The number of hours that it will take Alonso to drive 288 miles is 12 hours.
How to calculate the time?Since Alonso was driving down a road and after 4 hours he had traveled 96 miles, the speed will be:
Speed = Distance / Time
Speed = 96 / 4
Speed = 24 miles per hour.
Therefore, the time taken for 288 miles will be:
Time = Distance / Speed
Time = 288 / 24
Time = 12
The time taken is 12 hours.
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The doctor orders 100 units of a medication to administer daily. The vial is labeled 50 units/mL. How many mL will be administered if the patient stays in the hospital for a week?
350mL will be administered in a week.
Which of the following expressions has the greatest value
Answer:
2⁵ that is my answer for the question
Answer: 2^5
Step-by-step explanation:
3^3 = 27
1^10 = 1
2^5 = 32
5^2 = 25
Finding the slope and y-intercept of a line.
Answer:
Slope = -5/2
Y-intercept = -9
Step-by-step explanation:
Hello!
The equation is given in Slope-Intercept Form: y= mx + b
m = slopeb = y-interceptSince the slope is the coefficient of the x-term, the slope of this equation is -5/2, or -2.5
The y-intercept is the numerical constant, which is given the by the integer -9.
The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?
point a and point e are the two points representing extreme points on graph
Solve the system of equations by graphing
u=v
4u=2v-12
By using the graphing method, a solution to the given system of equations is equal to -6 and -6.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Next, we would simplify the equation as follows:
4u = 2v - 12
Dividing both sides of the equation by 4, we have:
4u/4 = (2v - 12)/4
u = v/2 - 3
By critically observing the graph of this system of equations, we can logically deduce that the point of intersection is at (-6, -6).
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the equation of the trend line is y= 0.36x + 12.6 use the equation of the trend line to predict the wind chill for a wind speed of 4 mi/h. Round your answer to the nearest degree. The wind chill at 4 mi/h is?? PLease help!!!! need this answer in less than 10 min!
The prediction of the wind chill for the wind speed 4 mi/h is 14 degrees
How to predict the wind chill for the wind speed?Here, we have the following parameters:
Equation of the trend line: y = 0.36x + 12.6
Where
x = Wind speed
y = Wind chill
Also, we have
x = 4 mi/h i.e. the wind speed
Substitute x = 4 in the equation y = 0.36x + 12.6
So, we have
y = 0.36 x 4 + 12.6
Evaluate the equation
y = 14.04
Approximate
y = 14
Hence, the wind chill is 14 degrees
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Consider the following observations on a receptor binding measure (adjusted distribution volume) for a sample of 13 healthy individuals: 22, 40, 41, 42, 43, 48, 51, 58, 62, 66, 67, 70, 71.
Calculate an interval for which you can be 95% confident that at least 95% of all healthy individuals in the population have adjusted distribution volumes lying between the limits of the interval. (Round your answers to three decimal places.)
Predict the adjusted distribution volume of a single healthy individual by calculating a 95% prediction interval. (Round your answers to three decimal places.)
The 95% confidence interval for the population mean adjusted distribution volume, using the t-distribution, is given as follows:
(43.479, 61.281).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the rule presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The sample is given as follows:
22, 40, 41, 42, 43, 48, 51, 58, 62, 66, 67, 70, 71.
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 13 - 1 = 12 df, is t = 2.1788.
Using a calculator with the sample, the parameters for the interval are:
[tex]\overline{x} = 52.38, s = 14.73, n = 13[/tex]
Hence the lower bound of the interval is calculated as follows:
52.38 - 2.1788 x 14.73/sqrt(13) = 43.479.
The upper bound of the interval is calculated as follows:
52.38 + 2.1788 x 14.73/sqrt(13) = 61.281.
