Answer:D) Under-root 25.Under-root 3
Step-by-step explanation
Under-root 25 = 5
Answer:
Answer D and B.
Step-by-step explanation:
[tex]{ \bf{5 \sqrt{3} }} \\ = { \bf{ \sqrt{ {5}^{2} } \times \sqrt{3} }} \\ = { \bf{ \sqrt{25} . \sqrt{3} }}[/tex]
If the mean, median, and mode are all the same for 4, 9, 7, 8, and x, what is the value of x?
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Explanation:
Since we have an odd number of values, this tells us that the median is part of the data set. It's the middle most item after we sort the values.
Recall that the mode is the most frequent item. Since the mode and median are the same, this must mean x can only be equal to one of the following
4, 9, 7 or 8
We can only pick one of those values.
----------------------
If x = 4, then the set {4,9,7,8,x} updates to {4,9,7,8,4} which sorts to {4,4,7,8,9}
The middle most item is in slot 3, which would be 7. So the median is 7.
The median 7 does not match with the mode 4.
So we cross x = 4 off the list.
-----------------------
If x = 7, then we have {4,7,7,8,9}
The mode is 7 and the median is 7. So far, so good.
Now let's compute the mean. Add up the values and divide by 5 because there are 5 items.
(4+7+7+8+9)/5 = 35/5 = 7
We've shown that the set {4,7,7,8,9} has mean 7.
Overall, that set has the same mean, median and mode. So the answer is confirmed.
I'll let you check the cases when x = 8 and x = 9.
The third term of an arithmetic sequence is $5$ and the eighth term is $-20$. What is the product of the 4th and 2015th terms?
Answer:
0
Step-by-step explanation:
Let n be the first term of this sequence and d the difference between two consecutive terms.
Following the arithmetic sequence formula,
The equation for the 3rd term:
n + 2d = 5
and the equation for the 8th term:
n + 7d = -20
We should start by finding d by subtracting the second equation from the first.
n + 2d - (n + 7d) = 5 - (-20)
-5d = 25
d = -5
We can then find the 1st term by plugging this number into the first equation.
n + 2 * -5 = 5
n - 10 = 5
n = 15
Now, using once again the arithmetic sequence formula, find the equation for the fourth term.
n + (4 - 1)*d
Plug in the values we found previously and solve:
15 + (4 - 1)*-5
= 15 + 3*-5
= 15 + (-15)
= 0
The 4th term is 0.
Remember that this problem is asking for the product of the 4th term and the 2015th term, and anything times zero equals to zero, so we don't even need to solve for the 2015th term!
Therefore, the answer to this problem is 0.
The product of the 4th and 2015th terms is 0 if the third term of an arithmetic sequence is 5 and the eighth term is -20.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
The third term of an arithmetic sequence is 5 and the eighth term is -20
a + 2d = 5
a + 7d = -20
After solving the equations:
a = 15
d = -5
4th term = 15 + 3(-5) = 0
2015th term = 15 + 2014(-5) = -10055
The product of the 4th and 2015th terms = 0(-10055) = 0
Thus, the product of the 4th and 2015th terms is 0 if the third term of an arithmetic sequence is 5 and the eighth term is -20.
Learn more about the sequence here:
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Will give brainliest answer
Yeahhhh I ain't dat smart
But that's why I got BRAINLY...
Anyways your welcome
Hope u have a good day
PLZZZZZ HURRY WILL GIVE BRAINLIEST!!!!
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds
Yes, because both figures are rectangles and all rectangles are similar.
No, because the center of dilation is not at (0, 0).
No, because corresponding sides have different slopes.
Answer:
option b
Step-by-step explanation:
both are rectangles and similar measures
Yes, because both figures are rectangles and all rectangles are similar
The rectangle EFGH is a result of the dilation of rectangle ABCD
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the first rectangle be represented as ABCD
Now , the rectangle is dilated by a scale factor k
And , the transformed rectangle is given by EFGH
where the center of origin is the scale factor of dilation
Now , the ratios of the sides of the rectangles will be similar
So , the rectangles ABCD and EFGH are similar
Hence , the dilated rectangle is EFGH
To learn more about dilation click :
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What is the difference between the temperature - 7 Celsius and - 12 Celsius on a scatter diagram
Answer:
I have to go get my car from the doctor office today
Class A has 9 pupils and class B has 24 pupils.
Both classes sit the same maths test.
The mean score for class A is 40.
The mean score for class B is 20.
What is the mean score (rounded to 2 DP) in the maths test across both classes?
