two angles are complementary. The measure of one angle is 15° more than one-half of the measure of the other. Find the measure of each angle.
Answer:
Step-by-step explanation:
First you have to know two definitions. Well, you only have to know one for this problem, but you should probably learn the 2nd just to be thorough.
Definition 1: Complementary angles are two angles whose sum is 90 degrees.
Definition 2: Supplementary angles are two angles whose sum is 180 degrees.
For this problem, we'll work with the definition that says two complementary angles have a sum of 90 degrees.
Soooo, here are the facts from your problem: if one angle is 15 degree more than 2 times the other.find the measure of two angles.
Let's let the larger angle equal this: 15 + 2(x) (<--See how it is 15 degrees MORE than 2 times the other?)
Let's let the smaller angle equal: x
SO now our total equation is:
15 + 2(x) + x = 90
3x + 15 = 90 (combined like terms)
3x = 75 (subtracted 15 from both sides)
x = 25 (divided both sides by 3)
Now we know that one angle is 25. The other angle must add to 25 to make 90 degrees, so 90 - 25 = 65.
Therefore, your two angles are 25 and 65 degrees.
Does this check out? Let's see...
First: 25 + 65 = 90 Therefore, this checks out.
Second: The angle that is 65 degrees must be 15 degrees more than twice the other. So, let's take twice the other...... 25 * 2 = 50. And, let's add 15....50 + 15 = 65. Therefore YES, the 2nd angle is 15 more than 2 times the angle that was 25 degrees.
I hope this is helpful. :-)
(3 points) Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson. Please upload your work for all of the parts at the end. (0.5 pts.) a) What is the probability that more than one accident occurs per year
Answer:
0.8743 = 87.43% probability that more than one accident occurs per year
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year.
This means that [tex]\mu = 3.1[/tex]
What is the probability that more than one accident occurs per year?
This is:
[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]
In which
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.6}*(3.6)^{0}}{(0)!} = 0.0273[/tex]
[tex]P(X = 1) = \frac{e^{-3.6}*(3.6)^{1}}{(1)!} = 0.0984[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0273 + 0.0984 = 0.1257[/tex]
[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1257 = 0.8743[/tex]
0.8743 = 87.43% probability that more than one accident occurs per year
-09
2 1 point
The amount of a radioactive substance y that remains after t years is given by the equation y = a (e)^kt, where a is the initial
amount present and k is the decay constant for the radioactive substance. If a = 100, y = 50, and k = -0.035, find t.
Answer:
19.80
Step-by-step explanation:
Given the equation :
y = a (e)^kt
If a = 100, y = 50, and k = -0.035, find t.
50 = 100(e)^(-0.035t)
50/100 = e^(-0.035t)
0.5 = e^-0.035t
Take the In
In(0.5) = - 0.035t
-0.693147 = - 0.035t
-0.693147 / - 0.035 = t
19.8042 = t
Hence, t = 19.80
y + x + z =762500
z : x = 15/9 : 2
y : x = 1 : 3/4
Step-by-step explanation:
true
for a science fair project javier is recording the amount of water that evaporate from a bucket in a month he creates a table like this i will give point for the best answer
week 1 2/16 inch
week 2 1/16 inch
week 3 3/16 inch
week 4 2/16 inch
how much water had evaported from the bucket at the end of week 2
what was the total amount of water that evaported in the four weeks
if javier orignally put 4 inches of water in the bucket how many inches of water were left after the experment was completed
Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]
Step-by-step explanation:
Given
Javier created a table for the amount of water evaporated in each week
After two weeks, the amount of water evaporated is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]
Total amount of water evaporated in four weeks is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]
If Javier originally puts 4 inches of water, amount of water left in the bucket
[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]
Negating conditional statement (a V ~ b) => c
Please show your work and give a proper answer
"p implies q" is equivalent to "(p and q) or not p", which in turn is equivalent to "(p or not p) and (q or not p)". But "p or not p" is always true, so the implication reduces completely to "not p or q". Negating an implication thus gives "not (not p or q)", which is equivalent to "p and not q".
