Solve log2(6-2x)-log2x=3
The sum of four consecutive even integer numbers is 84. find the four numbers.
84/4=21
now take the 2 even numbers below 21 and the 2 even numbers above 21
18 +20 + 22 +24 = 84
the numbers are 18, 20, 22 & 24
18 divided by 5593 equals 31-5400 = 193 what number should be placed in the box to help complete the division calculation?
The number that should be placed in the box to complete the division calculation is -7.
To find the number that should be placed in the box to complete the division calculation, let's analyze the given information:
- Dividend: 5593
- Divisor: 18
- Quotient: 31 (hundreds place is 3 and tens place is 1)
- When 5400 is subtracted from 5593, the result is 193.
- The box represents an unknown number in the ones place of the quotient.
To find the value in the box, we need to consider the units place. Since 5400 is subtracted from 5593 to give 193, the difference between the units places should be the value in the box.
193 - 5400 = -5207
So, the number that should be placed in the box to complete the division calculation is -7.
Correct question is:
What number should be placed in the box to help complete the division calculation?
Long division setup showing an incomplete calculation. 18 is in the divisor, 5593 is in the dividend, and 3 hundreds and 1 tens is written in the quotient.
5400 is subtracted from 5593 to give 193.
An unknown value represented by a box is being subtracted from 193.
juanita and lauren are painting a circular mural on one wall of the community center. the area of the mural is 66 square meters. what is the radius
Final answer:
The radius of Juanita and Lauren's circular mural with an area of 66 square meters is approximately 4.58 meters.
Explanation:
Juanita and Lauren's mural has an area of 66 square meters, and we need to find the radius of the circular mural. To find the radius, we can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Since the area of the mural is 66 square meters, we have:
66 = πr²
To solve for the radius (r), we divide both sides of the equation by π:
r² = 66 / π
Then, take the square root of both sides to get:
r = √(66 / π)
Using a calculator to compute this, we find:
r ≈ 4.58 meters (rounded to two decimal places)
Therefore, the radius of the circular mural is approximately 4.58 meters.
Please show work on how you got the answer
(30 Points) Paysly is studying a mosquito with a mass of 2.5×10^-6 kilograms and a housefly with a mass of 2×10^-5 kilograms. Which statement is true?
The tip of an 11-inch wiper blade wipes a path that is 31 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
2.8 radians is the answer.
The French club is sponsoring a bake sale. If their goal is to raise at least $135, how many pastries must they sell at $2.50 each in order to meet that goal? Write and solve an inequality.
The following two-way table shows the number of students of a school who have a video game and/or have a laptop:
Have Video Game Do Not Have Video Game Total
Have Laptop
15
50
65
Do Not Have Laptop
50
15
65
Total
65
65
130
Based on the table, how many students have both a laptop and a video game?
15
50
65
130
Based on the table given, the number of students who have both a laptop and a video game is 15 students.
Which students have both laptops and video games?In order to solve this question, look at the part of the table where the row on students who have laptops intersects with the column on those who have video games.
That part of the table has 15 in the cell. This means that 15 students have both video games and laptops.
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Solve x3 = 64 over 27.
±8 over 3
8 over 3
±4 over 3
The solution of the given equation is ±8/3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is x³= 64/27
x=±∛(64/27)
x=±∛(8³/3³)
x=±8/3
Therefore, the solution of the given equation is ±8/3.
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What are the phase shift and period for the function y = 3cos[4(θ + 60°)] − 2?
Phase shift = right 60°, period = 90°
Phase shift = right 60°, period = −90°
Phase shift = left 60°, period = 90°
Phase shift = left 60°, period = −90°
Start with a square piece of cardboard to produce a box that is 8 cm deep and whose capacity is exactly 1 liter. how large must the original square be
The formula for the volume of a square prism or box is calculated using the formula:
V = s^2 * h
where,
s is the measure of the sides of a square
h is the height of the prism or box = 8 cm
We are given that the volume capacity of the box must be 1 Liter. We know that 1 Liter is equivalent to 1000 cm^3. Therefore calculating for s:
1000 cm^3 = s^2 * (8 cm)
s^2 = 125 cm^2
s = 11.18 cm
Therefore the measure of the sides of the square must be about 11.18 cm. If the problem ask for the area of the square, A = s^2 = 125 cm^2.
