Question 5
Refer to the data that you recorded in part D. In each row, compare the slope of ABto the slope of the perpendicular line. What is the
relationship between the two slopes? What conclusion can you draw about the relationship between the slopes of any two perpendicular lines?
Ok

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: 8 \frac{1}{3}\:(or) \:8.333}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

[tex]3 \frac{3}{4} \times 2 \frac{2}{9} [/tex]

➺[tex] \: \frac{15}{4} \times \frac{20}{9} [/tex]

➺[tex] \: \frac{300}{36} [/tex]

➺[tex] \: \frac{25}{3} [/tex]

➺[tex] \: 8 \frac{1}{3} [/tex]

➺[tex] \: 8.333[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\pink{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

a. There are 1365 choices of eleven questions.

b. 1764 groups of eleven questions contain five that require proof and six that do not.

Step-by-step explanation:

The order in which the questions are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

a. How many different choices of eleven questions are there?

Eleven questions from a set of 15. So

[tex]C_{15,11} = \frac{15!}{11!4!} = 1365[/tex]

There are 1365 choices of eleven questions.

b. Suppose seven questions require proof and nine do not. How many groups of eleven questions contain five that require proof and six that do not?

5 from a set of 7 and 6 from a set of 9. So

[tex]C_{7,5}C_{9,6} = \frac{7!}{5!2!} \times \frac{9!}{6!3!} = 1764[/tex]

1764 groups of eleven questions contain five that require proof and six that do not.

Step-by-step explanation:

foctorized 990 = 9×10×11

so, (X+2)(X+3)(X+4)=9×10×11

we can choose one of the factors, and get the answer with the same x values

x+2 = 9 , => x =7

x+3 = 10, => x = 7

x+4 = 11, => x = 7

Answer:

c

Step-by-step explanation:

4/6 is reduced to two thirds

Answer:

1) 8 + 2i

2) -13

3) 15 + 3i

4) 1

5) 24 - 10i

Step-by-step explanation:

Working with imaginary numbers is similar to working with a variable when it comes to addition and subtraction, so for problems 1 and 3, it is a matter of combining like terms.

1) The like terms are 7i and -5i; 5 and 3. We can combine them.

8 + 2i

2) We can start to compute the problem by noticing it is a special product of difference of squares. The expression can also be written as:

(3i)^2 - (2)^2

9i^2 - 4

i is defined as the square root of negative 1, so i^2 is -1. We can substitute that in:

9(-1) - 4

-9 - 4

-13

3) We can combine the like terms, 12i and -9i; 5 and 10:

15 + 3i

4)The powers of i repeat every four numbers. For example:

i^1 = i

i^2 = -1

i^3 = -i

i^4 = 1

i raised to a power divisible by four is always 1, so i^24 is 1.

5) We can start by normally distributing in this problem:

12 - 18i + 8i - 12i^2

As said before, i^2 is -1:

12 - 10i + 12

24 - 10i

Answer:

What do you need help with?

Step-by-step explanation:

You didn't put a question

Step-by-step explanation:

he made a mistake in step 3 because you not supposed to add that value behind that division

and you divide first

Answer:

mistake is in step 4. he shouldn't have added first

Answer:

the fourth option

9, 30, 93, 282, 849

Step-by-step explanation:

a1 = 9

based on the sequence definition

a2 = 3×a1 + 3 = 3×9 + 3 = 27 + 3 = 30

the only answer option with a2=30 is the fourth one. all others must be therefore wrong.

check

a3 = 3×a2 + 3 = 3×30 + 3 = 93

a4 = 3×a3 + 3 = 3×93 + 3 = 282

a5 = 3×a4 + 3 = 3×282 + 3 = 849

confirmed.

Answer:

A. 25

Step-by-step explanation:

From the diagram given, we can deduce that <D EG = <F EG

Therefore:

3y + 4 = 5y - 10

Collect like terms and solve for y

3y - 5y = -4 - 10

-2y = -14

Divide both sides by -2

y = -14/-2

y = 7

✔️m<D EG = 3y + 4

Plug in the value of y

m<D EG = 3(7) + 4

m<D EG = 25°

Answer: D

Step-by-step explanation:

Answer:

Answer:

16 Miles

Step-by-step explanation:

For every week you simply multiply the number of miles from the previous week by 2, therefore

Week 1: 1

Week 2: 2

Week 3: 4

Week 4: 8

Week 5: 16

Answer:

iii) a=3b/2

Step-by-step explanation:

7a-2b= 5a+b

7a-5a=2b+b

2a=3b

a=3b/2

I hope this helps!

