Answer: they are abt the same its all abt percentage now- Pitcher A
Step-by-step explanation: more water lessens the strength
8^5 = 2^2m+3
Solve m
Answer:
[tex]m=6[/tex]
Step-by-step explanation:
Exponent properties:
We can use exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to solve this problem.
Rewrite [tex]8[/tex] as [tex]2^3[/tex], then apply exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to simplify:
[tex]2^{3^5}=2^{2m+3},\\2^{15}=2^{2m+3}[/tex]
If [tex]a^b=a^c[/tex], then [tex]b=c[/tex], because of log property [tex]\log a^b=b\log a[/tex]. Using this log property, you can take the log of both sides and divide by [tex]\log a[/tex] to get [tex]b=c[/tex]
Therefore, we have:
[tex]15=2m+3[/tex]
Subtract 3 from both sides:
[tex]12=2m[/tex]
Divide both sides by 6:
[tex]m=\frac{12}{2}=\boxed{6}[/tex]
Alternative:
Given [tex]8^5=2^{2m+3}[/tex], to move the exponent down, we'll use log properties.
Start by simplifying:
[tex]\log 32,768=2^{2m+3}[/tex]
Take the log of both sides, then use log property [tex]\log a^b=b\log a[/tex] to move the exponent down:
[tex]\log(32,768)=\log 2^{2m+3},\\\log (32,768)=(2m+3)\log 2[/tex]
Divide both sides by [tex]\log2[/tex]:
[tex]2m+3=\frac{\log (32,768)}{\log(2)}[/tex]
Subtract 3 from both sides:
[tex]2m=\frac{\log (32,768)}{\log(2)}-3[/tex]
Divide both sides by 2:
[tex]m=\frac{\log (32,768)}{2\log(2)}-\frac{3}{2}=\boxed{6}[/tex]
How many ways are there to put 9 differently colored beads on a $3\times3$ grid if the purple bead and the green bead cannot be adjacent (either horizontally, vertically, or diagonally), and rotations and reflections of the grid are considered the same
Answer:
20,160
Step-by-step explanation:
The arrangement of the 9 differently colored bead can be presented as follows;
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Where 1 is the purple bead and 2 is the green bead, the number of ways of arrangement where the green bead cannot be adjacent to the green either horizontally, vertically, or diagonally
Placing the purple bead at 1, the location of the green bead = 3, 6, 7, 8, or 9
The number of ways = 5 ways × 7! ways of arranging the other beads
With the purple bead at 2, the location of the green bead = 7, 8, or 9
The number of ways = 3 × 7!
With the purple at 3, we also have 5 × 7! ways
At 4, similar to 2, we have, 3 × 7! ways
At 5, we have, 0 × 7!
At 6, we have 3 × 7!
For 7, 8, and 9, we have, (5 + 3 + 5) × 7!
The total number of ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7! ways
However, placing the purple bead at 1, 2, 3, 4, 6, 7, 8, and 9, (8 positions) can be taken as reflection and rotation of each other and can be considered the same
Therefore, the total number of acceptable ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7!/8 = 20,160 ways
A tower is 543m from your house. The angle of elevation to the top of the tower is 33.4°. How high is the tower?
Answer:
358
Step-by-step explanation:
the step by step is in the photo so look at it
Can someone help with this
A store purchased a plasma screen TV and marked it up 95% from the original cost of $876.08. A week later, the
store placed the TV on sale for 70% off. What was the discount price?
Answer:
95%-70%=15%
$876.08×15% =$131.412
Answer:
512.51
Step-by-step explanation:
Hope this helps! :)
Which of the following values are in the range of the function graphed below?
Check all that apply.
O B. -1
O C. 5
D. 2
E. 1
Answer:
I believe the answer should be 0 to -1
Step-by-step explanation:
the range of a function is the lowest y value to the highest y value of that function. so in that example, the lowest y value you have on that curved line is at 0, and the highest y value you have on that curved line is 1, so the range should be from 0 to 1, or {0, 1}.
Convert
[−1,∞) to inequality notation use the variable x.
