Answer:
$1000
Step-by-step explanation:
$200 was saved on a new laptop
This was 20% of the original price of the laptop
Therefote the original cost of the laptop can be calculated as follows
= 20/100x = 200
= 0.2x= 200
Divide both sides by the coefficient of x which is 0.2
x= 200/0.2
= 1000
Hence the original cost of the laptop is $1000
This box is packed with cubes that measure one cubic foot.
enter the volume of the box in cubic feet.
Answer:
72ft^3
Step-by-step explanation:
I first took a single slice off the box and counted how many cubes there were. By looking at the blue side, I counted 12 cubes in that slice. I then counted how many slices were in the box, which were 6.
12* 6 = 72ft^3
Find an equation of the largest sphere with center (10, 8 , 7) that is contained completely in the first octant.
Answer:
The equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is [tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex].
Step-by-step explanation:
A sphere is described by its radius and center, the radius of the largest sphere contained in the first octant are determined by the least distance of the center with respect to an orthogonal axis, that is:
Distance regarding x-axis:
[tex]d_{x} = 10 - 0[/tex]
[tex]d_{x} = 10[/tex]
Distance regarding y-axis:
[tex]d_{y} = 8 - 0[/tex]
[tex]d_{y} = 8[/tex]
Distance regarding z-axis:
[tex]d_{z} = 7 - 0[/tex]
[tex]d_{z} = 7[/tex]
Hence, the radius of the sphere must have a measure of 7. The equation of the sphere is represented by the following geometric locus:
[tex](x-h)^{2} + (y-k)^{2} + (z - j)^{2} = r^{2}[/tex] (1)
Where:
[tex]h, k, j[/tex] - Coordinates of the center.
[tex]r[/tex] - Radius of the sphere.
If we know that [tex](h,k,j) = (10, 8, 7)[/tex] and [tex]r = 7[/tex], then the equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is:
[tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex]
A square storage unit has a volume of 607.5 ft3. The height of the unit is 7.5 ft. What are the length and width of the storage unit?
length of 1 ft; width of 81 ft
length of 2 ft; width of 40.5 ft
length of 3 ft; width of 27 ft
length of 9 ft; width of 9 ft
Answer:
9 ft by 9 ft
Step-by-step explanation:
Answer:
length of 9 ft; width of 9 ft
Step-by-step explanation:
It is because you see it says it is square storage, which means its length and width have to be the same, and when you do 607.5 divided by 7.5, you get 81 which you can guess is a length of 9 ft; width of 9 ft because 9 x 9 equals to 81. I hope it helps! :)
A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?
Answer:
The probability that the month starts with the letter J or the letter M is 41.66%.
Step-by-step explanation:
Given that a month of the year is chosen at random, to determine what is the probability that the month starts with the letter J or the letter M, the following calculation must be performed:
January - March - May - June - July = 5 months
(5/12) x 100 = X
0.4166 x 100 = X
41.66 = X
Therefore, the probability that the month starts with the letter J or the letter M is 41.66%.
Answer:
5/12
Step-by-step explanation:
Months that start with the letter M are March and May
Months that start with J are January, June, July
So, in total the months that start with J and M are 5 in number.
Total number of months = 12
Therefore the probability = 5/12 or 0.416 (bar on 6)
Hope u understood
Please mark as brainliest
Thank You
The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given sin 0 = 73, find cos 0.
27
cos 6 = 2
Simplify the fraction.
Answer:
1/2
Step-by-step explanation:
According to pythagoras theorem;
(sinx)²+(cosx)² = 1
Given that sinФ = √3/2
Substitute into the formula
(√3/2)²+(cosx)² = 1
3/4+(cosx)² = 1
(cosx)² = 1 - 3/4
(cosx)² = 1/4
cos x = √1/4
cos x = 1/2
Hence the value of cosФ is 1/2
Estimate 78.8X6.8 I neep help
Answer:
B. 500
Hope this helps!! :D
Answer:
The answer is B
explanation:
78.8 is nearly 80 and 6.8 is nearly 7
so an estimate would be 80 × 7
= 560
You have 3/4 a cup of flour in your cupboard. A recipe for bread calls for 1/5 cup of flour. How much flour would you have left if you made the bread?
Answer:
11/20 cups left
Step-by-step explanation:
first, we need to convert 3/4 and 1/5 into fractions with common denominators
so we would have:
15/20 and 4/20
now we need to subtract the fractions to get the difference
so we would do:
15/20 - 4/20 = 11/20
and that's the answer
hope that helped
Answer:
11/20 cup
Step-by-step explanation:
3/4 - 1/5
use common denominator of 20
15/20 - 4/20
11/20 cup
Which ones to select?
Answer:
<5, <1
Step-by-step explanation:
.............
........
Rewrite as an exponential equation.
Log3 1/81 = -4
Answer:
3`⁴ = 1/81
Step-by-step explanation:
________________
Please help! And hurry
Answer:
the answer is b
Step-by-step explanation:
Answer:
b: 78.5cm²
Step-by-step explanation:
answer is b my friend
Each question Sandra answers incorrectly changes her overall score by -3/4 points. Sandras overall score was -4 1/2 points , and then she answered the last question incorrectly. What was Sandras final score
A population of bacteria starts 8 and is doubling every 12 hours. What equation
represents how many bacteria there will be after x days?
