The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.
What is parabola ?
A parabola is a symmetric, U-shaped geometric shape.
a)V(1) = 38.4 = a(1)^2 + b(1) + c
V(2) = 21.6 = a(2)^2 + b(2) + c
V(3) = 9.6 = a(3)^2 + b(3) + c
Solving the system of equations, we get ,
a = -2.4 , b = 11.2 , c = 46 , V(t) = -2.4t^2 + 11.2t + 46.
b)We can find the initial volume of water in the tub by plugging in t = 0 into the function V(t) = -2.4t^2 + 11.2t + 46. This gives us V(0) = 46 liters, so the tub had 46 liters of water when the plug was pulled.
c)t = (-11.2 +/- sqrt(11.2^2 - 4*(-2.4)46))/(2(-2.4))
t = (11.2 +/- sqrt(124.48 + 552.8))/-4.8
t = (11.2 +/- sqrt(677.28))/-4.8 = (11.2 +/- 26.16)/-4.8 = -14.96 or 2.16
d)V(4.6667) = -2.4*(4.6667)^2 + 11.2*(4.6667) + 46 = -2.4*21.778 + 46.4 + 46 = -52.6667. So the least amount of water the model predict is -52.6667 liters. This number is not reasonable as the volume of water can't be negative.
e) The graph of the function V(t) = -2.4t^2 + 11.2t + 46 is a parabola that opens downward and has its vertex at (4.6667, -52.6667). Any portion of the graph for t < 0 or t > 2.
The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.
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Part B
The table holding Juanita's pennies gets bumped, and the stack becomes slanted.
How is the volume of the stack affected? Explain your reasoning
The volume of the stack affected will be 10,825.38 cubic millimeters.
Let r be the radius and h be the height of the cylinder.
Then the volume of the cylinder will be
V = π r²h cubic units
The table holding Juanita's pennies gets bumped, and the stack becomes slanted.
The radius of the cylinder is given as,
r = 19.05 / 2
r = 9.525 mm
Then the volume of the cylinder is calculated as,
V = π x (9.525)² x 38
V = 3.14 x 90.725 x 38
V = 10,825.38 mm³
The volume of the stack affected will be 10,825.38 cubic millimeters.
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Answer:
The volume of the stack affected will be 10,825.38 cubic millimeters.
Step-by-step explanation:
Describe the discontinuity of the graphed function. Be sure to indicate the location of each discontinuity and identify the type of discontinuity.
function f(x) is said to be discontinuous at a point ‘a’ of its domain D if it is not continuous there. The point ‘a’ is then called a point of discontinuity of the function.
he function of the graph which is not connected with each other is known as a discontinuous function.
A function f(x) is said to have a discontinuity of the first kind at x = a,
if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.
f(x) is said to have a discontinuity of the first kind from the left at x = a,
if the left hand of the function exists but not equal to f(a)
There are three types of discontinuity.
Jump Discontinuity
Infinite Discontinuity
Removable Discontinuity
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Given:2x-3y+z=03x+2y=354y-2z=14Which of the following is a solution to the given system?(2, 3, 5)(3, 2, 0)(1, 16, 0)(7, 7, 7)
The solution to the given system is (2, 3, 5). This can be determined by solving the system of equations using elimination.
First, add the first equation to the second equation to eliminate the y-term:
5x + z = 7
Next, add the third equation to the first equation to eliminate the x-term:
3y + z = 3
Finally, substitute the expression for z into the expression for x and solve for y:
y = 3
Now that we have the values for x and y, substitute them into one of the original equations to solve for z:
2(2) - 3(3) + z = 0
z = 5
The solution is (2, 3, 5).
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table. Consequently, .
If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage
X1: Gas mileage before using octane booster
X2: Gas mileage after using octane booster
The researcher is comparing X1 and X2, to determine if using an octane booster increases gasoline mileage.
