Answer:
21.75m
Step-by-step explanation:
14.5×150 =2175cm
1m =100cm
to convert into m divide 2175 by 100
=21.75m
rationalize root six divided by root three minus root two. [tex]\frac{\sqrt{6} }{\sqrt{3}-\sqrt{2} }[/tex]
Answer:
the answer is
[tex]3 \sqrt{2} + 2 \sqrt{3} [/tex]
Step-by-step explanation:
the explanation is given in the image.
Answer:
[tex]\huge\boxed{\dfrac{\sqrt6}{\sqrt3-\sqrt2}=3\sqrt2+2\sqrt3}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt6}{\sqrt3-\sqrt2}\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\\dfrac{\sqrt6}{\sqrt3-\sqrt2}\cdot\dfrac{\sqrt3+\sqrt2}{\sqrt3+\sqrt2}=\dfrac{\sqrt6(\sqrt3+\sqrt2)}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}=\dfrac{(\sqrt6)(\sqrt3)+(\sqrt6)(\sqrt2)}{(\sqrt3)^2-(\sqrt2)^2}[/tex]
[tex]\text{use}\ \sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\ \text{and}\ (\sqrt{a})^2=a[/tex]
[tex]=\dfrac{\sqrt{(6)(3)}+\sqrt{(6)(2)}}{3-2}=\dfrac{\sqrt{18}+\sqrt{12}}{1}=\sqrt{9\cdot2}+\sqrt{4\cdot3}\\\\=\sqrt9\cdot\sqrt2+\sqrt4\cdot\sqrt3=3\sqrt2+2\sqrt3[/tex]
Graph image of figure using transformation given. Reflection across x-axis.
Answer:
Q(1,1), N(3,2) A(2,5)
Step-by-step explanation:
Find the angle between (u= sqrt 5i) -8j and (v= sqrt 5i) +j. Round to the nearnest tenth of a degree.
Answer:
98.5
Step-by-step explanation:
The dude above do be wrong doh
helppppppppppp meeeeeeeeeeeeeeeee give bralienst
Answer:
Point C
Step-by-step explanation:
Point c is the only point on the number line which is in between 2 and 3.
Thus,
point c is the answer.
Hope this helps :)
is the perpendicular bisector of . What is the length of ?
A.
4
B.
6
C.
12
D.
7
Answer:
the answer is C. 12
Step-by-step explanation:
in the diagram AB =AD and
Answer:
AC ≅ AE
Step-by-step explanation:
According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.
Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.
Answer:
A). AC ≅ AE
Step-by-step explanation: took test on edge
What is the measure of JOK, given that GH=JK ?
A.
288
B.
108
C.
72
D.
18
Answer:
72 degrees.
Step-by-step explanation:
The angle marked as 72 degrees and the angle of JOK are considered vertically opposite angles in relation to each other. This relationship means that the angles are equal.
Answer:
[tex]\boxed{Option \ C}[/tex]
Step-by-step explanation:
Congruent arcs subtend congruent central angles.
So,
∠GOH ≅ ∠JOK
∠JOK = 72 degrees
Which value of x makes the equation 0.75( x + 20) = 2 + 0.5(x - 2) true?
Answer:
0.75x+15=2+0.5x-1
0.25x=1-15
0.25x=-14
x=-56
Step-by-step explanation:
Mark is solving the following systems Step 1: He multiplies equation (1) by 7 and adds it to equation (3). Step 2: He multiplies equation (3) by 2 and adds it to equation (2). Which statement explains Mark’s mistake? He added equation (3) instead of equation (2) in step 1. He did not multiply equation (3) by the same number as equation (1). He did not eliminate the same variables in steps 1 and 2. He added equation the equations in step instead of subtracting them.
Answer:
Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.
He makes such steps:
1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:
7x+7y+7x+4x-y-7z=14+16,
11x+6y=30.
2. He multiplies equation (3) 4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:
8x-2y-14z+3x+2y+z=32+8,
11x-13z=40.
