The time taken for Sam's family to get to Chicago, Illinois is 17.8 hours.
How many hours will it take Sam's family to get to Chicago, Illinois?Sam's family:
Total distance = 1,157 milesAverage speed = 65 mphTime taken = ?Average speed = Total distance / Time taken
65 = 1, 157 / time
cross product
65 × time = 1, 157
Time = 1,157 / 65
Time = 17.8 hours
Roshan's family:
Total distance = 1,250 milesAverage speed = 70 mphTime taken = ?Average speed = Total distance / Time taken
70 = 1,250 / Time
cross product
70 × time = 1,250
Time = 1,250/70
Time = 17.86 hours
Approximately,
17.9 hours
In conclusion, it will take Rohan's family 17.9 hours to get to Chicago, Illinois.
Read more on time taken:
https://brainly.com/question/4931057
#SPJ1
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Find the Sample standard deviation for Car 1 and Car 2
Answer:
he sample standard deviation for Car 1 is 8.2 miles and the sample standard deviation for Car 2 is 9.3 miles.
Step-by-step explanation:
Consider the rate law below. R=k(NO2)^2 what happens to the rate if the concentration is tripled?The rate increases by a factor of 9.The rate decreases by a factor of 6.The rate triples.The rate doubles.
The rate increases by a factor of 9 when the concentration is tripled.
It is given to us that the rate law is -
[tex]R=k(NO_{2} )^{2}[/tex] ----- (1)
We have to find out the change in the rate if the concentration is tripled.
When the concentration is tripled, we can rewrite the equation (1) as -
[tex]R_{new} =k(3*NO_{2} )^{2}\\= > R_{new} =9*k(NO_{2} )^{2}\\= > R_{new} =9R[/tex][From equation (1)]
Thus, we see that the rate increases by a factor of 9 when the concentration is tripled.
To learn more about factors visit
https://brainly.com/question/24182713
#SPJ9
A rectangular garden has an area of 360 square feet.
The length of the garden is 9 feet longer than the
width. Find the dimensions of the garden in feet.
24 ft by 15 ft
24 ft by 15 ft or -24 ft by - 15 ft
O 33 ft by 24 ft
49 ft by 40 ft
Answer:
24 ft by 15 ft
Step-by-step explanation:
Let l be the length of the garden. Then
l - 9 is the width of the garden.
[tex]l(l - 9) = 360[/tex]
[tex] {l}^{2} - 9l = 360[/tex]
[tex] {l}^{2} - 9l - 360 = 0[/tex]
[tex](l - 24)(l + 15) = 0[/tex]
[tex]l = 24[/tex]
[tex]l - 9 = 15[/tex]
(since l + 15 = 0 will give a negative value for l).
So the dimensions of this garden are 24 ft and 15 ft.
What is an equation of the line that passes through the points (4, 1) and (8, -4)?
Answer:
[tex]y=-\frac{5}{4}x+6[/tex]
Step-by-step explanation:
[tex]m=\frac{-4-1}{8-4}=-\frac{5}{4} \\ \\ y-1=-\frac{5}{4}(x-4) \\ \\ y-1=-\frac{5}{4}x+5 \\ \\ y=-\frac{5}{4}x+6[/tex]
Answer:
y=-1.25x+6
Step-by-step explanation:
use slope formula to find slope
y2-y1/x2-x1
-4-1/8-4
-5/4
-1.25
y=-1.25x is the equation we can make with this slope and fill in the equation with one of the coordinates to find y intercept
1=-1.25(4)
1=-5
We need to add 6 for this to be true so y intercept is 6
The equation is
y=-1.25x+6
Hopes this helps please mark brainliest
help meeeeeeeeee pleasee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
2. 18 = 4a + 10Solve equations
a=2
Explanation
[tex]18=4a+10[/tex]Step 1
subtract 10 in both sides
[tex]\begin{gathered} 18=4a+10 \\ 18-10=4a+10-10 \\ 8=4a \end{gathered}[/tex]Step 2
divide each side by 4
[tex]\begin{gathered} 8=4a \\ \frac{8}{4}=\frac{4a}{4} \\ 2=a \\ a=2 \end{gathered}[/tex]How much of an 8% solution should we use to make 100g of 3% solution?Please use the picture for the format :) thank you!!
x = -0.6
Explanation:The equation that represents this scenario is:
0.7x + 0.1*3 = 0.4(x + 3)
Solving for x, we have:
0.7x + 0.3 = 0.4x + 0.12
0.7x - 0.4x = 0.12 - 0.3
0.3x = -0.18
x = -0.18/0.3
= -0.6
37.5 is the answer for your question
Hello! Please see the picture to see the question, Thank you!
7)
The given function is
[tex]f(x)=2x^2+4x^3+3x+5[/tex]Recall that the degree of the polynomial is the highest power of the variable.
