[tex](x_1, y_1) = (6,-10),~~ (x_2, y_2) = (3,-13)\\\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-13 +10}{3 -6} =\dfrac{-3}{-3} =1[/tex]
What is the midpoint of the segment shown below?
A.(5,7/2)
B.(5,7)
C.(5/2,7)
D.(5/2,7/2)
Answer:
D
Step-by-step explanation:
[tex](x_{1},y_{1}) = (2 , 2)\\\\ (x_{2},y_{2}) = (3 , 5)\\\\\\Midpoint=\left(\dfrac{x_{1}+y_{1}}{2},\dfrac{x_{2}+y_{2}}{2} \right)\\\\\\=\left(\dfrac{3+2}{2},\dfrac{5+2}{2} \right)\\\\\\= \left(\dfrac{5}{2},\dfrac{7}{2} \right)[/tex]
There are 6 yellow, 9 blue, and 4 orange balls inside an urn. 8 balls are chosen from the urn without replacement. Let X, Y , and W denote the number of yellow, blue, and orange balls selected, respectively.
(a) Find P{X + W = 1}.
(b) Find P{X = 2, Y = W}
Using the probability concept, it is found that:
a) P{X + W = 1} = 0
b) P{X = 2, Y = W} = 0.0667
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, the order in which the balls are chosen is not important, hence, the combination formula is used to find the number of outcomes.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In total, 8 balls are chosen from a set of 19, hence:
[tex]T = C_{19,8} = \frac{19!}{8!11!} = 75582[/tex]
Item a:
1 from a set of 15.7 from a set of 4.Not possible, hence:
P{X + W = 1} = 0
Item b:
2 from a set of 6.3 from a set of 9.3 from a set of 4.Hence:
[tex]D = C_{6,2}C_{9,3}C_{4,3} = \frac{6!}{2!4!} \times \frac{9!}{3!6!} \times \frac{4!}{3!1!} = 5040[/tex]
Then, the probability is:
[tex]p = \frac{D}{T} = \frac{5040}{75582} = 0.0667[/tex]
P{X = 2, Y = W} = 0.0667
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This graph gives Selma's distance from home over time What does the slope of the line show in this situation? 20 18 16 Select from the drop-down menus to correctly complete each statement 14 12 Distance from home (miles) 100 For this situation, the slope of the line represents 81 60 Choose 40 20 The slope is Choose... which means that Selma's distance 0 from home Choose... by Choose... miles per hour.
Answer:
The amount Selma's distance from home changes per unit of time.
The slope is 38, which means that Selma's distance from home increases by 38 miles per hour.
Step-by-step explanation:
I just took the the test in k12 and I got it right.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. Selma's distance from home increases by 38 miles per hour.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points from graph are (2, 91) and (4,167)
x₁=2,y₁=91,x₂=4, y₂=167
Substitute in the formula
167-91/4-2
76/2
38
The amount Selma's distance from home changes per unit of time.
So slope is 38, which means that Selma's distance from home increases by 38 miles per hour.
Hence Selma's distance from home increases by 38 miles per hour.
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7. Tell whether the sequence is arithmetic. If it is, identify the common difference. (I point)
19.8. -3, -14,
Not arithmetic
Arithmetic, common difference is -11
Arithmetic, common difference is 5
Arithmetic, common difference is 17
Answer:
Arithmetic, common difference is -11
Step-by-step explanation:
19, 8, -3, -14
common difference = d = 8 - 19 = -11
-3 - 8 = -11
-14 - (-3) = -11
Arithmetic, common difference is -11
please someone helpppp meeeeee
Answer:
b
Step-by-step explanation:
236
Answer:
my answer is C/386
Step-by-step explanation:
x/2+74+42+77=x
Which term from the drop-down menu makes the statement true?
Select Choice triangles are similar.
A list of choices that appears on a computer screen when a person clicks on the menu title To print the document click on print in the file drop down menu
Which of the functions represents a function?
