The weight of each pile yesterday will be 6 and 8 pounds.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is Given that Yesterday the ratio of seeds in these piles was 3:4.
Let 3x and 4x represent the seeds.
If the 2 pounds of seeds are added in the bigger pile, then
4x + 2
He also ate 1/4 pound from the smaller pile,
3x - 1/4
The quantities of seeds in those piles is in the ratio of 5:16.
So, 4x + 2 = 5x
3x - 1/4 = 16x
Solve;
So, 4x + 2 = 5x
2 = 5x - 4x
x = 2
The weight of each pie will be
3x = 6 pound
4x = 8 pound
Hence, The weight of each pile yesterday would be 6 and 8 pounds.
Learn more about the unitary method;
brainly.com/question/23423168
#SPJ1
What is the range of y=sin(x)?
The range of y = sin(x) is [-1,1]
How to determine the range?The function is given as:
y = sin(x)
The above function is the parent function of a sine function.
A sine function has a minimum of -1 and a maximum of 1.
This is represented by the interval [-1,1]
Hence, the range of y = sin(x) is [-1,1]
Read more about range at:
https://brainly.com/question/10197594
#SPJ1
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.
Learn more about average speed here: https://brainly.com/question/4931057
#SPJ1
If f(x) = 3x − 1 and g(x) = x + 2, find (ƒ– g)(x)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]
[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]
Simple procedure :
[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]
[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]
[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
find the value of x
d:6
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \: 5x = 3x + 12[/tex]
[ by vertical opposite angle pair ]
[tex]\qquad \sf \dashrightarrow \: 5x - 3x = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 12 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 6[/tex]
Therefore, the correct choice is D. 6
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
the height of a toy rocket
Which of the following is a geometric sequence?
• A. 6, 18, 54, 162
O B. 1, 4, 5, 9, 14
O C. 3, 6, 9, 12, 15
O D. 3, 5, 8, 13, 21
Answer: A. 6, 18, 54, 162
Step-by-step explanation:
Each term is 3 times the last, meaning the common ratio is 3.
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].
Write an equation for the transformed logarithm shown below, that passes through (-2,0) and (0,-3)
Using translation concepts, the equation for the transformed logarithm is given by:
[tex]f(x) = \log{(x + 3)} - 3.48[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The logarithm function is given by:
[tex]f(x) = \log{x}[/tex].
We have that:
It passes through (1,0), and in this problem it passes through (-2,0), that is, it was shifted left 3 units, hence x -> x + 3.Hence:
[tex]f(x) = \log{x + 3} + b[/tex]
To find the shift up/down, we consider that f(0) = -3, hence:
[tex]-3 = \log{0 + 3} + b[/tex]
[tex]b = -3 - \log{3}[/tex]
b = -3.48.
Hence the function is given by:
[tex]f(x) = \log{x + 3} - 3.48[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
Item 6
A set of books sits on a shelf at a store. This line plot shows the thickness of each book. Juan buys one of the thickest books on the shelf. Min buys the third thinnest book on the shelf.
How much thicker is Juan’s book than Min’s book?
Answer:
There is no line plot
Step-by-step explanation:
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]
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?
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]
Plato trigonometry is crazy
Answer:
The answer is A. 21
i hope this can help you! :)
Answer:
a)21
-step explanation:
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]
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?
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.
1 x 1 x 99 x 100 hat is the awnser
What are the measures of ∠1 and ∠2? Show your work or explain your answers.
Answer:
angle 1 is 105degrees and angle 2 is 75degrees
Step-by-step explanation:
The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.
if n × 18 = ½ find n
Answer:
n = [tex]\frac{1}{36}[/tex]
Step-by-step explanation:
n × 18 = [tex]\frac{1}{2}[/tex]
To find the value of n we have to divide both sides by 18.
Let us solve it now.
18n = [tex]\frac{1}{2}[/tex]
[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18
n = [tex]\frac{1}{2}[/tex] ÷ 18
n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]
n = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]
n = [tex]\frac{1}{36}[/tex]
A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula
represents the volume of the pyramid?
A. V = 1/12 s ^3
B. V=1/6 s ^3
C. V=1/3s ^3
D. V=3s³
E. V=6s³
Answer:
The volume of the pyramid with a base area of s² and the heights iss
The formula for calculating the volume of a square based pyramid is expressed as:
Volume = 1/3* Base area* Height
Since it is a square-based pyramid, the base area is calculated as:
Base Area = s ^ 2
If the height of the pyramid is equal to of the length of a side on the base, hence h = s
Substituting the base area and the height into the formula for the volume, this will give;
V = BH / 3
V = (s ^ 2 * s)/3
V = (s ^ 3)/3
V = 1/3 * s ^ 3
Hence the volume of the pyramid with a base area of s ^ 2 and the height s is 1/3 * s ^ 3
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.
Learn more about function
here: https://brainly.com/question/17043948
#SPJ10
find the missing number in ?/4 = 27/36
[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]
The sequence an = 1(3)n − 1 is graphed below: coordinate plane showing the points 1, 1; 2, 3; and 3, 9 Find the average rate of change between n = 1 and n = 3. (6 points)
Answer:
4
Step-by-step explanation:
[tex] \frac{9 - 1}{3 - 1} = 4[/tex]
The average rate of change on the interval [3, 9] will be 4.
How to find the average rate of change?The average rate of change between two points is given by the slope formula:
m = average rate of change = (y2 -y1)/(x2 -x1)
The sequence an = 1(3)n − 1 is graphed below:
m = (9 -1)/(3 -1) = 8/2
m = 4
The average rate of change on the interval [3, 9] will be 4.
Learn more about average rate;
https://brainly.com/question/12395856
#SPJ1
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.
To know more about Parallel Lines
https://brainly.com/question/16701300
#SPJ1
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
Want to earn 20 points for correct answer CLICK ME
Answer:
64 is the answer
Step-by-step explanation:
Mark me brainliest answer pls
A cell phone towerbcast a shadow that is 40 feet long . An 10- foot- tall stop sign located near the tower casts a shadow that is 8 feet long. How tall is the cell phone tower?
Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:
8 feet - 10 feet
40 feet - h feet
Applying cross multiplication:
8h = 10 x 40
Simplifying by 8:
h = 10 x 5 = 50 feet.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
In the given figure, ABCD is a parallelogram. Find x, y and z.
Answer:
it is 18 by unknown number
Help me with this question please and thank you!! :)
[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].
We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).
This set is {3, 4, 11, 13, 14, 15, 17, 24}
