Step-by-step explanation:
A weather balloon is released and rises vertically such that its distance s (t) above the ground during the first 10 sec of flight is given by :
[tex]s(t)=6+2t+t^2[/tex] ...(1)
(a) We need to find velocity at t = 4 seconds
Differentiate equation (1) wrt t.
[tex]v=\dfrac{ds}{dt}\\\\v=\dfrac{d(6+2t+t^2)}{dt}\\\\v=2+2t[/tex]
At t = 4 seconds,
[tex]v=2+2(4)\\\\=10\ ft/s[/tex]
At t = 4 seconds, the velocity is 10 ft/s.
(b) When the balloon is 50 feet above the ground,
[tex]6+2t+t^2=50[/tex]
We need to find t.
[tex]6+2t+t^2=50\\\\t^2+2t-50+6=0\\\\t^2+2t-44=0[/tex]
It is a quadratic equation,
t = 5.708 and t = -7.708
Neglecting negative time, the instant time is 5.708 seconds.
Find the cost of tiling a rectangular plot of land 300 m long and 150 m wide at the rate of $6 per square m.
Answer:
$270,000
Step-by-step explanation:
First, find the area of the plot using the formula A = lw
A = lw
A = (300)(150)
A = 45,000
Then, multiply this by 6 to find the total cost:
45,000(6)
= 270,000
So, the cost to tile the plot is $270,000
Answer:
2700
Step-by-step explanation:
Length= 300m
width= 150 m
Area = Lx W = 300 x 150= 4500 sq m
rate per 100 sq meter= 6
so total cost = 4500/ 100 x 6
= 2700
hope it helps!
Noah has $5. Elena has 40% as much as Noah. How much does Elena have?
Answer:
Step-by-step explanation:
2 dollars
Answer:
$2.00
Step-by-step explanation:
Rose and Angel are caterers. Both Rose and Angel charge a flat fee plus a fee per guest. Rose charges a flat fee of $50 plus $12 per guest. The table shows how much Angel charges for different numbers of guests. Angel's Catering Charges Number of Guests Charge ($) 10 $180 15 $255 25 $405 30 $480 Part A Who charges the greater flat fee? O A. Rapse O B. Angel Part B Vhat is the difference in total charges between Angel and Rose for a party that includes 50 guests? Enter the answer in the box. Autohide sh Growth: Math 6+ GA 2015 Question ITU Shelf nositi
Answer:
a. Angel has a greater flat fee
b. Difference = $130
Step-by-step explanation:
Given
Rose:
[tex]Flat\ Fee = \$50[/tex]
[tex]Rate = \$12[/tex]
Angel
Guests --- Charges
10 -------- $180
15 -------- $255
25 -------- $405
30 -------- $480
Solving (a): Who charges the greater flat fee?
We have that the flat fee of Rose is:
[tex]Flat\ Fee = \$50[/tex]
For Angel, we need to determine the equation of the given table
Start by calculating the slope (m) of the table
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where x and y represent any two corresponding values of the guests and the charges.
[tex](x_1,y_1) = (10, 180)[/tex]
[tex](x_2,y_2) = (30, 480)[/tex]
So: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{480 - 180}{30 - 10}[/tex]
[tex]m = \frac{300}{20}[/tex]
[tex]m = 15[/tex]
Next, we calculate the equation using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 15[/tex]
[tex](x_1,y_1) = (10, 180)[/tex]
[tex]y - 180 = 15(x - 10)[/tex]
[tex]y - 180 = 15x - 150[/tex]
Add 180 to both sides
[tex]y - 180 + 180 = 15x - 150 + 180[/tex]
[tex]y= 15x + 30[/tex]
From the equation above:
The slope = 15 --- This represents the hourly rate
and
y intercept = 30 --- This represents the flat fee
This is better represented as:
Angel
[tex]Flat\ Fee = \$30[/tex]
[tex]Rate = \$15[/tex]
and
Rose:
[tex]Flat\ Fee = \$50[/tex]
[tex]Rate = \$12[/tex]
By comparison, Angel has a greater flat fee
Solving (b): Difference between total charges of 50 guests for both caterers.
For angel, the equation is:
[tex]y= 15x + 30[/tex]
and x = 50.