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-9x+2y =24
x = 10-4y
Answer: x = -2, y = 3
Step-by-step explanation:
Given that,
-9x+2y = 24..................................(i)
x = 10-4y.......................................(ii)
From equation (i)
-9(10-4y) + 2y = 24 [as x = 10-4y]
=> -90 +36y + 2y = 24
=> 38y = 90 + 24
=> 38y = 114
=> y = 114/38
Therefore, y = 3
Again,
x = 10 - 4(3) [as y = 3]
=> x = 10-12
Therefore, x = -2
Here, x = -2 and y = 3
Please help me! Christian, Freddy, and Skyler are all drinking orange juice from the same-size cartons in the cafeteria. Christian's carton is 3/7 packed. Freddy's carton is 3/10 complete. Kevin's carton is 3/4 full. Who has the least milk left in their carton?
Answer: Freddy
Step-by-step explanation:
Choose a common denominator for all the fractions. Let's use 140.
Christian: 3/7 = 60/140
Freddy: 3/10 = 42/140
Skyler: 3/4 = 105/140
The least value is 42/140
Carlos is making goodie bags for a party. Every goodie bag has exactly the same treats in it. Carlos has 72 granola bars and 48 small popcorn balls. What is the greatest umber of identical goodie bags Carlos can make? How many of each kind of treat is in each goodie bag?
The greatest number of identical goodie bags Carlos can make is 24.
Therefore will be 3 granola bars and 2 popcorn balls in each bag.
How to calculate the value?From the information, Carlos is making goodie bags for a party and every goodie bag has exactly the same treats in it.
Carlos has 72 granola bars and 48 small popcorn balls. It should be noted that the greatest common factor between 72 and 48 is 24.
Therefore, granola bars will be:
= 72/24
= 3 in each bag
Popcorn will be:
= 48/24
= 2 in each bag.
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In an economy, the price index in 2006 was 100 and the real gross domestic product (GDP) was $1,000. In 2010, the price index was 110 and the nominal GDP was $2,200. Based on that information, which of the
following can be inferred about the economy's nominal GDP in 2006 and real GDP in 2010?
A. Nominal GDP in 2006 = $2,000; Real GDP in 2010 = $1,000
B. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000
C. Nominal GDP in 2006= $1,100, Real GDP in 2010 = $2,420
D. Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,420
E. Nominal GDP in 2006 = $1,100; Real GDP in 2010 = $2,200
Please show your work.
The economy's nominal GDP in 2006 and real GDP in 2010 is option B) Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.
What does GDP Price Index mean?
A metric for gauging price inflation for American-made goods and services. The prices of American goods and services exported to other nations are included in the gross domestic product price index. This index excludes the costs Americans pay for imports.A country's gross domestic product that has been accounted for inflation is known as real GDP. Compare this to nominal GDP, which calculates GDP using today's prices without taking inflation into account.Nominal GDP in 2006=$1,000;
Real GDP in 2010=$2,000
Price index = (nominal GDP/real GDP) ×100
thus, nominal GDP in 2006=(price index × real GDP)/100
= (100×$1,000)/100
=$1,000
Real GDP in 2010= (nominal GDP/price index) ×100
= ($2,200/110) ×100
=$2,000.
Hence, the economy's nominal GDP in 2006 and real GDP in 2010 is option B) Nominal GDP in 2006 $1,000, Real GDP in 2010 = $2,000.
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Does the line for y = 6 have a negative slope ?
No, the slope of a horizontal line y=6 is, zero not negative.
What is a Slope?
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.
Slope Formula
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope, m = Change in y-coordinates/Change in x-coordinates = Δy/Δx
m = (y2 – y1)/(x2 – x1)
In the given equation of line y=6 .
The line crosses the y-axis at 6, as the line is always at that value. As it is a horizontal line, the slope is zero.
The equation y = 6 means for each and every value of x, y will be equal to 6.
This is the definition of a horizontal line.
By definition, the slope of a horizontal line is m = 0
When x = 0 then y = 6
Therefore, the y-intercept is: (0, 6).