The masses, in kg, of some bags on an airplane are shown below: 7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3 Jack made the following box plot to represent the masses: box plot shows minimum at 5.8, first quartile at 6.1, median at 6.3, third quartile at 6.8 and maximum at 7 Which of the following did Jack show incorrectly on his box plot?
Answer:
The value that Jack show incorrectly on his box plot is:
Median ( As he showed median is 6.3 but median is 6.2)
Step-by-step explanation:
We are given the mass of the bags as:
7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3
On arranging the data in the increasing order we have:
5.8 6.1 6.1 6.2 6.2 6.2 6.3 6.8 6.8 7
There are a total of 10 data points.
Also, the minimum value is: 5.8
Maximum value is: 7
The median is the central tendency of the data and lie in the middle of the data.
Hence, Median lie between 6.2 and 6.2
Hence, Median=6.2
Also, the lower set of data is: 5.8 6.1 6.1 6.2
The lower quartile or first quartile is the median of lower set of data is: 6.1
Also, the upper set of data is: 6.3 6.8 6.8 7
The upper quartile or Third quartile is the median of lower set of data is: 6.8
Hence, he showed median incorrectly in the box plot.
:)
find the solution to the two equations shown below y=16x-9 y=-4x+21
Answer: (1.5, 15)
Step-by-step explanation:
The given system of equations :-
[tex]y=16x-9...................(1)\\\\y=-4x+21..................(2)[/tex]
Substituting the value of y from equation (1) in equation (2), we get
[tex]16x-9=-4x+21[/tex]
Now, Adding 4x and 9 on both the sides , we get
[tex]16x+4x=21+9\\\\\Rightarrow\ 20x=30\\\\\Rightarrow\ x=\dfrac{3}{2}=1.5[/tex]
Substitute the value of x in equation (1), we get
[tex]y=16(1.5)-9=15[/tex]
Hence, the solution to the given system of equations : (1.5, 15)
The solution to the given system of equation is (1.5, 15).
The given system of equations are
y=16x-9 ---------(i)
y=-4x+21 ---------(ii)
From equation (i) and (ii), we get
16x-9=-4x+21
16x+4x=21+9
20x=30
x=30/20
x=1.5
Substitute x=1.5 in equation (i), we get
y=16×1.5-9
y=24-9
y=15
Therefore, the solution to the given system of equation is (1.5, 15).
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Triangle XYZ is a right triangle. Angle Z is a right angle and m∠X = 68°. What is m∠Y?
m∠Y is 22°
What is right triangle?Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.
Given,
ΔXYZ is a right triangle
m ∠Z = 90°
m∠X = 68°
Let m∠Y = x,
∵ Addition of interior angles of a triangle is 180°
So, m∠X + m∠Y +m ∠Z = 180°
Subsitute the values,
68° + x + 90° = 180°
x = 180 - 158
x = 22
Hence, m∠Y = 22°
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A sum of money amounting to $4.25 consists of dimes and quarters if there are 26 coins in all how many are quarters
d= dimes
q = quarters
d+q=26 coins
rewrite as d=26-q
0.25q +0.10d=4.25
0.25q+0.10(26-q)=4.25
0.25q+2.6-0.10q=4.25
0.15q=1.65
q=11
d=26-11=15
11*0.25 = 2.75, 15*0.10=1.50, 2.75+1.50=4.25
there are 11 quarters
Bicycle city makes custom bicycles. They charge $160 plus $80 for each day that it takes to build the bicycle. If you have $480 to spend on your new bicycle, how many days can it take Bicycle City to build the bike?
Please help with this question! thanks :)
the tallest line in the graph is 3
so 3 would be the answer
The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?
93
-7
50
7
Answer:
Option 4 - 7%
Step-by-step explanation:
Given : The function [tex]P(t) = 5000 (0.93)^t[/tex] is the value of a motor scooter t years after it is purchased.
To find : Which of the following values show the annual depreciation of the value of the motor scooter?