1. The researcher selected a random sample of seven cars and drove them for two weeks without using the octane booster (X1).
2. The researcher then drove the same seven cars for two weeks with the octane booster (X2).
3. The researcher then compared the data from X1 and X2 to see if there was an increase in gasoline mileage.
4. If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage.
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Which option distinguishes the element that needs to be adjusted on the chart in the following scenario?
Donna just completed her demographic chart for her final social studies project on population growth. Her
teacher returns it and says her independent variable is incorrect and needs to be changed.
title
O y-axis value
O legend
Ox-axis value
833
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An answer option which distinguishes the element that needs to be adjusted on the chart in the following scenario is: C. x-axis value.
What are the types of variables?In an experiment, there are two (2) main types of variables and these include the following:
Dependent variable.Independent variable.What is an independent variable?In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it is represented by the x-axis value on a graph.
In this scenario, we can reasonably infer and logically deduce that the independent variable (x-axis value) represents the element that should be adjusted on Donna's demographic chart on population growth.
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Find the margin of error for the given values of c, s, and n. c = 0.98, s = 3.3, n = 22 Click the icon to view the t-distribution table. The margin of error is . (Round to one decimal place as needed.)
The margin of error is 1.6393 for the supplied values of c, s, and n, which are 0.98, 3.3 and 22respectively.
what is margin ?
Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.
Given that,
standard deviation = s = 3.3
z is the 98% = z score = 2.33
Sample size = n =22
Margin of error is expressed using the formula;
M = z * √s²/n
M = 2.33* √3.3²/22
M = 2.33* 0.7035
M = 1.6393
Therefore, the margin of error is 1.6393 for the supplied values of c, s, and n, which are 0.98, 3.3 and 22respectively.
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medians are drawn from point $a$ and point $b$ in this right triangle to divide segments $\overline{bc}$ and $\overline{ac}$ in half, respectively. the lengths of the medians are 6 and $2\sqrt{11}$ units, respectively. how many units are in the length of segment $\overline{ab}$?
The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
What is right triangle ?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called legs, and one of them is the base and the other one is the height.
We know that the medians are 6 and $2\sqrt{11}$ units, respectively.
Therefore, the length of $\overline{ab}$ is twice the median length from $a$ to segment $\overline{bc}$ + twice the median length from $b$ to segment $\overline{ac}$
so the length of $\overline{ab}$ = 2(6) + 2($2[tex]\sqrt{11}[/tex]$) = 12 + 4$\sqrt{11}$
so the length of $\overline{ab}$ = 12 + 4$[tex]\sqrt{11}[/tex]$ units.
Hence , The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
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Which represents the polynomial written in standard form?
8x2y2 – 3x3y + 4x4 – 7xy3
4x4 – 3x3y + 8x2y2 – 7xy3
4x4 – 7xy3 – 3x3y + 8x2y2
4x4 + 8x2y2 – 3x3y – 7xy3
–7xy3 – 3x3y + 8x2y2 + 4x4
Answer:
Step-by-step explanation:
The correct answer is: 4x4 + 8x2y2 – 3x3y – 7xy3. This is the standard form for the polynomial, where the terms are written in descending order. The terms in this polynomial are the 4x4 term, the 8x2y2 term, the -3x3y term, and the -7xy3 term.
hello everyone, i need help can someone help me here please! thankyou
Answer:
1. 37, 44, 51
2. 24, 19, 14
3. 36, 49, 64
Step-by-step explanation:
The first rule is add 7
The second rule is subtract 5
The third rule is add 2 to every difference
Find the complex conjugates for each of the following numbers: a. - 19 = Preview b. -25i = Preview c. - 11 - 92i = Preview d. 413i - 37 Preview
The complex conjugates for each of the following numbers
a. - 19 = -19
b. -25i = +25i
c. - 11 - 92i = 11 + 92i
d. 413i - 37 = -413i - 37
The term complex number in math is defined as the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number.
