Monya and Kishi are hiking in the mountains and stop for lunch on a ledge 1000 feet above the valley below. Kishi decides to climb to another ledge 20 feet above Monya. Monya throws an apple up to Kishi, but Kishi misses it. The function h(t) = -16t2 + 30t + 1000 represents the height in feet of the apple at any given time in seconds.1. What is the maximum height of the apple? 2. How long did it take the apple to reach the maximum height? 3. How long did it take for the apple to hit the ground?
Answers
1) The function given is a quadratic function with negative leading coefficient, so its maximum value can be calculated using the formula for the y value of the vertex of a parabola:
\(\begin{gathered} y_v=-\frac{\Delta}{4a} \\ \Delta=b^2-4ac \end{gathered}\)Since the function is give, we can get the values for a, b and c:
\(\begin{gathered} y=ax^2+bx+c \\ h(t)=-16t^2+30t+1000 \end{gathered}\)So:
\(\begin{gathered} \Delta=30^2-4(-16)(1000)=900+64000=64900 \\ h_{\max }=-\frac{64900}{4(-16)}=-\frac{64900}{-64}=1014.0625 \end{gathered}\)So, the maximum height is 1014.0625 feet.
2) This is also the vertex of the parabola, but now the x value formula:
\(x_v=-\frac{b}{2a}\)So:
\(t_{\max }=-\frac{30}{2(-16)}=-\frac{30}{-32}=0.9375\)So, it take 0.9375 seconds to reach the maximum.
3) When it hits the ground, h(t) = 0, so this is the same as fiding the zero of the function, which we can do by using the quadratic formula:
\(\begin{gathered} t=\frac{-b\pm\sqrt[]{\Delta}}{2a}=\frac{-30\pm\sqrt[]{64900}}{2(-16)}=\frac{-30\pm254.754\ldots}{-32} \\ t_1=\frac{-30+254.754\ldots}{-32}=\frac{224.754\ldots}{-32}=-7.02358\ldots \\ t_2=\frac{-30-254.754\ldots}{-32}=\frac{-284.754\ldots}{-32}=8.89858\ldots \end{gathered}\)One of the results is negative, so it doen's make sence for this situation. So, the only solution is:
\(t=8.89858\ldots\approx8.8986\)So, it take approximately 8.8986 seconds for it to hit the gournd.
Related Questions
4.
fourteen hundredths + eighty and seventy-nine thousandths =
Answers
Answer:
80.219
Step-by-step explanation:
I might be wrong tho
Having done poorly on their Math finals in June, eight students repeat the course in summer school and take another exam in August. June 54 49 68 66 58 60 62 62 August 50 65 74 64 56 65 68 72 ! If we consider these students to be representative of all students who might attend this summer school in other years, do these results provide evidence that the program is worthwhile? (d) Set up the appropriate H0 and Ha. (e) Propose a formula to calculate the test statistic and report the result. (Assume the population follow a normal distribution) (f) Find the P-value and make your conclusion at α = .05.
Answers
The null hypothesis (H0) is that there is no significant change in the average score obtained by the students in June and August
Alternative hypothesis(H1): There is significant change(increase) in the average score obtained by the students from June to August
How to explain the hypothesisIn this case, paired sample test is to be used. For this the calculation is needed and attached.
t= 4.375*sqrt(8)/148.95
= 0.083
P-value will be:
= P(T>0.083)
= 0.468 (use t table or excel function = tdist( 0.083,7,1)
Since, p-value is greater than 0.05, null hypothesis is accepted. I.e. there is no significant change(increase) in average score of student at 5% level of significance. Hence, the program does not seem worthwhile.
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i need help thanks11!1!1!1!1!1
Answers
Answer:
A
Step-by-step explanation:
1
A line has a slope of 5 and a y-intercept of -2
Answers
Answer:
1
Step-by-step explanation:
Answer:
(2/5,0)
Step-by-step explanation:
The equation to find a line is mx+b=y. In this case m is 5, and b is -2.
5x+-2=y
Since we want to find the x-intercept, y has to be 0.
So: 5x+-2=0
5x=2
x=2/5
The ratio of two numbers is 5 to 6. If their sum is 88, what is the value of the smaller number?
Answers
Answer:
The smaller number is 40.
Step-by-step explanation:
The divisor is 5 + 6 = 11.
So one part = 88/11 = 8
So we need to find 5 parts and 6 parts.
The 2 numbers are:
5 * 8 = 40 and
6 * 8 = 48.
The function f(x)=4^x-6 is transformed to function G through a vertical compression by a factor of 1/2. Complete the equation of function G .  enter the correct answer in the box. Substitute  numerical values into the equation for a and k.
g(x) = a(4)^x-k
Answers
The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2
How to solve a function?
If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:
g(x) = a(4) raise to the power x-k/2
where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:
f(x) = g(x)/2
Substituting the expression for g(x) into this equation and simplifying, we get:
4raise to the power x - 6 = a(4)raise to the power x-k/2
To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:
f(0) = 4 - 6 = -5
f(1) = 4- 6 = -2
Using the equation g(x)/2 = f(x), we can write:
g(0)/2 = -5
g(1)/2 = -2
Substituting the expression for g(x) into these equations, we get:
a(4) raise to the power -k/2 = -10
a(4) raise to the power 1-k/2 = -4
Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":
(4)raise to the power -k/2 / (4) raise to the power 1-k/2 = -10 / -4
Simplifying this equation, we get:
4.raise to the power(1-k/2) = 5
Taking the logarithm of both sides (with base 4), we get:
1-k/2 = log4(5)
Solving for "k", we get:
k = 2 - 2 log4(5)
Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":
a = -10 / (4) raise to the power -k/2
Substituting the numerical value of "k", we get:
k = 2 - 2 log4(5) ≈ 0.872
a = -10 / (4) raise ti the power -k/2 ≈ 2.323
Therefore, the equation for the transformed function g(x) is:
g(x) = 2.323 (4)raise to the power x-0.872/2
or equivalently:
g(x) = 1.1615 (4) raise to the power -x0.872
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Answer:
g(x) = 1/2 (4)^x - 3
Step-by-step explanation:
A vertical compression by a factor of 1/2
means that the entire function f is multiplied by 1/2:
1/2 f (x) = 1/2 (4^x - 6)
= 1/2 (4)^x - 3
Find dy: y =
dy
=
x3 +52 +4
x²+4
Calculator
Check Answer
Jump to Answer
Answers
Given:
\(y=\frac{x^3+5x+4}{x^2+4}\)
Find:
\(dy=??\)
Rules/Methods that will be used:
Product rule: \(\Longrightarrow \frac{d}{dx}[\frac{f(x)}{g(x)} ] = \frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}\)
Power Rule: \(\Longrightarrow \frac{d}{dx}[x^n]=nx^{n-1}\)
Constant Rule: \(\Longrightarrow \frac{d}{dx}[k]=0\)
\(\Longrightarrow y=\frac{x^3+5x+4}{x^2+4} \Longrightarrow dy=\frac{(x^2+4)(\frac{d}{dx}[x^3+5x+4])-(x^3+5x+4)(\frac{d}{dx}[x^2+4] )}{(x^2+4)^2}\)
\(\Longrightarrow dy=\frac{(x^2+4)(3x^2+5)-(x^3+5x+4)(2x)}{(x^2+4)^2}\)
Simplify the expression.
\(\Longrightarrow dy=\frac{(x^2+4)(3x^2+5)-(x^3+5x+4)(2x)}{(x^2+4)^2} \Longrightarrow dy=\frac{(3x^4+17x^2+20)-(2x^4+10x^2+8x)}{(x^2+4)^2}\)
\(\Longrightarrow dy=\frac{x^4+7x^2-8x+20}{(x^2+4)^2}\)
The expression cannot be simplified further.
\(Thus, dy=\boxed{\frac{x^4+7x^2-8x+20}{(x^2+4)^2}} \therefore Sol.\)
Please find the area of the unshaded portion in the diagram above
Answers
Answer:
148 cm²Step-by-step explanation:
find the two areas and remove the shaded one
18 * 10 - 8 * 4 (remember pemdas)
180 - 32 =
148 cm²
Identify an equation in standard form for a hyperbola with center (0, 0), vertex (6, 0), and focus (10, 0).
Answers
Answer:
Step-by-step explanation:
a) Let X be a random variable that can assume only positive integer values, and assume its probability function is P(X -n) A/3^n for some constant A (n> 1). Find A.
b) Let X be a continuous random variable that can assume values between 0 and 3, and assume its density function is fx(x)- B(x2 +1) with some constant B (0< x ,3). Find B.
Answers
Answer:
a) The value of A = 2
b) The value of \(B = \dfrac{1}{12}\)
Step-by-step explanation:
a)
Given that:
X should be the random variable that assumes only positive integer values.
The probability function; \(P[X = n] = \dfrac{A}{3^n}\) for some constant A and n ≥ 1.
Then, let \(\sum \limits ^{\infty}_{n =1} P[X =n] = 1\)
This implies that:
\(A \sum \limits ^{\infty}_{n =1} \dfrac{1}{3^n}= 1\)
\(A \times \dfrac{\dfrac{1}{3}}{1 - \dfrac{1}{3}} = 1\)
\(A \times \dfrac{\dfrac{1}{3}}{\dfrac{2}{3}} = 1\)
\(A \times \dfrac{1}{2}=1\)
A = 2
Thus, the value of A = 2
b)
Suppose X represents a e constant A (n> 1). Find A.
b) Let X be a continuous random variable that can assume values between 0 and 3
Then, the density function of x is:
\(f_x(x) = \left \{ {{B(x^2+1)} \ \ \ 0 \le x \le 3 \ \ \ \atop {0} \ \ \ otherwise} \right.\)
where; B is constant.
Then, using the property of the probability density function:
\(\int ^3_0 \ B (x^2+1 ) \ dx = 1\\\)
Taking the integral, we have:
\(B \Big [\dfrac{x^3}{3} +x \Big ]^3_0 = 1\)
\(B \Big [\dfrac{3^3}{3} +3 \Big ]= 1\)
\(B \Big [\dfrac{27}{3} +3 \Big ] = 1\)
B [ 9 +3 ] = 1
B [ 12 ] = 1
Divide both sides by 12
\(B = \dfrac{1}{12}\)
Help please it’s important
Answers
Answer:
C
Step-by-step explanation:
Determine whether the following system of linear equations have no solution, infinitely many solution or unique solutions.x+2y=3,2x+4y=15A.No solutionB.Infinitely many solutionC.Unique solutionD.Cannot be determined
Answers
C. Unique solution. The system of linear equations have a unique solution because the equations are consistent and have the same number of variables and equations.
The given system of linear equations is x+2y=3 and 2x+4y=15. To determine whether the system of linear equations have no solution, infinitely many solution or unique solutions, we need to solve the system of equations. Firstly, we expand and simplify both equations to get x+2y=3 and 2x+4y=15. Then, we compare the coefficients of the equations to determine if the system of equations is consistent, inconsistent or dependent. Since the equations are consistent and have the same number of variables and equations, we can solve the system of equations. By isolating the variables and using the substitution method, we can solve the system of equations to get x=3 and y=3. This means that the system of linear equations have a unique solution.
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Which techniques can be used to evaluate the expression 12.75 = 1.5? Select all that apply.
Answers
pls answer correctly dont troll!!
Answers
Answer:
Yes
Step-by-step explanation:
To form a triangle : The sum of any two side lengths must be bigger than then the third side length and their difference smaller than the third side length.
19.6 + 1.6 > 18.7
19.6 - 1.6 < 18.7 and so on.
can you please help me
Answers
(Diversifying Portfolios MC)
worth points)
Name of Stock Symbol High Low Close
Stock A
105.19 103.25 103.38
Stock B
145.18 143.28 144.05
A
B
Last year, an investor purchase
difference in overall loss or ga
O The difference in overall gain is $207.00.
O The difference in overall loss is $207.00.
O The difference in overall loss is $200.70.
O The difference in overall gain is $200.70.
shares of stock A at $90 per share and 75 shares of stock B at $145 per share. What is the
ween selling at the current day's high price or low price?
Answers
The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.
To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.
Stock A:
High price = $105.19
Low price = $103.25
Close price = $103.38
Stock B:
High price = $145.18
Low price = $143.28
Close price = $144.05
The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.
To calculate the selling prices, we need to multiply the number of shares by the respective selling price.
Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50
Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50
Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50
Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00
Now, let's calculate the difference in overall gain or loss:
Difference in overall gain = Selling price at the high price - Selling price at the low price
= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)
= $16,148.00 - $15,908.50
= $239.50
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In a survey of 1914 adults, 38% responded "yes" to the survey question. How many adults answered "yes"? (round to the nearest whole person as needed)
Answers
Answer:
727 adults
Step-by-step explanation:
In a survey of 1914 adults, 38% responded "yes" to the survey question.
=> The number of adults who answered "yes":
N = 1914 x 38/100 = 727.32 = ~ 727
Answer:
727 adults
Step-by-step explanation:
Number of adults = 38% of 1914
= 0.38 * 1914
= 727.32
≈ 727 adults
There are five blue crayons, seven yellow crayons, and eight red crayons in a box. If one is randomly drawn and replaced 15 times, find the probability of drawing exactly four blue crayons.
Answers
0.2252
(Please mark me brainliest! thank you in advance!!)
Suppose the function h(x) = 2x - 9 is translated up 5 units to become a new function,
Xx). What's the equation of the new function?
A) x) = 7x-4
B)(x) = 2x - 14
C)(x) = 7x-9
D) (x)=2x-4
Answers
According to the given data the equation of the new function is (D) f(x) = 2x - 4.
What is meant by equation?An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.
According to the given information:If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:
f(x) = h(x) + 5
Substituting the definition of h(x) into this equation, we get:
f(x) = 2x - 9 + 5
Simplifying, we have:
f(x) = 2x - 4
Therefore, the equation of the new function is (D) f(x) = 2x - 4.
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What is the following sum?
16x²y +4/3/54x8,5
4x{X/)+12+y(2/28)
8x{X/Xy) + 12x2y? (1/6)
16x®y/2y2
[
48x©y(2/2)
PLEASE HELP!!!!!!!!
Answers
Answer:
the first one
Step-by-step explanation:
\(2(\sqrt[3]{16x^{3}y })+4(\sqrt[3]{54x^{6}y^{5} } )= 2(2x\sqrt[3]{2y })+4(3x^{2} y\sqrt[3]{2y^{2} } ) = 4x(\sqrt[3]{2y })+12x^{2} y(\sqrt[3]{2y^{2} } )\)
-5 1/4 -(-7 1/2) simplify
really fast pleas
Answers
-4 (2x + 13) + 3x = 80
How do you solve this out and get the answer
Answers
Answer:
-132/5
Step-by-step explanation:
-4(2x+13) + 3x = 80
-8x - 52 + 3x = 80
-5x = 80+52
5x = -132
x = -132/5
Feel free to mark this as brainliest! :D
A bag of baseballs costs $12. There are 15 balls in the bag. Another bag of baseballs costs $15 for 20 balls. Which bag prices individual baseballs lower?
Answers
Answer:
Step-by-step explanation:
For the first bag:
Price of the bag = $12
Number of balls in the bag = 15
Price per ball = Price of the bag / Number of balls
Price per ball for the first bag = $12 / 15 = $0.8
For the second bag:
Price of the bag = $15
Number of balls in the bag = 20
Price per ball = Price of the bag / Number of balls
Price per ball for the second bag = $15 / 20 = $0.75
Comparing the prices per ball, we find that the second bag has a lower price per baseball. Therefore, the second bag offers a better price for individual baseballs compared to the first bag.
Answer:
Step-by-step explanation:
To find out which bag prices individual baseballs lower, we can divide the total cost of each bag by the number of balls in the bag. This will give us the price per ball for each bag.
For the first bag, the price per ball is $12 / 15 = $0.80.
For the second bag, the price per ball is $15 / 20 = $0.75.
Therefore, the second bag prices individual baseballs lower.
What is the product?
(3a²b7)(5a³b³)
O 8a5b15
O 8a6b56
O 15a³b¹5
O 15a5b56
Answers
Answer:
15a^5 b^10
Step-by-step explanation:
The product is 15a⁵b¹⁰.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
When multiplying two terms with the same base, you add the exponents. Therefore:
(3a²b⁷)(5a³b³) = 3 x 5 x a⁵ x b ¹⁰
= 15a⁵b¹⁰.
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Evaluate the expression
if x = 2, y = 3, and z = 4.
2x²-y + 2(z-1)
Answers
Answer:
11
Step-by-step explanation:
Substituting the values of x, y, and z into the expression, we get:
2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)
= 2(4) - 3 + 2(3)
= 8 - 3 + 6
= 11
Therefore, if x = 2, y = 3, and z = 4, then the value of the expression 2x² - y + 2(z-1) is 11.
Answer:
11
Step-by-step explanation:
if x = 2, y = 3, and z = 4.
2x²-y + 2(z-1)
Substituting the given values of x, y, and z, we get:
2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)
= 2(4) - 3 + 2(3)
= 8 - 3 + 6
= 11
Therefore, the value of the expression when x = 2, y = 3, and z = 4 is 11.
BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) is used to determine the sequence of operations in a mathematical expression. It is used to avoid confusion and ensure that everyone obtains the same answer from a mathematical expression. The rule states that the operations inside the brackets must be done first, followed by orders, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).
A car sold 120 cars in April the dealership wants to increase the number of cars sold by 15% in may how many cars will the dealership need to sell to reach there goal
Answers
Answer:
18
Step-by-step explanation:
15 x 20%=18
Answer:
138
Step-by-step explanation:
because when you add 18 to 120 it is 138
Type the correct answer in each box.
Consider the expressions shown below.
A B C
Complete each of the following statements with the letter that represents the expression.
is equivalent to expression
.
is equivalent to expression
.
is equivalent to expression
.
Answers
Answer:
BAC
Step-by-step explanation:
The expression (3x² - 6x + 11) - (10x² - 4x + 6) is equivalent to the expression A, expression (-3x² - 5x - 3) - (-10x² - 7x + 2) is equivalent to the expression C, and expression (12x² + 6x - 5) - (5x² + 8x - 12) is equivalent to the expression B.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)
We have a polynomial shown in the picture.
A = -7x² - 2x + 5
B = 7x² - 2x + 7
C = 7x² + 2x - 5
The expression is:
= (3x² - 6x + 11) - (10x² - 4x + 6)
= -7x² - 2x + 5
= A
= (-3x² - 5x - 3) - (-10x² - 7x + 2)
= 7x² + 2x - 5
= C
= (12x² + 6x - 5) - (5x² + 8x - 12)
= 7x² - 2x + 7
= B
Thus, the expression (3x² - 6x + 11) - (10x² - 4x + 6) is equivalent to the expression A, expression (-3x² - 5x - 3) - (-10x² - 7x + 2) is equivalent to the expression C, and expression (12x² + 6x - 5) - (5x² + 8x - 12) is equivalent to the expression B.
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Line G passes through the point (7,11) and is parallel to the line given by y = 4(3x + 2). What is the equation of line G? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
Answers
Answer:
y = 12x - 73
Step-by-step explanation:
Pre-SolvingWe are given the line y=4(3x+2).
We want to find the equation of line G, which contains the point (7,11), and is parallel to y=4(3x+2) in the form y=mx+c. m is the slope, and c is the value of y at the y-intercept.
Parallel lines have the same slopes. So, we should start by finding the slope of y=4(3x+2).
SolvingWe can do the distributive property to distribute the 4 to both terms on the right side.
y=4(3x+2) => y=12x + 8
Notice how this equation is written in the form y=mx+c. As 12 is written in the place where m is, the slope of this line is 12.
It is also the slope of line G.
We can replace m in y=mx+c with 12 for line G. We'll get:
y=12x + c
Now, we need to find c.
We can use the point (7,11) to help us find c.
Substitute 7 for x and 11 for y.
11 = 12(7) + c
Multiply.
11 = 84 + c
Subtract 84 from both sides
-73 = c
Substitute -73 as c.
y = 12x - 73
A baker uses the equation y = 12x to predict the revenue generated from selling cakes. She uses equation y = 450+4.5x to model the cost to produce a cakes. What does (60, 720), the solution of the system y =12x y=450+4.5x represent?
Answers
The point (60, 720) means that the break even is when 60 cakes are produced. That is when 60 cakes are sold, the revenue is equal to the cost of $720
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The slope intercept form of the linear equation is:
y = mx + b
where m is the slope and b is the initial value.
A baker uses the equation y = 12x to predict the revenue generated from selling cakes. She uses equation y = 450+4.5x to model the cost to produce a cakes.
The solution to the system y = 12x and y = 450 + 4.5x represent the point at which there is break even, that is cost is equal to revenue
The point (60, 720) means that the break even is when 60 cakes are produced. That is when 60 cakes are sold, the revenue is equal to the cost of $720
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williams has 32 coins that are all either quarter or dimes the coins have a value of $5 how many dimes does williams have
Answers
Answer:
20 dimes
Step-by-step explanation:
1 dime = $0.1
1 quarter = $0.25
Let there be x dimes
Then the number of quarters is 32-x
Also, $5 = 0.1x + 0.25(32-x)
⇒ 5 = 0.1x + 8 - 0.25x
⇒ 0.25x - 0.1x = 8 - 5
⇒ 0.15x = 3
⇒ x = 3/0.15
⇒ x = 20