Using the identity. (a - b) ²= (a² - 2ab + b²), evaluate 699²​

Answer:

250 options to create an even number

375 options to create an odd number

Answer:

Hence , the means of Largemouth Bass and Smallmouth Bass are significantly different.

Step-by-step expl;anation:

From the question we are told that:

Largemouth Bass:

[tex]\=x_1 =164.8[/tex]

[tex]s_1=96.4[/tex]

[tex]n_1=125[/tex]

Smallmouth Bass:

[tex]\=x_2 =272.8[/tex]

[tex]s_2=40[/tex]

[tex]n_2=97[/tex]

Assume

[tex]\alpha =0.05[/tex]

Generally The hypothesis is given as

H_0: The Largemouth Bass and Smallmouth Bass are equal  

H_1: The Largemouth Bass and Smallmouth Bass are  not equal

Generally the equation for Test statistics is mathematically given by

[tex]T=frac{( \=x_2 - \=x_1 )}{\sqrt{\frac{s^{1}}{n_1} + \frac{s_1^{2}}{n_2}}}[/tex]

[tex]T =\frac{(272.8 - 164.8)}{\sqrt{\frac{96.4^{2}}{125} + \frac{40^{2}}{97}}}[/tex]

[tex]T=\frac{108}{9.530925}[/tex]

[tex]T=11.33[/tex]

Therefore

From table

Critical Value

[tex]T_{\alpha,n_2-1}[/tex]

[tex]T_{0.05,96}=1.661[/tex]

Conclude

Since 11.33 is greater that 1.661 we eject the null hypothesis that the means are the same.

Hence , the means of Largemouth Bass and Smallmouth Bass are significantly different.

Answer:

bias

Step-by-step explanation:

the wording of the question may be misleading. the way the question is phrased influences the way the person who is being surveyed answers.

The wording of the questions can introduce (C) Bias.

Learn more about Bias brainly.com/question/3749477 here

#SPJ2

Answer:

Step-by-step explanation:

Answer:

40 mph

Step-by-step explanation:

40 mins to bike usually, which means he bikes 10 miles. He needs to bike at a minimum of 10 miles in 15 mins, which translates to 40 miles in an hour.

P.S. He is going to surely be late.

Answer:

20

Step-by-step explanation:

I assume y is 4/3 of z.

x = 7/6 y

y = 48

x = 7/6 * 48

x = 7 * 8

x = 56

y = 4/3 z

4/3 z = y

z = 3/4 y

z = 3/4 * 48

z = 36

x - z = 56 - 36 = 20

Given:

The geometric sequence is:

[tex]n[/tex]              [tex]a_n[/tex]

1                        -4

2                      20

3                     -100

To find:

The explicit formula and list any restrictions to the domain.

Solution:

The explicit formula of a geometric sequence is:

[tex]a_n=ar^{n-1}[/tex]            ...(i)

Where, a is the first term, r is the common ratio and [tex]n\geq 1[/tex].

In the given sequence the first term is -4 and the second term is 20, so the common ratio is:

[tex]r=\dfrac{a_2}{a_1}[/tex]

[tex]r=\dfrac{20}{-4}[/tex]

[tex]r=-5[/tex]

Putting [tex]a=-4,r=-5[/tex] in (i), we get

[tex]a_n=-4(-5)^{n-1}[/tex] where [tex]n\geq 1[/tex]

Therefore, the correct option is B.

Answer:

25

Step-by-step explanation:

40/24 = x/15

x = 15•40/24

x = 25

Answer:

25

Step-by-step explanation:

just use the facts that both triangles are similar

Answer:

Step-by-step explanation:

to cross the x-axis you need to solve f(x)=0

x(x+4)(x+7)*5=0 which means you will have x=0  ,x+4=0 or x+7=0

so the final answer is

x=0 or x=-4 or x=-7

Answer:

(x+7)^2+(y-10)^2=9

Step-by-step explanation:

The distance between the two points is sqrt((-7+7)^2+(10-7)^2)=3 which is in turn the radius of the circle

Answer:

2x + 1.