Here we have given that the list of complex number and here we need to find the complex conjugates for each of the following numbers:
As we all know that conjugate in Mathematics is formed by changing the sign of one of the terms in a binomial.
Based on the definition, here we have the general form a + bi as the conjugate as a - bi.
From this one we have identified that here we have only changed the sign of imaginary pat.
So, the complex conjugate of the given complex numbers are written as
=> a. - 19 = -19
Here we have only the number part so the sign remains constant
b. -25i = +25i
Here we have only the imaginary part so we have changed it to positive.
c. - 11 - 92i = 11 + 92i
Based on the complex conjugate rule the term must be changed.
d. 413i - 37 = -413i - 37
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work out the value of r in the equation below
5.8/r=tan 19
give your answer in 1d.p.
Answer: 16.8
Step-by-step explanation:
[tex]\frac{5.8}{r}=\tan 19^{\circ}\\\\\frac{r}{5.8}=\frac{1}{\tan 19^{\circ}}\\\\r=\frac{5.8}{\tan 19^{\circ}}}\\\\r \approx 16.8[/tex]
11 is 25% of what number?
Answer:
44 is your answer
Step-by-step explanation:
Write an equation relating the total amount in a in Terry’s account to the number of years,t. Is the relationship proportional?Explain
An equation relating the total amount in a in Terry’s account to the number of years, t is A = P + P*(r/100)*t. Yes, the relationship is proportional.
what is an equation?An equation is a well-formed formula that connects two expressions with the equals sign to express the equality of those two expressions. For example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
An equation relating the total amount in a in Terry’s account to the number of years, t is A = P + P*(r/100)*t.
Where, A is total amount,
P is amount which Terry deposit,
r is rate of interest,
and t is number of years.
Yes, the relationship is proportional.
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What is the equation of a circle with a center (−3, −2) and radius of 5?
HELPPPPPPP!!!!!!
(x − 3)2 + (y − 2)2 = 25
(x − 3)2 + (y − 2)2 = 5
(x + 3)2 + (y + 2)2 = 5
(x + 3)2 + (y + 2)2 = 25
which of the following shows the correct first step to solve x^2-16x=-21 by completing the square? I'LL GIVE YOU BRAINLLEST PLEASE HELP ASAP!!!!!!!!!!!!!!!!!
Answer: B. [tex]x^{2} - 16x + 64 = -21 + 64[/tex]
Step-by-step explanation:
Please, help me! I need help in this solve
Answer:
Step-by-step explanation:
15x² - 2x - 1 = 0
15x² - 5x + 3x - 1 = 0
5x(3x - 1) + 3x - 1 = 0
(5x + 1)(3x - 1) = 0
x = -1/5, 1/3
8x² - 10x - 3 = 0
8x² - 12x + 2x - 3 = 0
4x(2x - 3) + 2x - 3 = 0
(4x+1)(2x-3) = 0
x = -1/4 , 3/2
16x² - 8x + 3 = 0
This question has complex answers as the D = 64 - 192 < 0
So, ignore this question. It is wrong or it has complex answers.
Use the quadratic formula for it.
9x² - 6x - 2 = 0
This also needs the quadratic formula as the answer is in roots.
8x² - 2x - 3 = 0
8x² - 6x + 4x - 3 = 0
2x ( 4x - 3) + 4x - 3 = 0
(2x + 1)(4x-3) = 0
x = -1/2 , 3/4
Pls help will get grounded if I fail ☹ Write the rule for the linear. Remember a function rule written using f(x).
raquel wants to make a rectangular garden with a area of 12m, but using the least amount of fencing. Each has to be a whole (ie not decimals). What will the dimensions of the garden be?
Answer:
Step-by-step explanation:
The dimensions of the garden will be 4m by 3m. To determine the dimensions of the garden, we need to use the formula A = l x w, where A is the area of the garden (12m), l is the length of the garden and w is the width of the garden.