Answer:
[tex]-1\leq x<\infty[/tex]
Step-by-step explanation:
We want to convert the interval [-1, ∞) to inequality notation using x as the variable.
The interval [-1, ∞) reads: "All real numbers between -1 and positive infinity."
In other words, it is all numbers greater than or equal to -1 and less than positive infinity.
Therefore:
[tex]-1\leq x<\infty[/tex]
Note that we do not use "or equal to" for the infinity as we can never really "equal" infinity.
mila first stands on a diving board is 3 feet above surface of the water .she then dives to the bottom of the pool to a depth of 10 feet
Answer:
She Dives 13 Feet
Step-by-step explanation:
3+10=13
Mila's depth from the diving board to the bottom of the pool is 13 feet.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Mila first stands on a diving board 3 feet above the surface of the water .she then dives to the bottom of the pool to a depth of 10 feet.
The total depth will be calculated as below:-
Depth = 3 + 10
Depth = 13 feet
Therefore, Mila's depth from the diving board to the bottom of the pool is 13 feet.
To know more about expression follow
https://brainly.com/question/878985
#SPJ2
Can somebody help me please?!!
Answer:
Step-by-step explanation:
Which expressions are equivalent to 2 Superscript 5 times 2 Superscript 4? Check all that apply.
Note: Consider the given figure attached with this question.
Given:
The expression is:
[tex]2^5\times 2^4[/tex]
To find:
The equivalent expression.
Solution:
We have,
[tex]2^5\times 2^4[/tex]
It can be written as:
[tex]2^5\times 2^4=2^{5+4}[/tex]
[tex]2^5\times 2^4=2^{9}[/tex]
So, option A is correct and option B is incorrect.
Similarly, in options C, D, E,
[tex]2\cdot 2^9=2^{10}[/tex]
[tex]2^{10}\cdot 2^2=2^{12}[/tex]
[tex]2^{-2}\cdot 2^{11}=2^{9}[/tex]
So, options C and D are incorrect but option E is correct.
The given expression can be written as:
[tex](2\cdot 2\cdot 2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2\cdot 2)[/tex]
So, option F is correct.
Therefore, the correct options are A, E F.
Help and explain !!!!!
Answer:
yeah the answer is one of those just pick one
How can I solve this problem
Answer:
x = 27
Step-by-step explanation:
I'm going to use letters to label the parts of the triangle while explaining how to solve for x:
Angle A = x (bottom left angle of the triangle)
Angle B = 4x (top angle of the triangle)
Angle C = empty angle (bottom right angle of the triangle)
Angle D = 3x + 54 (angle outside of the triangle)
A line has a angle measurement of 180 degrees.
Angle C & D make up the line, meaning Angle C + Angle D = 180 degrees.
To find Angle C, we would subtract Angle D's equation from 180 like this:
180 - (3x + 54)
Now Angle C equals 180 - (3x + 54)
Now we have all the angles inside the triangle. To find x, we are going to sum up Angle A, B, & C and set it equal to 180.
We set the equation to 180 because a the sum of the interior angles for a triangle is 180.
The equation looks like this:
(180 - (3x + 54)) + 4x + x = 180
Now we use basic algebra to solve it:
(180 - (3x + 54)) + 4x + x = 180
(distribute the - to (3x + 54))
180 - 3x - 54 + 4x + x = 180
(add like terms on the left side of the equation)
126 + 2x = 180
(subtract 126 from both sides)
2x = 54
(divide both sides by 2)
x = 27
To prove this answer is correct, plug it back in the original equation and you'll see that it ends up equaling 180, which is the sum of interior angles for triangle.
Hope it helps (●'◡'●)
4. Given the perimeter find the missing side.
Answer:
x^2 + 3x + 5
Step-by-step explanation:
sum of the two given side = 2x^3 + 3x^2 + 3x -2
missing side = 2x^3 + 4x^2 + 6x + 3 - 2x^3 - 3x^2 - 3x + 2 = x^2 + 3x + 5
he time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places. (a) What is the probability that more than three aircraft arrive within an hour? Enter your answer in accordance to the item a) of the question statement (b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals? Enter your answer in accordance to the item b) of the question statement
Answer:
A) 0.019
B) 0.563
Step-by-step explanation:
a) We will use Poisson distribution formula to solve this;
The formula is given as;
P(X = x) = ((e^-λ) × (λˣ))/x!