Step-by-step explanation:

Average = sum of the expression / number of expressions

= [(4 - 2x) + (-7 - 3x) + (11x + 6)] / 3

= (-2x - 3x + 11x + 4 - 7 + 6) / 3

= 6x + 3 / 3

= 2x + 1

Answer:

2x+1

Step-by-step explanation:

(4-2x), (-7-3x),(11x+6)

Add the three expressions

(4-2x)+ (-7-3x)+(11x+6)

Combine like terms

-2x-3x+11x+4-7+6

6x+3

Divide by the number of expressions which was 3

(6x+3)/3

2x+1

The average is 2x+1

Answer:

a) 0.321 = 32.1% probability of obtaining a negative daily return, on any given day.

b) 0.103 = 10.3% probability of having a negative daily return for two days in a row.

c) (-$1449.68, $3109.68)

d) A bonus of $4,488.174 is needed.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with mean = $830 and standard deviation = $1,781.

This means that [tex]\mu = 830, \sigma = 1781[/tex]

(a) What is the probability of obtaining a negative daily return, on any given day?

This is the p-value of Z when X = 0, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0 - 830}{1781}[/tex]

[tex]Z = -0.466[/tex]

[tex]Z = -0.466[/tex] has a p-value 0.321.

0.321 = 32.1% probability of obtaining a negative daily return, on any given day.

(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row?

Each day, 0.3206 probability, so:

[tex](0.321)^2 = 0.103[/tex]

0.103 = 10.3% probability of having a negative daily return for two days in a row.

(c) Give the boundaries of the interval containing the middle 80% of daily returns

Between the 50 - (80/2) = 10th percentile and the 50 + (80/2) = 90th percentile.

10th percentile:

X when Z has a p-value of 0.1, so X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = -1.28*1781[/tex]

[tex]X = -1449.68[/tex]

90th percentile:

X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = 1.28*1781[/tex]

[tex]X = 3109.68[/tex]

So

(-$1449.68, $3109.68)

d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus?

The 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.054 = \frac{X - 830}{1781}[/tex]

[tex]X - 830 = 2.054*1781[/tex]

[tex]X = 4488.174 [/tex]

A bonus of $4,488.174 is needed.

9514 1404 393

Answer:

  30 small chairs and 24 large chairs

Step-by-step explanation:

Let x and y represent the numbers of small chairs and large chairs built in a day. Then the relations for using available time are ...

  20x +50y = 30×60

  60x +90y = 66×60

Removing common factors, these can be written in standard form as ...

  2x +5y = 180

  2x +3y = 132

Subtracting the second equation from the first gives ...

  2y = 48

  y = 24 . . . . . divide by 2

Using the first equation to find x, we have ...

  2x +5(24) = 180

  2x = 60 . . . . . . . . . . subtract 120

  x = 30 . . . . . . . . divide by 2

The company can build 30 small chairs and 24 large chairs in a day.

If 6ˣ = 5, then

(6ˣ)³ = 6³ˣ = 5³ = 125,

and

6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500

Answer:

D

Step-by-step explanation:

we first dilate it, making it the same size, then translate it to the right. I hope I have helped :)

Answer:

for D, the slope of (2,5) (3,6) it is one

Step-by-step explanation:

i can't really get much, but i can give basic info

Answer:

First term a = 3

Sum of first 20 term = 440

Step-by-step explanation:

Given:

8th term of AP = 17

12th term of AP = 25

Find:

First term a

Sum of first 20 term

Computation:

8th term of AP = 17

a + 7d = 17 ....... EQ1

12th term of AP = 25

a + 11d = 25 ...... EQ2

From EQ1 and EQ2

4d = 8

d = 2

a + 7d = 17

a + 7(2) = 17

First term a = 3

Sum of first 20 term

Sn = [n/2][2a + (n-1)d]

S20 = [20/2][(2)(3) + (20-1)2]

S20 = [10][(6) + 38]

S20 = [10][44]

S20 = 440

Sum of first 20 term = 440

Answer:

f

Step-by-step explanation:

Answer:

S = 62.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan S = opp side / adj side

tan S = sqrt(42)/ sqrt (11)

tan S = sqrt(42/11)

Taking the inverse tan of each side

tan ^ -1( tan S) =  tan ^-1(sqrt(42/11))

S=62.89816

Rounding to the nearest tenth

S = 62.9

"RS tangent to circle a..." is first statement          Reason: Given

Second Reason: "Radius perpendicular to tangent"

Second Statement: "AR is parrallel to BS"      Reason: "2 lines perpendicular..."