We can then rearrange the formula to solve for either l or w. We can rearrange the formula to solve for l by dividing both sides of the equation by w: A/w = l.
We know that the area is 12m, so we can substitute 12m for A in the equation. We need to find the dimensions that use the least amount of fencing, so let's set w equal to 3m. We can then substitute 3m for w in the equation and solve for l: 12m/3m = 4m.
Therefore, the dimensions of the garden are 4m by 3m.
Why is 1 A common factor of every number?
A number multiplied by 1 is the number itself. So,1 is a factor of every number.
1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.
1 is the greatest factor of itself and the smallest factor of any other number.
There are some properties of factors one:
Every whole number is the product of 1 and itself so, each number is a factor of itself. Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.Every number other than 1 has at least two factors, namely the number itself and 1.To know more about common factors:
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Bonjour je suis entrain de faire la distributivité et je bloque sur ce calcul quelqu'un pourrait m'aider svp.
4x+[3-(7-x)]-[4x-(x-2)]
Merci
Answer:
Step-by-step explanation:
beaucoup pour votre aide !
Pour résoudre cette expression, nous allons appliquer la distributivité, c'est-à-dire multiplier chaque terme entre parenthèses par le nombre devant les parenthèses.
On commence par 4x + [3 - (7-x)], ce qui donne:
4x + (3 - 7 + x)
Ensuite, nous pouvons appliquer la distributivité à 4x-(x-2):
4x + (3 - 7 + x) - (4x - x + 2)
Enfin, nous pouvons réorganiser les termes pour simplifier l'expression:
4x + 3 - 7 + x - 4x + x - 2
En réarrangeant, nous obtenons:
-2 - 4 + 5x
Donc, l'expression complète est: -2 - 4 + 5x.
find the vector, not with determinants, but by using properties of cross products. (i × j) × k
(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.
What is cross product?The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.
A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.
As we know,
i × j = | i | × | j | × sin 90° × k
or, i × j = 1 × 1 × 1 × k
or, i × j = k
thus, (i × j) × k = k × k
or, (i × j) × k = 0
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what is the answer for this question? answer ASAP
Answer:
1÷(5/2×(2×(8-2/5)-1))
1÷(5/2×(2×(6/5)-1))
1÷(5/2×(12/5-1))
1÷(5/2×7/5)
1÷(35/10)
1÷35/10
1×10/35
10/35
2/7
1) Rustam has three times as many carrots as Pio. Rustam has 5 fewer carrots that Claudine.
Form an equation relating the number of carrots that Pio has compared to Claudine.
b. Use your equation to find out how many carrots Pio has, if Claudine has 20?
C. Use your equation to find out how many carrots Claudine has, if Pio has 10?
3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and if pio has 10 then the number of carrots with Claudine are 35
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Rustam has three times as many carrots as Pio
R=3P
Where is Rustam, P is Pio and C is Claudine.
Rustam has 5 fewer carrots that Claudine.
R=C-5
3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine.
Now let us find the number of carrots Pio has when Claudine has 20
3P=20-5
3P=15
Divide both sides by 3
P=5
Pio has 5 carrots when Claudine has 20.
Now if pio has 10 then the number of carrots with Claudine
3(10)=C-5
30+5=C
35=C
Hence, 3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and if pio has 10 then the number of carrots with Claudine are 35
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Dr. Jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left in the culture dish each hour. If the initial bacteria count was 100, what was the bacteria count after 5 hours? Round to the nearest whole number
The bacteria count after 5 hours, given the initial bacteria count and the rate that the bacteria are disappearing is 59 bacteria
How to find the bacteria count ?First, find the rate at which the bacteria are disappearing from the culture dish every hour. This rate is:
= 100 % - 90 %
= 10 %
This means that every hour, 10% of the bacteria are removed from the culture dish on account of the antibiotic.