Hence , the the slope of a horizontal line , m = 0.
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A bag has 2 red, 3 green, and 6 orange balls. If a ball is randomly selected from the bag, what is the theoretical probability
that it is the color specified in parts (a) through (d).
Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.
In the given question,
A bag has 2 red, 3 green, and 6 orange balls.
So total number of balls = 2+3+6 = 11
We have to find the theoretical probability.
(a) We have to find the theoretical probability of selecting green ball.
P(G) = Total number of green balls/Total number of balls
P(G) = 3/11
Hence, the probability of selecting green ball is 3/11.
(b) Now we have to find the theoretical probability of not selecting green ball.
Except green ball there is having red and orange i.e.
Total remaining balls except green = 2+6 = 8
P(G) = Total number of balls except green balls/Total number of balls
P(G) = 8/11
Hence, the probability of not selecting green ball is 8/11.
(c) Now we have to find the theoretical probability of selecting orange ball.
P(G) = Total number of orange balls/Total number of balls
P(G) = 6/11
Hence, the probability of selecting green ball is 6/11.
(d) Now we have to find the theoretical probability of not selecting orange ball.
Except orange ball there is having red and green balls i.e.
Total remaining balls except orange = 2+3 = 5
P(G) = Total number of balls except orange balls/Total number of balls
P(G) = 5/11
Hence, the probability of not selecting orange ball is 5/11.
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Robert bought a used car for $10,332 with an added sales tax of 2.5%. What was the
original price of the car?
A $11,080
B. $10,080
C. $20,800
D. $15,416
If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.
Option (B) is correct.
What is a percentage?
A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is the one-hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.
Robert bought a used car for $10,332 with an added sales tax of 2.5%.
so the additional amount would be = 10,332 * 2.5%
= 10332 * 0.025
= $258.3
So the original price of the car would be = 10332 - 258.3
≈ $10,080.
Hence, If Robert bought a used car for $10,332 with an added sales tax of 2.5%. Then the original price of the car would be around $10,080.
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A 2-pound bag of candy costs $6.04. What is the unit price?
per pound
Answer:
it would be $3.02
Step-by-step explanation:
you pretty much do $6.04/2 Ib
therefore, your answer would be $3.02
Answer:
Step-by-step explanation:
6.04 divded by 2= 3.02 per pound
A company orders 20 boxed lunches from a deli for $234.00. If each boxed lunch
costs the same amount, how much do 16 boxed lunches cost?
16 boxed lunch cost $187.2.
Given that a company orders 20 boxed lunches from a deli for $234.00.
Each boxed lunch costs the same amount.
20 boxed lunches from a deli for $234
1 boxed lunches from a deli for $234/20 = $11.7
Hence the cost of 16 boxed lunch is = $11.7*16 = $187.2
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This square root equation has 2 solutions. What is the extraneous solution?
√x+12 −6=x
Enter your answer in the box.
x = - 8 is not a root of √(x + 12) - 6 = x, since it is an extraneous solution.
How to find the extraneous solution of a radical equation
In this question we have a radical equation that offer two possible roots. A root is an extraneous solutions when it brings out an absurd (i.e. 1 = 4) when the expression is evaluated. First, write the radical equation:
√(x + 12) - 6 = x
Second, use algebra properties to find the possible roots of the radical equation:
√(x + 12) - 6 = x
√(x + 12) = x + 6
x + 12 = x² + 12 · x + 36
x² + 11 · x + 24 = 0
(x + 3) · (x + 8) = 0
x = - 3 or x = - 8
Third, evaluate the radical equation at each root:
√(- 3 + 12) - 6 = - 3
√9 - 6 = - 3
3 - 6 = - 3
- 3 = - 3 (TRUE)
√(- 8 + 12) - 6 = - 8
√4 - 6 = - 8
2 - 6 = - 8
- 4 = - 8 (FALSE)
x = - 8 is an extraneous solution.