Answer:
mean ≈ 25.45
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
We require the sum for both classes
class A
mean = [tex]\frac{sum}{9}[/tex] = 40 ( multiply both sides by 9 )
sum = 9 × 40 = 360
class B
mean = [tex]\frac{sum}{24}[/tex] = 20 ( multiply both sides by 24
sum = 24 × 20 = 480
Total sum for both classes = 360 + 480 = 840 , then mean for both classes is
mean = [tex]\frac{840}{33}[/tex] ≈ 25.45 ( to 2 dec. places )
Use the Laplace transform to solve the given system of differential equations.
Let X(s) and Y(s) denote the Laplace transforms of x(t) and y(t), respectively. Then taking the transform of both sides of both equations gives
LT[dx/dt + 5x + dy/dt] = LT[1]
==> s X(s) - x (0) + 5 X(s) + s Y(s) - y (0) = 1/s
==> s X(s) + 5 X(s) + s Y(s) = 1/s
==> (s + 5) X(s) + s Y(s) = 1/s
LT[dx/dt - x + dy/dt - y] = LT[exp(t )]
==> s X(s) - x (0) - X(s) + s Y(s) - y (0) - Y(s) = 1/(s - 1)
==> s X(s) - X(s) + s Y(s) - Y(s) = 1/(s - 1)
==> (s - 1) X(s) + (s - 1) Y(s) = 1/(s - 1)
Solve for X(s) and Y(s). Using elimination, you would get
X(s) = (1 - 2s) / (5s (s - 1)²)
Y(s) = (7s - 1) / (5s (s - 1)²)
Now take the inverse transforms of each. Start by getting the partial fraction decompositions:
(1 - 2s) / (5s (s - 1)²) = 1/5 (a/s + b/(s - 1) + c/(s - 1)²)
-2s + 1 = a (s - 1)² + bs (s - 1) + cs
-2s + 1 = (a + b) s ² + (-2a - b + c) s + a
==> a + b = 0, -2a - b + c = -10, a = 5
==> a = 1, b = -1, c = -1
==> X(s) = 1/5 (1/s - 1/(s - 1) - 1/(s - 1)²)
Similarly, you would find
Y(s) = -1/5 (1/s - 1/(s - 1) - 6/(s - 1)²)
Now for the inverse transforms:
LT⁻¹ [1/s] = 1
LT⁻¹ [1/(s - 1)] = exp(t )
LT⁻¹ [1/(s - 1)²] = t exp(t )
Putting everything together, we have
LT⁻¹ [X(s)] = x(t) = 1/5 - 1/5 exp(t ) - 1/5 t exp(t )
and
LT⁻¹ [Y(s)] = y(t) = -1/5 + 1/5 exp(t ) + 6/5 t exp(t )
What is
the solution to the system of equations graphed below?
3/9 and 5/15 are they equivalent
Answer:
yes
Step-by-step explanation:
3/9 Divide the top and bottom by 3
1/3
5/15 Divide the top and bottom by 5
1/3
They are equal
determine the values of X which the sequence
[tex]log3. \: log {3}^{3}. \: log {3}^{x} [/tex]
is (I) arithmetic (II) geometric
Answer:
arithmetic
hyj
bhhm
bm.hg
hgjm
hgjgshmih
mhh
jhuu
Suppose $1,000 was deposited into an account compounded quarterly that grew to $1,490 at rate of 6%. How long did it take for this to occur?
Answer:
A (1 + i)^n = 1490 time for amount to reach 1490
(1 + i)^n = 1.49 since A = $1000
n log (1 + .06/4) = log 1.49 take log of both sides at 1.5% per quarter
n = log (1.49) / log 1.015 = 26.78 periods or 6.695 years
(compare to 6.843 years compounded annually)
[tex]t = ln(A/P) / n[ln(1 + r/n)]\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.06/4)] )\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.015)] )\\t = 6.7 years[/tex]
It would take around 6 years 8 months to get $1,490 from $1,000 at 6%.
I hope I've helped! :)
HELP ME WITH THIS MATHS QUESTION
IMAGE IS ATTACHED
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Each point moves to the same distance on the other side of the mirror line. The slope of the mirror line is 1, so the points move along a line perpendicular to that, one with a slope of -1. You can make sure the distances are the same by counting the grid squares.
Derive
Somebody could help me?
check that
////////////////////////
A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose 26 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants
Answer:
27405
Step-by-step explanation:
There are 6 different variants available for each croissant. There are 26 croissants in all out of which 1 is plain. We use combination and permutation technique to identify different ways to choose croissant.
