Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the tunnel is initially full, how long will it take for it to be one-third full? What is the height of the water level? Assume the radius to be 3 inches and the altitude of the cone to be 4 inches.
A ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth
The length of the ladder is 11.66 ft.
What is the Pythagoras theorem?The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
a² + b² = c²
Given that a ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house.
Let the length of the ladder be x
Therefore, using Pythagoras theorem
x² = 10² + 6²
x² = 100 + 36
x = [tex]\sqrt{136[/tex]
x = 11.66 ft
Hence, the length of the ladder is 11.66 ft.
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A child is to receive a dose of 0.5 teaspoon of cough medicine every 6 hours. If the bottle contains 24 doses, how many days will the medicine last?
An object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet high. Write a model for the object? How many seconds until the maximum height is reached? What will be the maximum height? How many seconds until the object hits the ground
The model for the object's motion is [tex]h(t) = -16t^2 + 64t + 80[/tex]. It reaches its maximum height of 144 feet at 2 seconds. The object will hit the ground after 5 seconds.
To model the vertical motion of the object, we use the equation:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
where:
h(t) is the height at time t64 ft/s is the initial velocity80 ft is the initial height[tex]16t^2[/tex] represents the effect of gravity (since the gravitational acceleration is approximately 32 ft/s2, and here it is halved to be per second squared)Time to Reach Maximum Height
The time to reach the maximum height can be found by using the formula:
[tex]t = \frac{v_0}{|g|} = \frac{64}{32} = 2 seconds[/tex]
Maximum Height
Plug t = 2 seconds into the height equation:
[tex]h(2) = -16(2)^2 + 64(2) + 80 = 144 feet[/tex]
Time to Hit the Ground
To find when the object hits the ground (h(t) = 0), solve:
[tex]-16t^2 + 64t + 80 = 0[/tex]
Using the quadratic formula:
[tex]t = \frac{-64\pm\sqrt{64^2-4(-16)(80)} }{2(-16)}[/tex]
Simplifies to:
t = 5 seconds (since the negative value does not make sense in this context)
The object will hit the ground after 5 seconds.
use the model to write an equivalent fraction 3 over 4
6/8 , 9/12 are the equivalent fraction 3 over 4
What is Fraction?A fraction represents a part of a whole.
The given fraction is 3/4.
In the given fraction the numerator is three and denominator is four.
We need to find the equivalent fractions of 3/4.
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.
Let us multiply with same number in numerator and denominator to find the equivalent fractions.
3/4×2/2=6/8
3/4×3/3=9/12
Hence, 6/8 , 9/12 are the equivalent fraction 3 over 4
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if the quotient of -20 and 4 is decreased by 3 what number results
quotient is division
-20/4 = -5
-5 -3=
-8
the number is -8
Can you use the values in Pascal’s triangle to find the powers of 11? Explain.
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Yes!
Ultimately (it states) all numbers in existence can be extracted from Pascal's Triangle. Using his binomial formation of: (a + b)^0 = 1 , where y is the number you are using. and (a + b)^x is the equation you use to find the answer of that row... the usage of that row, and the formation of its components is how you find the powers of numbers in a given row...
You would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution, and
If you look at the images below you will notice that to find a power of 11 at it's 6th power, you look at the 6th row of Pascal's Triangle... Although not completely relevant, I also added an image of using his Triangle to find the Powers of 2...
Remember, The images below are of only smaller versions of Pascal's Triangle, as his Triangle is of infinite size...
Yes, we can use the values in Pascal’s triangle to find the powers of 11
What is Pascal triangle?Pascal triangles contains coefficient of (x + 1)'s expanded form's terms.
For first row, we have:
Thus, 1 is the value in the first row of Pascal triangle.
(x + 1) = 1
The variable x has coefficient 1, and that 1 itself, so second row of Pascal triangle has 1 , 1 as values.
It states that all numbers in existence can be extracted from Pascal's Triangle.
Using his binomial formation;
(a + b)^0 = 1 , where y is the number
(a + b)^x is the equation that use to find the answer of that row. the usage of that row, and the formation of its components isto find the powers of numbers in a given row.