Answer:
letter A or B but I think it's letter b
Answer:
The answer is A
Step-by-step explanation:
on edge 2021
Solve
46+(-4)
A. 50
B. 42
C. -42
D. -50
we have 46 + (-4) = 46 - 4 = 42
so the answer is B
ok done. Thank to me :>
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $37.27
what is the amount of the tip is approximately
the numbers one through 10 are written on individual cards and place in a bag. If you reach into the bag to pull out card what is the probability that it will be a 7
Answer:
1 in 10 chance
Step-by-step explanation:
There are 10 cards, so since you reach into the bag and pull out only 1 card, there is a 1 in 10 chance.
Patient”s wt: 60 lbs Medication order: 0.5 mg/kg Stock medication : 10 mg/mL, How many mL will you give them?
Answer:
Needs 13.6077 mg/mL, but they have in stock only 10 mg/mL, so will be short 3.6077 mg/dL.
Step-by-step explanation:
1 lb= 0.45359 kg
60lbs converted to kg= 60lb = 27.2154 kg
Medication order 0.5 mg x kg = 0.5 mg x 27.2154 kg = 13.6077 mg/mL
In stock only 10 mg/mL= 13.6077 mg/mL - 10 mg/mL= 3.6077 mg/mL
Will be short 3.6077 mg/mL
Jessica has 23,450 stickers in her sticker collection. Her sister has 20,993 stickers in her collection. Who has the most stickers?
Answer:
Jessica (23,450 stickers)
Solve: m = 5 – (-10).
Answer:
m=15
Step-by-step explanation:
help! giving brainliest!!!
The area of a rectangle is 4y+10.A.Represent the area of the rectangle in factored form.B.Use the factored form to give one possible set of dimensions for this rectangle
Answer:
2 ( 2y + 5 )
Step-by-step explanation:
→ Take out 2 as a factor
2 ( 2y + 5 )
Answer:
A = 2(2y + 5)2 and 11 (when y = 3)Step-by-step explanation:
The area equation is:
A = lwGiven:
A = 4y + 10This can be factored as:
A = 2(2y + 5)Let y = 3, then the dimensions are:
2 and 2*3 + 5 = 11Math experts please simplify this thank you
Answer:
t+4 / t-4
Step-by-step explanation:
(t^2 - 16) / (t^2 -8t +16)
=( t^2 - 4^2) / (t^2 - 2*4*t + 4^2)
by formula a^2 - b^2 = (a+b)(a-b)
= (t+4)(t-4) / (t-4)^2
= (t+4)(t-4) / (t-4)(t-4)
= t+4 / t-4
Let E be the region bounded cone z = â 6 â ( x 2 + y 2 ) and the sphere z = x 2 + y 2 + z 2 . Provide an answer accurate to at least 4 significant digits. Find the volume of E.
Answer:
Step-by-step explanation:
Solve the inequality and express your answer in interval notation.
x2 - 12x + 5 <0
Answer:
([tex]6 - \sqrt{31}[/tex], [tex]6 + \sqrt{31}[/tex])
Step-by-step explanation:
[tex]x^{2}-12x+5 < 0[/tex]
To solve this inequality, we can start by completing the square. To do this, we divide the x coefficient (-12) by 2 and then square it. We then add the result to the left side of the equation. To ensure the inequality remains true, we also subtract it.
[tex]x^{2}-12x+(-6^{2})-(-6^{2}) + 5 < 0\\x^{2}-12x+36-36 + 5 < 0\\[/tex]
We can then express the first trinomial as a perfect square.
[tex](x-6)^{2} - 31 < 0[/tex]
Add 31 to both sides:
[tex](x-6)^{2}< 31[/tex]
Then take the square root of both sides:
[tex]x-6<[/tex] ± [tex]\sqrt{31}[/tex]
Finally, add 6 to both sides:
x < 6 + [tex]\sqrt{31}[/tex]
x > 6 - [tex]\sqrt{31}[/tex]
The solution to the inequality in interval notation is shown by option A
What is inequality?