In five hours therefore, the bacteria count on the culture dish would be:
= Starting number of bacteria x ( 1 - rate of decrease per hour) ^ number of hours
= 100 x ( 1 - 10 %) ⁵
= 100 x 90 %⁵
= 59 bacteria
In conclusion, after 5 hours of the antibiotic working on the culture dish, the number of bacteria left would be 59 bacteria.
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What are the values of the constants in the vertex form of the quadratic equation that models the bird's path? with answers.
h = 0
k = 20
a = -0.12
next question
which system of equations could you use to determine where the paths intersect? b.
y = 0.8x and y = -0.12x2 + 20
The point of intersection of the bird's paths can be found by setting up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20 and solving for x. The x-coordinate of the point of intersection is approximately 3.33.
y = 0.8x
and
y = -0.12x2 + 20
First, set the two equations equal to each other:
0.8x = -0.12x2 + 20
Next, subtract 20 from both sides of the equation:
0.8x = -0.12x2
Then, divide both sides by 0.8:
x = -0.15x2
Finally, solve for x by dividing both sides by -0.15:
x = 10/3 or x ≈ 3.33
To find the point of intersection of the bird's paths, we can set up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20. We then set the two equations equal to each other and solve for x. Subtracting 20 from both sides of the equation, we get 0.8x = -0.12x2. We then divide both sides of the equation by 0.8, giving us x = -0.15x2. Finally, by dividing both sides of the equation by -0.15, we can solve for x to find the point of intersection, which turns out to be x = 10/3 or approximately 3.33. In other words, the paths intersect at a point with a x-coordinate of approximately 3.33.
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Pretty please someone answer this! Based on the graph shown, which of the following statements is true?
For the graph of data given option C: The median 300 is the middle number is correct.
What is median?
In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.
Draw the median table for the graph of values given -
Number Frequency ∑f
100 14 14
200 6 20
300 18 38
400 12 50
500 2 52
600 12 64
700 8 72
The formula for median is -
Median = [n/2 + (n/2 + 1)] / 2
Median = [72/2 + (72/2 + 1)] / 2
Median = [36 + (36 + 1)] / 2
Median = 73/2
Median = 36.5
According to the table the ∑f value 36.5 corresponds to 300.
Therefore, the median 300 is the middle number.
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Three fathers-Paul, Johnson, and Nicolas have between them a total of 15 children of which 9 are boys. Paul has 3 girls and Johnson has the same number of boys. Johnson has 1 more child than Paul who has 4 children. Nicholas has 4 more boys than girls and the same number of girls as Paul has boys. How many boys each do Nicolas and Paul have?
Answer:
Nicholas has 5 boys, and Paul has 1 boy
Step-by-step explanation:
We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:
[tex]p + j + n = 15[/tex] (1st Equation)
[tex]p_{g} = j_{b} = 3[/tex] (2nd Equation)
[tex]j = p + 1 (p = 4)[/tex] (3rd Equation)
[tex]n_{b} = n_{g} +4[/tex] (4th Equation)
[tex]n_{g} = p_{b}[/tex] (5th Equation)
Whew! That was a lot. We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:
b = g + 4 and b + g = 6
So, we substitute the first equation into the second equation, giving us:
g + 4 + g = 6
2g = 2
g = 1
So, Nicholas has one girl, meaning he has 5 boys.
So, Nicholas has 5 boys, and Paul has 1 boy.
Hope this helped!
please help me answer this ty :)
12. Susan has 8 eggs in her fridge.
Two of the eggs have passed their sell by date and are "bad".
She selects 3 eggs at random to bake a cake.
(a) Complete the probability tree diagram.
(b) Work out the probability that Susan will select 3 "good" eggs.
(c) Work out the probability that Susan will select at least one "bad" egg.
The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4
How do you calculate probability?Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.
What are probability and examples?The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). Writing P(heads) = 12
Hence,
The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4
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select all the examples of exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
Answer:
Select all the examples of the exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
