Answer:
Width = 10 inches
Step-by-step explanation:
A cube is a six-sided shape where each side consists of a square. Since the length of a square is the same measure of the width, then the cube will "work the same way", and the length, width, and height of the cube will all be the same length.
Please I need a lot of help
Answer:
that's a computer I'm sorry di ko po Alam
Step-by-step explanation:
ty sa points
I need help!! I will give 5.0 star
So, here we need to differentiate tan³[tex](\theta)[/tex], wr.t.[tex]\theta[/tex], but let's recall some identities which will be very useful in this question :
[tex]{\boxed{\bf{\dfrac{d}{dx}\{\tan (x)\}=\sec^{2}(x)}}}[/tex][tex]{\boxed{\bf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}[/tex][tex]{\boxed{\bf{\sec^{2}(\theta)=\tan^{2}(\theta)+1}}}[/tex]Coming back on the question, consider :
[tex]{:\implies \quad \sf \dfrac{d}{d\theta}\{\tan^{3}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{3-1}(\theta)\dfrac{d}{d\theta}\{\tan (\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\sec^{2}(\theta)}[/tex]
Using the identity ;
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\{1+\tan^{2}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)+3tan^{4}(\theta)}[/tex]
[tex]{:\implies \quad \sf 3\tan^{4}(\theta)+3\{\sec^{2}(\theta)-1\}}[/tex]
[tex]{:\implies \quad \boxed{\bf 3\tan^{4}(\theta)+3\sec^{2}(\theta)-3}}[/tex]
Hence, Proved
Leila wanted to order her IFTAR meal from La Gondola, Al Khobar. The menu stated that their pasta is a blend of wheat and corn. La Gondola does not disclose the percentage of each ingredient in the blend but we know that the wheat in the blend contains 5% protein, and the corn in the blend contains 10% protein. Overall, each 57 gram serving of pasta contains 4 grams of protein.
Leila told her sister that there was more wheat than corn in the pasta. Use multiple representations to justify if this is a true statement. (You may use DESMOS for graphing. You must also put in the algebraic solution and a table.)
Step-by-step explanation:
Let the amount of wheat is x and amount of corn is y.
The total amount of pasta is
x + y = 57Amount of protein in same pasta is
5% of x + 10% of y = 4or
0.05x + 0.1y = 4The graphical solution is attached
x = 34, y = 23It is easy to solve the system by substitution
y = 57 - x0.05x + 0.1(57 - x) = 40.05x + 5.7 - 0.1x = 40.1x - 0.05x = 5.7 - 40.05x = 1.7x = 1.7/0.05x = 34Then the value of y is
y = 57 - 34 = 23As we see x > y, so Leila is right
The above problem is solved using Multiple Representations. Multiple representations are used to achieve a deeper comprehension of concepts related to the same operation.
How do we evaluate the veracity of Leila's assertion?We can arrive at whether the statement is true or false by solving for the value of Y using the graphical method. Where Y is the amount of wheat and X is the amount of corn.
Our function is given as follows:
X + Y= 57. ..........1
Recall that the total amount of pasta is 57 grams
Recall as well that the total amount of protein in the pasta is given as:
0.05x + 0.1y= 4grams.......2
By inputting equations 1 and 2 into the Desmos Graph, we have x to be equal to = 34, and y = 23. (please see the attached image).
Recall that Leila's assertion was that there is more corn in the Pasta. Since x is the amount of corn, then Leila's assertion is True that: x>y.
The algebraic solution is arrived at using substitution.
Rewriting equation (1), we have
y = 57 - x .......................(3)
Let us substitute y into equation (2) above. That gives us:
0.05x + 0.1(57 - x) = 4.........................(4)
Expanding the brackets, we obtain
0.05x + 5.7 - 0.1x = 4
Collecting like terms, we can rewrite the quation as:
0.1x - 0.05x = 5.7 - 4
0.05x = 1.7
Rewriting the equation such that it is subject to x, we have
x = 1.7/0.05
x = 34
If from the above, x = 34, inputting that into equation (3) above, we have
y = 57 - 34; Therefore,
y = 23
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Height of a Toy Rocket A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec. a. Give the function that describes the height of the rocket in terms of timet b. Determine the time at which the rocket reaches its maximum height and the maximum height in feet. c. For what time interval will the rocket be more than 300 ft above ground level? d. After how many seconds will it hit the ground?
