Answer:
$400
Step-by-step explanation:
Cash = $2200
$600 + ($100*20) = 2600
$2600 - $2200 = 400
if a = 10 , than a2 =
Step-by-step explanation:
if a = 10
a² = 10²= 100
Hope it will help :)
Answer:
a^2 = 100
a * 2 = 20
Step-by-step explanation:
If a = 10 , than a2 =
a^2 = 100 because 10 ^2 = 10 * 10 = 100
a * 2 = 10 * 2 = 20
Chef Selena is making her special dish that requires pasta, sauce, and onions. She has 5 1/8 pounds of pasta, 6 pounds of sauce, and 4 7/8 pounds of onions. How many servings of her dish can she make if each serving is 1/2 pound? Which two equations are needed to solve the problem?
Answer:
[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]
Step-by-step explanation:
The Weight of Ingredients to be used by Chef Selena are:
[tex]5\frac{1}{8}[/tex] pounds of pasta, 6 pounds of sauce; and [tex]4\frac{7}{8}[/tex] pounds of onions.Total Weight of Food Made, x
[tex]=5\frac{1}{8}+6+4\frac{7}{8}\\=5+6+4+\frac{1}{8}+\frac{7}{8}\\=16 \: Pounds[/tex]
Since each serving is [tex]\frac{1}{2} Pounds[/tex]
Number of Servings of her dish, y
[tex]16 \div \frac{1}{2}\\ =32 \: Servings[/tex]
The two equations needed to solve the problem are therefore:
[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]
Calculate the area of the shaded region. Use 3.14 for pi. Round your answer to the nearest hundredth if necessary
Based on the diagram shown above, the area of the shaded region rounded to the nearest hundredth is 1.34 square meter.
In Mathematics and Euclidean Geometry, the area of a square can be calculated by using this formula;
A = [tex]s^2[/tex]
Where:
A is the area of a square.s is the side length of a square.By substituting the given side lengths into the formula, we have;
Area of square, A = 2.5 × 2.5
Area of square, A = 6.25 square meters.
In Mathematics and Geometry, the area of a circle can be calculated by using this formula:
Area of circle = π[tex]r^2[/tex]
Where:
r represents the radius of a circle.
By substituting, we have;
Radius of circle = diameter/2 = 2.5/2
Radius of circle = 1.25 m.
Area of circle = π × [tex]1.25^2[/tex]
Area of circle ≈ 4.91 square meters.
Area of the shaded region = Area of square - Area of circle
Area of the shaded region = 6.25 - 4.91
Area of the shaded region = 1.34 square meter.
The area of the shaded region is Area = 1.34 [tex]m^2[/tex].
To find the area of the shaded region (the area outside the circle but inside the square), we need to calculate the area of the square and the area of the circle, then subtract the area of the circle from the area of the square.
Given:
Side length of the square [tex]\(s = 2.5\)[/tex] meters
Use [tex]\( \pi = 3.14 \)[/tex]
1. Calculate the area of the square:
[tex]\[ \text{Area of the square} = s^2 = 2.5^2 = 6.25 \text{ square meters} \][/tex]
2. Calculate the radius of the circle:
Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.
[tex]\[ \text{Diameter of the circle} = 2.5 \text{ meters} \][/tex]
[tex]\[ \text{Radius of the circle} = \frac{2.5}{2} = 1.25 \text{ meters} \][/tex]
3. Calculate the area of the circle:
[tex]\[ \text{Area of the circle} = \pi r^2 = 3.14 \times (1.25)^2 \][/tex]
[tex]\[ \text{Area of the circle} = 3.14 \times 1.5625 = 4.90625 \text{ square meters} \][/tex]
4. Calculate the area of the shaded region:
[tex]\[ \text{Area of the shaded region} = \text{Area of the square} - \text{Area of the circle} \][/tex]
[tex]\[ \text{Area of the shaded region} = 6.25 - 4.90625 = 1.34375 \text{ square meters} \][/tex]
Rounded to the nearest hundredth:
[tex]\[\text{Area of the shaded region} \approx 1.34 \text{ square meters}\][/tex]
The complete question is:
Calculate the area of the shaded region. Use 3.14 for pi. Round your answer to the nearest hundredth if necessary.