So:
[tex]y = 15 * 50 + 30[/tex]
[tex]y = 750 + 30[/tex]
[tex]y = 780[/tex]
For Rose,
First, we need to determine the equation.
[tex]Flat\ Fee = \$50[/tex]
[tex]Rate = \$12[/tex]
The equation is:
[tex]y = Flat\ Fee + Rate * x[/tex]
[tex]y = 50 + 12 * x[/tex]
So, the total charges for 50 guests is:
[tex]y = 50 + 12 * 50[/tex]
[tex]y = 50 + 600[/tex]
[tex]y = 650[/tex]
The difference is then calculates as:
[tex]Difference = 780 - 650[/tex]
[tex]Difference = \$130[/tex]
The probability distribution for a
random variable x is given in the table.
Answer: 60%
Step-by-step explanation:
the probability is -2 is less than or equal to x and x is less than or equal to 2 so you would include .33, .16, and .10 in your problem
.33 + .16 + .11 = .6
.6 x 100 = 60
(if your using acellus don’t forget the % sign or it’ll mark it wrong!)
A pair of boots has an original price of $95. They are on sale for 35 percent off. What number can you multiply $95 by to equal the discounted price of $61.75? 0.35 0.60 0.65 0.95 I WILL GIVE BRANLIEST
Answer:
it will be 0.65
Step-by-step explanation:
Answer:
The Answer is .35 or 35%
Step-by-step explanation:
PLS HELP Which number has a product of -6/5 when multiplied by -12/5
A. -18/5
B -1/2
C 1/2
D 2/1
on Wednesday, James slept for [tex]\frac{3}{8}[/tex] of the day.
how many hours did James spend sleeping?
Answer:
I believe he slept for 9 hours of the day
Step-by-step explanation:
⅜ of 24
24 ÷ 8 = 3
3 × 3 = 9
The number of hours James slept is 9 hours.
What is an expression?In mathematics, an expression is a combination of symbols and numbers, often containing variables, that represents a quantity or a relationship between quantities.
Expressions can be simple or complex, and they can involve a variety of mathematical operations such as addition, subtraction, multiplication, and division.
The number of hours will be calculated as,
E = ⅜ of 24
E = 3 x ( 24 ÷ 8 )
E = 3 × 3
E = 9 hours
Therefore, the number of hours will be 9.
To know more about an expression follow
https://brainly.com/question/30672422
#SPJ3
Question
Mark's grade went from 65% to 90%. What was his percent increase?
25%
28%
38%
90%
Jill and Erika made 5 gallons of lemonade for their lemonade stand.
Part1: How many quarts did they make?
Part2: If they charge $2.00 per quart, how much money will they make if they sell it all?
can u pls help me with this question
Answer:
3 miles per hour
Step-by-step explanation:
his speed is 12/4 (or 3) miles an hour. What you do, is you have to multiply 15 by four to go from 15 min to one hour, and you also have to multiply 3/4 by four.
Consider two bases B = {b1, b2, b3} and C = {c1, c2, c3} for a vector space V such that
b1 = c1 + 3c3, b2 = c1 + 4c2 - c3, and b3 = 5c1 - c2. Suppose vector x = b1 + 6b2 + b3. That is,
suppose space left square bracket bold italic x right square bracket subscript B space equals open square brackets table row 1 row 6 row 1 end table close square brackets . Find space left square bracket bold italic x right square bracket subscript B space, the coordinates of the vector x in basis C.
A motocross ramp is 16 feet tall and 24 feet long what is the slope of the ramp
Determine the two ordered pair solutions of the equation y = 2x2 + 3x , given (0, ), and (-2, ).
Answer:
We conclude that the two ordered pairs (0, 0) and (-2, 2) are the solutions of the equation y = 2x² + 3x.
Step-by-step explanation:
Given the expression
y = 2x² + 3x
Substituting x = 0
y = 2(0)² + 3(0)
y = 0+0
y = 0
so when x = 0, y = 0Thus, the ordered pair is: (0, 0)
Now, substituting x = -2
y = 2x² + 3x
y = 2(-2)² + 3(-2)
y = 8 - 6
y = 2
so when x = -2, y = 2Thus, the ordered pair is: (-2, 2)
Therefore, we conclude that the two ordered pairs (0, 0) and (-2, 2) are the solutions of the equation y = 2x² + 3x.