It would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution.
Yes, we can use the values in Pascal’s triangle to find the powers of 11
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90=20+70 use the distributive property and the GCF OF 20 and 70 to write another related expression for 90 could you write another expression with a different common factor?
Final answer:
To write another expression for 90 using the distributive property and the GCF of 20 and 70, distribute the GCF to each term. Another expression with a different common factor can be written by multiplying each term by a different common factor.
Explanation:
To write another expression for 90 using the distributive property and the GCF of 20 and 70, we can rewrite 90 as (20 + 70). Using the distributive property, we can distribute the GCF to each term inside the parentheses, resulting in 20*(GCF of 20 and 70) + 70*(GCF of 20 and 70). The GCF of 20 and 70 is 10, so the expression becomes 20*10 + 70*10, which simplifies to 200 + 700, equaling 900.
Yes, we can write another expression with a different common factor. Let's say we use the GCF of 20 and 70, which is 10, to rewrite the expression. Instead of multiplying each term by 10, we can multiply 20 and 70 by a different common factor, such as 5. This gives us 20*5 + 70*5, which is equal to 100 + 350, resulting in 450.
Given the piecewise function shown below, select all of the statements that are true.
The statements f(1) = 0 and f(-1) = 2 are true based on the piecewise function.
Options B and C are the correct answer.
We have,
The piecewise function:
f(x) = -x + 1, x < 0
f(x) = -2, x = 0
f(x) = x² - 1. x > 0
Now,
f(-2) = 0
False.
When x = -2, we are in the first condition, so f(-2) = -(-2) + 1 = 3, not 0.
f(1) = 0
True
When x = 1, we are in the third condition, so f(1) = (1)² - 1 = 0.
f(-1) = 2
True
When x = -1, we are in the first condition, so f(-1) = -(-1) + 1 = 2.
f(4) = 7
False.
When x = 4, we are in the third condition, so f(4) = (4)² - 1 = 15, not 7.
Therefore,
The statements f(1) = 0 and f(-1) = 2 are true.
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Will the opposite of a opposite always be positive?
Yes, the opposite of an opposite will always return you to the original value, making it positive if you started with a positive number.
The question refers to the concept of opposites in Mathematics. When considering opposite numbers, the opposite of a positive number is negative, and vice versa. To answer the query, let’s break it down into steps.
First Opposite: The opposite of a positive number, say +5, is -5.Second Opposite: The opposite of -5 is, again, +5.So, yes, the opposite of an opposite will always be positive if you start with a positive number. Similarly, the opposite of an opposite will be negative if you start with a negative number, returning to the original number. This concept is crucial in understanding signed numbers and their roles in arithmetic and algebra.
Ok folks 4 questions and 50 points up for grabs for correct answers....Need quickly thanks!!!
1. 2*0.8 = 1.6 PQ = 1.6
2. arctan(14/12) = 49.4 degrees
3. 15 * cos(70) = 5.1 feet
4. x = 30 * cos(40) = 22.9813 = 23.0 miles
y = 30 *sin(40) = 19.2836 = 19.3 miles
What is the value of digit 0 in 175,028
Answer:
its in the hundreads place but it has no value becuase its 0
Step-by-step explanation:
Solve the equation, and check the answer
5g+4(-5+3)=1-g
A produce store sold 63 red apples. If the ratio of red apples to green apples sold was 7:2, what is the combined amount of red and green apples sold?
The total number of apples sold if, A produce store sold 63 red apples, The ratio of red apples to green apples sold was 7:2, which is 81.
What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.
Given:
A produce store sold 63 red apples,
The ratio of red apples to green apples sold was 7:2,
Assume the total number of apples sold is x then,
Total number of apple sold = 7x + 2x
But the number of red apples sold is given so,
7x = 63
x = 63 / 7
x = 9
Put the value of x in the above equation,
Total number of apple sold = 7 × 9 + 2 × 9
Total number of apple sold = 63 + 18
Total number of apples sold = 81
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Evaluate the expression for the given value.
36 ÷ m when m = 9
A.
324
B.
45
C.
27
D.