The degree of the given polynomial function is 3.
we know that a cubic function is a polynomial function with degree 3.
Hence the given function is a cubic function.
Option D is correct.
When connected of Wi-fi, Julian's smart phone downloaded 32 songs in 4 minutes. How many songs can bedownloaded per minute
8 songs
Explanation:number of songs = 32
time = 4minutes
let the number of song per minute = y
32 songs = 4 minute
y = 1 minute
Cross multiply:
32(1) = 4(y)
32 = 4y
32/4 = 4y/4
y = 8
This means the number of songs that can be downloaded per minute is 8yna
1. On a clearance rack, t-shirts cost $5 and shorts cost $9. You have $35 to spend. Write an equation
that models the possible combinations of t-shirts, t, and shorts, s, you can buy.
The inequality that represents the situation is [5x + 9y ≤ 35] where x and y are the number of t-shirts and shorts purchased.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
So, we know that:
The T-shirts cost $5.
The shorts cost $9.
The total budget is $35.
Then, the inequality can be:
5x + 9y ≤ 35
Where x and y are the number of t-shirts and shorts purchased.
5(3) + 9(2) ≤ 35
15 + 18 ≤ 35
33 < 35
Therefore, the inequality that represents the situation is [5x + 9y ≤ 35] where x and y are the number of t-shirts and shorts purchased.
Know more about inequality here:
https://brainly.com/question/28964520
#SPJ1
Correct question:
On a clearance rack, t-shirts cost $5 and shorts cost $9. You have $35 to spend. Write a correct inequality that models the possible combinations of t-shirts, t, and shorts, s, you can buy.
what is the product of 2 2/3 and 1 1/6
Answer:
Step-by-step explanation: you can rewrite 2/3 plus 1/6 as: 2 3 + 1 6 To add fractions you need to have a common denominator (the bottom half of the fraction). In this case 6 is a common denominator.
The emission veat of local zoo was $1.50 for children and $4.00 for adults, on a certain day 3000 people enter the zoo in $9250 is collected how many children adults attended?
1100 children and 1900 adults attended the local zoo on that day.
A system of equations or an equation system is a finite set of equations for which common solutions are sought.
Given:
A local zoo's admission fee is $1.50 for children and $4.00 for adults.
On a certain day, 3000 people enter the zoo and $9250.00 is collected.
We have to determine how many children and how many adults attended?
Solution:
Let number of children enter the zoo = x
Then number of adults enter the zoo = 3000-x
Total collection = $9250
Collection from children + Collection from adults = 9250
1.50 × x + 4(3000-x) = 9250
1.5x + 12000 – 4x = 9250
1.5x - 4x = 9250 - 12000
-2.5x = -2750
2.5x = 2750
X =2750/2.5
X = 1100
Number of children enter the zoo = x = 1100
Number of adults enter the zoo = 3000 - x = 3000 - 1100 = 1900
Therefore 1100 children and 1900 adults attended the local zoo on that day.
To learn more about the system of equations visit
https://brainly.com/question/24065247
#SPJ1
three friends go grocery shopping together and each buys the same kind of oranges. lamar buys 2 pounds and pays $3.00 enrico buys 5 pounds and pays $7.50 anna buys 3 pounds and pays $4.50
The cost of 1 pound of orange will be $1.5. The total payment was $15. The total weight of orange was 10 pounds.
What is unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Here,
cost of 2 pound of orange=$3
cost of 5 pound of orange=$7.50
cost of 3 pound of orange=$4.50
Therefore,
The cost of 1 pound of orange is $1.5
The total payment made=$7.50+$4.50+$3
=$15
The total weight of oranges=2+3+5
=10 pounds
One pound of oranges will cost $1.5. $15 was paid in total. Orange weighed ten pounds in total.
To know more about unitary method,
https://brainly.com/question/22056199?referrer=searchResults
#SPJ1
. The volume of the prism is 45 cubic inches.What is the length of each side?
Given:
The volume of the cubic prism is 45 cubic inches.
Let the side length = x
So,
[tex]volume=x^3=45[/tex]Taking the cubic root of 45
[tex]x=^3\sqrt[]{45}\approx3.557[/tex]So, the answer will be the side length = 3.557 inches
Determine the exact value of (sin 45 °) (cos 45 ) + (sin 30°) (sin 60°)
(Don't leave radicals in the denominator)
Answer:
[tex]\frac{1}{2}+ \frac{\sqrt{3} }{4}[/tex]
Step-by-step explanation:
Refer to the triangle diagrams I attached. Use SOH CAH TOA
[tex]sin(45)*cos(45)+sin (30)* sin (60)[/tex]
The exact value of sin(45) is [tex]\frac{\sqrt{2} }{2}[/tex]
[tex]\frac{\sqrt{2} }{2}*cos(45)+sin (30)* sin (60)[/tex]
The exact value of cos(45) is [tex]\frac{\sqrt{2} }{2}[/tex]
[tex]\frac{\sqrt{2} }{2}*\frac{\sqrt{2} }{2}+sin (30)* sin (60)[/tex]
Multiply [tex]\frac{\sqrt{2} }{2}*\frac{\sqrt{2} }{2}[/tex].
