The length of a rectangle is 12 m and its diagonal is 15 m. find
the breadth and area of the rectangle.

Answer:

There is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.

Step-by-step explanation:

The hypothesis :

H0 : μ1 = μ2

H1 : μ1 > μ2

Given :

n1 = 35 ; x1 = 75.1 ; s1 = 12.8

n2 = 50 ; x2 = 72.1 ; s2 = 14.6

Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)

df1 = n1 - 1 = 35 - 1 = 34

df2 = n2 - 1 = 50 - 1 = 49

(x1 - x2) ÷ Sp(√(1/n1 + 1/n2))

Sp² = (34*12.8^2 + 49*14.6^2) / (35+50-2)

Sp² = (5570.56 + 10444.84) / 83

Sp² = 192.95662

Sp = √192.95662

Sp = 13.89

Test statistic = (75.1 - 72.1) / 13.89 * √(1/35 + 1/50)

Test statistic = 3 / (13.89 * 0.2203892)

Test statistic = 0.980

df = n1 + n2 - 2

df = 35 + 50 - 2 = 83

Using the Pvalue calculator :

Pvalue(0.980, 83) = 0.165

α = 0.1

Pvalue > α ; We fail to reject the H0; and conclude that there is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.

Answer:

Well, divide the shape into rectangles,

triangles or other shapes after that, you can find the area of and then add the areas back together.

Step-by-step explanation:

The area of composite shapes is defined as the area covered by any composite shape. A composite shape is made up of basic shapes put together. Thus, the area of the composite shape is found by individually adding all the basic shapes.

To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together.es

Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.  

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)  

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) [tex]Z=2.45[/tex]

b) [tex]P Value=0.0073[/tex]

Step-by-step explanation:

From the question we are told that:

Probability of Wishart and Leach [tex]P=21.4=>0.214[/tex]

Population Size [tex]N=498[/tex]

Sample size [tex]n=12[/tex]

Therefore

[tex]P'=\frac{129}{498}[/tex]

[tex]P'=0.2590[/tex]

Generally the Null and Alternative Hypothesis is mathematically given by

[tex]H_0:P=0.214[/tex]

[tex]H_a:=P>0.214[/tex]

Test Statistics

[tex]Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex]

[tex]Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}[/tex]

[tex]Z=2.45[/tex]

Therefore P Value is given as

[tex]P Value =P(Z\geq 2.45)[/tex]

[tex]P Value =1-P(Z\leq 2.45)[/tex]

[tex]P Value =1-0.99268525[/tex]

[tex]P Value=0.0073[/tex]

Answer:

The purchase value at the 30th percentile=34.24

Step-by-step explanation:

We are given that

Mean,[tex]\mu=41.34[/tex]

Standard deviation,[tex]\sigma=13.54[/tex]

We have to find the purchase value at the 30th percentile.

[tex]xth percentile =\mu+Z\times \sigma[/tex]

Where Z is the critical value of x% confidence interval

x=30

Critical value of Z at 30% confidence interval=-0.5244

Using the formula

30th percentile=[tex]41.34+(-0.5244)(13.54)[/tex]

30th percentile=[tex]41.34-7.100376[/tex]

30th percentile[tex]\approx 34.24[/tex]

Hence,  the purchase value at the 30th percentile=34.24

Answer:

3.142

Step-by-step explanation:

Succinctly, pi which is written as the Greek letter for p, or π is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.142.

Answer:

[tex]{ \tt{y = 8 - 3x}} - - - (i) \\ \\ = > 7x - 4(8 - 3x) = 6 \\ 7x - 32 + 12x = 6 \\ 19x - 32 = 6 \\ 19x = 38 \\ x = 2 \\ \\ = > y = 8 - 3(2) \\ y = 2[/tex]

Answer:

[tex]g(x) = -x^2 + 3[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2[/tex]

Required

Determine g(x)

First, shift f(x) down by 3 units

The rule is:

[tex]f'(x) = f(x) - 3[/tex]

So:

[tex]f'(x) = x^2 - 3[/tex]

Next, reflect f'(x) across the x-axis to get g(x)

The rule is:

[tex]g(x) = -f(x)[/tex]

So, we have:

[tex]g(x) = -(x^2 - 3)[/tex]

Open bracket

[tex]g(x) = -x^2 + 3[/tex]

Answer:

D

Step-by-step explanation:

I figured out the hard way

Answer:

y = 5x + 1

Step-by-step explanation:

Given the coordinate points (0,1) and (5,0)

First, get the slope

Slope m =(0-1)/5-0

m = -1/5

Since the required line is perpendicular, then the required slope is;

M = -1/(-1/5)

M = 5

Since 1the y intecept id (0,1) i.e. 1

Required equation is y = mx+b

y = 5x + 1

This gives the required equation

Note that the coordinate (0,1) was used instead os (0,0)

Answer:

a) P(man asked for a raise) = 0.21.

b) P(man received raise, given he asked for one) = 0.6.

c) P(man asked for raise and received raise) = 0.126.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

21% asked for a raise, so:

P(man asked for a raise) = 0.21.