The height of the toy is an illustration of the height function
The function of the toy velocityThe given parameters are:
Initial velocity, Vo = 200 ft per secInitial height, H = 50 ftThe function of the height is calculated as:
h(t) = -16t² + Vot + H
This gives
h(t) = -16t² + 200t + 50
Hence, the velocity function is h(t) = -16t² + 200t + 50
The time of maximum heightIn (a), we have:
h(t) = -16t² + 200t + 50
Differentiate
h'(t) = -32t + 200
Set to 0
-32t + 200 = 0
Subtract 200 from both sides
-32t = -200
Divide both sides by -32
t = 6.25
Substitute 6.25 for t in h(t)
h(6.25) = -16 *6.25² + 200 * 6.25 + 50
h(6.25) = 675
Hence, the time to reach the maximum height is 6.25 seconds and the maximum height is 675 feet
When the rocket will be at a height more than 300This is represented as
h(t) >300
So, we have:
-16t² + 200t + 50 > 300
Subtract 300 from both sides
-16t² + 200t - 250 > 0
Using a graphical calculator, we have:
t = 11.09s and t = 1.41 s
Hence, the rocket will be at a height more than 300 at 11.09s and 1.41 s
When it will hit the ground?This means that
h(t) = 0
So, we have:
-16t² + 200t + 50 = 0
Using a graphical calculator, we have:
t = 12.75
Hence, the rocket will hit the ground at 12.75s
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The average gas mileage (mpg) for vehicles produced by a particular automotive company is 26 mpg, with a standard deviation of 2 mpg. What percentage of the vehicles produced by the automotive company have a gas mileage greater than 24?
Note: Assume that a Normal model is appropriate for the distribution of the gas mileages for the vehicles.
Answer:
above 84°/. of the vehicles have a gas mileage greater then 24 mpg
Looking for good answer on this
[tex]\dfrac{6x-24}{16-x^2}\\\\=\dfrac{6(x-4)}{4^2 -x^2}\\\\=\dfrac{6(x-4)}{(4+x)(4-x)}\\\\=-\dfrac{6(x-4)}{(x+4)(x-4)}\\\\=-\dfrac{6}{x+4}[/tex]
please help
Find the volume of each prism. Round to the nearest tenth if nessary
Stuck on this math question can anyone help me please?!?
Answer:
1) f(-6) = 8
2) f(3) = -2
3) f(x) = -5 when x = 4
Write the equation of the line that is parallel to the line y=3x+7 and passes through the
point (-4,-14).
Answer:
Step-by-step explanation:
hello :
note :
Use the point-slope formula.
y - y_1 = m(x - x_1) when : x_1= -4 y_1= -14
m= 3 (parallel means same slope)
an equation in the point-slope form is : y +14 =3(x+4)
please help I will give brainiest pls
A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot.
Please explain how to solve this problem, not just the answer.
The area of the square pyramid building is the amount of space on it
The maximum base length of the building is 67.42 cm
How to determine the maximum side length?The given parameters are:
Base = b
Slant height (l) = 5b
The lateral surface area is calculated using:
L = 2bl
So, we have:
L = 2 * b * 5b
Evaluate the product
L = 10b^2
The total surface area is calculated using:
T = L + b^2
So, we have:
T = 10b^2 + b^2
Evaluate the sum
T = 11b^2
The maximum surface area is 50,000 square feet
So, we have:
11b^2 = 50000
Divide both sides by 11
b^2 = 50000/11
Take the square root of both sides
b = 67.42
Hence, the maximum base length of the building is 67.42 cm
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Answer: 71 feet
Step-by-step explanation:
Let's assume that the side length of the base of the square pyramid is x. Then, the slant height of the pyramid would be 5x, as given in the problem.