So
not [(a or not b) implies c] <==> (a or not b) and not c
Why is underfind the square root of a negative number?
Answer:
The square root of a negative number is undefined, because anything times itself will give a positive (or zero) result. Note: Zero has only one square root (itself). Zero is considered neither positive nor negative
Answer:
sjshzhshshdhdgdgdhdhdgshshshshshwywhwhw
Find the equivalent exponential expression.
(543
Answer:
(5) we have multiple the powers
Screenshot of the question
9514 1404 393
Answer:
x = 1, x = 7
Step-by-step explanation:
You can see from the graph that the x-intercepts of f(x) are ...
0 = f(-3)
0 = f(3)
To find the corresponding values of x for f(x-4), we can solve ...
0 = f(x -4)
x -4 = -3 ⇒ x = 1
x -4 = 3 ⇒ x = 7
The x-intercepts of the function after translation 4 units right are ...
x = 1, x = 7
__
Your sketch will be the same curve moved 4 units to the right. (Add 4 to every x-value shown.)
If f(x) = 4x and gx) = 2x- 1, what is g(f(-2))?
-17
-13
-8
-5
Answer:
-17
Step-by-step explanation:
We are given these following functions:
[tex]f(x) = 4x[/tex]
[tex]g(x) = 2x - 1[/tex]
g(f(-2))
First we find f when x = -2, then we find g for this value(f when x = -2). So
[tex]f(-2) = 4(-2) = -8[/tex]
[tex]g(f(-2)) = g(-8) = 2(-8) - 1 = -16 - 1 = -17[/tex]
Thus -17 is the answer.
There are 3 boxes on stage that appear identical, but one is Lucky. The boxes are full of tickets; some are labeled "win" and the others are labeled "lose." In the Lucky box, ninety percent of the tickets are winners. In each of the other two boxes, only twelve percent of the tickets are winners.
1. You will pick a box at random and draw one ticket from it at random.2. What is the probability you will draw a winning ticket? 3. If you do draw a winning ticket, what is the chance it came from the Lucky box?
Answer:
2.-P = 0.38
3.-P [ Lb | Wt ] = 0.788
Step-by-step explanation:
1.-Probability of choosing any box is, 1/3. So the probability of choosing the lucky box is 1/3
Let´s say the lucky box is the number 2 box ( that consideration does not in any way change the problem generality)
Then we have
p₁ probability of choosing box 1 is 1/3 p₁´ Probability of win ticket is 0.12
p₂ probability of choosing box 2 is 1/3 p₂´Probability of win ticket is 0.90
p₃ probability of choosing box 3 is 1/3 p₃´ Probability of win ticket is 0.12
Then
P (of choosing a winning ticket is) = p₁*p₁´ + p₂*p₂´ + p₃*p₃´
P = 1/3*0.12 + 1/3*0.9 + 1/3*0.12
P = 0.04 + 0.3 + 0.04
P = 0.38
3.- if I draw a winning ticket what is the probability it came from Lucky box
According to Bayes theorem
P [ Lb | Wt ] = P(Lb) * P[ Wt|Lb]/ P(Wt)
P(Lb) = 1/3 = 0.33333
P[Wt|Lb] = 0.9
P(Wt) = 0.38
Then By substitution
P [ Lb | Wt ] = 0.333 * 0.9 / 0.38
P [ Lb | Wt ] = 0.788
f(x)=2x1 + 16x2 + 7x3 + 4x4 -> min
Step-by-step explanation:
f(x)=(2x-1)square=0
it can be 0 or greater than 0
Hence,maximum value of (2x- 1)square=0
maximum value of (2x- 1square)+3=0+3=3
Find the missing length (picture below)
Answer:
Step-by-step explanation:
because these are similar triangles, that is, one is a bigger of smaller version of the other, then we know, that the bigger triangle is just 2 times bigger than the smaller, or 2x of any side of the small one
sooo 2(20) =40
so we know that side n of the bigger triangle is 40
A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?
