[tex]\text{First I would recommend replacing the question mark with x}\\\text{We have two ratios, }\\\text{and we need to solve that hard-looking equation}\\\text{in terms of x}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{We can multiply x times 36:: 36x}\\\text{We can multiply 4 times 27:: 108}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{Now it's easier to solve for x:: 36x=108; x=3}\\\text{ (we divided by 36 on both sides of the = sign)}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The missing number is 3}[/tex]
Uniform Distibution
The mail arrival time to a department has a uniform distribution over 0 to 60 minutes. What is the probability that the mail arrival time is more than 20 minutes on a given day? Answer: (Round to 2 decimal places.)
Step-by-step explanation:
Let X be the mail arrival time to a department that follows uniform distribution over 0 to 60 minutes.
The probability function of X is:
f
(
x
)
=
1
60
,
0
<
x
<
60
Now, the probability that the mail arrival time is more than 40 minutes on a given day is calculated below:
P
(
X
>
40
)
=
∫
60
40
1
60
d
x
=
[
x
60
]
60
40
Calculate the length of the diagonal of the state of Wyoming.
The length of the diagonal of the state of Wyoming is 457 miles.
What is the length of the diagonal?The length of the diagonal of the diagonal can be determined using Pythagoras theorem.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse√365² + 275² = 457 miles
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Plato trigonometry is crazy
Answer:
The answer is A. 21
i hope this can help you! :)
Answer:
a)21
-step explanation:
my sis needs help asap SHOW WORK! :)
Step-by-step explanation:
el resultado le puedo ayudar si sabe Spanish
Answer:
see below
Step-by-step explanation:
White = 1 1/3 = 4/3 = 16/12
Color = 3/4 = 9/12
white - color == 16/12 - 9/12 = (16-9) / 12 = 7/12 of a scoop more for the white load
A cliff on the seashore is eroding at the rate of 17 cm per year. Write and solve an equation to find the number of years in which the cliff will erode 85cm.
Answer: 0.2 years
Step-by-step explanation:
what is (x^2y^3)^1/3 / 3 sqrt x^2
Answer: y/(3x^1/3)
Step-by-step explanation:
The figure below shows parallel lines cut by a transversal:
A pair of parallel lines is shown with arrowheads on each end. A transversal cuts through these two lines. An angle formed between the top parallel line and the transversal on the inner left side is marked 1. Another angle formed between the bottom parallel line and the transversal on the inner right side is marked 2.
Which statement is true about ∠1 and ∠2?
∠1 and ∠2 are congruent because they are a pair of adjacent angles.
∠1 and ∠2 are complementary because they are a pair of adjacent angles.
∠1 and ∠2 are congruent because they are a pair of alternate interior angles.
∠1 and ∠2 are complementary because they are a pair of alternate interior angles.
∠1 and ∠2 are congruent because they are a pair of alternate interior angles , Option C is the right answer.
What are Parallel Lines ?When two lines do not meet at any point and the distance between them remains constant , then the two lines are called parallel to each other .
It is given that the parallel lines are cut by a transversal and the angles are marked
The angle 1 and angle 2 are congruent because they are pair of alternate interior angles .
Therefore Option C is the right answer.
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Identify each pair of angles as corresponding, alternate interior, alternate exterior, same-side interior, vertical, or adjacent
1) Alternate exterior
2) Corresponding
3) Alternate exterior
4) Alternate exterior
5) Vertical
6) Corresponding
7) Adjacent
8) Corresponding
9) Corresponding
10) Alternate interior
What error did Lucia make?
Answer:
See below
Step-by-step explanation:
She combined 3x and - 9x incorrectly
she should have gotten - 6 x not - 12 x
In the given figure, ABCD is a parallelogram. Find x, y and z.
Answer:
it is 18 by unknown number
also can someone check this too? just want to make sure i got the the first part right before proceed further
Answer:
the answers are all right
If each pound of beef costs $3.69, how much does 2 pounds cost? Round to the nearest cent.
Answer: Two pounds of beef costs $7.38.