The lateral surface area of a square pyramid can be calculated using the formula:
Lateral surface area = (perimeter of base) × (slant height) / 2
The perimeter of the square base is 4x. So, the lateral surface area of the square pyramid can be written as:
Lateral surface area = 4x × (5x) / 2 = 10x^2
We are told that the construction material used for the outside of the building is between 20,000 square feet and 50,000 square feet. So, we can set up the following inequality:
20,000 ≤ 10x^2 ≤ 50,000
Dividing both sides by 10, we get:
2000 ≤ x^2 ≤ 5000
Taking the square root of both sides, we get:
44.7 ≤ x ≤ 70.7
Since we are looking for the maximum possible value of x, we can round 70.7 up to the nearest foot, which is 71 feet.
Therefore, the maximum possible side length of the base of the building is 71 feet.
the function f(x)=2^x and g(x)=f(x)+k if k=2 what can be concluded about the graph of g(x)?
please help me find Find AB
Answer:
AB=4
Step-by-step explanation:
[tex]\frac{10+x}{2}[/tex][tex]=7[/tex]
Multiply both sides by 2.
10+x=14
x=14-10
x=4
Simplify the following expression.
6.64 ÷ 8
A.
1.245
B.
0.664
C.
0.83
D.
0.93
Answer:
[tex]0.83[/tex]
Step-by-step explanation:
[tex]6.64 \div 8[/tex]
[tex]0.83[/tex]
Answer:
The answer should be C.)0.83, hope this helps.
The area of circles
Answer:
Formula for the area of a circle;
A = π[tex]r^{2}[/tex]Where 'π' represents pi(3.14 or 22/7), and 'r' represents the radius which is being squared.
Plug in the radius into this formula:-
A = π[tex]r^{2}[/tex]
Note: I will be using 3.14 as pi(π).A = 3.14(4^2)
A = 3.14(16)
A = 50.24 centimetres is the area for this circle.
A swimming pool is in the shape of a cylinder 7 feet deep and 9 feet in radius. Find the exact volume of the pool.
Answer:
16
Step-by-step explanation:
Hope this helps
You would use a back-to-back stem-and-leaf plot when you want to analyze the heights of the boys on the basketball team.
False
True
Answer:
true because there are going to be many heights already
Step-by-step explanation:
i it's true
this is because already there will be
so many heights
what number equals 2/9?
Heather invested $11,600 in an account that pays 5% simple interest. If she invests the money for 6 years, how much will she have?
The total amount in the account after 6 years is $______?
Answer
$15080
Step-by-step explanation:
ok so i havent done these in a while but basically.
First, we need to find out what the 6% is.
[tex]\frac{5}{100} \times \frac{11600}{1}[/tex]
5/100 because it's PERCENT, and well we need to put the 11600 out of 1.
Wich gives us
$580. THen, we multiply that by 6, (6 years). Which gives us
$3480. Now, we add that to the $11600. WHich gives us
$15,080.
Hope this helps!
Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the explicit rule for this sequence in simplified form?
What is the recursive rule?
The required recursive function will be expressed as an = 3000 + 500n
How to write recursive functionsGiven the following parameters
First year salary = $30,000
If it increases by $500 each year, let the number of years be "n", then the increment after "n" years is 500n
The required recursive function will be expressed as an = 3000 + 500n
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Write a Pseudo code for average speed
Answer:
SEQUENCE represents linear tasks sequentially performed one after the other.
WHILE a loop with a condition at its beginning.
REPEAT-UNTIL a loop with a condition at the bottom.
FOR another way of looping.
IF-THEN-ELSE a conditional statement changing the flow of the algorithm.
CASE the generalization form of IF-THEN-ELSE
Step-by-step explanation:
Always capitalize the initial word (often one of the main 6 constructs).
Have only one statement per line.
Indent to show hierarchy, improve readability, and show nested constructs.
Always end multiline sections using any of the END keywords (ENDIF, ENDWHILE, etc.).
Keep your statements programming language independent.
Use the naming domain of the problem, not that of the implementation. E.g., “Append the last name to the first name” instead of “name = first+ last.”
Keep it simple, concise, and readable.
