Answer:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Step-by-step explanation:
To find:
Simplified product of:
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]
Solution:
First of all, let us have a look at some of the formula:
1. [tex](a+b) (c+d) = ac+bc+ad+bd[/tex]
2. [tex]a^b\times a^c =a^{b+c }[/tex]
3. [tex]\sqrt{a^{2b}} = \sqrt{a^b.a^b}=a^b[/tex]
4. [tex]\sqrt a \times \sqrt b = \sqrt{a\times b}[/tex]
Now, let us apply the above formula to solve the given expression.
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\\Rightarrow(\sqrt{10x^4})(2\sqrt{15x^4})+(\sqrt{10x^4})(\sqrt{3x^3})-(x\sqrt{5x^2})(2\sqrt{15x^4})-(x\sqrt{5x^2})(\sqrt{3x^3})\\\\\Rightarrow2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\\Rightarrow\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
The answer is:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Answer:
Its D
Step-by-step explanation:
To compare the teaching methodologies of two of its eighth-grade math teachers, a school decides to compare student test scores from the two classes throughout the year.
Which type of statistical study is the school conducting?
a) Matched-pair design study
b) Meta-analysis
c) Retrospective observational study
d) Prospective observational study
Answer:
D) Prospective observational study
Step-by-step explanation:
A study which gathers data moving forward is called a prospective study. Since the data is gathered on students without controlling the setting moving forward, it is a prospective observational design.
To determine her water pressure, Denise divides up her day into three parts: morning, afternoon, and evening. She then measures her water pressure at 2 randomly selected times during each part of the day.What type of sampling is used?a. Simple random b. Cluster c. Stratified d. Convenience e. Systematic
Answer:
The correct answer is:
Stratified (c.)
Step-by-step explanation:
Stratified sampling technique is one in which the groups of data are divided into smaller groups or strata, based on shared common characteristics in these groups, and the samples randomly selected from each group in a proportional way. In this example, the sub-groups used is "times of the day" ie. morning, afternoon or evening. Other strata that can be used are; age, gender, continents etc. Stratification is done when the researcher wants to understand the relationships between the two or more groups. Stratified random sampling is also known as proportional random sampling or quota random sampling.
find the measure of a
Answer:
Hello,
answer D 48°
Step-by-step explanation:
In the right triangle down, a+42°=90° ==> a=90°-42°=48°
Find the equation (in terms of x) of the line through the points (-2,-3) and (4,-1)
Answer:
y = 1/3x - 7/3
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - (-3) / 4 - (-2)
2/6
= 1/3
y = 1/3x + b
-1 = 1/3(4) + b
-1 = 4/3 + b
-7/3 = b
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answer:
x = 2 is the solution to x + 1.5 = 3.5
Step-by-step explanation:
x + 1.5 = 3.5
-1.5 -1.5
--------------------
x = 2
the box plots shows the price for two different brands of shoes
Answer:
A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.
Step-by-step explanation:
The most appropriate measure that can be used to compare the SPREAD of the data of the 2 brands plotted on a box plot, is the Interquartile range (IQR).
Interquartile range is the difference between Q3 and Q1.
Q3 is the value which lies at the end of the rectangular box, while the Q1 lies at the beginning of the box.
From the box plot given,
IQR for brand A = 80 - 70 = $10
IQR for brand B = 50 - 25 = $25
Therefore, the correct option is "A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25."
Simplify the product. (–7) + (–7) + (–7) + (–7)
Answer:
-28
Step-by-step explanation:
(–7) + (–7) + (–7) + (–7)
=> -7 -7 -7 -7
=> - 28
solve the equation
Answer:
x = 10
Step-by-step explanation:
2x/3 + 1 = 7x/15 + 3
(times everything in the equation by 3 to get rid of the first fraction)
2x + 3 = 21x/15 + 9
(times everything in the equation by 15 to get rid of the second fraction)
30x+ 45 = 21x + 135
(subtract 21x from 30x; subtract 45 from 135)
9x = 90
(divide 90 by 9)
x = 10
Another solution:
2x/3 + 1 = 7x/15 + 3
(find the LCM of 3 and 15 = 15)
(multiply everything in the equation by 15, then simplify)
10x + 15 = 7x + 45
(subtract 7x from 10x; subtract 15 from 45)
3x = 30
(divide 30 by 3)
x = 10
. One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, what is the value of Cohen’s d?