Answer:
a = 8 * (2)^(2x)
Step-by-step explanation:
There are 2 12hours periods in a day
a = 8 * (2)^(2x)
LaVilla is a village in the Italian Alps. Given its enormous popularity among Swiss, German, Austrian, and Italian skiers, all of its beds are always booked in the winter season, and there are, on average, 1562.664 skiers in the village. On average, skiers stay in LaVilla for 17.8 days. How many new skiers are arriving - on average - in LaVilla every day
Answer:
87.79
Step-by-step explanation:
Given :
Number of skiers in the village = Inventory = 1562.664
Stay time in LaVilla = 17.8 days
The number of new skiers arriving on average per day is :
According to Little's theorem :
Inventory / flow time
1562.664 / 17.8
= 87.79
Hence, 87.79 arrive LaVilla per day on average
1)An octagon can be divided into 8 congruent triangles with base angles that are 67.5°. This octagon has a side length that is 8 cm.
2)What is the area of each triangle?
3)What is the area of the octagon?
4) Use your work from above to derive a generic formula for any octagon with side length that is n units.
Answer:
(a) [tex]Area = 14.7824cm^2[/tex]
(b) [tex]Area = 118.2592cm^2[/tex]
(c) [tex]Area = 4nh[/tex]
Step-by-step explanation:
Given
[tex]\theta = 67.5[/tex]
[tex]b= 8cm[/tex] --- base
[tex]n = 8[/tex] --- triangles
Solving (a) The area of each triangle
First, calculate the height (h) of each triangle using:
[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle
[tex]\sin(67.5) = \frac{h}{8/2}[/tex]
[tex]\sin(67.5) = \frac{h}{4}[/tex]
Solve for h
[tex]h =4*\sin(67.5)[/tex]
[tex]h =4*0.9239[/tex]
[tex]h =3.6956[/tex]
The area of each triangle is:
[tex]Area = \frac{1}{2} *b * h[/tex]
[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]
[tex]Area = 14.7824cm^2[/tex]
Solving (b): Area of the octagon
This is calculated as:
Area = 8 * area of 1 triangle
[tex]Area = 8 * 14.7824cm^2[/tex]
[tex]Area = 118.2592cm^2[/tex]
Solving (c): Area of octagon of side length n
In (a), we have:
[tex]Area = \frac{1}{2} *b * h[/tex]
Replace b with n
[tex]Area = \frac{1}{2} *n * h[/tex]
Multiply by 8 (the sides) to get the area of the octagon
[tex]Area = 8 * \frac{1}{2} *n * h[/tex]
[tex]Area = 4nh[/tex]
A rectangular garden has an area of 37 square miles. If its length is 28 miles, what is its width?
Input your answer as a fraction.
Answer:
[tex]\frac{37}{28}[/tex] miles
Step-by-step explanation:
Use the area formula, A = lw, where l is the length and w is the width.
Plug in the area and length into the formula, and solve for w:
A = lw
37 = 28w
37/28 = w
So, as a fraction, the width of the garden is [tex]\frac{37}{28}[/tex] miles
Answer:
37/28 =w
Step-by-step explanation:
Area for a rectangle is given by
A = l*w
Substitute in what we know
37 = 28*w
Divide each side by 28
37/28 = 28w/28
37/28 =w
Please show steps on how to solve
log7 -2b-9=-6
Answer: b= - -log10(7)+3/2
Step-by-step explanation: log 10 (7) -2b-9=-6 : b= - -log10(7)+3/2 (Decimal : b = -1.07745...)
so these are the steps how I got it I did log 10 (7)-2b-9=-6 subtract log 10 (7) -9 from both sides log 10 (7)-2b-9-(log10(7)-9)=-6-(log 10 (7) -9)
Simplify -2b= -log10(7)+3
Divide both sides by -2 -2b/2= - log 10(7)/-2+ 3/-2 if you simplify it should give you b= - -log10(7)+3/2 that should be your answer but i'm not sure those I think that's how you do it let me know if you got it right bye!
c. Solve 1/2 x - (x+3)<1/3(x-1)
Answer: x = 28
Step-by-step explanation:
Let's solve your equation step by step!
3/8x + 15/2 = 18
Step 1: Subtract 15/2 from both sides.
3/8x + 15/2 - 15/2 = 18 - 15/2
3/8x = 21/2
Step 2: Multiply both sides by 8/3
(8/3) * (3/8x) = (8/3) * (21/2)
Step 3. Calculate
x = 28
First person will get brainiest
Answer:
341.6
Step-by-step explanation:
This problem asks one to subtract (58.4) from (400).
400 - 58.4 = 341.6
Less than is subtraction.