Area = ____ [tex]m^2[/tex].
If I am going 70 miles per hour and I am talking to someone for 66 seconds and 513 milliseconds how long would it take for my car to travel with the extra time
Answer:
Car would have traveled [tex]1.283[/tex] miles more with the extra time
Step-by-step explanation:
Given
Speed of the car - [tex]70[/tex] miles per hour
Speed of car in miles per second
[tex]\frac{70}{60* 60}[/tex]
[tex]= 0.0194[/tex] miles per second
Time wasted in talking instead of travelling
[tex]66[/tex] seconds and [tex]513[/tex] milliseconds
Total time wasted in seconds
[tex]66 + \frac{513}{1000} \\66 + 0.513[/tex]
[tex]66.153[/tex] seconds
Distance that would have been traveled in this time instead of talking
[tex]0.0194[/tex] miles per second [tex]* 66.153[/tex] seconds
[tex]= 0.0194 * 66.153[/tex] miles
[tex]= 1.283[/tex] miles
Edward and Tiffany were comparing the distance they ran over a week. If Edward ran
11.90 miles and Tiffany ran 7.9 miles, how far did they run total?
Answer:
18.9 miles
Step-by-step explanation:
11.90 + 7.9 = 18.9
Which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? Select two options.
Answer:
its 4xy and 12x
( options B and C)
hope that helped :)
Answer:
its 4xy and 12x
Step-by-step explanation:
can someone help me please? Thanks!
Which expression is the result of factoring the expression below by taking out its greatest common factor? 16x^2-8x=
Answer:
8x(2x - 1)
Step-by-step explanation:
Step 1: Write expression
16x² - 8x
Step 2: Find GCF
We can factor and 8 out of both terms and also an x out of both terms.
GCF = 8x
Step 3: Factor
8x(2x - 1)
To factor the expression [tex]16x^2[/tex] - 8x, the greatest common factor is 8x, resulting in the factored expression 8x(2x - 1).
To factor the expression [tex]16x^2[/tex] - 8x by taking out the greatest common factor (GCF), we first identify the largest factor that divides both coefficients. Here, 8 is the GCF of 16 and 8, and since both terms also include a factor of x, the GCF is 8x. We then divide each term by 8x to find the factored expression:
[tex]16x^2[/tex] ÷ 8x = 2x
-8x ÷ 8x = -1
So, the expression factored by its greatest common factor is 8x(2x - 1).
There are 100 senators in the 115th Congress. Democrats make up $\frac{46}{100}$ of the senators, and Republicans make up $\frac{13}{25}$ of the senators. The rest are Independents. What fraction of the senators are Democrat or Republican?
Answer: The fraction that makes up Democrats or Republicans is 49/50.
Step-by-step explanation: There are 100 senators in total. We have 46/100 representing the Democrats, and 13/25 representing the Republicans. The number representing the Republicans can be made into an equivalent fraction of the other simply by multiplying both numerator and denominator by 4 (in order to make the denominator the same, that is 100). Hence the fraction of Republicans is 52/100, while the rest are Independents. The independents are
Ind = 100 - (46/100 + 52/100)
Ind = 100 - 98/100
Ind = 2/100
{Total = 46/100 + 52/100 + 2/100}
{Total = 100/100}
However, the fraction of all senators that are Democrats or Republicans is derived as follows;
Dems = 46/100
Reps = 52/100
Total fraction = 46/100 + 52/100
Total fraction = 98/100
Total fraction = 49/50
Final answer:
To find the fraction of senators who are Democrat or Republican, we add the fractions representing Democrats and Republicans. The fraction is $rac{49}{50}$.
Explanation:
To find the fraction of senators who are Democrat or Republican, we need to add the fractions representing Democrats and Republicans. The fraction of senators who are Democrats is $rac{46}{100}$, and the fraction of senators who are Republicans is $rac{13}{25}$.
To add these fractions, we need a common denominator. The least common multiple of 100 and 25 is 100, so we can rewrite the fractions with denominators of 100. $rac{46}{100}$ is equivalent to $rac{46}{100} imes rac{1}{1}$, and $rac{13}{25}$ is equivalent to $rac{13}{25} imes rac{4}{4}$ (since $25 imes 4 = 100$).