Thus, he did not eliminate the same variables in steps 1 and 2.
Answer: correct choice is he did not eliminate the same variables in steps 1 and 2.
Hope this helps you :)! If you would mark me brainliest, that would be awesome!
Answer:
correct answer is c
Step-by-step explanation:
edge 2020
6th grade math help me, please :D
Answer:
option: D
51200
Step-by-step explanation:
64000 x 80/100 = 51200
Answer:
Hi there!!!
your required answer is option D.
explanation see in picture.
I hope it will help you...
In a regional high school swim meet, women’s times (in seconds) in the 200-yard freestyle ranged from 108.5 to 140.6. Estimate the standard deviation, using the Empirical Rule. (Round your answer to 2 decimal places.)
Answer: Estimated the standard deviation α = 5.35
Step-by-step explanation:
According to Empirical rule, the largest value is approximately:
ц + 3α
And the smallest value is approximately:
ц + 3α
Based on the given figures in the question, we can say
ц + 3α = 140.6
ц - 3α = 108.5
Now subtracting these two; we have
ц + 3α - ( ц - 3α ) = 140.6 - 108.5
ц + 3α - ц + 3α = 32.1
6α = 32.1
α = 32.1 / 6
α = 5.35
Estimated the standard deviation α = 5.35
What is the value of x plz help
Solve for one half on the triangle with height 6 and base would be 4/2 = 2
Use the Pythagorean theorem:
X = sqrt( 6^2 + 2^2)
X = sqrt( 36 + 4)
X = sqrt(40)
The answer is D
an organisms population in the year 2000 was about 9 billion and was increasing with a double time of 20 years. Suppose the population continued this growth pattern from the year 2000 into the future. Complete part a through d
Answer:
For this case we know that at the starting year 2000 the population was 9 billion and we also know that increasing with a double time of 20 years so we can set up the following model:
[tex]18 =9(b)^20[/tex]
And if we solve for b we got:
[tex] 2 = b^20[/tex]
[tex]2^{1/20}= b[/tex]
And then the model would be:
[tex] y(t) = 9 (2)^{\frac{t}{20}}[/tex]
Where y is on billions and t the time in years since 2000.
And for this equation is possible to find the population any year after 2000
Step-by-step explanation:
For this case we know that at the starting year 2000 the population was 9 billion and we also know that increasing with a double time of 20 years so we can set up the following model:
[tex]18 =9(b)^20[/tex]
And if we solve for b we got:
[tex] 2 = b^20[/tex]
[tex]2^{1/20}= b[/tex]
And then the model would be:
[tex] y(t) = 9 (2)^{\frac{t}{20}}[/tex]
Where y is on billions and t the time in years since 2000.
And for this equation is possible to find the population any year after 2000
Line j is a straight line. Which equation represents the relationship between the measures of Angle w and Angle z? A) Measure of angle w = measure of angle z b) Measure of angle w + measure of angle z = 90 degrees c) Measure of angle w + measure of angle z = 100 degrees d) Measure of angle w + measure of angle z = 180 degrees
Answer:
Measure of angle W + measure of angle Z = 180°
Step-by-step explanation:
The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)
Answer:
D is your answer
Step-by-step explanation:
I have no explanation
Write the partial fraction decomposition of the rational expression. Check your result algebraically.
Answer:
See below.