Subtract 58.4 from 400
400 - 58.4 = 341.6
The answer is 341.6
Write the fraction 2/3 as the sum of unit fraction
9514 1404 393
Answer:
1/2 + 1/6
Step-by-step explanation:
2/3 = 1/2 + 1/6
__
The sum of unit fractions is called an Egyptian Fraction. There are several different algorithms for finding such a sum. Here, we are starting with the form ...
2/p
where p is a small prime. Then the sum can be written as ...
1/((p+1)/2) +1/(p(p+1)/2) = 1/(4/2) +1/(3(4/2)) = 1/2 + 1/6
A different algorithm is used when p is a composite number.
__
Using the "greedy" algorithm, we can find the largest unit fraction less than 2/3 to be ...
1/ceil(3/2) = 1/2
Then the largest unit fraction in the remainder is similarly found. The remainder is ...
2/3 -1/2 = 1/6 . . . . already a unit fraction
So, the sum is ...
2/3 = 1/2 + 1/6
(-6 - 4) divided by 2 simplified
Answer:-5
Step-by-step explanation:
Hello!
-6-4/2 = -10/2=-5
Hope this helps, have a great day!
-2x +9y=8
x=y+3
Step by step
I REALLY NEED HELP PLS I NEED THIS DONE TODAY!!! JUST LOOK AT THE PICTURE!!!
Which scatterplot shows a negative correlation?
Answer:
Plot B
Step-by-step explanation:
Plot B has a negative slope.
NEED HELP ASAP! Translate into symbols
1. Fifteen more than a number
2. Decreased the quotient of forty eight and 6 by two is six
Answer:
x-6+6(6+6+6)X I am a pro boiiiiii
Rico has 2 plants. He buys 13 more.
If he puts 3 plants in each row, how many
rows will he have?
Total number of plants,
= 13 + 2 = 15
Number of plants in a row = 3
Hence, Total Number of rows,
= 15 ÷ 3= 5Therefore, he will have five rows.
The diagonal and the longer side of a rectangle make an angle of 43.2°. If the longer
side is 12.6cm. Find the length of the shorter Side.
Answer: The shorter side = 11.83 cm
Step-by-step explanation:
The diagonal of a rectangle creates a right triangle with its adjacent sides.
Given: The diagonal and the longer side of a rectangle make an angle of 43.2°. If the longer side is 12.6cm.
According to trigonometry,
[tex]\tan x=\frac{\text{Side opposite to x}}{\text{Side adjacent to x}}[/tex]
[tex]\tan 43.2^{\circ}=\frac{\text{Shorter side}}{12.6 }\\\\0.93906251=\frac{\text{Shorter side}}{12.6}\\\\ \text{Shorter side}=12.6\times 0.93906251\\\\=11.832187626\approx11.83\ cm[/tex]
Hence, the shorter side = 11.83 cm
A circular fountain has a radius of 9.4 feet. Find its diameter and circumference to the nearest tenth.
Please Help.
Answer:
diameter = 18.8 ft
circumference = 56.1 ft
Step-by-step explanation:
diameter = 2 x radius = 2 x 9.4 = 18.8 ft
circumference = 2[tex]\pi[/tex]r = 2[tex]\pi[/tex](9.4) = 56.061 rounded to the nearest tenth is 56.1
Use the box method to distribute and simplify (4x + 6)(- 6x ^ 4 - 4x - 6x ^ 3 + 6 + 4x ^ 2) . Drag and drop the terms to the correct locations of the table.
Answer:
= -24x^5 -60x^4 - 20x^3 + 8x^2+36
Step-by-step explanation:
Given the expression
(4x + 6)(- 6x^4 - 4x - 6x ^ 3 + 6 + 4x ^ 2)
Expand
4x(- 6x^4 - 4x - 6x ^ 3 + 6 + 4x ^ 2)+6(- 6x^4 - 4x - 6x ^ 3 + 6 + 4x ^ 2)
= -24x^5 -16x^2-24x^4+24x+16x^3 - 36x^4 -24x-36x^3+36+24x^2
= -24x^5 -24x^4 - 36x^4+16x^3-36x^3 -16x^2+24x^2+24x-24x+36
= -24x^5 -60x^4 - 20x^3 + 8x^2+36
This gives the required expression
what is the arc length of the subtending arc for an angle of 72 degrees on a circle of radius 4?
Step-by-step explanation:
We can set up the ration of the radian angle θ in your problem in terms of degrees given as the ratio: (Θ/2·pi) = (72/360), solving for Θ we get Θ = 1.26 radians. Then for the arc length s = Θ·r using this value gives s = 1.26·4 = 5.04
(10 points) help plz
Answer:
(c) No; There is an exponent on a variable x that is not a whole number
Step-by-step explanation:
Given
[tex]f(x) = x^2 - \sqrt[5]{x}[/tex]
Required
Determine if the function is a polynomial function of not
A polynomial function is represented as:
[tex]f(x) =ax^n + bx^{n-1} + cx^{n-2}+........+z[/tex]
Where n is an integer and the least power is 0
So, we have:
[tex]f(x) = x^2 - \sqrt[5]{x}[/tex]
The degree of x is [tex]\frac{1}{5}[/tex] ----- i.e. not an integer
Hence, the function is not a polynomial