Solution :
We are given a function p(t) which is represented as:
[tex]P(t) = 5000 (0.93)^t[/tex]
Where, p(t) is the value of a motor scooter t years after it is purchased.
Depreciation is the amount that has been deducted from the cost of an item.
The rate of change is 1-0.93=0.07 i.e. 7%.
So, The function P(t) has 7% of the amount has been deducted each year and the value of the motor scooter is 93% of the amount of the previous year.
Therefore, The annual rate of depreciation is 7%.
So, option 4 is correct.
PLEASE HELP!!!!!!!
f(x)=x^2−3x+9
g(x)=3x^3+2x^2−4x−9
Find (f−g)(x)
Select one:
a. −3x^3−x^2+x+18
b. 3x^3+3x^2−7x
c. 3x^3+x^2−x−18
d. 3x^3−x^2−x
cot^2x-csc^2x=-1 for all values of x true or falsse
The original equation cot^2x - csc^2x = -1 is true for all values of x.
How to determine if cot^2x-csc^2x=-1 for all values of xThe equation cot^2x - csc^2x = -1 is true for certain values of x, but not for all values of x.
To see why, let's break down the equation using trigonometric identities:
cot^2x - csc^2x = -1
Using the reciprocal identities, we can rewrite cot^2x and csc^2x in terms of sine and cosine:
(cos^2x / sin^2x) - (1 / sin^2x) = -1
Now, let's simplify:
(cos^2x - 1) / sin^2x = -1
Using the Pythagorean identity cos^2x + sin^2x = 1, we can substitute cos^2x with (1 - sin^2x):
(1 - sin^2x - 1) / sin^2x = -1
-sin^2x / sin^2x = -1
Now, we can cancel out the sin^2x terms:
-1 = -1
This equation holds true for all values of x. Therefore, the original equation cot^2x - csc^2x = -1 is true for all values of x.
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If n is a positive integer and the product all the integeres from 1 to n inclusive is a multiple of 990 what is the least possible value of n
Planes Q and R are parallel. Explain how you know lines a and b are skew.
Sample Response: Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew
Sample Response:
Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.
Which sample fairly represents the population? CHECK ALL THAT APPLY.
--measuring the heights of every fiftieth person on the school roster to determine the average heights of the boys in the school
--calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment
--observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses
--sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town
--taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch
Answer:
The population is defined by: The set of all possible individuals who are likely to be selected for a study and who also share some observable characteristic. In this way, the correct answer is:
Taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch
Step-by-step explanation:
The coordinates of a point are (4, –1). which matrix expression represents translating the point 3 units to the left and 7 units up?
How do I simplify this problem?
The line y = x − 6 y=x−6 has exactly one point in common with the circle x 2 + y 2 = r 2 x2+y2=r2. what is the value of r 2 r2?
Find two positive numbers such that their product is 192 and their sum is a minimum pre-calc
The two numbers with a product equal to 192 such that their sum is minimized are:
A = √192 and B = √192
How to find the two numbers?
Let's define A and B as our two numbers, we know that their product must be equal to 192, then we have:
A*B = 192.
Now, the sum of these two numbers is:
A + B.
And we want to minimize this, to do it, we need to use the first equation to rewrite one variable in terms of the other. For example, if we isolate A, we get:
A = 192/B
Replacing this in the sum, we get:
192/B + B
To minimize this, we need to find the values of B that make 0 the differentiation of the above expression.
The differentiation is:
-192/B^2 + 1
Then we need to solve:
-192/B^2 + 1 = 0
192/B^2 = 1
192 = B^2
√192 = B
To get the value of A, we use:
A = 192/B = 192/√192 = √192
Then we can conclude that the two positive numbers such that their product is 192, and their sum is minimized, is:
A = √192 and B = √192.
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The length of a rectangular lawn is measured to twice its width. the perimeter of the lawn is given as 30 m. find the length and width of the lawn.
How many different selections of 4 books can be made from a bookcase displaying 12 books?
(12 x 11 x10 x9) / (4 x3 x 2 x 1) = 495
there are 495 different ways to select 4 books