Answer:

khai niem hinh cat don gian?

Answer:

Amount gained = $900

Step-by-step explanation:

Let the cost price be = x

Given selling price = 8400

And profit% = 12%

Profit = selling price - cost price

        = 8400 - x

[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]

Therefore , cost price of the radio $7500

The amount she gained = 8400 - 7500 = $ 900

Answer:

A

Step-by-step explanation:

Recall that for a quadratic equation of the form:

[tex]0=ax^2+bx+c[/tex]

The number of solutions it has can be determined using its discriminant:  

[tex]\Delta = b^2-4ac[/tex]

Where:

We have the equation:

[tex]2x^2+5x-k=0[/tex]

Thus, a = 2, b = 5, and c = -k.

In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:

[tex]b^2-4ac=0[/tex]

Substitute:

[tex](5)^2-4(2)(-k)=0[/tex]

Solve for k. Simplify:

[tex]25+8k=0[/tex]

Solve:

[tex]\displaystyle k = -\frac{25}{8}[/tex]

Thus, our answer is indeed A.

Answer:

B

Step-by-step explanation:

substitute the values in the eq. Ot is also arithmetic progression.

sfddssdfa63434daasfdfddfsa

Use the change-of-base property for logarithms to write

logₓ(16) log₂(x) = (ln(16) / ln(x)) (ln(x) / ln(2)) = ln(16)/ln(2) = log₂(16)

Then since 2⁴ = 16, we hvae

log₂(16) = log₂(2⁴) = 4 log₂(2) = 4

Answer:

a. 3 and 56, respectively.

Step-by-step explanation:

The computation of the degrees of freedom for the numerator and denominator for the critical value of F is given below:

k = 4

n = 15

Total degree of freedom is

= nk - 1

= 59

For numerator, it is

= k -1

= 4 - 1

= 3

and for denominator it is

= T - (k -1 )

= 59 - 3

= 56

Answer:

2.5%

Step-by-step explanation:

Thorazine is available in the strength of 25mg/mL.

To find out the percentage strength,

W/V = g/mL  (weight in grams of solute/milliliters of solute.)

1mL of Thorazine contains 25mg.

Dissolve Thorazine with the 100mL solution.

Therefore, 25 x 100 = 2500mg

Which is equals to 2.5g

100mL solution contains 2.5g of Thorazine.

Percentage Strength (W/V) = 2.5 / 100 x 100 = 2.5%.

The percentage strength of Thorazine 25mg/mL has 2.5%

Step-by-step explanation:

Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t

Now, we are given that the savings is =Rs 500

So, According to our assumption, 2t=500

⇒t=250

Hence, the income of the family is =7×250=Rs 1750

And the expenditure is =Income−Savings

=Rs 1750−Rs 500

=Rs 1250

Answer:

A sample of 784 is required to estimate the mean usage of water.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The standard deviation is 2 gallons

This means that [tex]\sigma = 2[/tex]

They would like the estimate to have a maximum error of 0.14 gallons. How large of a sample is required to estimate the mean usage of water?

This is n for which M = 0.14. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.14 = 1.96\frac{2}{\sqrt{n}}[/tex]

[tex]0.14\sqrt{n} = 1.96*2[/tex]

[tex]\sqrt{n} = \frac{1.96*2}{0.14}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*2}{0.14})^2[/tex]

[tex]n = 784[/tex]

A sample of 784 is required to estimate the mean usage of water.