Mean is 1. Thus;
λ = 1 aircraft/hour.
Thus, the probability that more than three aircrafts will arrive within an hour is written as; P(X > 3)
Thus;
P(X > 3) = 1 - P(X ≤ 3)
Thus;
1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
Solving through online calculator, we have;
P(X > 3) = 1 - 0.98101
P(X > 3) = 0.01899
To 3 decimal places, we have; P(X > 3)= 0.019
b) Probability of one 1-hour interval not containing more than 3 arrivals is, let's first find;
P(X ≤ 3) = 1 - P(X > 3)
P(X ≤ 3) = 1 - 0.01899
P(X ≤ 3) = 0.98101
Since there are 30 one-hour intervals, then we have;
Probability that none of the thirty 1-hour intervals will contain more than 3 arrivals;
(P ≤ 3) = (0.98101)³⁰
(P ≤ 3) = 0.5626
Approximating to 3 decimal places, we have;
(P ≤ 3) = 0.563
is y=9x proportinal?
Answer:
yeah it is
y is directly proportional to x
proportionality constant is 9
Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.
Leon needs to save more than $350 to buy a new bike. He has $130 saved so far, and he plans to save $20 each week until he has enough. The inequality below represents x, the number of weeks he must save to have the extra money needed.
Answer:
11 weeks
Step-by-step explanation:
350=X*20+130
220=X*20
11=x
A circle has a diameter with endpoints (-8,2) and (-2,6). What is the equation of the circle?
Answer:
the equation would be (x+5)2+(y−4)2=r2
Step-by-step explanation:
The equation would be
(x+5)2+(y-4)2=r2
(d) Statement one: Two adult tickets and three children tickets cost $43.00
Statement two: One adult ticket and one ticket for a child cost $18.50
(i) Let x represent the cost of an adult ticket and y the cost of a ticket for a child.
Write TWO equations in x and y to represent the information. (2mks)
(ii) Solve the equation to determine the cost of an adult ticket
Answer:
The cost of an adult ticket is $12.50
Step-by-step explanation:
The given information are;
The cost of two adult tickets and three children tickets = $43.00
The cost of one adult ticket and one child ticket = $18.50
Whereby the cost of an adult ticket is represented by x and the cost of a child's ticket is represented by y, we get the following two simultaneous equations;
2·x + 3·y = 43.00...(1)
x + y = 18.5...(2)
(ii) Multiplying equation (2) by 2 and subtracting the result from equation (1) gives;
2·x + 3·y - 2×(x + y) = 43 - 2×18.5 = 6
2·x - 2·x + 3·y - 2·y = 0 + y = 6
∴ y = 6
The cost of each the children ticket = $6.00
From equation (2), where y = 6, we get;
x + y = 18.5
∴ x + 6 = 18.5
x = 18.5 - 6 = 12.5
The cost of an adult ticket, x = $12.50.
Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.
PLEASE HELP!!
Wesley initially filled a measuring cup with 5/6 of a cup of syrup from a large jug. Then he poured 1/2 of a cup back into the jug. How much syrup remains in the measuring cup?
Answer:
2/6 or 1/3
Step-by-step explanation:
We start off with 5/6 of a cup of syrup in a measuring cup.
Then Wesley pours out 1/2 of the syrup in the measuring cup.
Our equation looks like this:
5/6 - 1/2 = ?
However, we can't use this equation because the denominators (6 & 2) aren't the same. So we will find the LCD (least common denominator).
Mulitiples of 6: 6, 12, 18, 24
Multiples of 2: 2, 4, 6, 8
6 is the LCD for the both of them.
Multiply 3 to the numerator and denominator of 1/2 (because to get from 2 to 6 using multiplication, you mulitiply 3)
1/2 x 3/3 = 3/6
Now we can substitue 3/6 into our original equation and solve it:
5/6 - 3/6 = 2/6
It's better to use the simplified answer, 1/3.