Step-by-step explanation:
Multiply the cost for one pound by the amount of pounds you need.
$3.69×2=$7.38
I hope this helps!!
PLEASE HELP ME WITH MY MATH
The definition for the graphed function is the one shown in option d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Which piecewise function coincides with the graph?Here we have a piecewise function, where for the first part we have a linear equation with a negative slope (for x < 1, we know that the symbol "<" must be used because of the open dot at the end of the line).
Then, we have another linear equation with a negative (and steeper) slope. This time there is a closed dot, so the domain for this second part is x ≥ 1.
With that we can conclude that the correct option is:
d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Where you can see that the second part has a larger (in module) slope, and the domains are defined as we saw above.
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After 8 points are added to each score in a sample.
the mean is found to be M = 40. What was the
value for the original mean?
Challenge time! Isn't time to give your brains a break? Its a fun challenge! EARN 20 POINTS NOW
Answer:
The answer is 64
Step-by-step explanation:
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it's easy 64 the key is in the pic.
URGENT + 20 Points! The regression equation for water being poured into a large, cone-shaped cistern is In(volume) = -1.327 +2.993 In(Time). What is the predicted volume for a time of 12 seconds?
- There is a line above "(volume)"
1.810 cm3
6.110 cm3
34.589 cm3
450.485 cm3
The predicted volume for a time of 12 seconds of the large, cone-shaped cistern is; V = 450.485 cm³
How to Solve Regression Equations?We are given the regression equation;
In V = -1.327 + 2.993 In T
Where;
V is volume
T is time
At T = 12, we have;
In V = -1.327 + 2.993 In 12
In V = -1.327 + 7.4373
In V = 6.1103
V = e^(6.1103)
V = 450.485 cm³
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A rectangular prism and a cylinder both have a height of 8m, and their cross-sectional areas are equal at every level parallel to their respective bases.
Complete the steps to find the prism.
1) [tex]V=lwh=5(x)(8)=\boxed{40x}[/tex]
2) [tex]V=\pi r^{2}h=(\pi)(3^{2})(8)=\boxed{72}\pi[/tex]
3) [tex]40x=72\pi\\\\x=\frac{72\pi}{40} \approx \boxed{5.7}[/tex]
Does this graph show a function explain how you know
The correct option is Option D: Yes, the graph passes the vertical line test.
The function is a relationship between two distinct sets X and set Y which can be many-one or one-one. here set X is called the domain and set Y is called the codomain.
The vertical line test states that
If we draw a straight vertical line( which is also parallel to the y-axis) and it touches the graph at only one point at all locations, then that relation is said to be a function and this relation will be also one-one.
So here in this function shown in the graph.
If we draw a vertical line parallel to the y-axis in this at any location then it crosses the graph only once. So, it passes vertical line test. And this graph is a function. Therefore option D is correct.
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What was the initial quantity of vanadium-49, which has a half-life of 330 days, if after 540 days there is a 1,750 g sample remaining?a.)5,440.42g b.)3,500g C.) 8,700g d.)2,863.63g e.)98g
Answer:
(a) 5440.42 g
Step-by-step explanation:
The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...
Q = Q₀(1/2)^(t/330) . . . . . where t is in days
__
The amount after 540 days is ...
1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀
Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g
The initial quantity was about 5440.42 grams.
George buys a computer. He pays a deposit of £200 and six monthly instalments of £55_
How much does George pay for his computer in total?
How many miles per hour does a sneeze travel? 1 10 100 1000
The average speed of sneeze is about 100 miles per hour.
What is the average speed of sneeze?
The average speed of sneeze is determined from the total distance traveled by the sneeze to the total time of motion of the sneeze.
Averagely a sneeze can travel as fast as 100 miles in an hour, which is equivalent to 44.7 m/s.
Thus, the average speed of sneeze is about 100 miles per hour.