Please assist me with these question. I am having a hard time
Step-by-step explanation:
[tex] \frac{1}{3x} + \frac{7}{ {x}^{2} } + \frac{x + 2}{x} [/tex]
[tex] \frac{x}{ {3x}^{2} } + \frac{21}{3 {x}^{2} } + \frac{3 {x}^{2} + 6x}{3 {x}^{2} } [/tex]
[tex] \frac{ {3x}^{2} + 7x + 21 }{ {3x}^{2} } [/tex]
Choice D
What is the scale factor of the enlargement of shape A to shape B?
Answer:
scale factor = 6
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, shape B to shape A
base of shape A = 1 , base of shape B = 6 , then
scale factor = [tex]\frac{6}{1}[/tex] = 6
After finding the ratio of their corresponding sides of triangles the scale factor we get is 6.
The difference in scale between an original item's scale and a new object that is its representation but is larger or smaller is known as a scale factor.
From figure
For small triangle:
base = 1 units
For large triangle:
base = 6 units
Now the scale factor = ratio of adjacent sides
Scale factor = (Base of large triangle)/(Base of small triangle)
Scale factor = 6/1
Scale factor = 6
Hence,
The scale factor is 6.
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#SPJ4
it takes 1 1/2 hours to fill 1/2 of a tank how long will it take to fill 2 tanks completely
Answer:
15
Step-by-step explanation:
hope this helps
A 2-pack of jump ropes costs $1.80. What is the unit price?
$
per jump rope
Answer:
90 cents
Step-by-step explanation:
you divide 1.80 by 2 and get .9 which is equal to 90 cents
Answer:
$0.90
Step-by-step explanation:
literally just divide by 2
Please answer .....
there are 5 blue, 4 red, 1 yellow and 2 green bead in a bag.
A) Find the probability that a bead chosen at random from the bag is blue?
B) Find the probability that a bead chosen at random from the bag is red or yellow?
C) Find the probability that a bead chosen at random from the bag is white?
D) Find the probability that a bead chosen at random from the bag is NOT yellow?
Q4) A fruit bowl contains 4 apples, 3 oranges, and 8 bananas, find the probability of
a) Randomly selected orange
b) Randomly selected apples
c) Randomly selected apple or banana
d) Randomly selected orange ,replace it then select banana
Q5) a number cube labeled by the numbers (3,3,3,3,5,5),what is the probability of
a) The number cube shows a 5
b) The number cube shows a 3
c) Having 5 and then 5 when the number cube rolled twice
d) Having 5 and then 3 when the number cube rolled twice
Answer:
A) 5/12
B) 5/12
C) 0/12
D) 11/12
-------------
Q4.
A) 3/15
B) 4/15
C) 12/15
D) 8/15
-----------------
Q5.
A) 2/6 or 1/3
B) 4/6 or 2/3
C)
D)
Step-by-step explanation:
i need help please !!
Answer:
22x + 155
Step-by-step explanation:
9(x-3)+ 13(x+14) use distributive law
9x - 27 + 13x + `182 gather 'like' terms
(9x+13x) + ( -27+ 182) simplify
22x + 155
Evaluate each expression if f = –4, g = 2, and h = 7.
h – f
Answer:
11
Step-by-step explanation:
h - f = 7 - (-4) = 7 + 4 = 11
A game requires rolling a six-sided die numbered 1 to 6 and flipping a coin. What is the
probability rolling an even number and flipping a head
Answer:
1/4
Step-by-step explanation:
on flipping a coin, we either get a heads or a tails and both the events are equally likely. So the probablity of getting a tails is 1/2.
Now
On rolling a die, we can get 6 possible outcomes(1,2,3,4,5,6)
But the favourable outcomes (an even number) are only 3. So the probablity of getting an even number is 3/6=1/2
In case. we have 2 events that need to occur together, we simply need to multiply their individual probablities to get the probablity of getting both the events together
So our required answer is
p(even number)× p(tails)= 1/2 × 1/2 = 1/4
A chef used one-half of a bag of potatoes for a meal. If the potatoes fed 2 people, what
fraction of the bag did each person get?
(Help plss as soon as you can)
Answer: 1/4
Step-by-step explanation: each person had half of the half of bag.
