area of a equalatiral triangle with 1 cm on each side
Answers
Answer:
side=a=1cm(let)
area of a equalatiral triangle=√3/4a²=√3/4×1²=√3/4cm²
Related Questions
Burning Brownie has five varieties of cakes as Chocolate fudge cake (Cake 1), Nutella-filled Cake (Cake 2), Marble Cake (Cake 3), Cheese cake (Cake 4) and Fruit Cake (Cake 5) at their store. The selling prices of each of the cakes are $9, $12, $4, $5, $8 respectively. a. Formulate the Revenue function If it takes 4 cups of milk, 7 cups of sugar, 1 egg, 3 cups flour & 4 cups cream to make Cake 1; 3 cups milk, 4 cups sugar, 2 egg, 4 cups flour & no cream to make Cake 2; 1 cups milk, 5 cups sugar, 3 eggs, 2 cups flour & 1 cup cream to make Cake 3; 5 cups milk, no sugar, 4 eggs, 4 cups flour & 5 cups cream for Cake 4; & lastly 4 cups milk, 8 cups sugar, 5 eggs, 6 cups flour & 3 cups cream to make Cake 5; Which types of cakes to be baked such that we get maximum Revenue? Keep in mind that the store has availability of maximum 280 cups milk, 300 cups sugar, 80 eggs, 250 cups flour & 190 cups cream at their disposal. b. Formulate the constraints of the scenario. c. Solve the system if linear inequalities using Excel Solver.
Answers
A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5
B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0
How did we get these values?To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:
a. Revenue Function:
Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.
The revenue function can be formulated as:
Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)
In equation form:
Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5
b. Constraints:
The constraints for the availability of ingredients can be formulated as follows:
Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280
Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300
Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80
Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250
Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190
Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0
c. Solve the system of linear inequalities using E x c e l Solver:
To solve the system of linear inequalities using E x c e l Solver, follow these steps:
1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:
| | A | B |
|-----|-----------|-----------------|
| 1 | Cakes | Selling Price |
| 2 | Cake 1 | $9 |
| 3 | Cake 2 | $12 |
| 4 | Cake 3 | $4 |
| 5 | Cake 4 | $5 |
| 6 | Cake 5 | $8 |
| | | |
| | | Formula |
| 9 | Milk | 280 |
| 10 | Sugar | 300 |
| 11 | Eggs | 80 |
| 12 | Flour | 250 |
| 13 | Cream | 190 |
2. In cell B16, enter the formula for the revenue:
=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11
3. In cell B18, enter the formula for the milk constraint:
=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6
4. In cell B19, enter the formula for the sugar constraint:
=7×B2 + 4×B3 + 5×B4
5. In cell B20, enter the formula for the egg constraint:
=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6
6. In cell B21, enter the formula for the flour constraint:
=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6
7. In cell B22, enter the formula for the cream constraint:
=4×B2 + 5×B4 + B5 + 3×B6
8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:
=B2
9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:
=B3
=B4
=B5
=B6
10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.
11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).
12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).
13. Click on the "Add" button in the "Subject to the Constraints" section.
14. In the Constraint window, select the range B18:B22 for the constraint cells.
15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.
16. Set the Solver options as desired, and click on the "Solve" button.
E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.
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An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. He believes that the mean income is $23.7, and the standard deviation is known to be $9.1. How large of a sample would be required in order to estimate the mean per capita income at the 98% level of confidence with an error of at most $0.44
Answers
Answer:1442
Step-by-step explanation:
Given,
Mean is,
Standard deviation,
,
Margin of error(E) = 0.54,
For 98% level of confidence,
Thus, the sample size would be,
Write the decimal expansion of 3/5
Answers
Answer:0.6
Step-by-step explanation:
To convert any fraction to decimal form, we just need to divide its numerator by denominator. Here, the fraction is 3/5 which means we need to perform 3 ÷ 5. This gives the answer as 0.6. So, 3/5 as a decimal is 0.6.
When Jake picked from the
numbers below, he got the number
one 6 times out of 10 picks. What is
the experimental and theoretical probability?
Answers
Answer:
Probability isn't my strong subject, so please review carefully.
Step-by-step explanation:
The possible numbers:
Number Count Probability Chance
1 2 2/5 40%
3 1 1/5 20%
5 2 2/5 40%
Sum 5 1 100% [chance you'll get any number]
The probability of getting the number 1 is 2/5 or 40% on the first draw. The probability of getting 6 1's in 10 draws is:
\((2/5)^{10}\) = 0.0001049
Try it to determine the experimental probability. After 10,000 tries you should have at least one success.