Hope it helps and good luck (●'◡'●)
find the area of the shape below
Answer:
34?
Step-by-step explanation:
I think 34 because 3×3 is equal to 9. 5×5 is equal to 25. If you add 9+25, you would get 34.
Answer:
24 cm²
Step-by-step explanation:
the area = ½× (3+3) × (5+3)
= ½× 6×8
= 3×8
= 24 cm²
Can someone help with 3 and 9
Answer:
9= 512m/1000m
SIMPLIFY IT
Step-by-step explanation:
Which is the equation of a line perpendicular to the line with the equation: y = −14x + 7
y = -4x - 7
y = 4x + 2
y = 14x − 12
y = −14x + 3
which describes the graph of y=-(x+5)^2+3
Answer:
Maximum at (-5, 3)
Step-by-step explanation:
The quadratic equation is in vertex form, which specifically shows the vertex.
Since the a is negative, you get a maximum y value of 3.
Vertex form: y=a(x-h)^2+k
Find the area of the triangle from the coordinate plane.
Y
A
10-
5-1
с
B.
0
-20
-15
-10
-5
Answer:
Find the area of the triangle from the coordinate plane.
Y
A
10-
5-1
с
B.
0
-20
-15
-10
-5Step-by-step explanation:
the question is in the photo
[tex]\displaystyle\bf 3x+7\geq 52 \ ; \ x>15 \\\\3x\geq 45\\\\x\geq 15 \ \ \ and \ \ \ x>15[/tex] here is a contradiction because in one inequality x can be equal to 15 ; and in the other it cannot
Evaluate function from their graph
Answer:
f(-5) = 7
Step-by-step explanation:
f(-5) means find the y value when x = -5
y = 7 when x = -5
Use the elimination method to solve the system of equations.
A. (1.5,-8)
B. (-6,-13)
C. (0,0)
D. (4.5,-6)
Answer:
(4.5,-6)
Step-by-step explanation:
[tex]2x-3y = 27\\4x+3y = 0[/tex]
6x = 27
x = 27/6=4.5
9-3y = 27
-3y = 18
y = -6
A(-1,-5), B(5,-2) and C(1, 1).
ABCD is a trapezium.
AB is parallel to DC and angle BAD is 90°.
Find the coordinates of D.
Answer:
D(-3, -1)
Step-by-step explanation:
The given coordinates are;
A(-1, -5), B(5, -2) and (1, 1)
The coordinates and the coordinates of the point D form a trapezium
The parallel sides of the trapezium ABCD = AB and DC
The angle ∠BAD = 90°
The coordinates of the point D = Required
Let (x, y) represent the x and y-coordinates of the point D, by the given information, we get;
The slope of the line DC = The slope of the line AB
The slope of AB = (-2 - (-5))/(5 - (-1)) = 3/6 = 1/2
∴ The slope of CD, m = 1/2
From the point C(1, 1),the equation of the line CD is therefore;
y - 1 = (1/2)·(x - 1)
∴ y = x/2 - (1/2) + 1 = x/2 + 1/2
y = x/2 + 1/2
Given that ∠BAD is 90°, therefore, AD is perpendicular to DC and we have;
The slope of AD = -1/m
∴ The slope of AD = -1/(1/2) = -2
From the point A(-1, -5), the equation of the line AD is therefore;
y - (-5) = -2·(x - (-1))
y = -2·x - 2 - 5 = -2·x - 7
y = -2·x - 7
Equating both (simultaneous) values of y to find the value of x gives;
y = y, therefore;
x/2 + 1/2 = -2·x - 7
x/2 + 2·x = 5·x/2 = -7 - (1/2) = -15/2
∴ 5·x/2 = -15/2
x = (-15/2) × (2/5) = -3
x = -3
From y = -2·x - 7, and x = -3, we get;
y = -2 × (-3) - 7 = 6 - 7 = -1
The coordinates of the point D(x, y) = (-3, -1).