9514 1404 393
Answer:
36.6 km
Step-by-step explanation:
We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(35°) = (21 km)/XZ
XZ = (21 km)/sin(35°) ≈ 36.61 km
The distance from X to Z is about 36.61 km.
_____
The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.
Joan has raised $306 by selling 34 equally priced boxes of chocolate for the team fund-raiser. Which of the following equations can be used to find the price, n, of each box of chocolate?
n ÷ 34 = 306
34n = 306
n − 34 = 306
n + 34 = 306
Answer:
34n=306
Step-by-step explanation:
Use inverse operation to find it, 306÷34= 9, check again 34(9)=306, so it's correct!
Choose the best graph that represents the linear equation:
y + 3 = 0
Graph A
On a coordinate plane, a line goes through (0, 3) and (1, 3).
Graph B
On a coordinate plane, a line goes through (negative 3, 0) and (negative 3, 1).
Graph C
On a coordinate plane, a line goes through (0, negative 3) and (1, negative 3).
Graph D
On a coordinate plane, a line goes through (0, 0) and (1, negative 3).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
PLEASE HELP!!! Please select the best answer from the choices provided
A
B
C
D
Graph B is the best graph that represents the linear equation
Answer:
m=2b=1y=2x+1
just enter it
7. What is given in the problem?
A. Radius of 80m C. Radius of 80 ft.
B. Diameter of 40 ft. D. Diameter of 40 m paki sagot
Answer:
radius of 80cm is the answer
A grinding stone completes 175 revolutions before coming to a stop. How many radians did the stone complete
Answer:
175 * 2 * [tex]\pi[/tex]
350[tex]\pi[/tex] radians
Step-by-step explanation:
The number of radians completed by the stone will be 350 radians.
What is an angle in radians?The angle subtended from a circle's centre that intercepts an arc with a length equal to the circle's radius is known as a radian.
Given that a grinding stone completes 175 revolutions before coming to a stop.
The number of the revolutions in radians will be calculated as:-
Multiply the number by 2π to convert it into the radians.
Number of revolutions = 175 x 2 x π
Number of revolutions = 350 radians
Therefore, the number of radians completed by the stone will be 350 radians.
To know more about an angle in radians follow
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the slope of line is
Answer:
there is no file attached
Step-by-step explanation:
Determine the domain of the function graphed above.
Answer:
the domain of given f is (-2,4)
No more than one state of nature can occur at a given time for a chance event. This indicates that the states of nature are defined such that they are
a. conservative events.
b. mutually exclusive.
c. independent outcomes.
d. collectively exhaustive.
Answer:
b. mutually exclusive.
Step-by-step explanation:
The given description is an illustration of mutually exclusive events.
Take for instance, when you roll a die;
It is impossible to have an outcome of 2 and 6 at the same time; these means that 2 and 6 are mutually exclusive.
In a nutshell, when two or more sates of events/states of nature can not happen at the same time; such events/states of nature are mutually exclusive.
The perimeter of a square and rectangle is the same. The width of the rectangle is 6cm and it's area is 16cmsquare less than the area of the square. Find the area of the square
Answer:
Area of square = 100 square cm
Step-by-step explanation:
Let the sides of a square be = a
Perimeter of a square = 4a
Let area of square = [tex]a^2[/tex]
Let the Length of rectangle be = [tex]l[/tex]
Given: width of the rectangle = 6 cm
Area of rectangle = length x breadth
Perimeter of rectangle and square is equal.
That is,
[tex]2(length + width) = 4a\\\\2(l + 6) = 4a\\\\l + 6 = 2a\\\\l = 2a - 6[/tex]
Therefore ,
Area of rectangle
[tex]= Length \times width \\\\= (2a - 6) \times 6\\\\=6(2a - 6)[/tex]
Given area of rectangle is 16 less than area of square.