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what's the constant of proportionality: the table represent the linear relationship between the number of seconds a paper airplane is in the sky and the total distance it will fly
PLEASE HURRY!!!!!!!!!!!!!!!!!!! i need to complete this it im studying it for my test tomorrow
The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
What is constant of proportionality?When two or more parameters are directly or indirectly proportional to one another, their relationship is expressed as a = kb or a = k/b, where k indicates the nature of the relationship between the two variables. This k is referred to as the proportionality constant.
For example, the number of apples in a crop is proportional to the number of trees in an orchard, with the ratio of proportionality being the average number of apples per tree.
This can be illustrated as:
Let's say y = 4
Let's say x = 2
y = kx
4 = 2k
Divide
k = 4/2
k = 2
The constant is 2.
Note that an overview was given as the information is incomplete.
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Annie's current earnings are shown in the table.
She was offered a new job that will pay $7.25 per hour. Assume
that her earnings vary directly with the number of hours worked.
Which job pays more an hour?
Answer:
Annie's new job pays more an hour.
Step-by-step explanation:
They tell us that her new job pays $7.25 per hour. So to determine which job pays her more, we need to find how much she earns in her current job.
There are a few ways to find this (none of them are hard.) But this is the easiest way in my opinion.
The chart tells you that Annie earns $13 in 2 hours. We need to find how much she earns in 1 hour. All you need to do is divide $13 by two.
13/2 = 6.5
6.5 = $6.50
If her current job pays her $6.50 an hour and her new job pays $7.25 an hour, she should consider higher paying jobs.
But, yes, the new job pays her more an hour.
Write equations for the horizontal and vertical lines passing through the point (2, -6).
horizontal line: 0
vertical line:
Continue
0
00
X
0=0
3
The equation of the horizontal line passing through the point (2, -6) is :
y = -6
and the equation of the vertical line passing through the point (2, -6):
x = 2
We need to write equations for the horizontal and vertical lines passing through the point (2, -6)
For a vertical line the value of x will never change. This will be true for any value of y.
So, the equation for a vertical line passing through this point is:
x = 2
Similarly, for a horizontal line the value of y will never change. This is true for any value of x.
So, the equation for a horizontal line passing through this point is:
y = -6
Therefore, the equation of the horizontal line passing through the point (2, -6) is y = -6
and the equation of the vertical line passing through the point (2, -6) is x = 2
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I need some help with this problem please
Answer:
the answer is 135
Step-by-step explanation:
Dave and LaVontae are saving money. Dave has $10, and LaVontae has $5. Write an
equation expressing the relationship between the amount that LaVontae has, x, and
the amount that Dave has, y.
9. The seventh-grade class is raising money to
have a class trip at the end of the year. They
began the year with $1,500. Now they have
$1,650 in the account.
a. What is the percent of increase for the
money the class has raised?
b. Make Sense and Persevere The class
figured out that if the percent increase is
99% from the beginning of the year, the
class will have enough money for every
student to go on the field trip. How
much money will the class need to raise
for every student to go.
The percentage increase for the money the class has raised is 10% and they will need $ 2115 to make the percentage increase to 99%.
According to the question,
We have the following information:
Initial price in the year = $1500
Final price they have = $1650
a) Now, we know that following formula is used to find the percentage increase in the price:
Percentage increase = 100*(final price-initial price)/initial price
Percentage increase = 100*(1650-1500)/1500
Percentage increase = 100*(150)/1500
Percentage increase = 10%
b) Now, we will find the final price when the percentage increase is 99%.
Let's take the final price to be $x.
99 = 100*(x-1500)/1500
99 = (x-1500)/15
Using the cross multiplication method:
x-1500 = 15*99
x-1500 = 615
x = 615+1500
x = 2115
Hence, the percentage increase for the money the class has raised is 10% and they will need $ 2115 to make the percentage increase to 99%.