Question b:

Event A: Asked for a raise.

Event B: Received a raise:

21% had asked for a raise and 60% of the men who had asked for a raise received the raise:

This means that [tex]P(A) = 0.21, P(A \cap B) = 0.21*0.6[/tex], thus:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.21*0.6}{0.6} = 0.6[/tex]

P(man received raise, given he asked for one) = 0.6.

Question c:

[tex]P(A \cap B) = 0.21*0.6 = 0.126[/tex]

P(man asked for raise and received raise) = 0.126.

Answer:

sin²2θ. (cos θ sin θ). cos 2θ

Step-by-step explanation:

finding g'(x)

g'(x)

= 4 (cosθsinθ)³ . { cosθ. (sinθ)' + sinθ. (cosθ)' }

= 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}

= 4 (cosθsinθ)³{ cos²θ - sin²θ}

= (4 cosθ sinθ)². (cosθ sinθ). { cos²θ - sin²θ}

= sin²2θ. (cos θ sin θ). cos 2θ

Answer:

That number is 39

Answer:

y - 1 = -6(x - 1)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 1)

Slope m = -6

Step 2: Find Equation

Answer:

[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]

Step-by-step explanation:

[tex] (2 + i) \div (1 - 4i) = [/tex]

[tex] = \dfrac{2 + i}{1 - 4i} [/tex]

[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]

[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]

[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]

[tex] = \dfrac{2 + 9i - 4}{17} [/tex]

[tex] = \dfrac{-2 + 9i}{17} [/tex]

[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]

Answer:

(1) Ordinal

(2) Such data should not be used for calculations such as an average.

Step-by-step explanation:

Given

[tex]1 \to Low[/tex]

[tex]2 \to Medium[/tex]

[tex]3 \to High[/tex]

[tex]Average = 1.3[/tex]

Solving (a): The level of measurement

When observations are presented in ranks such as:

[tex]1 \to Low[/tex]

[tex]2 \to Medium[/tex]

[tex]3 \to High[/tex]

The level of measurement of such observation is ordinal

Solving (b): What is wrong with the computation?

Ordinal level of measurement are not numerical values whose average can be calculated because they are used as ranks.

Hence, (a) is correct

Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]

Step-by-step explanation:

Given

In equality is [tex]x^3+4x>5x^2[/tex]

Taking terms one side

[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]

Using wavy curve method

[tex]x\in (0,1)\cup (4,\infty)[/tex]

Answer:

(x - 3)^2 + (x + 2)^2 = 4

Step-by-step explanation:

Equation of circle:

(x - h)^2 + (x - k)^2 = r^2

(h, k) = (3, -2)

r = 2

(x - 3)^2 + (x - (-2))^2 = 2^2

(x - 3)^2 + (x + 2)^2 = 4

Answer:

2 < x < 6

Step-by-step explanation:

x/10

1/5 = 2/10

.6 = 6/10

2 < x < 6

Answer:

1st blank=[tex]y_{1}[/tex]

2nd blank=[tex]x_{1}[/tex]

3rd blank= [tex]y_{2}[/tex]

3*27=81

so 1*[tex]y_{1}[/tex]=81

hence [tex]y_{1}[/tex]=81

9* [tex]x_{1}[/tex]= 81

[tex]x_{1}[/tex]=9

27*[tex]y_{2}[/tex]=81

[tex]y_{2}[/tex]=3

Thus solved.

Hope this helps.

Please mark me as brainliest.

Explanation:

There are 4 choices for first place, 3 choices for second place, and 2 choices for third place. Overall, there are 4*3*2 = 24 permutations.

Answer:

4/3

Step-by-step explanation:

Substitute in 4.

(1/3)4

Multiply

4/3

I hope this helps!

Answer:

Step-by-step explanation:

so let the equation equal 13

13 = 3[tex]x^{3}[/tex]-12x+13

so when ever 3[tex]x^{3}[/tex]-12x=0  then this is equation is true, soooo

x (3[tex]x^{2}[/tex] - 12) =0

so when x = 0  this is true, but also when

3[tex]x^{2}[/tex]-12=0   also

3[tex]x^{2}[/tex] = 12

[tex]x^{2}[/tex] = 4

x = 2

so when x = 2  or -2  or 0  ,  then this is true

Answer:

x =[tex]x =(\frac{c}{4} )^{1/3} \\[/tex]

input 2  output 32

output 256 input 4

Step-by-step explanation:

Answer:

2 1/8

Step-by-step explanation:

7/8 is the same as 0.875 and therefore you need 0.125 also known as 1/8 to make it a whole number. When you add it to the already existing whole 2 you get three. Subtract three from five to make two which is what you need to add on top to finally get 5.