What type of transformation
has this figure Madeo
Answers
Answer:
Rotation it almost has Rotate in the word, Reflection is a mirror of itself, Translation is when the Object stays the same, But is moved
Step-by-step explanation:
A movie membership costs $10 a month plus an additional $5 for each movie purchased. If you have only budgeted to spend a maximum of $25 this month, how many movies can you purchase?
Answers
Answer:
3
Step-by-step explanation:
25-10/3=3
Answer:
3 movies
Step-by-step explanation:
You can pay for 3 movies because
5*3=15 and you have to pay for the membership which is 10 so
10+15=25
Can someone help me Solve:
-2√3+√75=
Answers
Answer:
\(3\sqrt{3}\)------------------
Simplify in below steps:
\(-2\sqrt{3} +\sqrt{75} =\)\(-2\sqrt{3} +\sqrt{25*3} =\)\(-2\sqrt{3} +\sqrt{5^2*3} =\)\(-2\sqrt{3} +5\sqrt{3} =\)\(3\sqrt{3}\)need help really please someone
Answers
Answer:
6/8 and 12/16
Step-by-step explanation:
This is because 3/4 x 2/2 = 6/8 and 3/4 x 4/4 = 12/16
Answer:
6/8 and 9/12 are both equal to 3/4
Step-by-step explanation:
You can't simplify but you can make it bigger.
3/4 x 2/2 = 6/8
and
3/4 x 3/3 = 9/12
it should be correct because 3/3 and 2/2 are both equal to 1 which is why they are equivalent.
At 10:00 AM, you enter the highway at mile marker 160 and drive north (the direction in which the mile markers increase) for 3 hours at 50 miles per hour to visit your friend. You visit for your friend for 4 hours, and then at 5:00 PM you enter the highway (at the same location you exited 4 hours ago) and head south for 2 hours at 60 miles per hour, before you come to stop at a restaurant to eat dinner.
Draw a graph of your car's position (relative to the highway mile markers) as a function of time between 10:00 AM and 7:00 PM that day.
What is the mile marker on the highway for the exit to the restaurant at which you ate?
At what time(s) did you pass the 250-mile marker that day?
Answers
The exit to the restaurant is at mile marker 190. The car passed the 250-mile marker twice, once at 1:48 PM and again at 1:50 PM.
Describe Distance?Distance is a measure of the physical space between two points or objects. It is often measured in units such as meters, feet, or miles, depending on the system of measurement being used. Distance can be measured in a straight line, also known as the "as-the-crow-flies" distance, or it can be measured along a curved path, such as a road or a hiking trail.
Here's a graph of the car's position as a function of time:
| .
| .
| .
| .
| .
| .
| .
| .
----+---------------------------> Highway Mile Markers
160 x y
The car travels north from mile marker 160 at a rate of 50 mph for 3 hours, so it covers a distance of 150 miles and reaches mile marker 310 at 1:00 PM. Then, the car travels south at a rate of 60 mph for 2 hours, covering a distance of 120 miles. The location of the restaurant can be found by subtracting the distance traveled south from mile marker 310: 310 - 120 = 190. So the exit to the restaurant is at mile marker 190.
To find the time(s) the car passed the 250-mile marker, we can set up two equations:
Northbound: 160 + 50t = 250
Southbound: 310 - 60t = 250
Solving the first equation gives t = 1.8 hours, or 1:48 PM. Solving the second equation gives t = 1.83 hours, or 1:50 PM. So the car passed the 250-mile marker twice, once at 1:48 PM and again at 1:50 PM.
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Aman borrowed rs.30,000 for 2 years at 10% P.A compounded annually. he paid only half of the principle at the end of 2 years. He paid the remaining principle and interest at the same rate at the end of the next 2 years. How much amount did he pay. Atlast to clear the debt??
Answers
The amount Aman paid to clear the debt, at last, was Rs. 25,773, including compounded interest of Rs.10,773.
What is compound interest?Compound interest is a type of interest system in that accumulated interest attracts interest.
With compounding, interest is paid on interest, unlike the simple interest system.
To compute compound interest, we use the following formula: CI = P( 1 + r/100)^n - P, where CI is compound interest, P is the principal, r is the compound interest rate and n is the number of years.