Step-by-step explanation:
First, distribute:
[tex]=\frac{1}{x(x+1)}[/tex]
Now, perform partial fraction decomposition. This is only two factors, so we only need linear functions:
[tex]\frac{1}{x(x+1)} =\frac{A}{x}+\frac{B}{x+1}[/tex]
Now, multiply everything by x(x+1):
[tex]1=A(x+1)+B(x)[/tex]
Now, solve for each variable. Let's let x=-1:
[tex]1=A(-1+1)+B(-1)[/tex]
[tex]1=0A-B=-B[/tex]
[tex]B=-1[/tex]
Now, let's let x=0:
[tex]1=A(0+1)+B(0)[/tex]
[tex]A=1[/tex]
So:
[tex]\frac{1}{x(x+1)}=\frac{1}{x}-\frac{1}{(x+1)}[/tex]
Double Check:
[tex]\frac{1}{x}-\frac{1}{(x+1)}=\frac{(x+1)}{x(x+1)}-\frac{x}{x(x+1)}[/tex]
[tex]=\frac{x-x+1}{x(x+1)} =\frac{1}{x^2+x}[/tex]
Which of the following is the product of the rational expressions shown here? X/x-2•3/x-2
Answer:
[tex] \boxed{\sf \frac{3x}{ {x}^{2} - 4x + 4}} [/tex]
Step-by-step explanation:
[tex] \sf Product \: of \: the \: rational \: expression: \\ \sf \implies \frac{x}{x - 2} \times \frac{3}{x - 2} \\ \\ \sf \implies \frac{3x}{(x - 2)(x - 2)} \\ \\ \sf (x - 2)(x - 2) = (x)(x - 2) - 2(x - 2) : \\ \sf \implies \frac{3x}{ \boxed{ \sf (x)(x - 2) - 2(x - 2)}} \\ \\ \sf (x)(x - 2) - 2(x - 2) = (x)(x) - (2)(x) - 2(x) - (2)( - 2) : \\ \sf \implies \frac{3x}{ \boxed{ \sf (x)(x) - (2)(x) - 2(x) - (2)( - 2) }} \\ \\ \sf \implies \frac{3x}{ \boxed{ \sf {x}^{2}} - 2x - 2x - (2)( - 2)} \\ \\ \sf (2)( - 2) = - 4 : \\ \sf \implies \frac{3x}{ {x}^{2} - 2x - 2x - \boxed{ \sf - 4}} \\ \\ \sf - ( - 4) = 4 : \\ \sf \implies \frac{3x}{ {x}^{2} - 2x - 2x + \boxed{ \sf 4}} \\ \\ \sf - 2x - 2x = - 4x : \\ \\ \sf \implies \frac{3x}{ {x}^{2} - 4x + 4} [/tex]
X/(x - 2) × 3/(x - 2) = 3x/(x² + 4x + 4). So, the correct option is A.
The product of the rational expressions shown here X/x-2•3/x-2
X/(x - 2) × 3/(x - 2)
3x/(x - 2)²
by the (a - b)² = a² + b² -2ab
(x - 2)² = x² + 4 - 4x
3x/(x² + 4 - 4x).
Therefore, the correct answer is 3x/(x² + 4 - 4x).
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Use the Product Rule of Logarithms to write an expression equivalent to In(6a+ 9b). Make sure to use parenthesis around your logarithm functions In(x +y)
Answer:
The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].
Step-by-step explanation:
Let be [tex]r = \ln (6\cdot a + 9\cdot b)[/tex], which is now solved as follows:
1) [tex]\ln(6\cdot a + 9\cdot b)[/tex] Given.
2) [tex]\ln [3\cdot (2\cdot a + 3\cdot b)][/tex] Distributive property.
3) [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex] ([tex]\ln (x\cdot y) = \ln x + \ln y[/tex]) Result.
The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].
We want to find an equivalent expression to ln(6a + 9b). We will get:
ln(6a + 9b) = ln(3) + ln(2a + 3b)
Here we will be using the rule:
ln(x) + ln(y) = ln(x*y)
Now let's see our expression:
ln(6a + 9b) = ln(3*(2a + 9b))
Now we use the above rule to write:
ln(3*(2a + 3b)) = ln(3) + ln(2a + 3b)
Then the equivalent expression is:
ln(6a + 9b) = ln(3) + ln(2a + 3b)
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Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
(A) If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.
(B) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.
Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) = [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]
= [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]
= [tex]\frac{0.3025}{0.4825}[/tex]
= 0.63
Customers can pick their own pumpkins at the great pumpkin patch. They pay $4 to enter and $3 per pound for the pumpkins they pick. Write an equitation to model the total cost, y, for x pounds of pumpkins.