That is ,
[tex]( 6(2a- 6) ) = a^2 - 16\\\\12a - 36 = a^2 - 16\\\\a^2 - 12a +20= 0\\\\a^2 - 2a -10a + 20 = 0\\\\a(a - 2) - 10(a - 2) = 0\\\\(a -10) ( a-2) = 0\\\\a = 10 , \ a = 2[/tex]
Check which value of 'a ' satisfies the equation:
[tex]\underline {when \ a = 2 }\\\\Length\ of \ rectangle \ l = 2a - 6 = 2 ( 2 ) - 6 = 4 - 6 = - 2. \\\\Length \ cannot \ be \ negative \ number. \\\\ \underline{ when \ a = 10 }\\\\Length \ of \ rectangle \ , l = 2a - 6 = 2 (10) - 6 = 20 - 6 = 14\\\\satisfies \ the \ conditions. \\\\Therefore , a = 10[/tex]
That is , side of the sqaure = 10
Therefore , area of the square = 10 x 10 = 100 square cm.
Which would result in a lower price to first discount an item by 10% and then by a further 15%, OR to first discount an item by 15% and then by a further 10%. Justify your reasoning.
Answer:
Neither one. They will both result in the same price.
Step-by-step explanation:
To discount an item 10%, you charge 90% of the price of the item. To find 90% of a price, you multiply the price by 0.9.
To discount an item 15%, you charge 85% of the price of the item. To find 85% of a price, you multiply the price by 0.85.
Since multiplication is commutative, multiplying a number by 0.9 and then by 0.85 is the same as multiplying the number by 0.85 first and then by 0.9.
Let's say the item costs x.
Take off the 10% discount first: 0.9x
Now take off the 15% discount: 0.85 * (0.9x)
Now do it the other way.
Take off the 15% discount first: 0.85x
Now take off the 10% discount: 0.9 * (0.85x)
Since 0.85 * 0.9 * x = 0.9 * 0.85 * x, the results are the same.
Answer: neither
I’ll mark u plz help
Answer:
D is the answer
Step-by-step explanation:
all sides and angles are equal
hope it helps!! let me know if it does
p{x:x is a natural number x (9
Answer:
you need a photo my dude
Step-by-step explanation:
Will give brainliest answer
Answer:
A
Step-by-step explanation:
the proof of the answer is shown above
The value of y varies with x and z, and y=8, when x=4 and z=10. What is the value of y when x=5 and z=11
The formula for the lateral area of a right cone is LA = pi rs, where is the radius of the base and s is the slant height of the cone.
Answer:
r is the radius of the base and s is the slant height of the cone. From the options given, We can make s the subject of the formula. Hence: Option a) s equals StartFraction L A Over pi r EndFraction
Two equivalent equations are s = LA/πr and r = LA/πs
What is cone?A cone is a shape formed using a series of line segments or lines that connect a common point, called a apex or vertex, to all points on the base of a circle that do not contain a vertex. The distance from the apex of the cone to the base is the height of the cone. A circular base has a measured radius value. And the length from the apex of the cone to any point around the base is the height of the slope. Equations for the surface area and volume of a cone can be derived from these quantities
Volume(V) = ⅓ πr²h cubic units
The total surface area of the cone = πrs + πr²
where, r is radius of the base, s is slant height and h is height of the cone
Given,
Lateral area of cone is denoted by LA
Lateral area of cone = πrs
where r is radius and s is slant height
⇒ LA = πrs
⇒ s = LA/πr
⇒ r = LA/πs
Hence, s = LA/πr and r = LA/πs are two equivalent equations in the given options.
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The surface area of a roof with dimensions of 40 feet long by 28 feet wide is how many times the surface area of a floor where the dimensions are 16 feet long by 7 feet wide?
Answer:
10 times
Step-by-step explanation:
Multiply 40 by 28
1120
Multiply 16 by 7
112
Divide the two numbers
You get 10
Hope this helps!
An airplane can travel 350 mph in still air. If it travels 1995 miles with the wind
in the same length of time it travels 1505 miles against the wind, what is the speed of the wind?
Answer:
49 mph
Step-by-step explanation:
RT=D
T = D/R
[tex]\frac{1995}{(350 + x) } =\frac{1505}{350-x}[/tex]
1995(350-x) = 1505(350+x)
x=49