An inequality in mathematics describes how two expressions relate to one another by indicating whether one expression is greater, smaller, equal to, or not equal to the other. Inequalities are denoted by symbols.
We have to use the quadratic formula that states that;
x < (-b ± √([tex]b^2[/tex] - 4ac)) / 2a
So we have that;
x < [12 ± √([tex](-12)^2[/tex] - 4 * 1 * 5)] / 2 * 1
Thus we would obtain in the end;
6 - √31 < x < 6 + √31
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Write an equation in slope-intercept form of the line shown.
Answer:
y=-3/2x+5
Step-by-step explanation:
The line intersects with points (2,2) and (4,-1). Slope intercept form is y=mx+b, where m is slope and b is the y intercept. The y intercept appears to be at (0,5), so b=5. As for the line, the formula for calculating slope is y2-y1/x2-x1 (the order of the points you use actually does not matter; you just have to make sure both coordinates from the same point are placed in the same part of the formula). -1-2/4-2=-3/2. Therefore, the slope is -3/2 (or -1.5 if you want a decimal).
Scientific notation question in mathematics please answer
A newly discovered planet has a mass of 4.8743 · 10 22 kilograms. It's estimated that there is water on the surface and that, the water's mass is only 4 · 10 -2 percent of the planet's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.
Answer:
1.94972 × 10¹⁹ kgStep-by-step explanation:
Mass of the planet:
4.8743 × 10²² kgThe water's mass:
4×10⁺²%Mass of the planet's water:
4.8743 × 10²² * 4×10⁺² / 100 = 19.4972 × 10²²⁺²⁺² = 19.4972 × 10¹⁸ = 1.94972 × 10¹⁹What is 953 divided by 6
Answer
158 with a remainder of 5 ( also expressed as 953/6 OR 158.333333333333)
Step-by-step explanation:
I wasn't sure if you wanted a fraction, so I put two forms of the answer.
find the derivative of (Cosx/1+sinx)^5
Use the Chain Rule:
[tex]\frac{d}{dx} [f(g(x))] = f'(g(x)) * g'(x)[/tex]
Given Information:
[tex]f(x) = x^5\\ g(x) = \frac{cos(x)}{1} +sin(x)\\ f(g(x)) = ( \frac{cos(x)}{1} +sin(x))^5\\ \\ f'(x)=5x^4\\ g'(x)=\frac{-sin(x)}{1} + cos(x)\\f'(g(x))*g'(x)=5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]
The answer is:
[tex]5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]
negative two B subtracted by C plus four B plus three C
Answer:
First we should make this word problem into an equation.
. * (_poof_) *,
-2b - c + 4b + 3c There we go. . . much better.
Now we can simplify the equation by combining like terms.
( - 2b + 4b ) + ( - c + 3c ) = ( 2b ) + ( 2c )
So the simplified form of this would be 2b + 2c.
Step-by-step explanation:
hope this helps. . . <3
good luck! uωu
Nghiệm của Phương trình sĩn= -1
Answer:
sinx=−1⇔x=−π2+k.2π,k∈Z ( mà ông người VN đúng không =)))
Step-by-step explanation:
SUBIECTUL I
1. 1p Să se determine primul termen al unei progresii aritmetice (an
)n≥1 știind că rația este
egală cu 5 și suma primilor zece termeni ai progresiei este egală cu 245.
2. 1p Să se determine punctele de intersecție ale graficului funcției
f: R → R, f (x) = x
2 − 7x + 12, cu axele de coordonate.
3. 1p Să se determine numărul real a pentru care vectorii
u⃗ = (a − 2)i + (3a − 1)j și v = 2i +4j sunt coliniari.
4. 1p Să se calculeze ctg x, știind că sin x =
√3
2
, x ∈ (0, 90°
).
5. 1p Să se determine soluțiile reale ale ecuației 49x+2 = 7
x
2+5
.
6. 1p Să se rezolve ecuația : Ax
2+Cx
2 = 0, x∈ N , x≥ 2.