Answer:

[tex](a)\ \bar x_1 - \bar x_2 = 2.0[/tex]

[tex](b)\ CI =(1.0542,2.9458)[/tex]

[tex](c)\ CI = (0.8730,2.1270)[/tex]

Step-by-step explanation:

Given

[tex]n_1 = 60[/tex]     [tex]n_2 = 35[/tex]      

[tex]\bar x_1 = 13.6[/tex]    [tex]\bar x_2 = 11.6[/tex]    

[tex]\sigma_1 = 2.1[/tex]     [tex]\sigma_2 = 3[/tex]

Solving (a): Point estimate of difference of mean

This is calculated as: [tex]\bar x_1 - \bar x_2[/tex]

[tex]\bar x_1 - \bar x_2 = 13.6 - 11.6[/tex]

[tex]\bar x_1 - \bar x_2 = 2.0[/tex]

Solving (b): 90% confidence interval

We have:

[tex]c = 90\%[/tex]

[tex]c = 0.90[/tex]

Confidence level is: [tex]1 - \alpha[/tex]

[tex]1 - \alpha = c[/tex]

[tex]1 - \alpha = 0.90[/tex]

[tex]\alpha = 0.10[/tex]

Calculate [tex]z_{\alpha/2}[/tex]

[tex]z_{\alpha/2} = z_{0.10/2}[/tex]

[tex]z_{\alpha/2} = z_{0.05}[/tex]

The z score is:

[tex]z_{\alpha/2} = z_{0.05} =1.645[/tex]

The endpoints of the confidence level is:

[tex](\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}[/tex]

[tex]2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}[/tex]

[tex]2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}[/tex]

[tex]2.0 \± 1.645 * \sqrt{0.0735+0.2571}[/tex]

[tex]2.0 \± 1.645 * \sqrt{0.3306}[/tex]

[tex]2.0 \± 0.9458[/tex]

Split

[tex](2.0 - 0.9458) \to (2.0 + 0.9458)[/tex]

[tex](1.0542) \to (2.9458)[/tex]

Hence, the 90% confidence interval is:

[tex]CI =(1.0542,2.9458)[/tex]

Solving (c): 95% confidence interval

We have:

[tex]c = 95\%[/tex]

[tex]c = 0.95[/tex]

Confidence level is: [tex]1 - \alpha[/tex]

[tex]1 - \alpha = c[/tex]

[tex]1 - \alpha = 0.95[/tex]

[tex]\alpha = 0.05[/tex]

Calculate [tex]z_{\alpha/2}[/tex]

[tex]z_{\alpha/2} = z_{0.05/2}[/tex]

[tex]z_{\alpha/2} = z_{0.025}[/tex]

The z score is:

[tex]z_{\alpha/2} = z_{0.025} =1.96[/tex]

The endpoints of the confidence level is:

[tex](\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}[/tex]

[tex]2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}[/tex]

[tex]2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}[/tex]

[tex]2.0 \± 1.96 * \sqrt{0.0735+0.2571}[/tex]

[tex]2.0 \± 1.96* \sqrt{0.3306}[/tex]

[tex]2.0 \± 1.1270[/tex]

Split

[tex](2.0 - 1.1270) \to (2.0 + 1.1270)[/tex]

[tex](0.8730) \to (2.1270)[/tex]

Hence, the 95% confidence interval is:

[tex]CI = (0.8730,2.1270)[/tex]

Answer:

Uh, think you can give a picture?

Step-by-step explanation:

Answer:

The mean is the better center for the given dot plot.

What is Dot plot?

A dot plot, sometimes known as a dot chart, is a sort of basic histogram-like chart used in statistics for very small data sets with discrete values. To create a dot plot, count the number of data points in each bin and draw a stack of dots with that number of dots on top for each bin.

Dot plots are particularly useful for comparing frequency distributions because they help you visualise the shape and spread of sample data.