The amount of the loan = Rs.30,000
Loan period = 4 years
Annual percentage rate = 10%
Compounding period = Annual
Amount after two years = P( 1 + r/100)^n
= Rs. 30,000 x (1 + 0.1)^2
Rs. 36,300 (Rs. 30,000 x 1.21)
Payment after two years = Rs.15,000 (Rs. 30,000 x 50%)
Balance = Rs. 21,300 (Rs. 36,300 - Rs. 15,000)
Amount after another two years = Rs. 21,300 x (1 + 0.1)^2
= Rs. 25,773 ($21,300 x 1.21)
Total payments = Rs. 40,773 (Rs. 25,773 + Rs. 15,000)
Compounded interest = Rs. 10,773 (Rs. 40,773 - Rs. 30,000)
Thus, to settle the loan, lastly, Aman paid Rs. 21,300.
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In a 30°-60°-90° triangle, the length of the hypotenuse is 30. Find the length of the shorter leg.
Answers
Answer:
15
Step-by-step explanation:
30 --> r
60 --> r√3
90 --> 2r
If z = 25, solve z + 5
Answers
Answer:
z + 5 = 30
Step-by-step explanation:
Substitute z = 25 into z + 5.
z + 5 = 25 + 5
= 30
Answer:
30
Step-by-step explanation:
if z = 25
then,
25 + 5 = 30
hope it helpful
Neal invested $120,000 in stocks and bonds. He earned 18% on his stock investments and 12% on his bond investments. If Neal's combined profits on both types of investments were $17,400, how much did he invest in stocks?
Answers
Answer:
$50,000
Step-by-step explanation:
The given relations can be used to write and solve an equation for the amount invested in stocks.
SetupLet s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...
0.18s +0.12(120,000 -s) = 17,400
SolutionSimplifying the equation, we have ...
0.06s +14,400 = 17,400
0.06s = 3000 . . . . . . . . . . subtract 14,400
s = 50,000 . . . . . . . . . . . . divide by 0.06
Neal invested $50,000 in stocks.
__
Additional comment
The amount invested in bonds was 70,000. The profit earned was ...
0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400
it takes billy an hour to rase to his friends house and two hours if he went 20 mph slower how far away does billy's friend live?
Answers
you are doubling the amount of time it takes when it’s -20mph, so multiply 20 by 2 to get 40 miles
For a large order, Mr. Magoo made 3/8 kg of fudge in his bakery. He then got 1/6 kg from his sister’s bakery. If he needs a total of 1 1/2 kg, how much more fudge does he need to make? Put your answer in fraction form. Example: Mr. Magoo needs to make #/# more fudge.
(PS: Please show your work)
Answers
Answer:
Amount fudge he needs = 23/24 kg
Step-by-step explanation:
Given:
Total fudge wants = 1\(\frac{1}{2}\) = 3/2 kg
His sister gave = 1/6 kg
He make = 3/8 kg
Find:
Amount fudge he needs
Computation:
Amount fudge he needs = Total fudge wants - His sister gave - He make
Amount fudge he needs = 3/2 - 1/6 - 3/8
Amount fudge he needs = 23/24 kg
Donna wants to save $700 to buy a TV. She saves $17 cach week. The amount, A (in dollars), that she still needs after w weeks is given by the following
function
A(w)= 700 - 17w
Answer the following questions.
(a) How much money does Donna still need after 6 weeks?
s
(b) If Donna still needs $411, how many weeks has she been saving?
Answers
Answer:
Part A:
She would need $598 after 6 weeks of collecting money.
Part B:
She would have waited 17 weeks to have $411 left.
Step-by-step explanation:
Part A:
Replace w in 700 - 17w with 700 - 17(6).
This would give you $598 left until $700 has been reached.
Part B:
Replace w in 700 - 17w with 700 - 17(17).
This would give you $411 left until $700 has been reached.
....Help Please......
Answers
Answer:
9984000
Step-by-step explanation:
subtract the total by the other number (coverage)
Answer:
1.6e+16
Step-by-step explanation:
16k km = 1.6e+9 (1600000000)
1600000000 x 10,000,000
=1.6e+16
Solve the following quadratic inequality x^2+x-6>0
Answers
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
Help will give Brainly points
Answers
Answer:
(D
Step-by-step explanation:
Calculator in the picture below.
kiniwih426
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10∘ to the horizontal. Calculate the length of the zip wire.
Answers
The length of the zip wire is approximately 25.42 meters.
To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.
Given:
Distance between the two posts: 25m
Angle of the zip wire to the horizontal: 10°
We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.
In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.