Answer:
y=3x+4
Step-by-step explanation:
4 is the y intercept and 3 is the slope which is how much per pound. The equation you can use is y=mx+b, m is the slope so you fill it in with 3 and b is the y intercept so you fill it in with 4.
Write the point slope equation of the line with the given slope that passes through the given point
M= -3, (3,5)
Answer:
y - 5 = -3(x - 3).
Step-by-step explanation:
The point-slope form is y - y1 = m(x - x1).
In this case, y1 = 5, x1 = 3, and m = -3.
y - 5 = -3(x - 3).
Hope this helps!
Answer:
[tex]\boxed{y-5= -3(x-3)}[/tex]
Step-by-step explanation:
Point-slope is in the general form:
[tex]y-y_1 = m(x-x_1)[/tex]
The values are given.
[tex]m=-3\\x_1=3\\y_1=5[/tex]
Plug in the values,
[tex]y-5= -3(x-3)[/tex]
1,580 milliliters (mL) is equal to how many liter (L)?
Answer:
1.580 Liters
Step-by-step explanation:
We know that 1000 mL = 1 Liter
1580 ml * 1L/1000 ml
1.580 Liters
Answer:
1.58
Step-by-step explanation:
1 milliliter = .001 liter
Evaluate the expression. 1/2 x (4+8)
Answer:
Hey there!
1/2 x (4+8)
1/2 x (12)
6
Hope this helps :)
Answer: 6x
Step-by-step explanation:
.5x*(4+8)
.5x*(12)
6x
Hope it helps <3
Rationalize the denominator and simplify.
7
3
Answer:
[tex]\frac{\sqrt{21}}{3}[/tex] is the answer.
Step-by-step explanation:
To rationalize the denominator of [tex]\sqrt{\frac{7}{3}}[/tex] we will remove the square root or cube root from the denominator.
For which we multiply with the same value given in the denominator to numerator and denominator both.
[tex]\sqrt{\frac{7}{3}}=\frac{\sqrt{7} }{\sqrt{3} }[/tex]
[tex]\frac{\sqrt{7}}{\sqrt{3}}=\frac{\sqrt{7}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]=\frac{\sqrt{7\times 3}}{(\sqrt{3})^2}[/tex]
[tex]=\frac{\sqrt{21}}{3}[/tex]
[tex]\frac{\sqrt{21}}{3}[/tex] is the rationalized form.
Therefore, [tex]\frac{\sqrt{21}}{3}[/tex] will be the answer.
Use completing the square to solve the equation x^2+16x=-44.
we need to add 64 on both sides and required equation is x=-8±2√5-8
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x²+16x=-44
Now we need to make the coefficient of x variable half and to square it.
(16/2)²=8²=64
Now add 64 on both the sides
x²+16x+64=-44+64
x²+16x+64=20
(x+8)²=20
x+8=±√20
x+8=±2√5
Now subtract 8 on both sides
x=-8±2√5-8
Hence, we need to add 64 on both sides and required equation is x=-8±2√5-8
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6. Assume that the probability of a driver getting into an accident is 6.4%, the average cost of an
accident is $13,991.05, and the overhead cost for an insurance company per insured driver is $95.
What should this driver's insurance premium be?
Answer:
This driver's insurance premium should be at least $990.43.
Step-by-step explanation:
We are given that the probability of a driver getting into an accident is 6.4%, the average cost of an accident is $13,991.05, and the overhead cost for an insurance company per insured driver is $95.
As we know that the expected cost that the insurance company has to pay for each of driver having met with the accident is given by;
The Expected cost to the insurance company = Probability of driver getting into an accident [tex]\times[/tex] Average cost of an accident
So, the expected cost to the insurance company = [tex]0.064 \times \$13,991.05[/tex]
= $895.43
Also, the overhead cost for an insurance company per insured driver = $95. This means that the final cost for the insurance company for each driver = $895.43 + $95 = $990.43.
