Using the identity. (a - b) ²= (a² - 2ab + b²), evaluate 699²
Answers
Step-by-step explanation:
hope it helps you.......
[tex]\\ \sf\longmapsto 699^2[/tex]
[tex]\\ \sf\longmapsto (700-1)^2[/tex]
[tex]\\ \sf\longmapsto 700^2-2(700(1)+(1)^2[/tex]
[tex]\\ \sf\longmapsto 490000-1400+1[/tex]
[tex]\\ \sf\longmapsto 488600+1[/tex]
[tex]\\ \sf\longmapsto 488601[/tex]
Related Questions
Dr. Burger rides his bike to work in the mornings. Usually, he leaves his house at 8:20 and gets to the office at 9:00 riding at a rate of 15 miles an hour. On this particular morning he has overslept and leaves at 8:45. How fast does he need to ride to avoid being late
Answers
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.
The 8th term in the arithmetic sequence is 17, the 12th term is 25. Find the first term, and the sum of the first 20 terms.
Answers
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
Thorazine is available in a strength of 25 mg/mL. Express this strength as a percent.
Answers
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%
khai niem hinh cat don gian ?
Answers
Answer:
khai niem hinh cat don gian?
Simplify to the extent possible: (
logx16)(log2 x)
Answers
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
Write the standard form of the equation of the circle with center (−7,10) that passes through the point (−7,7)
Answers
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
Random samples of of outh bass and smallmouth bass were taken from a lake, and their lengths in millimeters) were deter mined. We wish to know if the mean standard length differs between the two species in this lake. The results were as follows:
Largemouth Bass Smallmouth Bass
x 164.8 272.8
s 96.4 40.0
n 97 125
Answers
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.
As one once said Another one
Answers
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
Please help me I don’t understand and my tutor is gonna tell me mom please help number 12
Answers
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
At which root does the graph of f(x) = (x + 4)^6(x + 7)^5 cross the x-axis?
O -7
O -4
O 4
Ο 7
Answers
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
A day trading firm closely monitors and evaluates the performance of its traders. For each $10,000 invested, the daily returns of traders at this company can be modeled by a Normal distribution with mean = $830 and standard deviation = $1,781.
(a) What is the probability of obtaining a negative daily return, on any given day? (Use 3 decimals.)
(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? (Use 3 decimals.)
(c) Give the boundaries of the interval containing the middle 80% of daily returns: (use 3 decimals) ( , )
(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? (Use 3 decimals.)
Answers
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.
(x²-9)(√x-2)=0 ??????????
Answers
sfddssdfa63434daasfdfddfsa
E. The ratio of monthly income to savings of a family is 7:2. If the savings is Rs. 500, find the monthly income and expenditure.
Answers
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
Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.
n an
1 −4
2 20
3 −100
an = −5(−4)n − 1 where n ≥ 1
an = −4(−5)n − 1 where n ≥ 1
an = −4(5)n − 1 where n ≥ −4
an = 5(−4)n − 1 where n ≥ −4
Answers
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.
If $6^x = 5,$ find $6^{3x+2}$.
Answers
If 6ˣ = 5, then
(6ˣ)³ = 6³ˣ = 5³ = 125,
and
6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500
6. Find average of the following
expressions (4-2x), (-7-3x), and
(11x+6)
Answers
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
easy! plz help me tho
In a survey, the wording of the questions can introduce
Validity
Randomness
Bias
Uniformity
Answers
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.
What are bias questions?A question that is worded or expressed in a way that affects the respondent's opinion is considered biased. Such inquiries could offer details that influence a respondent's perspective on the topic.What are the types of bias?Bias in selection- When a sample is used in research that does not accurately reflect the larger population, selection bias arises. Aversion to Loss - People with loss aversion, which is a widespread human tendency, dislike losing more than they enjoy winning.Anchoring Bias. Framing Bias.Learn more about Bias brainly.com/question/3749477 here
#SPJ2
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the standard deviation is 2 gallons and the mean is 16 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water
Answers
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.
A furniture company makes large and small chairs. A small chair takes 20 minutes of machine time and 60 minutes of labor to build. A large chair takes 50 minutes
of machine time and 90 minutes of labor to build. The company has 66 hours of labor time and 30 hours of machine time available each day. How many of each
type of chair is built in a day?
Answers
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.
Help please, I attached the question. Is it a!?

Answers
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:
If the discriminant is positive, we have two real solutions. If the discriminant is negative, we have no real solutions. And if the discriminant is zero, we have exactly one solution.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.
Which one goes where?
Answers
"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..."
Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain
Answers
What is the explicit formula for the sequence ? -1,0,1,2,3
Answers
Answer:
B
Step-by-step explanation:
substitute the values in the eq. Ot is also arithmetic progression.
By selling a radio for $8400 a dealer gained 12% .how much money did she gain
Answers
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
Using the digits 5, 6, 7, 8, 9 and repetition is allowed how many options are there to
Create a 4 digit even number?
[2]
Create a 4 digit odd number?
Answers
Answer:
250 options to create an even number
375 options to create an odd number
What is the value of x?
Enter your answer in the box.
units
Answers
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
Kevin has 17 trading cards. Billy has t more trading cards than Kevin. Choose the expression that shows how many trading cards
Billy has
Answers
Answer:
Step-by-step explanation:
ABC ~ DEF. What sequence of transformations will move ABC ~ DEF
Answers
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 :)
Can y’all help me again I’m sorry I just want to pass summer school guyss<33
Answers
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
An ANOVA procedure is applied to data obtained from four distinct populations. The samples, each comprised of 15 observations, were taken from the four populations. The degrees of freedom for the numerator and denominator for the critical value of F are:___________
a. 3 and 56, respectively.
b. 3 and 59, respectively.
c. 4 and 21, respectively.
d. 4 and 60, respectively
Answers
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