Now we can add the fractions: $rac{46}{100} + rac{13}{25} = rac{46}{100} + rac{52}{100} = rac{98}{100}$.
So, $rac{98}{100}$ of the senators are Democrat or Republican, which simplifies to $rac{49}{50}$.
Eugene spent $6 on a magazine and some candy bars. If the magazine
cost $2 and each candy bar cost $2, then how many candy bars did he
buy?
What is the slope of the line that passes through the points (-1, -10)(−1,−10) and (-1, -2) ?(−1,−2)? Write your answer in simplest form.
Answer:
undefined
Step-by-step explanation:
We can find the slope of the line using
m = (y2-y1)/(x2-x1)
= (-2 - -10)/(-1 - -1)
= (-2+10)/(-1+1)
= 8/0
When we have a 0 in the denominator the slope is undefined
Can someone help me on this
Michael is packing his bags for his vacation. He has 6 unique toy animals, but only 5 fit in his bag. How many different groups of 5 toy animals can he take?
Answer:
6 different groups of toy animals
Step-by-step explanation:
In this question, we are to calculate the number of different groups of toy animals Michael can take.
Since we are selecting, this is clearly a COMBINATION question. Now from the question, we are trying to select 5 toy animals from a group of 6 different animals to fit in the bag
The number of ways we can do this is 6C5 ways
Mathematically, if we have to select a number of r items from a group of n items, the number of ways this can be done is;
nCr = n!/(n-r)!r!
Using the case in the question, we have; 6!/5!(6-5)! = 6!/5!1! = 720/120 = 6 groups
Answer:
6 different groups of toy animals
Step-by-step explanation:
The question above can be solved by applying the Combination technique
Combination technique uses the formula:
nCk = n! /k!(n-k)!
Where in the question above:
n = 6
k = 5
Therefore we have , 6C5
= 6! / 5! (6-5)!
= 6!/ 5!(1!)
6! = 6×5×4×3×2×1
5! = 5×4×3×2×1
Hence,
= (6×5×4×3×2×1) / (5×4×3×2×1)(1)
= 6
Hence, Michael can take 6 different groups of toy animals with him on his vacation.
3. What is x?
E
4x+ 5
H
Simplify the following rational expression
Answer:
= 5 (-2y+3) / -y+3
Step-by-step explanation:
If you need more help, you can look at this website called "symbolab".
Jose Has scored 28,24,26,27,and 21 Points in his five basketball game so far. How many points does he need to score in his next game so that his average mean is 25 points per game
Answer:
The correct answer is 24.
Step-by-step explanation:
Jose wants to have an average mean of 25 points per game in his 6 basket ball matches.
Total points Jose plans to achieve in 6 games is 25 × 6 = 150.
Points score by him in the first five matches are 28, 24, 26, 27 and 21.
Total points in 5 matches is 126.
Thus the points he need to score in his next game to have an average mean of 25 is given by 150 - 126 = 24.
What is the area of a circle with a diameter of eight
Answer:
16 pi or approximately 50.24
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
r = d/2 where d is the diameter
r = 8/2 =4
So plugging into the equation for the area
A = pi (4)^2
A = 16pi
Using 3.14 as an approximation for pi
A = 16*3.14 =50.24
do you guys mind helping ?
Answer:
m = -7
Step-by-step explanation:
1) expand: 2/9m-16/9=2/3m+4/3
2) add 16/9 to both sides:
2/9m-16/9+16/9=2/3m+4/3+16/9
3) simplify: 2/9m=28/9+2/3m
4) subtract 2/3 m from both sides:
2/9m-2/3m= 28/9+2/3m-2/3m
5) simplify: -4/9m=28/9
6) m=-7
5/7 = p + 4/7
p =
Solve the equation.
Step-by-step explanation:
p=5/7-4/7
7p=1
p=1/7
hope it helps
Answer:
Step-by-step explanation:
{y = x - 4
{Y = 6x - 10
Answer:
x = 6/5
y = -14/5
Step-by-step explanation:
y = x -4
y - x = -4
y = 6x -10
y - 6x = -10
y - x = -4
y - 6x = -10
_________--
5x = 6
x = 6/5
y - x = -4 | ×6 |
y - 6x = -10 | ×1 |
6y - 6x = -24
y - 6x = -10
__________--
5y = -14
y = -14/5
Donatello starts with a marble cube of side length $10.$ He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length $s.$ Find $s.$ [asy] import three; size(7cm); unitsize(1 cm); currentprojection
The side length, s, of the resulting polyhedron is (20√3)/3 cm.