Find the area of the triangle.
7 yd
24 yd
Answer:
A=84 square yards
Step-by-step explanation:
A=1/2bh
A=1/2(7x24)
A=1/2(168)
A=84
What is the numerical expression of 28
Answer:
the answer is 5 i think
Step-by-step explanation:
Use a fives fact to help you solve 7x6.
Answer:
42
Step-by-step explanation:
Since 7x5=35, then 7x6=42. This is known as the fives fact rule, and I used it to figure it out.
Hope this helps! :)
Following are the facts to solve the given expression:
Given:
[tex]\to 7 \times 6[/tex]
To find:
facts=?
Solution:
[tex]\to 7 \times 6=42[/tex]
Fact 1:
[tex]\to 42= 6 \times 7[/tex]
Fact 2:
[tex]\to 42= 3 \times 2 \times 7[/tex]
Fact 3:
[tex]\to 42 =(4 \times 10)+ (2\times 1)[/tex]
Fact 4:
[tex]\to 42= (5\times 8) + (2\times 1 )[/tex]
Fact 5:
[tex]\to 42=(3 \times 12)+(2 \times 3)[/tex]
Learn more about facts for solving equations:
brainly.com/question/8648763
If 3 times the difference of x and y is -30, and 2/3 of x plus 1/2 of y is 19, what are x and y
Answer:
x = 12 and y = 22
Step-by-step explanation:
It is given that,
3 times the difference of x and y is -30
3(x-y) = -30
3x-3y = -30 ....(1)
2/3 of x plus 1/2 of y is 19.
[tex]\dfrac{2x}{3}+\dfrac{y}{2}=19\\\\\dfrac{4x+3y}{6}=19\\\\4x+3y=114\ ...(2)[/tex]
Add equation (1) and (2).
3x-3y + 4x+3y = -30 +114
7x = 84
x = 12
Put the value of x in equation (1)
3x-3y = -30
3(12)-3y = -30
36+30 = 3y
3y = 66
y = 22
Hence, the value of x and y are 12 and 22.
If f(x)=34x+56 , what is f(12)?
Answer:
f(x)= 34x +56 34(12) +56=464
Step-by-step explanation:
4. Which of the following represents a function?
(8,3), (8,3), (-8, -3), (-8, -3)
0 (-5, 6), (-5, 6), (-5, -6), (-5, -6)
O (3,9), (-7, 1), (6, 12), (-3, -9)
O (5, 1), (5,2), (5, 3), (5, 4)
Refer to - KLMN
2x
M
101
-3
2y
P
y + 3 cm
60°
К.
N
x + 4 cm
mZ1 + m22 =
Answer:
[tex]m∠1 + m∠2 = 180[/tex]
Step-by-step explanation:
[tex]m∠1 = m∠3 \\ m∠2 = m∠4[/tex]
[tex]m∠ 1 = m∠3 \\ 60 = 60[/tex]
[tex]360 - m∠1 + m∠3 = m∠2 + m∠4[/tex]
[tex]360 - 60 + 60 = m∠2 + m∠4[/tex]
[tex]360 - 2(60) = m∠2 + m∠4[/tex]
[tex]360 - 120 = m∠2 + m∠4[/tex]
[tex]240 = m∠2 + m∠4[/tex]
[tex] \frac{240}{2} = m∠2 = m∠4[/tex]
[tex]120 = m∠2 = m∠4[/tex]
[tex]m∠2 = 120 \\ m∠4 = 120[/tex]
[tex]m∠1 = 60 \\ m∠3 = 60[/tex]
[tex]m∠2 = 120 \\ m∠4 = 120[/tex]
[tex]m∠1 + m∠2 + m∠3 + m∠4 { = }^{?} 360[/tex]
[tex]60 + 120 + 60 + 120 { = }^{?} 360[/tex]
[tex]2(60) + 2(120) { = }^{?} 360[/tex]
[tex]120 + 240 { = }^{?} 360[/tex]
[tex]360 = 360[/tex]
[tex]m∠1 + m∠2 [/tex]
[tex]60 + 120 = 180[/tex]
[tex]m∠1 + m∠2 = 180[/tex]
(sec(π/3) + tan(-7π/4))/(1-cos(2 π/3))
Answer:
3
Step-by-step explanation:
3+3_3=3
after that 3+2+6+7+7+8+8+9+9+9+9+9+0+0+8+6+5+4+ 5=?