Using the cosine function:
cos(angle) = adjacent/hypotenuse
cos(10°) = 25m/hypotenuse
To find the hypotenuse (length of the zip wire), we can rearrange the equation:
hypotenuse = 25m / cos(10°)
Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.
Therefore, the length of the zip wire is:
hypotenuse = 25m / 0.9848 ≈ 25.42m
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what is the solution to the equation:
5(n - 1/10) = 1/2
a. n= 13/5
b. n= 3/25
c. n= 0
d. n= 1/5
Answers
\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)
\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)
\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)
\( \sf \longrightarrow \: \: 100n =20\\ \)
\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)
\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)
Answer:-
Answer:- D) n = ⅕ ✅To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:
Step 1: Distribute the 5 on the left side:
\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)
Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:
\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)
\(\sf 5n = 1 \\\)
Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):
\(\sf \frac{5n}{5} = \frac{1}{5} \\\)
\(\sf n = \frac{1}{5} \\\)
Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).
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Let's play Cooking Diary! Together we'll rock the culinary world! https://social-cd.mytonagames.com/4gx9R8
Answers
Please help!
Simplify the expression. Show all steps to simplify the expression.
Answers
Answer:
3^5
Step-by-step explanation:
substract the index of the number
if a(x) = 3x+1 and b(x) = \(square root of x-4\), what is the domain of (boa)(x)
Answers
The domain of (boa)(x) is [1, ∞].
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
Based on the information provided above, we have the following functions:
a(x) = 3x+1
\(b(x) = \sqrt{x-4}\)
Therefore, the composite function (boa)(x) is given by;
\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [1, ∞] or {x|x ≥ 1}.
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![if a(x) = 3x+1 and b(x) = [tex]square root of x-4[/tex], what is the domain of (boa)(x)](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/gGe6IRGOQUF4aKHR4HvpxeklJAqlYD78.png)
By visual inspection, determine the best-fitting regression model for the
scatterplot.
10
-10
A. Linear
B. No pattern
so
ОООО
C. Quadratic
D. Exponential
Answers
Answer:
Option A linear is your answer ☺️☺️
The best-fitting regression model for the scatterplot is,
⇒ Linear
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Scatter plot is shown in image.
Now, We can see by the scatterplot,
The best-fitting regression model for the scatterplot is,
⇒ Linear
Thus, The best-fitting regression model for the scatterplot is,
⇒ Linear
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x = -9 and y = 2 plz help me plz
Answers
Answer: 9 and -2
Step-by-step explanation: because of the way it's writen.
Calculate the area of one triangle so that you can begin building the tabletop .What is the area of each triangle in square inches
Answers
A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
The area of each triangle is 200 square inches.
What is a right triangle?A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
We have,
The area of a right triangle is given by:
= 1/2 x base x height
We have from the figure,
Base = 20 inches
Height = 20 inches
Area = 1/2 x 20 x 20
Area = 10 x 20
Area = 200 square inches
Thus the area of each triangle is 200 square inches.
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The complete question is:
You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches?
A. 200 square inches
B. 400 square inches
C. 570 square inches
D. 2,800 square inches
E. 5,600 square inches
Write 13.13.13.13.13 in exponential form?
Answers
13.13.13.13.13 in exponential form is 13^5
How to rewrite the expression?The expression is given as:
13.13.13.13.13
The factors of the above expression are 13.
And each factor is grouped by product
There are five 13s in the expression.
So, we have:
13.13.13.13.13 = 13^5
Hence, 13.13.13.13.13 in exponential form is 13^5
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A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet.
The letter selected will be recorded as the outcome.
Consider the following events.
Event X: The letter selected comes before "D".
Event Y : The letter selected is found in the word "CAGE".
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
Answers
a) The only outcome that satisfies both events X and Y is the letter C.
b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.
c) The complement of event X is {D, E, F, G}.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
The outcomes for each of the following events are:
(a) Event "X and Y": {C}
To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.
(b) Event "X or Y": {A, B, C, E, G}
The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.
(c) The complement of event X: {D, E, F, G}
The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.
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Weight of three books are 23⁄4 kg, 35⁄6 kg and 23⁄8 kg. Find the total weight of all the three books.
Answers
Answer:
12.54kg
Step-by-step explanation:
(23/4 + 35/6 + 23/8)kg
\( = \frac{(23 \times 6) + (35 \times 4) + (23 \times 3)}{24} \)
\( = \frac{92 + 140 + 69}{24} \)
= 301/24
= 12.54kg