To find the value of s, the side length of the resulting polyhedron, we can analyze the original cube's corners and the pyramids that Donatello slices off. Each corner of the cube contributes one-eighth of a pyramid to the polyhedron. These pyramids are similar, and their base is an equilateral triangle with side length s/2, and the height is s/2.
Considering one of these pyramids, we can use the Pythagorean theorem to find its slant height (the side length of the original cube):
(s/2)^2 + (s/2)^2 + (s/2)^2 = 10^2
Simplifying:
3/4 * s^2 = 100
Now, solve for s:
s^2 = (4/3) * 100
s^2 = 400/3
s = √(400/3)
s = 20/√3
To rationalize the denominator, multiply by (√3/√3):
s = (20/√3) * (√3/√3)
s = (20√3)/3
So, the side length s of the resulting polyhedron is (20√3)/3 cm.
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The side length of the resulting polyhedron after slicing off corner pyramids is [tex]\( \frac{10}{3} \).[/tex]
Of course, here's the solution in LaTeX:
To find the side length ( s ), we can break down the process step by step:
1. Start with a cube of side length ( 10 ).
2. Slice off a pyramid from each corner.
Since all the edges of the resulting polyhedron have the same length, let's find the side length of the pyramid. Consider one of the corner pyramids:
- It has a square base, with side length ( x , which is also equal to the side length of the cube.
- It has four congruent triangular faces.
If we draw a cross-section through the pyramid and the cube, we'll see that the cross-section of the pyramid is an isosceles right triangle with legs of length ( x ).
Given this, we can use Pythagoras' theorem to find the height of the pyramid. The hypotenuse of the right triangle is ( x ), and the legs are each x ). So, we have:
[tex]\[ x^2 = x^2 + x^2 + h^2 \][/tex]
Solving for \( h \), the height of the pyramid, we get:
[tex]\[ h = \sqrt{x^2 - x^2} = \sqrt{x^2 - \left(\frac{x}{\sqrt{2}}\right)^2} \]\[ h = \sqrt{x^2 - \frac{x^2}{2}} = \sqrt{\frac{x^2}{2}} = \frac{x}{\sqrt{2}} \][/tex]
Now, we know that the height of the pyramid is [tex]\( \frac{x}{\sqrt{2}} \).[/tex]
When we remove the corner pyramid, the remaining shape is a pentagonal pyramid with a square base. This means the side length of the square base of the remaining polyhedron is [tex]\( 10 - 2x \).[/tex]
The height of this pentagonal pyramid is the same as the height of the corner pyramid, which is [tex]\( \frac{x}{\sqrt{2}} \).[/tex]
So, we can set up an equation for the height of the remaining pyramid:
[tex]\[ 10 - 2x = \sqrt{2} \cdot \frac{x}{\sqrt{2}} \]\[ 10 - 2x = x \][/tex]
Solving for \( x \):
[tex]\[ 10 = 3x \]\[ x = \frac{10}{3} \][/tex]
So, the side length [tex]\( s \) of the polyhedron after slicing off the corner pyramids is \( \boxed{\frac{10}{3}} \).[/tex]
A cylinder has a radius of 1 inch and a height of 1 inch. What is the approximate volume of the cylinder? Round to the nearest hundred. Use 3.14 for pie
Find the area of the irregular polygon.
8 ft
4 ft
12 ft
Answer:
120
Step-by-step explanation:
you multiply base times height of the rectangle to get 96 then you do 1/2 bh for the triangle to get 24 and then you add them to get 120
The area of the irregular polygon is 120ft^2
We are given that;
The figure with triangle on top and rectangular base
Height of triangle=4ft
Base* height= 12*8
Now,
Area of triangle= 1/2 * base * height
=1/2 * 12 * 4
=24
Area of rectangle= 12 * 8
=96
Total area= 24+96
=120
Therefore, by the given polygon answer will be 120ft^2.