[tex]\frac{\sqrt{2}^{2} }{4}+sin (30)* sin (60)[/tex]
Rewrite [tex]{\sqrt{2}^{2}[/tex] as 2.
[tex]\frac{2}{4} +sin (30)* sin (60)[/tex]
Simplify
[tex]\frac{1}{2} +sin (30)* sin (60)[/tex]
The exact value of sin(30) is [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2} +\frac{1}{2} * sin (60)[/tex]
The exact value of sin(60) is [tex]\frac{\sqrt{3} }{2}[/tex]
[tex]\frac{1}{2} +\frac{1}{2} * \frac{\sqrt{3} }{2}[/tex]
Simplify
[tex]\frac{1}{2}+ \frac{\sqrt{3} }{4}[/tex]
Cindy's beginning balance in her checkbook was $463.18. She madedeposits of $265, wrote checks for $198.73, and had to pay a bankcharge of $2.50. What was her ending balance for the month?a. $519.27b. $526.95c. $381.73d. $911.73
Given,
The initial balance in the checkbook is $463.18.
The deposite money is $265.
The amount of check is $198.73.
The charge paid for bank is $2.50.
The ending balance at the month end is,
[tex]\begin{gathered} \text{Ending balance=}463.18+265-198.73-2.50 \\ =526.95 \end{gathered}[/tex]Hence, option b ($526.95) is correct.
what is the scale factor of Triangle ABC to Triangle DEF?A. 3 B. 1/2C. 2D. 1/3
If we have the triangle ABC and we want to obtain the triangle DEF, we need to multiply every side of the triangle ABC by 3 as:
5 * 3 = 15
4 * 3 = 12
3 * 3 = 9
So, the scale factor of triangle ABC to triangle DEF is 3
Answer: 3
Label the missing side length of the figure below. Click each dot on the image to select an answer. A sculpture made up of 2 rectangular prisms. Color is used to show the rectangular prisms that make up the figure. The first rectangular prism is green and has dimensions of an unknown length of 2 meters width by 3 meters height. The second rectangular prism is purple and has dimensions of 10 meters in length by 4 meters in width by 7 meters in height. Find the volume of the entire figure by adding the importance of the separate figures. \text{Volume}=Volume=start text, V, o, l, u, m, e, end text, equals {}+ \purpleD{280}=+280=plus, start color #7854ab, 280, end color #7854ab, equals \text{ cubic meters} cubic meters create text, space, c, u, b, i, c, space, m, e, t, e, r, s, end text
Answer:
Your answer is A now.
Step-by-step explanation:
Alicia watched a drone take off from a bridge. The height of the drone (in meters above the ground)minutes after takeoff is modeled byh(t) = −3+^2 + 12t +96Alicia wants to know when the drone will land on the ground.1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number inthe equation.h(t) =2) How many minutes after takeoff does the drone land on the ground?
a.
Function:
[tex]h(t)=-3t^2+12t+96[/tex]Factoring -3, we have:
[tex]\begin{gathered} h(t)=-3t^2+12t+96 \\ h(t)=-3(t^2-4t-32) \end{gathered}[/tex]Middle term facotizing the term inside parenthesis:
[tex]\begin{gathered} h(t)=-3(t^2-4t-32) \\ h(t)=-3(t-8)(t+4) \end{gathered}[/tex]This is the factored form.
b.
h(t) is the height.
When it lands on the ground, the height (h(t)) is 0, so we have:
[tex]\begin{gathered} h(t)=-3(t-8)(t+4) \\ 0=-3(t-8)(t+4) \end{gathered}[/tex]If we solve this equation for t, we get the line drone lands on the ground.
Let's do this:
[tex]\begin{gathered} -3(t-8)(t+4)=0 \\ t=8,-4 \end{gathered}[/tex]Time can't be negative, so the solution is t = 8 seconds.
Answer:
h(t) = -3(t-8)(t+4) and 8 minutes
Step-by-step explanation:
Enjoy ur answer have a great day please mark as brainliest :D !!!
I need help its due today at 11:59 PM!!
Answer:
attached at point A; forms a right angle; attached at point B; forms a right angle; same; yes
Step-by-step explanation:
Amelia is saving up to buy a new $105 iPad pen. Her best friend gave her $12 and she saves $20 per week from her babysitting job. How many weeks will she have to save money in order to buy the iPad? Write an inequality to solve.