[5 + 26 - 1 ] 26 = 30C26 = 27405.
Evaluating linear piecewise functions
Henry wants to buy a new table saw for his carpentry shop. he saved $360 which is 2/3 of the price of the saw.how much does the table saw cost?
Answer:
Step-by-step explana
540
Solve 2x2 - 9x - 5 = 0 by factoring.
AS IN THE PICTURE...........
If the integer $152AB1$ is a perfect square, what is the sum of the digits of its square root?
9514 1404 393
Answer:
13
Step-by-step explanation:
152AB1 is not a square in hexadecimal, so we assume A and B are supposed to represent single digits in decimal.
If A=B=0, √152001 ≈ 389.9
If A=B=9, √152991 ≈ 391.1
The least significant digit of 152AB1 being non-zero, we know it is not the square of 390. Hence, it must be the square of 391.
For 152AB1 to be a perfect square, we must have ...
152AB1 = 391² = 152881
The sum of the digits of the square root is 3+9+1 = 13.
A linear regression equation and multiple linear regression equations can be used to calculate y if one is given the x values. However, a logistic regression equation cannot be used to calculate y when one is given x value.
a. True
b. False
Answer:
FALSE
Step-by-step explanation:
First, define y and x.
In statistics, we have what we call variables. Variables are items or symbols that can take on various values. We have dependent variables - whose values are derived from other variables in an equation - and independent variables - whose values are given and are used to determine the values of dependent variables.
Usually, y represents the dependent variable while x represents the independent variable. So the simplest form of regression equation is
y = f (x)
Said as "y is a function of x"
A logistic regression equation can be used to calculate y when x values are given.
Here, the independent variable function (the X function) is a logistic function and it is used to find a binary dependent variable (a Y value, out of two possible values).
In logistic regression equations, the value of Y is not numerical like 1, 0.2, 3/4, and so on. It is categorical, e.g.
Black/White, Gain/Lose, Pass/Fail, Eat/Drink, etc.
pls help me REALY unrgent
Answer:
[tex]269 \frac{1}{4} [/tex]
Step-by-step explanation:
the solution is found above in the diagram.
What is 10 + 15k equivalent
Plz hurry
Answer:
if you mean 15k as is 15 thousand then the answer would be 15,010
How do you do 7-7(-4)
Answer:
35
Step-by-step explanation:
7-7(-4)
Using PEMDAS
Multiply first
7 +28
Then add
35
Jessica always uses the same ratio of green beads to blue beads when she makes necklaces. The graph shows these equivalent ratios.
Which table shows the same data?
Need help due tomorrow
Answer:
[tex]Given:[/tex] Δ ABC ≈ ΔDEF
[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²
⇒ 34/A(ΔDEF)=9²/(13.5)²
⇒34/A(ΔDEF)=81/182.25
⇒A(ΔDEF)=34×182.25/81
⇒Area of ΔDEF=76.5 cm²
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Hope it helps...
Have a great day!!!
Perform the following series of rigid transformations on ∆ABC: Translate ∆ABC by moving it 5 units to the right and 2 units up. Draw the line y = -x, and reflect ∆A'B'C' across the line. Rotate ∆A''B''C'' counterclockwise about the origin by 270°.
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is translated a units right and b units up, the new point is at A'(x + a, y + b).
If a point A(x, y) is reflected across the line y = -x, the new point is at A'(-y, -x).
If a point A(x, y) is rotated counterclockwise by 270 degrees, the new point is at A'(y, -x).
Let us assume that triangle ABC has vertices at A(-6, -1), B(-3, -3) and C(-1, -2).
If it is moved 5 units to the right and 2 units up, the new point is at A'(-1, 1), B'(1, -1) and C'(3, 0). If it is reflected across the line y = -x, the vertices are at A"(-1, 1), B"(1, -1) and C"(0, -3). If it is then rotated counterclockwise about the origin by 270°, the new point is at A'"(-1, -1), B"'(1, 1), C"'(3, 0)
These 2 questions confuse me.
Can anyone help with some 3D trigonometry?