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Give one combination of two factors whose product is 0.24, if one of the factors is a whole number greater than 1.
Answer:
Step-by-step explanation:
so they are just asking for some numbers multiplied together to get 0.24
any two , as long as one is great than 1 soo , try 2
2 * ? = 0.24
I suspect you can see the answer now?
Macmillan Learning
Holly is deciding between 2 yoga studios. If she chooses Life Studio, she will pay a $60 initial sign-up fee and $30 each
month. If she chooses Yoga Mind, she will pay $40 each month and no initial sign-up fee. If Holly thinks she will do yoga
for 6 months, which studio should she join to pay less money?
She will pay the same amount at both.
Life Studio
Yoga Mind
Answer:
She will pay the same amount at both
Step-by-step explanation:
For Life Studio,
the initial sign up fee + $30 each month
= $30 = 30 × 6 = $180
Hence, $60 + $180 = $240
For Yoga Mind,
$40 each month for 6 months
= $40 × 6
$40 × 6= $240
Therefore, she will pay the same amount at both
A candy company sells peanut brittle and almond bark. The information for both types of candy is shown.
graph labeled Peanut Brittle with x axis labeled weight in ounces and y axis labeled cost in dollars with a line from point 0 comma 0 going through 10 comma 10
Almond Bark
Weight (ounces) 2 6 14
Cost (dollars) 3 9 21
Determine how much more one candy costs per ounce than the other candy.
Peanut brittle costs $0.50 more per ounce than almond bark.
Almond bark costs $0.50 more per ounce than peanut brittle.
Peanut brittle costs $0.33 more per ounce than almond bark.
Almond bark costs $0.33 more per ounce than peanut brittle.
Peanut brittle costs $0.33 more per ounce than the almond bark option (C) is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A candy company sells peanut brittle and almond bark.
Almond: $6/(10 oz) = $0.60/oz
Bark: $9/(10 oz) = $0.90/oz
0.90 - 0.60 = $0.90
Peanut brittle costs $0.33 more per ounce than almond bark.
Thus, peanut brittle costs $0.33 more per ounce than the almond bark option (C) is correct.
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Answer:
Almond bark costs $0.50 more per ounce than peanut brittle.
Step-by-step explanation:
Nate and Gavin are playing a video game. Gavin has scored eleven more than twice the number of points Nate has. If they scored 692 points altogether, have many points has Gavin scored?
Answer: gavin scored 465 points
Step-by-step explanation:
Can someone help me with this question please like explain it to me ?
Using the trigonometry relation, the value of sin2x=4√2/9, cos2x=7/9 and tan2x=4√2/7.
In the given question, we have to find the value of sin(2x), cos(2x) and tan(2x).
The given value of six=1/3, x in quadrant first.
We firstly finding the value of cosx.
cosx = √1-(sinx)^2
Now putting the value of sinx
cosx = √1-(1/3)^2
cosx = √1 -1/9
cosx = √(9-1)/9
cosx = √8/9
cosx = 2√2/3
We know that;
sin2x=2sinxcosx
sin2x=2* 1/3 * 2√2/3
sin2x=4√2/9
Now finding the value of cos2x
We know that;
cos2x=1-2(sinx)^2
cos2x=1-2(1/3)^2
cos2x=1 -2/9
cos2x=(9-2)/9
cos2x=7/9
Now finding the value of tan2x
As we know that
tan2x=sin2x/cos2x
tan2x=(4√2/9)/(7/9)
tan2x=4√2/7
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Julia is a motived worker, and she is caring, considerate and cooperative most times. These are just a few of her positive,
A. typical responses
B. inherited responses
C.personality traits
D.measurable traits
HELP ASAP!! Find the sum of the series
Answer:
225
Step-by-step explanation:
a1 = 1
a15 = 29
sum = n/2 ( a1 + a15) = (15/2) ( 1 + 29) = 225