EXPLANATION
Let's see the facts:
Ipad pen cost = -$105
Best friend ----> +$12
---------------
-$93
Babysitting Saves +$20/week
We are still needing $93 dollars to buy the pen, so, if she earns $20 peer week, then she should work:
$93 = 20 $/week * number of weeks
Calling x to the number of weeks and turning this into an inequality:
12 + 20x ≥ 105
Subtracting -12 to both sides:
20x ≥ 105-12
Simplifying:
20x ≥ 93
Dividing both sides by 20:
x ≥ 93/20
Simplifying:
x ≥ 4.65
Answer: Amelia should at least work 5 weeks in order to save the money to buy the Ipad pen.
whats 4x4x4x4x4 so yea
Find the value of x in the triangle show below
Answer:
A
Step-by-step explanation:
a^2 + b^2 = c^2
2^2 + x^2 = 4^2
4 + x^2 = 16
x^2 = 12
x = √12
y=2x+6
y = 2x-1
Solve for X and Y
Answer:
no solution
Step-by-step explanation:
y = 2x + 6 → (1)
y = 2x - 1 → (2)
substitute y = 2x + 6 into (2)
2x + 6 = 2x - 1 ( subtract 6 from both sides )
2x = 2x - 7 ( subtract 2x from both sides )
0 = - 7 ← not possible
This indicates the system of equations has no solution
What is the length of RS?
RA
Figure not drawn to scale
OA. 8
0 в.
O C. 16
OD. 20
10
16
Applying the Pythagoras Theorem, the length of RS = 8 units.
According to the figure,
Diameter = 16 +4 = 20 units
So, the Radius = Diameter/2 = 20/2 = 10 units
Now,
Let the center be M, then
MT = 10 - 4 = 6 units
RT = x units
The radius is perpendicular to the chord,
So, MTR will be a right-angled triangle,
We will apply the Pythagoras theorem,
So, we have :
[tex]RT^{2} +TM^{2} =RM^{2}[/tex]
Here, RT = x units
TM = 6 units and RM = radius = 10 units
Putting these values in the Pythagoras theorem,
[tex]x^{2} +6^{2} =10^{2}\\x^{2} + 36 = 100 \\x^{2} = 100 - 36 = 64\\x^{2} = 64 \\x = 8[/tex]
Thus, the length of RS = 8 units.
To read more about Pythagoras's theorem, visit https://brainly.com/question/343682
#SPJ9
the question is in the pic! it must be simplified, decimalized, and percentaged
Answer
Explanation
Probability of an event is calculated as the number of elements in an event divided by the total number of elements in the sample space.
P(quarter)
Number of quarters = 4
Total number of coins in the jar = 6 + 14 + 16 + 4 =
A large glass holds 5/6 cup of water spouse you have 8 cups of water you want to fill both glasses how many of each size glass can you fill
PLEASEE HURRY ANYONE???
The number of large glasses that will be filled is 10 glasses.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator, as well as the denominator, are both integers.
Given that the large glass holds 5/6 cup of water and you have 8 cups of water. The number of glasses filled will be:
= 8 ÷ 5/6
= 8 × 6/5
= 48/5
= 9.6
= 10 glasses approximately
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
-12 + 8x less than or greater than -44
Could be the two
For example for less than we will obtain -12+8x<-44
For the greater than -12+8x>-44
Find the slope of the line that contains the following points: (17, -12) and (7, 8)
Answer: -2
Step-by-step explanation:
To find the slope of a line, we use the formula [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
{x(2),y(2)} coordinates of second points in line
{x(1),y(1)} coordinates of first points in line
So to solve, you take any set of your coordinates given and you chose one to be your second set and your first set. Then you take the y from your 1st set, and you subtract it from the y from your 2nd set. Then you take that and you put it over from what you get when you take the x from the 1st set, and you subtract that from the x in your 2nd set.
So when I solve using this the coordinates given, I get -12-8/17-7
This equals to -20/10, and that equals to -2.
So you find the slope of the line as -2
Ben is making waffles for breakfast. The recipe calls for 1-1/2 cups of water for every 2 cups of AuntJemina pancake mix. How many cups water would he need for only one cup of Pancake mix? Show your work
3/4 cups of water would need for only one cup of Pancake mix.
From the question, we have
1-1/2 cups water would he need for every 2 cups of pancake mix.
3/2 cups water would he need for every 2 cups of pancake mix.
Required cups water for only one cup of Pancake mix = 3/(2*2)
=3/4
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ9
Answer:
3/4 cups of water would need for only one cup of Pancake mix.
From the question, we have
1-1/2 cups water would he need for every 2 cups of pancake mix.
3/2 cups water would he need for every 2 cups of pancake mix.
Required cups water for only one cup of Pancake mix = 3/(2*2)
=3/4
Step-by-step explanation: