Answer:
The time it takes for the cannonball to hit the ground is 6.49 seconds.
Step-by-step explanation:
You know that the height of the cannonball above the ground, h, in meters, in time, t, in seconds, is found by the function h(t) = -4.9t² + 30.5t + 8.4. You want to calculate the time it takes for the cannonball to hit the ground, that is, the time it takes for the bullet to reach zero height. So, being h(t) = 0 you have:
0 = -4.9t² + 30.5t + 8.4
To solve a quadratic function 0=a*x² + b*x +c, the expression is applied:
[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
In this case, being a = -4.9, b =30.5 and c =8.4 you have:
[tex]\frac{-30.5+-\sqrt{30.5^{2} -4*(-4.9)*8.4} }{2*(-4.9)}[/tex]
Solving you get:
t1= -0.26 seconds and t2=6.49 seconds
Since time does not have a negative value, then the time it takes for the cannonball to hit the ground is 6.49 seconds.
If x is positive and x^2 = 729, what is the value of x? Please help
Answer:
X= 27
Step-by-step explanation:
Square root both sides
x = + or - 27
but since it’s positive x=27
The soccer team boughtt-shirts at cost for $7.50. They want to sellthem as a fundraiser for between $11.00 and $15.00. What percent increase could they charge?
Answer:
47% or 100%Step-by-step explanation:
Step one:
given data
cost of T-shirt = $7.50
they could sell for either $11.00 and $15.00.
Required
The percent increase in the price
% increase = (cost-sales)price/cost price
% increase = (7.5-11)/7.5*100
% increase = 3.5/7.5*100
% increase = 0.47*100
% increase =47%
OR
% increase = (7.5-15)/7.5*100
% increase = 7.5/7.5*100
% increase = 7.5/7.5*100
% increase =1*100
% increase =100%
The increase could be 47% or 100%
In the bakery 4 cupcakes in one box. If 6 cups
were placed in the box, there would be 20 boxes left
empty. If 3 cupcakes were placed in each box, it
would run out of 20 boxes. Calculate how many
cupcakes were
in the bakery.
Answer:
There were 240 cupcakes in the bakery
Step-by-step explanation:
Assume that the number of boxes used is x
∵ If 6 cups were placed in the box, there would be 20 boxes left
∴ The number of cups in each box = 6
∴ The number of boxes used = (x - 20)
→ Multiply the number of cups in each box by the number of boxes
used to find the total number of cups
∵ The number of cups = 6(x - 20)
∴ The number of cups = 6x - 120 ⇒ (1)
∵ If 3 cupcakes were placed in each box, it would run out of 20 boxes
∴ The number of cups in each box = 3
∴ The number of boxes used = (x + 20)
→ Multiply the number of cups in each box by the number of boxes
used to find the total number of cups
∵ The number of cups3(x + 20)
∴ The number of cups = 3x + 60 ⇒ (2)
∵ The number of cups is the same in the two cases
→ Equate the right sides of (1) and (2)
∴ 6x - 120 = 3x + 60
→ Add 120 to both sides
∴ 6x = 3x + 180
→ Subtract 3x from both sides
∴ 3x = 180
→ Divide both sides by 3 to find x
∴ x = 60
∴ The number of boxes used is 60
∵ In the bakery 4 cupcakes in one box
∵ The number of boxes is 60
∴ The number of cupcakes = 4 × 60
∴ The number of cupcakes = 240
∴ There were 240 cupcakes
If f(x) = 8 – 10x and g(x) = 5x + 4, what is the value of (fg)(–2)? –196 –168 22 78
Answer: Hey buddy it's -168 or B. Hope that helps.
Step-by-step explanation:
edge 2020
The value of (fog)(-2) is -292
What is a composite function ?A composite function is a combination of two or more than two functions where the output of the previous function is the input to the next function.
Given
f(x) = 8 - 10x and g(x) = 5x + 4
To find
(fog)(x) where x = - 2
First we will find (fog)(x)
putting the value of g(x) in f(x)
(fog)(x) = 8 - 10(5x + 40)
= 8 - 50x - 400
= -50x - 392
(fog)(-2) = -50(-2) - 392
= 100 -392
= -292
Learn more about Composite functions here:
https://brainly.com/question/20379727
#SPJ6
hellllllp
awarding brainllest and +100 points
Answer: -45/4 = -11 1/4
I NEED HELP WITH THIS!!
A movie theater used y=1.83x to calculate how much money they made selling buckets of popcorn where y is the total and k is the price per bucket. How much would they make if they sold 8 buckets?
Group of answer choices
$10.98
$16.47
$12.81
$14.64
$14.64
Step-by-step explanation:
Am I right or wrong
Devaughn's age is three times Sydney's age. The sum of their ages is 68. What is Sydney's age?
Answer:
16
Step-by-step explanation:
Devaughn's age is three times Sydney's age. The sum of their ages is 68. What is Sydney's age?
Assume lines p and q intersect to form adjacent angles 1 and 2.
If m∠1=(7x+6)°
and m∠2=(8x−6)°,
find the value of x such that p is perpendicular to q.
Answer:
x=12
Step-by-step explanation:
To make these 2 lines perpendicular to each other, one of their angles must be equal to 90 degrees.
Therefore, we can set up an equation with one of the angles:
7x+6=90
7x=84
x=12
The information of the other angle is useless in this case, but we can use it to check by plugging in 12 for x, and seeing if it equals to 90:
8*12-6=96-6=90
Therefore, x=12.
Sarthak wants to complete his design
project to be able to graduate. He works on
his project 20 minutes every three hours. If
his project requires 10 hours of work, how
long will he take to finish his project?
Answer:
Step-by-step explanation:
3 times 60 = 180 minutes
10 * 60 = 600 minutes
600/20 = 30 * 3 = 90 hours
Given that 1 kilogram = 2.2 pounds, which statements are true?
Two kilograms is equal to 4 pounds.
Three kilograms is greater than 6 pounds.
Four kilograms is less than 8 pounds.
Five kilograms is equal to 11 pounds.
Answer:
the second and fourth statements
Step-by-step explanation:
What are the zeros of f(x) = x2 - x - 20?
Answer:
(-4,0) and (5,0)
Step-by-step explanation:
Factor.
f(x) = x^2 -x - 20
Factors of -20 that when are added they equal -1
-5 and 4
(x-5) (x+4)
x=5 and x=-4
What is the result when 16x3 + 12x2 + 14x + 3 is divided by 4x + 1?
Answer: i think that is the ans
Step-by-step explanation:
5y=35+10x in standard form
Answer:
5y-10x=35
Step-by-step explanation:
The standard way to write a linear relationship between the x and y variables is through a homogeneous equation as a combination of the x and y variables with real coefficients.
7
Slope
6'
y-intercept (0, – 6)
What is the equation
Answer:
y = 7x - 6
Step-by-step explanation:
We are given the slope of 7 and the y-intercept of (0, -6).
We can easily write this in slope-intercept form.
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Replace 'm' with '7' and 'b' with '-6'.
[tex]y=mx+b\rightarrow \boxed {y=7x-6}[/tex]
Hope this helps.
Statistics Probability
A survey of a freshmen English class asked students whether or not they ate breakfast the morning of the survey. The results are included in the table to the right.
(a) What is the probability that a randomly selected student ate breakfast?
(b) Of all students, what is the probability that a randomly selected student is female and ate breakfast?
(c) What is the probability a randomly selected student is male, given that the student ate breakfast?
(d) What is the probability that a randomly selected student ate breakfast, given that the student is male?
(e) What is probability of "is male" or "did not eat breakfast"?
(f) What is the probability of "is male and did not eat breakfast?
Answer:
Explained below.
Step-by-step explanation:
Denote the variable as follows:
M = male student
F = female student
Y = ate breakfast
N = did not ate breakfast
(a)
Compute the probability that a randomly selected student ate breakfast as follows:
[tex]P(Y)=\frac{n(Y)}{N}\\\\=\frac{198}{330}\\\\=0.60[/tex]
(b)
Compute the probability that a randomly selected student is female and ate breakfast as follows:
[tex]P(F\cap Y)=\frac{n(F\cap Y)}{N}\\\\=\frac{121}{330}\\\\=0.367[/tex]
(c)
Compute the probability a randomly selected student is male, given that the student ate breakfast as follows:
[tex]P(M|Y)=\frac{n(M\cap Y)}{n(Y)}\\\\=\frac{77}{198}\\\\=0.389[/tex]
(d)
Compute the probability that a randomly selected student ate breakfast, given that the student is male as follows:
[tex]P(Y|M)=\frac{n(Y\cap M)}{n(M)}\\\\=\frac{77}{154}\\\\=0.50[/tex]
(e)
Compute probability of the student selected "is male" or "did not eat breakfast" as follows:
[tex]P(M\cup N)=P(M)+P(N)-P(M\cap N)\\\\=\frac{n(M)}{N}+\frac{n(N)}{N}-\frac{n(M\cap N)}{N}\\\\=\frac{n(M)-n(N)-n(M\cap N)}{N}\\\\=\frac{154+132-77}{330}\\\\=0.633[/tex]
(f)
Compute the probability of "is male and did not eat breakfast as follows:
[tex]P(M\cap N)=\frac{n(M\cap N)}{N}\\\\=\frac{77}{330}\\\\=0.233[/tex]
please answer me after you click on the image
Answer:
2x - 3
Step-by-step explanation:
The missing side is the value of the perimeter subtract the sum of the 2 given sides, that is
? = 10x + 1 - (5x - 2 + 3x + 6)
= 10x + 1 - (8x + 4) ← distribute parenthesis by - 1
= 10x + 1 - 8x - 4 ← collect like terms
= 2x - 3
5.
Find the exact value of sin 267° cos 27°
COS 267° sin 27°.
sin 267° cos 27º – cos 267° sin 27°
Enter your next step here
When dividing 82 by 43, Linda estimated the quotient to be 2. Examine Linda’s work, and explain what
she needs to do next. On the right, show how you would solve the problem.
Answer:
82/43 = 1 and 39/43
Step-by-step explanation:
When dividing 82 by 43 , the operation follows;
82/43 = 1 and 39/43
This means the quotient is 1 and reminder is 39
However;
82/43 = 1.907 ------nearest whole number is 2.
so the quotient can be approximated to the nearest whole number as 2.
1/2 + 1/6 what is it pls help!!!!
Answer:
4/6
Step-by-step explanation:
1/2 = 3/6. 3/6 + 1/6 = 4/6
Answer:
4/6
Step-by-step explanation
a music teacher gathered data from several clarinet players about the time they spent practicing their instruments and the number of errors they made on a performance assessment. the data and the line of the best fit are shown in the scatter plot
Answer:
The answer is A. Yes, because the points in the plot are all very close to the line, which indicates a strong association.
Step-by-step explanation:
plouto answer
Answer:
Yes, because the points in the plot are all very close to the line, which indicates a strong association.
Step-by-step explanation:
When the points in a scatter plot are very close to the line of best fit, there is a strong association between the two variables and the line of best fit can be expected to make reliable predictions.
So, yes, the line of best fit could be used to make reasonable predictions, because the points in the plot are all very close to the line, which indicates a strong association.
The length of the base of an isosceles triangle is x. The length of a leg is 2x-6 The perimeter of the triangle is 23. Find x.
Answer: 2.20
Step-by-step explanation:
An isosceles triangle has two of its side equal. Since the length of of a leg is 2x-6, it means that the other length is also 2x-6 while the base is x.
We the add the sides together. This will be:
x + 2x - 6 + 2x - 6 = 23
5x - 12 = 23
5x = 23 - 12
5x = 11
x = 11/5
x = 2.20
Chanelle deposits $7,500 into the bank. She does not withdraw or deposit money for 6 years. She earns 6% interest during that time.
a. How much interest will she have earned at the end of 6 years?
Answer:
2700
Step-by-step explanation:
Helppppppppp plzzz I need this done very soon
Answer:
For every 10 on the x axis, there is 80 on the y axis
Step-by-step explanation:
Zainab runs her own business where she leads guided day-long tours for small groups of tourists in her city. Each tour has a maximum of 333 guests. Let XXX represent the number of customers Zainab gets on a randomly chosen day. Based on previous data, here is the probability distribution of XXX along with summary statistics: X=\text{\# of customers}X=# of customersX, equals, start text, \#, space, o, f, space, c, u, s, t, o, m, e, r, s, end text 000 111 222 333 P(X)P(X)P, left parenthesis, X, right parenthesis 0.200.200, point, 20 0.100.100, point, 10 0.400.400, point, 40 0.300.300, point, 30 Mean: \mu_X=1.8μ X =1.8mu, start subscript, X, end subscript, equals, 1, point, 8 Standard deviation: \sigma_X\approx1.08σ X ≈1.08sigma, start subscript, X, end subscript, approximately equals, 1, point, 08 It costs Zainab \$5$5dollar sign, 5 each day to pay for her own transportation to her business, and then each customer she gets pays her \$60$60dollar sign, 60. Let YYY represent Zainab's net gain on a randomly chosen day. What are the mean and standard deviation of YYY?
An
μ Y=103 dollars
σ Y≈64.8 dollars
Step-by-step explanation:
We can find her income by multiplying the number of customers by 606060, and then subtracting her fixed transportation cost to get her net gain:
Y=60X-5Y=60X−5Y, equals, 60, X, minus, 5
How will this transformation impact the mean and standard deviation?
Hint #22 / 4
Effect on mean
Multiplying by 606060 and subtracting 555 both impact the mean:
\begin{aligned} \mu_Y&=60\left(\mu_X\right)-5 \\\\ &=60\left(1.8\right)-5 \\\\ &=108-5 \\\\ &=103 \end{aligned}
μ
Y
=60(μ
X
)−5
=60(1.8)−5
=108−5
=103
Hint #33 / 4
Effect on standard deviation
Multiplying by 606060 impacts the standard deviation, but subtracting 555 does not — adding or subtracting a constant only shifts data, which doesn't affect the spread.
\begin{aligned} \sigma_Y&=60\left(\sigma_X\right) \\\\ &\approx60\left(1.08\right) \\\\ &\approx64.8 \end{aligned}
σ
Y
=60(σ
X
)
≈60(1.08)
≈64.8
The ansa
μ 103 dollars
σ 64.8 dollars
the length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle
Answer:
26x47
Step-by-step explanation:
To calculate the length of the rectangle we would do 2(2x - 5) + 2(x) = 146
We simplify and get 6x - 10 = 146,
then divide both side by 6 and plus 10 both sides,
we will get
x = 26
Now we've found one of the length,
to find the other side we do 26 * 2 = 52, and subtract 52 from 146,
which would get 94, then we divide it by 2
94/2 = 47
The dimensions is 26x47
-7(a - 3) = 11 - 7a
what’s the answer
Answer:
the statement is false there is no solution
Step-by-step explanation:
step 1 -7(a-3)=11-7a
step 2 -7a+21=11-7a
step 3 cancel out the -7a's
step 4 you are left with 21=11 which does not work so it is false
−4p + 9 = −5
what is the answer
Answer:
p = -1
Step-by-step explanation:
-5 - -9 = 4
-4p/4 = -1
p = -1
Carol Ate 25% of the candies in the bag iF Carroll ate 24 Candies how many candies were there total in the bag
Answer:
96
Step-by-step explanation:
A factor divides evenly into another number without a ________ left over.
Answer: remainder
Step-by-step explanation:
whats the answer ?
[tex]2(x^2 - 3) - 8 = - 6[/tex]
Step-by-step explanation:
Remove the parentheses
2x^2-6-8= -6
Cancel equal terms
2x^2-8=0
Move the constant to the right
2x^2=8
Divide both sides by 2
x^2=4
Simplify the equation
x=+2 or -2