Hence, this driver's insurance premium should be at least $990.43.
Answer:115
Step-by-step explanation:
if a/b and c/d are rational expressions then a/b divided by c/d =a times d/b times c true or false
Answer:
(a d)/(bc)
Step-by-step explanation:
a/b ÷ c/d
Copy dot flip
a/b * d/c
ad / bc
x^2-y^2=3y in polar form
Answer:
Step-by-step explanation:
put x=r cos θ
y=r sin θ
r²cos²θ-r²sin²θ=3rsin θ
r²(cos²θ -sin²θ)=3r sin θ
r²cos 2θ=3rsinθ
r cos 2θ=3 sin θ
r=3sec 2θ sin θ
Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.)
24.5
Calculator =
Differentials =
Answer:
With calculator;√24.5 = 4.9497
With differentials;With calculator;√24.5 = 4.95
The value of the square root gotten using differentials is an approximate value of the one gotten with a calculator
Step-by-step explanation:
With calculator;√24.5 = 4.9497
Using differentials;
The nearest number to 24.5 whose square root can be taken is 25, so let us consider that x = 25 and δx = dx = - 0.5
Now, let's consider;
y = √x - - - (eq 1)
Differentiating with respect to x, we have;
dy/dx = 1/(2√x) - - - - (eq 2)
Taking the differential of eq 2,we have;
dy = (1/(2√x)) dx
Using the values of x = 25 and dx = 0.5,we have;
dy = (1/(2√25)) × 0.5
dy = 0.05
Now;
√24.5 = y - dy
√24.5 = √x - dy
√24.5 = √25 - 0.05
√24.5 = 5 - 0.05
√24.5 = 4.95
Find two numbers with difference 62 and whose product is a minimum.
Answer:
31 and -31
Step-by-step explanation:
The two numbers with a difference of 62 and whose product is a minimum are; 31 and -31
Let the two numbers be x and y.We are told that their difference is 62.
Thus; x - y = 62 ---(1)
We want their products to be minimum. Thus;f(x,y) = xy
From eq, making y the subject gives us;
y = x - 62
Thus;
f(x) = x(x - 62)
f(x) = x² - 62x
For the product to be minimum, let us find the derivative of f(x) and equate to zero. Thus;f'(x) = 2x - 62
At f'(x) = 0
2x - 62 = 0
2x = 62
x = 62/2
x = 31
Thus;
y = 31 - 62
y = -31
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An arrow is shot upward at a rate of 220 feet per second. Use the projectile formula h=−16t^2+v_0t to determine when the height of the arrow will be 400 feet. Round your answer to the nearest tenth.
Answer:Explanatory help v
Step-by-step explanation:The question gives you V0 as 220, so plug that in first.
h=-16t2+220t.
Then it says to find the time (solve for t), when the height is 400 ft. Plug 400 ft in as h and solve for t.
400=-16t2+220t.
To solve this, set the quadratic equal to 0 by subtracting 400 from both sides (0=-16t2+220t-400) and use the quadratic formula!
Answer:
The arrow reaches 400 feet in its way up at about 2.2 seconds after being launched.
Step-by-step explanation:
Since we want to find the time at which the arrow will reach 400 feet, we use this information in the equation for the height;
[tex]400=-16\,t^2+220\,t\\16\,t^2-220\,t+400=0[/tex]
and now use the quadratic equation to solve for the unknown time (t). Notice that been a quadratic equation we expect up to two answers, and then we will need to decide which answer to pick.
[tex]t=\frac{220}{2\,(16)} +/- \frac{\sqrt{(-220)^2-4 \,(16)(400)}}{2\,(16)} \\ \\t= 2.156\,sec\,\,\,or\,\,\, t=11.594\,sec[/tex]
This means that as the arrow goes up, it takes 2.156 seconds to reach 400 feet, and afterwards, after the arrow reaches it maximum height, it falls back due to acceleration of gravity, going through the same 400 feet height before reaching the ground.
We round the answer to the nearest tenth as requested.