Answer:
Cohen's d : 1.00
Step-by-step explanation:
We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.
The formula to solve for the value of Cohen's d is as follows,
d = M₁ - M₂ / S - pooled,
d = 18 - 14 / 4 = 4 / 4 = 1
Therefore the value of Cohen's d = 1
Determine x&y
(2+i) (x+yi) = -7+3i
Answer:
x = -11/5 or -2.2
y = 13/5 or 2.6
Step-by-step explanation:
well, start by doing the multiplication. then we will see better.
2x + 2yi + xi + yii = -7 + 3i
2x + 2yi + xi - y = -7 + 3i
this is because, remember, i = sqrt(-1), and ii = -1.
now we group the i-factors and the terms without i and compare it to the corresponding parts on the right side.
2x - y = -7
2yi + xi = 3i
=> 2y + x = 3
x = 3 - 2y
and that we use ihr the first equation again
2×(3-2y) - y = -7
6 - 4y - y = -7
-5y = -13
y = 13/5
x = 3 - 2×13/5 = 3 - 26/5 = 15/5 - 26/5 = -11/5
The average price of a college math textbook is $158 and the standard deviation is $26. Suppose that 40 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 48, find the probability that the average price is between $153 and $155.
Find the first quartile for the average textbook price for this sample size. $ (round to the nearest cent)
For part b), is the assumption that the distribution is normal necessary? Yes No
Please only answer if you are able to answer correctly and entirely.
The probability that the average price is between $153 and $155 is 0.04.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The average price of a math textbook =$158
The standard deviation =$26
The mean= 158
n =number of textbooks randomly chosen which is 40
n=10
Then
σ = 26
σₓ = σₓ/√n
= 26/√40
Therefore. σₓ² = 16.90
For the group of 48, find the probability that the average price is between $153 and $155.
The probability that the average price is between $153 and $155
= 0.04
Learn more about probability here;
https://brainly.com/question/11234923
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Please help me with this ,
Answer:
(a) -2.3°/min
(b) -2.9°/min
Step-by-step explanation:
The average rate of change is the ratio of the difference in R values to the difference in the corresponding t values.
(a) m = (157.6 -226.6)/(30 -0) = -69/30 = -2.3 . . . degrees per minute
__
(b) m = (61.6 -119.6)/(70 -50) = -58/20 = -2.9 . . . degrees per minute
If your starting salary is $40000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn one the first 16 years that you work
Answer:
Total amount in dollars= $64614.00
Step-by-step explanation:
Initial starting salary is $40000.
Rate of increase is 3%
Number of years is 16 years
The salary is compounded yearly.
Amount A after 16 years is given as
A= p (1+r/n)^ (nt)
A=40000(1+0.03/16)^(16*16)
A= 40000(1.001875)^(256)
A=40000(1.61534824)
A= 64613.92959
Total amount in dollars= $64614.00
Answer: the answer is $806275
Step-by-step explanation:
A p e x
What is the US TREASURY BONDS pretax expected return?
Answer:
this is the return on an investment that does not include the taxes the investor must pay on this return
Complete parts (a) through (c) below.
(a) Determine the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.
(b) Determine the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 level of significance based on a sample size of n = 20.
(c) Determine the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.
Answer:
(a) 1.341
(b) -2.539
(c) -2.160 and 2.160
Step-by-step explanation:
(a) We have to find the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%
Now, looking in the t table with P = 10% and [tex]\nu[/tex] = 15, we get the critical value of 1.341.
(b) We have to find the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%
Now, looking in the t table with P = 1% and [tex]\nu[/tex] = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.
(c) We have to find the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.
Since the degrees of freedom are included here, so we will use t table here for a population mean test.
In the table there are two values given, one is the degrees of freedom and another is the value of P.
P is the level of significance at which the critical values are calculated.
So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is [tex]\frac{0.05}{2}[/tex] is 0.025, i.e. P = 2.5%.
Now, looking in the t table with P = 2.5% and [tex]\nu[/tex] = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.