u will do the answer and it will be done
The cost of 3 scarves is $26.25. What is the unit price? (cost per scarf)
$8.75 because 26.25 divided by 3 equals $8.75.
hope this helps
In Santana's last basketball game he made a total of 22 baskets. Santana
scored a combination of 2-point baskets and 3-point baskets for a total
of 54 points. How many 2-point baskets did Santana score?
Answer:
Santana scored 12 2-point baskets.
Step-by-step explanation:
Given that Santana converted 22 baskets in his last basketball game, totaling 54 points at the end of the game, and that in basketball the baskets are worth 2 and 3 points, to determine the number of baskets of each value that Santana converted, the following logic reasoning must be done:
If all the baskets were 2 points, the total of points made would have been 44 (22 x 2). Now, there are 10 more points, which are attributable to the 3-point baskets (that is, each extra point is a 3-point basket). Therefore, since 54 minus 44 equals 10, Santana made 10 3-point baskets and 12 2-point baskets.
This is verified through the following calculation:
(10 x 3) + (12 x 2) = X
30 + 24 = X
54 = X
A researcher wants to estimate the mean commute time of residents in Westchester County. The researcher samples 40 commuters and find the mean commute time to be 25 minutes. Assume the population standard deviation for commute time is 12.5 minutes. Construct a 90% confidence interval for the mean commute time of residents in Westchester County. What is the Lower Bound of the confidence interval
Answer:
21.759
Step-by-step explanation:
Given that :
Mean (m) = 25
Standard deviation (s) = 12.5
Sample size (n) = 40
α = 90%
The confidence interval is obtained using the relation:
Mean ± Zcritical * s/sqrt(n)
Zcritical at 90% confidence interval = 1.64
25 ± 1.64 * (12.5/sqrt(40))
Lower boundary : 25 - 1.64(1.9764235) = 21.75866546
Upper boundary : 25 + 1.64(1.9764235) = 28.24133454
(21.759, 28.241)
Hence, lower bound of confidence interval is : 21.759
5/6 - (-2/3)
Steps please
Answer:
9/6
Steps:
5/6 - (-2 x 2)
____. = 9/6
3 x 2
As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than 10 hours per week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and
x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply.
Answer:the line x+y<10 has a negative slope and a positive y intercept
The line representing 20x+25y>200 is solid and the graph is shaded above line
The overlapping region contains the point (4,5)
Step-by-step explanation:
;)
Answer:
The answers are B, C, and E.
Step-by-step explanation:
I got it right on edge
9+x=12 Can you guys please tell me the answer
Answer:
X=3
Step-by-step explanation:
9+x=12
x=12-9
so x is 3
Answer:
3
Step-by-step explanation:
Let's go through this together.
Step 1) Rearrange Terms (Optional)
9 + x = 12
x + 9 =12
Step 2) Subtract 9 from both sides of the equation
x + 9 = 12
-9 -9
Step 3) Simplify
If we subtract 9 on both sides, we end up with:
x + 0 = 3
Since 0 no longer has any part in the equation, we can conclude that:
x = 3
help me please!!!!!!!!!
Answer:5.6
Step-by-step explanation:112 divided by 20=5.6
Mike and Joe each receive money for their lunch. Mike receives $100 and spends $3 each day on his lunch. Joe receives $20 and then an additional $5 each day. Joe saves his
money and does not buy lunch. How many days will it take for Mike and Joe to have the same amount of money?
what is the value of x in the eqation 3 [2x+5]=3x+4x
Answer:
x = 15
Step-by-step explanation:
3 ( 2x + 5 ) = 3x + 4x
Distribute;
3 ( 2x + 5 ) = 3x + 4x
6x + 15 = 3x + 4 x
Combine like terms;
6x + 15 = 3x + 4x
6x + 15 = 7x
Inverse operations;
6x + 15 = 7x
-6x -6x
15 = x