Answer:
Q2) 29 degree as unrounded to nearest degree is 28.95 degree
Q3) 69 degree as unrounded to nearest degree is 68.56 degree
Step-by-step explanation:
QU 2)
When they speak of plane we see ABCD and also see ABC
So we need the length of AB and BC to find the diagonal CA
AB^2 + BC^2 = CA^2
16.4^2 + 9.1^2 = sqrt 351.77
CA^2 = sqrt 351.77 = 18.8 cm
We know CG = 10.4cm
We identify the hypotenuse for ACG triangle
We do trig tan x = opp/adj for CGA angle
Tan x = tan-1 10.4/18.8 = 28.95099521 degree
Tan x = tan-1 18.8/10.4 = 61.04900479 degree
so we know one is much smaller than the other
We also know ACG angle is 90 degree and that angle from ABCD that meets line AG is the smaller angle.
Answer therefore must be 28.95 degree = or 29 degree
QU 3)
we are basically looking for angle where VB meets BC line or AVB meets ABC we have the slant length, so step 1 is find the height by first dividing square base by 2 then finding the height.
= 7.6/2 = 3.8 cm
Then Pythagoras
BV^2 - 1/2 BC = height
10.4^2 - 3.8^2 = height
Height = sq rt 93.72 =9.68090905 = 9.7cm
Which means V to midpoint VC = V to midpoint AB
They are the same and the midpoints are 90 degree angles.
To find the required angle for VB + BCmidpoint or we wont be able to determine the right angle hypotenuse.
We do the same as last question determine the hypotenuse and where the angle sought is is where we use the trig function = adj/hyp
Because if it was the midpoint angle then it would be opp/adj like the question 1 so this time its cos of x.
cos x = adj/hyp = cos-1 (3.8/ 10.4) = 68.5687455
Answer is 68.56 degree
The reason we show the height is so we can check by doing opp/hyp
= sin of x = sin-1 (9.68090905/3.8) = 23.11171135
and 90 -23.11171135 = 66.8882887
= 67 degree
So we go with the first one and assume 9.68 was already simplified to 9.7cm
= sin-1 (3.8/9.7) = 23 degree 90-23 = 67 degree
but when rounded to 10.4cm for slant we get the same
= sin-1 (3.8/10.4)
So we realise here trig functions -1 doesn't work on the same 90 degree angle for both lines that meet such 90 degree angle.
We try the sin-1 (10.4/ 9.68090905) = 68.5687455 = 69 degree
and that where the lines join away from the 90 degree angle we can always find true answer, and see it is a match with the first cos trig function we did.
This proves that cos line 1/line2 = sin line 1/line 2 are the same when the larger number is numerator for sin representing the hypotenuse slant for sin as shown and when the larger of the sides is numerator for cos di
and smallest side acts as denominator for both trig functions.
What are the solutions to the equation?
x3 – 6x2 – 9x + 54 = 0
Answer:
x = -3 or x = 3 or x = 6
Step-by-step explanation:
x3 – 6x2 – 9x + 54 = 0
There is no common factor to factor out. There are 4 terms. We try factoring by grouping. Factor a common factor out of the first two terms. Factor a common factor out of the last two terms.
x^2(x - 6) - 9(x - 6) = 0
x - 6 is a common factor, so we factor it out.
(x^2 - 9)(x - 6) = 0
x^2 - 9 is the difference of 2 squares, so we factor it.
(x + 3)(x - 3)(x - 6) = 0
x + 3 = 0 or x - 3 = 0 or x - 6 = 0
x = -3 or x = 3 or x = 6
Answer:
x=6 x=3 x=-3
Step-by-step explanation:
x^3 – 6x^2 – 9x + 54 = 0
Factor by grouping
x^3 – 6x^2 – 9x + 54 = 0
x^2(x-6) -9(x-6 ) =0
Factor out x-6
(x-6)(x^2 -9) =0
Notice x^2 -9 is the difference of squares
(x-6)(x-3)(x+3) = 0
Using the zero product property
x-6 =0 x-3 =0 x+3 =0
x=6 x=3 x=-3
For what value of w is4w = 2w - 8
Answer:
w =-4
Step-by-step explanation:
4w = 2w - 8
Subtract 2w from each side
4w-2w = 2w-2w - 8
2w = -8
Divide by 2
2w/2 = -8/2
w = -4
Out of 100 people sampled, 42 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to three places.
Answer:
The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Out of 100 people sampled, 42 had kids.
This means that [tex]n = 100, \pi = \frac{42}{100} = 0.42[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.293[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.547[/tex]
The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).
What is the distance between U(-1,9) and V(4,7)leave answer in radical form
Answer:
[tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\=\sqrt{(4-(-1))^{2}+(7-9)^{2} } \\\\=\sqrt{(5)^{2}+(-2)^{2}} \\\\=\sqrt{25+4} \\\\=\sqrt{29}[/tex]