Answer:  [tex]_{13} P _{13}[/tex]

Another acceptable answer is 13! where the exclamation mark is needed.

The numeric form is 6,227,020,800 which is a little over 6 billion.

==============================================================

Explanation:

Let's lump those four songs together to form a so called "mega song". So we treat those four items as one single item. This is ensure that those songs are played in the order we want. The other songs aren't treated this way.

We start with 16 songs and drop to 16-4 = 12 songs when taking out those four named songs. Then we add 1 to get 12+1 = 13 since we're adding in that "mega song" block.

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

So to recap so far, we've gone from 16 songs to 13 songs. The goal is to find out how many arrangements of 13 songs are possible. Order matters.

We'll use the nPr permutation function

[tex]_{n} P _{r} = \frac{n!}{(n-r)!}\\\\[/tex]

where in this case n = 13 and r = 13. Your teacher doesn't want you to evaluate this function. You simply need to state the symbolic form. So that's why we go from [tex]_{n} P _{r}[/tex] to [tex]_{13} P _{13}[/tex]

If you wanted to answer this in terms of factorial notation, then you could say this

[tex]_{n} P _{r} = \frac{n!}{(n-r)!}\\\\_{13} P _{13} = \frac{13!}{(13-13)!}\\\\_{13} P _{13} = \frac{13!}{(0)!}\\\\_{13} P _{13} = \frac{13!}{1}\\\\_{13} P _{13} = 13!\\\\[/tex]

So we can see that the notations [tex]_{13} P _{13}[/tex] and [tex]13![/tex] mean the exact same thing.

If you wanted to know the actual number of permutations, then,

13! = 13*12*11*10*9*8*7*6*5*4*3*2*1 = 6,227,020,800

which is a little over 6 billion permutations.

Answer:

ya the equation divides y as a function of x

Answer:

The price of 1 exercise book is $122.45.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the price of one exercise book.

y is the price of one textbook.

Total cost of 10 exercise books and 2 textbooks is $1400.00.

This means that:

[tex]10x + 2y = 1400[/tex]

Since we want x:

[tex]2y = 1400 - 10x[/tex]

[tex]y = 700 - 5x[/tex]

One also finds the total cost of 3 textbooks and 30 exercise books is $3000.

This means that:

[tex]3x + 30y = 3000[/tex]

Since [tex]y = 700 - 5x[/tex]

[tex]3x + 30(700 - 5x) = 3000[/tex]

[tex]3x + 21000 - 150x = 3000[/tex]

[tex]147x = 18000[/tex]

[tex]x = \frac{18000}{147}[/tex]

[tex]x = 122.45[/tex]

The price of 1 exercise book is $122.45.

Answer:

option D

Step-by-step explanation:

[tex]sin^2 ( \frac{3\pi}{2}) + cos^2(\frac{3\pi}{2}) = 1\\\\( -1)^2 + 0^2 = 1[/tex]

Explanation:

[tex]sin x = cos( \frac{\pi}{2} - x)\\\\sin(\frac{3\pi}{2}) = cos ( \frac{\pi}{2} - \frac{3\pi}{2})\\[/tex]

            [tex]=cos(\frac{\pi - 3\pi}{2})\\\\ =cos(\frac{2\pi}{2})\\\\=cos \ \pi\\\\= - 1[/tex]

Therefore ,

               [tex]sin^2( \frac{3\pi}{2}) = ( - 1)^2[/tex]

Answer: B. Cannot be determined

Explanation:

We can't use SAS since we don't have two pairs of proportional sides. We only know one pair of sides. This also rules out SSS as well since we'd need 3 pairs of proportional sides.

We can't use AA because we don't have two pairs of congruent angles.

Currently, we simply don't have enough information to determine if the triangles are similar or not.

Answer:

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]

Step-by-step explanation:

Given

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2[/tex]

Required

Solve

Start with the bracket

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ (9.1)^2-(-1.4)^2[/tex]

Evaluate all exponents

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ 82.81-1.96[/tex]

Evaluate all products

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 2.4+ 82.81-1.96[/tex]

[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]

Answer:

36

Step-by-step explanation:

2x is an exterior angle

Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).

Put symbolically

<LEG = <EGF + <EFG

<EFG = 180 - 4x           In this case you need to find the supplemtnt

<LEG = x + 180 - 4x

2x = 180 - 3x                Add 3x to both sides

5x = 180                       Divide by 5

x = 36