4
Describe and correct the error made in solving the system of equations by elimination
The error that was made is that the constant term in the second equation was not multiplied by 5.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method and Addition Method.
Based on the information provided, we have the following system of linear equations:
5x + 3y - z = 15 .........equation 1.
-x + 2y + 3z = 10 .........equation 2.
By multiplying the second equation by 5, we have the following:
(-x + 2y + 3z = 10) × 5 = -5x + 10y + 15z = 50 .........equation 3.
By adding equation 1 and equation 3, we have the following:
5x + 3y - z = 15
-5x + 10y + 15z = 50
13y + 14z = 65
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What is the e-file rejection error for an Invalid bank account or routing transit numbers?
Answer;
The Error code "0019".
Explanation;
-The e-file rejection error for an invalid bank account or routing transit numbers is error code "0019".
-This error code may be caused by a variety of reasons and is present in tax accounting software, where an e-file sent to the IRS is rejected, hence the error name. An incomplete installation might be one of the several reasons behind an e-file rejection error.
The tax rate as a percent, r, charged on an item can be determined using the formula – 1 = r, where c is the final cost of the item and p is the price of the item before tax. Louise rewrites the equation to solve for the final cost of the item: c = p(1 + ). What is the final cost of a $40 item after an 8% tax is applied?
Answer:$43.20
Step-by-step explanation:
Commutative property across multiplication for 2x10x7
what is 15.2 rounded to the nearest tenth
charlie wants to order lunch for his friend. hell order 5 sandwiches and a $3 kids meals for his little brother. charlie has $28. how much can he spend on each sandwich if they are all the same price?
Answer:4 or less
Step-by-step explanation:
6x+3>27
your grandmother is in the hospital and is on a liquid diet. After examining her chart, a mistake is found stating that her weight is 500kg. what is the equivalent weight in pounds
Tamara’s dosage of medication has recently decreased 20 milligrams per day. What is the total decrease in Tamara’s medication at the end of the week? Show your work.
Type answer here
A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inches wide. How far is the house from the other side of the lot?
Answer:
132
123
Step-by-step explanation:
Corresponding range of Celsius temperature C
how do i use parentheses to rewrite 16 - 4 × 3 + 7 so that it equals 120?
(16-4) x (3+7) =120
when we subtract 16 and 4 you get 12.
When we add 3+7 you get 10.
After multiplying them together we get 120.
What are parentheses those called?
parentheses
Parentheses are a pair of punctuation marks that might be most customarily used to feature extra nonessential information or an aside to a sentence. Parentheses resemble two curved vertical lines: ( ). An unmarried one of these punctuation marks is called a parenthesis.
How do you operate parentheses?Use parentheses to surround additional or supplemental data that clarifies or illustrates a point. Use parentheses to offer a digression or afterthought.Use parentheses to surround numbers or letters introducing objects in a list or outline.Learn more about parentheses here: https://brainly.com/question/1473593
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6×12=(6×7)+(6×_)=answer plz
(09.05) A golf ball is hit from the ground with an initial velocity of 208 feet per second. Assume the starting height of the ball is 0 feet. How long will it take the golf ball to hit the ground?
The amount of Time that it would take for the golf ball to hit the ground using the given parameters is; 13 seconds
How to solve projectile problems?
We are given;
Initial Velocity = 208 feet per second
Initial height = 0 ft
Now, the general equation to be used here is;
h(t)= -16t² + 208t
Factorizing the equation gives;
h(t) = -16t(t - 13)
At h = 0, we have;
-16t(t - 13) = 0
Thus;
t = 13 seconds
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PRE-CAL/CAL MASTER NEEDED
f ( 2x − 1 ) = 4x^2 − 10x + 6
from f(x)=x^2-3x+2, h(x)=2x-1, f(h(x))
How is this: f ( 2x − 1 ) = 4x^2 − 10x + 6 derived from ^
Simplify and determine the coefficient of (-x)(3y)(-2x).
a.-4
b.1/3
c.1
d.4
well.. i just got the same problem.. With the same multiple choice.. I'm going to put one. I might update with my score on the test after i finish. (this is an old question that i thought i might answer with my guess)