The mean temperature for the first 4 days in January was 8°C. The mean temperature for the first 5 days in January was 7°C. What was the temperature on the 5th day? SOMEONE HELP FIRST ANSWER BRAINLIEST THIS TIME I PROMISE LOL
Answer:
The temperature of the 5th day was 3°C
Step-by-step explanation:
Mean temperature of the first 4 days = 8°C
Note that:
Mean = Sum of temperatures ÷ number of days
∴ 8 = sum of temperature ÷ 4
[tex]= 8 = \frac{sum\ of\ temperatures}{4}[/tex]
[tex]= sum\ of\ temperatures\ = 8\ \times\ 4 = 32[/tex]
Therefore the sum of the first 4 days = 32
Let the temperature of the next day (the fifth day) be m
Hence,
sum of the temperatures of first 5 days = 32 + m - - - - (1)
Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:
Mean temperature of the first 5 days = 7
[tex]Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)[/tex]
Now, you will notice that equation (1) = equation (2)
∴ 32 + m = 35
m = 35 - 32 = 3
therefore, the temperature of the 5th day was 3°C
Which point slope form equations could be produced with the points (3,2) and (4,6)
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of a line given two points first find the slope of the line and use the formula
y - y1 = m( x - x1) to find the Equation of the line using any of the points given
Slope of the line using points
(3,2) and (4,6) is
[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]
So the equation of the line using point
( 3 , 2 ) and slope 4 is
y - 2 = 4( x - 3)Hope this helps you
I need help please. Thank you
Answer:
0.0009765625
Step-by-step explanation:
This is what i got its probally incorrect
A laboratory tested n = 98 chicken eggs and found that the mean amount of cholesterol was LaTeX: \bar{x}x ¯ = 86 milligrams with σ = 7 milligrams. Find the margin of error E corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.
Answer:
1.3859
Step-by-step explanation:
The formula for Margin of Error is given as:
Margin of Error = Critical value × Standard Error
Critical value = z score
In the question, we are given a confidence interval of 95%.
Z score for a 95% confidence level is given as: 1.96
Hence, critical value = 1.96
Standard Error = σ / √n
Where n = number of samples = 98 chicken eggs
σ = Standard deviation = 7 milligrams
Standard Error = 7/√98
Standard Error = 0.7071067812
Hence, Margin of Error = Critical value × Standard Error
Margin of Error = 1.96 × 0.7071067812
Margin of Error = 1.3859292911
Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859
(x
3
+y
3
)(xy
4
+7)
Answer:
question is not proper
Step-by-step explanation:
question is
Please help. I’ll mark you as brainliest if correct!
Answer: x= -1, z=2, y= -4
Step-by-step explanation:
System of equations:
-5x - 4y - 3z= 15 +
-10x + 4y + 6z= 6
-15x + 3z = 21 ------> 3 (-5x + z) = 7.3
-5x + z = 7
now,
-10x + 4y + 6z= 6
2(-5x + z) + 4y + 4z = 6
14 + 4y + 4z = 6
7 + 2y + 2z = 3
2y + 2z= -4
y+z=-2
Now we were using the equation: 20x + 4y + 4z = -28
20x + 4(y+z) = 20x -8= - 28
20 x = -20
x= -1
With this we can find y and z
X=-1
-5x + z = 7
z= 2
y+z=-2
y=-4
Finally we have: x= -1, z=2, y= -4
I hope this can help you.
Thank you
A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix. A number line goes from 65 to 115. Crackers's whiskers range from 70 to 100, and the box ranges from 75 to 85. A line divides the box at 80. Cookies's whiskers range from 70 to 115, and the box ranges from 90 to 105. A line divides the box at 100. Which statement is true about the box plots
OPTIONS:
A. The interquartile range of the trail mix data is greater than the range of the cracker data.
B. The value 70 is an outlier in the trail mix data.
C. The upper quartile of the trail mix data is equal to the maximum value of the cracker data.
D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
Answer:
D.
Step-by-step explanation:
With the given information about how the box plot looks like, let's examine each option to see if they are true or not.
Option A: "The interquartile range of the trail mix data is greater than the range of the cracker data."
The interquartile range of trail mix data = 105 - 90 = 15
Range of cracker data = 100 - 70 = 30
Option A is NOT TRUE.
Option B: "The value 70 is an outlier in the trail mix data."
This is NOT TRUE. There are not outliers as 70 is the minimum value if the ranges of the data set for the trail mix.
Option C: "The upper quartile of the trail mix data is equal to the maximum value of the cracker data."
Upper quartile of the trail mix data = 105
Max value of cracker data = 100
This statement is NOT TRUE.
Option D: "The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers."
The greater the range value, the greater the variation. Thus,
Range value of the trail mix data = 115 - 70 = 45
Range value of the cracker data = 100 - 70 = 30
This is statement is correct because trail mix data have a greater range value, hence, it has a greater variation in the number of calories.
Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answer:
u= 2 ; v = 1
Sen 60 = [tex]\frac{\sqrt{3}}{u}[/tex] so u=2
Using the pythagoras theorem [tex]u^{2} =v^{2} +\sqrt{3}^{2}[/tex] so v =[tex]\sqrt{2^{2} - 3}[/tex] =1
PLEASE PLEASE PLEASE HELP ME ANSWER THIS QUESTION QUICK!! The picture of the question is down below. The answer choices are increased or decreased.
Answer:
NEGATIVE; DECREASED.
Step-by-step explanation:
A correlation coefficient of -0.76 indicates that there is a "fairly" strong negative relationship between the daily temperature and the number of people who visit the store.
This implies that, as the daily temperature increases, number of customers who come to the store decreases.
Therefore, the interpretation of the situation is:
"There is a NEGATIVE association between x and y. As the high temperature of the day increases across days, the number of customers who come to the store DECREASED.
A cyclist rides her bike at a speed of 30 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 2
minutes? Do not round your answers.
Answer:
0.5 km/min and 1km
Step-by-step explanation:
30 km in an hour
30 km in 60 mins, 30/60 km in one minute so she cycle 0.5km/min. They will cover 1 km in 2 minutes
Find the midpoint of the segment with the given endpoints.
(7,10) and (-1,- 8)
Answer:
(3,1) is the midpoint
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(7+-1)/2 = 6/2 =3
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(10+-8)/2 = 2/2 = 1
(3,1) is the midpoint
Answer:
(3, 1)
Step-by-step explanation:
We can use the formula [ (x1+x2)/2, (y1+y2/2) ] to solve for the midpoint.
7+(-1)/2, 10+(-8)/2
6/2, 2/2
3, 1
Best of Luck!
simplify √-18
A 3i√2
B 9i√2
C -3√2
[tex]\\ \rm\longmapsto \sqrt{-18}[/tex]
[tex]\\ \rm\longmapsto \sqrt{18}i[/tex]
[tex]\\ \rm\longmapsto \sqrt{9\times 2}i[/tex]
[tex]\\ \rm\longmapsto \sqrt{3(3)(2)}i[/tex]
[tex]\\ \rm\longmapsto 3i\sqrt{2}[/tex]
Answer:
A. [tex]\displaystyle 3i\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sqrt{-18} → \sqrt{[2][-1][9]}\\ \\ 3i\sqrt{2}[/tex]
As you can see, you need a perfect square to wourk with, which in this case is 9. Now, [tex]\displaystyle \sqrt{-1}[/tex] comes out as an imaginary number [tex]\displaystyle [i],[/tex]so pull it out of the radical alongside 3, [tex]\displaystyle \sqrt{9}.[/tex]
I am joyous to assist you at any time.
in triangle JKL, angle JKL is a right angle, line KM is an altitude, JL=20, ML=4. Find KM
9514 1404 393
Answer:
KM = 8
Step-by-step explanation:
The ratio of long side to short side is the same for all of the triangles in this geometry:
KM/ML = JM/KM
KM² = ML·JM = 4(20-4) = 64
KM = √64 = 8
The length of KM is 8 units.
Find the equation of the circle in standard form for the given center (h, k) and radius R:(H,K)=(4/3,-8/8),R=1/3
Answer:
The answer is option BStep-by-step explanation:
Equation of a circle is given by
( x - h)² + ( y - k)² = r²
where r is the radius and
( h , k) is the center of the circle
From the question the radius R = 1/3
the center ( h ,k ) = (4/3 , -8/3)
Substituting the values into the above equation
We have
[tex](x - \frac{4}{3} )^{2} + {(y - - \frac{8}{3}) }^{2} = ({ \frac{1}{3} })^{2} [/tex]
We have the final answer as
[tex](x - \frac{4}{3} )^{2} + {(y + \frac{8}{3}) }^{2} = \frac{1}{9} [/tex]
Hope this helps you
PLS HELP IM CONFUSED
Given the graph of a radical function, which statement is correct?
Radical function going from the point negative 3 comma negative 2 up to the right through the point comma 0
A. R colon open bracket y is an element of all real number close bracket
B. R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
C. R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 2 close bracket
D. R colon open bracket y is an element of all real numbers such that y is greater than or equal to 1 close bracket
Answer:
The answer to your question will be the choice "D."