SUBIECTUL II
1 Se consideră matricea A(a) = (
1 0 √a
1 0 1
a 1 1
), unde a ∈ (0, ∞).
a) 0.5p Arătați că det(A(4)) = 1.
b) 0.5p Demonstrați că det(A(a) ∙ A(1) − A(a + 1)) > 0, pentru orice a ∈ (0, ∞).
2. Pe mulțimea de numere reale se definește legea de compoziție asociativă
x ∘ y = √3(xy + 4) − 3(x + y).
a) 0.5p Arătați că √3 ∘ 2 = √3.
b) 0.5pDemonstrați că x ∘ y = √3(x − √3)(y − √3) + √3, pentru orice numere reale x și y.
SUBIECTUL III
1 0.5p Se consideră funcția f: R → R, f(x) = e
2x
(x − 5).
Arătați că f
′
(x) = e
2x
(2x − 9), x ∈ R .
2. 0.5p Se consideră funcția f: R → R, f(x) =
x
√x
2+1
.
Arătați că ∫ f(x)√x
2 + 1
2
0
dx = 2.
Answer:
there was a tipikal answers of this question
Please help me ASAP please please
Answer:
x = 67°
Step-by-step explanation:
angle FGD and angle CGE are vertical angles, meaning that they both have the same value. This concludes that angle FGD must be 23°. Now, we have to find angle x. We know that angle x and angle FGD are complementary, meaning they sum to 90°. Therefore, x = 90° - 23° = 67°.
Write an equation in point-slope form of the line that passes through the point (4,−9) and has a slope of 6.
The equation is y−
Answer:
Step-by-step explanation:
Okay, so the point-slope form is
(y - y1) = m(x - x1)
Where m = the slope of the line
and where (x1, y1) is a point on the line
So, if the slope is 6, then m = 6
Now, you plug that and the point (4, -9) into the equation above.
(y -(-9)) = 6(x - 4)
y + 9 = 6(x - 4)
This is the point slope form of the line
The angle of depression from the top of a cliff to a
nearby town is 12 degrees. If the top of the cliff is
277 feet above the town, how far is the town from
the base of the cliff?
Round your answer to the nearest tenth of a foot
Answer:
Step-by-step explanation:
d = 277/tan12 = 1,303.1825... m = 1.3 km
The nearest tenth of a foot, the distance from the town to the base of the cliff is approximately 1337.3 feet.
The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
The angle of depression is 12 degrees, and the side opposite the angle is the height of the cliff (277 feet), while the side adjacent to the angle is the distance from the town to the base of the cliff (which we want to find).
Let's denote the distance from the town to the base of the cliff as "d."
The tangent of the angle of depression is given by:
tan(12°) = opposite / adjacent
tan(12°) = 277 / d
Now, solve for "d":
d = 277 / tan(12°)
Using a calculator:
d ≈ 1337.25 feet
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Simplify these expressions
a) 5 x x
b) 6 x x xy
c) 2 x x 3 y
Maximize z=200x+300y subject to x+2y<10 ,x+y<6,x>4 and x>0 ,y>0
Answer:
In theory I would have started looking at the critical points of the function, ie where the tangent plane is horizontal. Trick is, since the function is linear in both x and y the tangent plane is the curve itself, and it's never horizontal. We have to parametrize the border and look in there.
From the last two conditions ([tex]x>0; y>0[/tex]) we are looking only at the first quadrant. Let's start drawing lines.
The various restrains are color coded in the graph ([tex]x+2y<10[/tex] is red, [tex]x+y<6[/tex] is blue, [tex]x>4[/tex] is orange). That leads to the right triangle with a grey border that gets parametrized as shown. Due to the linearity of the original function, the maximum is at one of the extremes (upper or lower depending if the coefficient of the parameter is positive or negative). At this point is just calculating the values, pick up the largest, and see which points correspond to that value of the parameter.
Number crunching done, the maximum is at (4,2)