Learn more about polygons;
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What is this???): pls help
Answer:
sin D= 12/15
sin E= 9/15
cos D=9/15
Step-by-step explanation:
Use SOH CAH TOA
Sine= opposite/hypotenuse
Cosine= adjacent/hypotenuse
Tangent= opposite/adjacent
10•f(7)+9•g(-1)? What’s the answerrr
Answer:
= 70f - 9g
Step-by-step explanation:
1. Remove parentheses
2. Multiply the numbers
3. Multiply the numbers
Answer:
-1
Step-by-step explanation:
Brad can type 1260 words in 1/2 hour. What is Brad’s average typing rate in words per minute?
Brad average typing rate in words per minute is 21
1260 divided by 60 = 21
(In case you meant 30 minutes)
1260 divided by 30 = 42
If the figure below is a regular polygon, find the value of x.
Answer:
Sum of the interior angles of a regular polygon is given by = (n-2)180°
where n is the no. of sides.
In the above figure, n= 10
Therefore, sum of the interior angles = (10-2)×180°
= 8×180°
= 1440°
Measure of each angle = 1440/10= 144°
Therefore, 10x+4=144
=> 10x= 140
=> x= 14
For the given figure the value of x is 14
Given a regular polygon
A regular polygon is a polygon which has all sides equal and each side subtends equal interior angle at the center.
According to the figure
We are given a regular polygon with 10 sides
The angle subtended at the center is given as
(10x + 4)°
[tex]\rm The\; Sum \; of \; Interior\; angles = \bold {(n-2) \times 180\textdegree} ......(1) \\Where n = Number \; of \; sides \;of\; a \;polygon[/tex]
The Sum of interior angles = ( 10-2) [tex]\times 180\textdegree[/tex]= 1440°
So the angle subtended by one side at the center is given as follows
1440°/ 10 = 144°
Since the angle subtended at the center = 144° = (10x + 4)°
so by solving this we can get
140 = 10x
x = 14
For more information please refer to the link below
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Jake ran 145 meters before lunch and 389 meters after lunch. How many kilometers did Jake run in all? 0.00534 km 0.0534 km 0.534 km 5.34 km
Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.
Step-by-step explanation:
The given is,
Jake ran 145 meters before lunch.
389 meters after lunch.
Step:1
Total distance ran by Jake,
Total distance = Jake run before lunch + Jake run after lunch...(1)
Where,
Jake run before lunch = 145 meters
Jake run after lunch = 389 meters
Equation (1) becomes,
Total distance = 145 + 389
= 534
Total distance = 534 meters
Step:2
1 kilometer = 1000 meters
Total distance ran by Jake = 534 meters
= [tex]\frac{534}{1000}[/tex] kilometers
= 0.534
Total distance ran by Jake = 0.534 km
Result:
Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.
Answer:
0.534
Step-by-step explanation:
I did the work
You walk 1/3 miles to a clothing store. Then you walk another 1/4 miles to a shoe store. How many miles have you walked in all?
answer as a fraction in simplest form.
-1 3/5 divided by (- 2/3)
Answer:
2 2/5
Step-by-step explanation:
-1 3/5 ÷ -2/3
First change the mixed number to an improper fraction
1 3/5 = (5*1 +3)/5 = 8/5
-8/5 ÷ -2/3
Copy dot flip
-8/5 * -3/2
Multiply the numerators then the denominators
24/10
Dividing the top and bottom by 2
12/5
Changing this back to a mixed number
10/5 +2/5
2 + 2/5
2 2/5
Pls mark Brainliest.
Answer:
12/5 or 2 2/5 is the answer.
Step-by-step explanation:
-1 3/5 divided by -2/3.
First, we must turn the mixed fraction into an improper fraction so we are able to perform operations without the hassle of an extra whole.
-1 3/5 = -8/5
Now let's divide. Division is the same as multiplying the dividend by the reciprocal of the divisor. The divisor is the latter, or the number we are dividing the other number by, i.e. -2/3.
The reciprocal of -2/3 is -3/2.
Now let's multiply.
-8/5 * -3/2 = 24/10, which simplifies into 12/5.
12/5 or 2 2/5 is the answer.