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f(x) = x² + (k-6) x +9, k * 0. The roots of the equation f(x) = 0 are a and B. (a) Find, in terms of k, the value of (i) a² + ß² (ii) a² ß² Given that 9(a²+ B²) = 2a²p². find the value of k. (b) (c) Using your value of k, and without solving the equation f(x) = 0. form a quadratic equation, with integer coefficients, which has roots and 33² f ( x ) = x² + ( k - 6 ) x +9 , k * 0 . The roots of the equation f ( x ) = 0 are a and B. ( a ) Find , in terms of k , the value of ( i ) a² + ß² ( ii ) a² ß² Given that 9 ( a² + B² ) = 2a²p² . find the value of k . ( b ) ( c ) Using your value of k , and without solving the equation f ( x ) = 0 . form a quadratic equation , with integer coefficients , which has roots and 33²
(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as
[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]
Expand the right side and match up coefficients:
[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]
Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that
[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]
and
[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]
(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then
[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]
Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].
(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is
[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]
which expands to
[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]
Reusing the identity from (a-i) and the result from part (b), we have
[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]
We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].
So, the simplest quadratic that fits the description is
[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]
To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].
Find the ratio of 18 inches to 2 yards B
A. 3/4 B. 1/4
C. 1/5 D. 2/5
Answer:
B. 1 / 4
Step-by-step explanation:
Step 1: We can turn 2 yards into 6 feet.
Step 2: Then we can turn 6 feet into 72 inches.
Step 3: We plug it into the ratio, getting 18 / 72.
Step 4: Simplify. We get 1 / 4 as the answer. Therefore, we choose B.
The set of all numbers greater than or equal to −5 and less than 5.
Answer:
No. greater than of equal to (-5) = -4,-3,-2,-1,0,1,2,3,4,5,6...........
No. less than 5 = 4,3,2,1 ,0,-1......
{ -4,-3,-2,-1,0,1,2,3,4}
Problem
Suppose that J is between H and K. If HJ=2x+4, JK=3x+3, and KH=22, find the lengths of HJ and JK. Remember to always draw an image first and to pay attention to what the question is asking for!
Solution
Find the Segment Addition Postulate
Use the Segment Addition Postulate and then substitute what we know. Do not use any spaces in your answers.
HJ+JK= Answer
( Answer
)+( Answer
)= Answer
Find x
Once we combine our like terms we get:
Answer
x+ Answer
= Answer
x= Answer
Find HJ and JK
Our questions asked us for the lengths of HJ and JK so we must plug in the value of x to solve for those values. We were given HJ=2x+4 and JK=3x+3.
HJ=2x+4
HJ=2( Answer
)+4
HJ= Answer
And
JK=3x+3
JK=3( Answer
)+3
JK= Answer
3x-4
Check Work
View checked work
Answer:
The lengths of HJ and JK are 50 and 72 respectively.
Given:
J is between H and K.
HJ=2x+4
JK=3x+3
HK=22
Step-by-step explanation:
The total length is given as:
HJ+JK=HK
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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The lengths of HJ and JK are 50 and 72 respectively.
Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.
The line HJ and JK are collinear then the total length is given as: HJ+JK=HK
substitute values
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)? The equation of the line in slope-intercept form is y =-5/3 x + ____
Substituting into point-slope form,
[tex]y+5=-\frac{5}{3}(x-15)\\\\y+5=-\frac{5}{3}x+25\\\\\boxed{y=-\frac{5}{3}x+20}[/tex]
Solve the equation on the
interval [0, 2π).
√2 cos x - 1 = 0
Answer:
Step-by-step explanation:
[tex]\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}[/tex]
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Answer:
64 is the answer
Step-by-step explanation:
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Hassan put 437.2 grams of brown sugar into a canister. Then he carefully measured out 430.43 grams of it to use in a recipe for cookies. How much brown sugar is left in the canister?
Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Answer:
Step-by-step explanation:
slope of line ⊥ to y=-8x+2
is -1/-8=1/8
eq. of line with slope 1/8 thro' (-4,1) is
y-1=1/8 (x+4)
8y-8=x+4
8y=x+4+8
8y=x+12
y=1/8 x+12/8
or
y=1/8 x+3/2