First the mean of the data

= (1+ 2+ 3+ 4+ 5)/ 5

= 15 /5

= 3

So, the mean is 3.

Thus, the data is skewed and there are outliers.

Hence, the mean a better center for this data.

Step-by-step explanation:

Answer:

isosceles

Step-by-step explanation:

Two sides are the same length as indicated by the lines on the sides.

This tells use that the triangle is isosceles

Answer:

Hi, this an isoceles triangle

Step-by-step explanation:

An isoceles triangle has 2 equal sides

A right angled one has a right angle (90 degrees)

An equilateral traingle has all of his sides equal

A scalene has all of his sides different.

So this must be an isoceles triangle because there is basically a proof of the two equal sides (the bars).

Hope its clear!

Answer:

30.00×.06=1.8+30.00=31.8

Answer:

1.tenisha

2.1\5+1\3=1\×

3.n-12=1\3(n+2)

4.500×=120

Answer:

I thinks they take 5 hours to meet each other

Answer:

14.50 cm

Step-by-step explanation:

Based on the midsegment theorem:

The midsegment connecting two sides of triangle is parallel to the third side of the triangle and the length of the midsegment line is half the length of the third side parallel to the midsegment.

From the diagram ;

QR // ZY

XY = 2 * 2.93 = 5.86

RS // XZ

XZ = 2 * 2.04 = 4.08

QS // XY

XY = 2 * 2.28 = 4.56

The perimeter :

(XY + XZ + XY)

5.86 + 4.08 + 4.56

= 14.50 m

Answer:

d

Step-by-step explanation:

Answer:

It is one-half the area of a rectangle with sides 6 units × 2 units.

Step-by-step explanation:

Area of the triangke ABC = 6

Answer:

2 -> 3

14 -> -3

7 -> -2

-1 -> 2

Step-by-step explanation:

Given the function

f(x) = x² - 2x - 1

If x = 2

f(x) = 2² - 2(2) - 1

f(x) = 4 - 4 - 1

f(x) = -1

If x = -2

f(x) = (-2)² - 2(-2) - 1

f(x) = 4 + 4 - 1

f(x) = 7

If x = 3

f(x) = 3² - 2(3) - 1

f(x) = 9 - 6 - 1

f(x) = 2

If x = -3

f(x) = (-3)² - 2(-3) - 1

f(x) = 9 + 6 - 1

f(x) = 14

Answer:

True

Step-by-step explanation:

When conducting Analysis of Variance test (ANOVA) ; our hypothesis are stated as follows ;

The null hypothesis; H0 ; stats that there is no difference in means between any of the population ;

H0 : μ1 = μ2

While the alternative hypothesis which is the opposite of the null hypothesis will be of the claim that ; atleast one of the population means is different from another.

Hence, once there is sufficient evidence to indicate that atleast one of the population means is different from another, then we reject the Null.

Answer: a) a) 0.700, (0.676, 0.724)

Step-by-step explanation:

Confidence interval for population proportion p :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]\hat{p}[/tex] = Sample proportion, n= sample size, z* = Critical value.

Let p denote the proportion of all people who voted.

As per given, n= 1000

[tex]\hat{p}=\dfrac{700}{1000}\\\\=0.7[/tex]

z* for 90% confidence = 1.645

Required confidence interval :

[tex]0.7\pm (1.645)\sqrt{\dfrac{0.7(1-0.7)}{1000}}\\\\=0.7\pm(1.645)\sqrt{0.00021}\\\\=0.7\pm (1.645)(0.0145)\\\\=0.7\pm 0.0238525\\\\=(0.7-0.0238525,0.7+0.0238525)\\\\=(0.6761475,\ 0.7238525)\approx(0.676, 0.724)[/tex]

hence, the correct option is a) a) 0.700, (0.676, 0.724)

Answer:

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Answer:

(x - 12)²

Step-by-step explanation:

Given

x² - 24x + 144

Required

Factorize

Start by expanding the expression

x² - 12x - 12x + 144.

Factorize.

x (x - 12) - 12(x - 12)

Factor out x - 12

(x 12)(x - 12)

Rewrite as

(x - 12)²

Answer:

20

Step-by-step explanation:

i dont know

look it up