The distance travelled was 225 miles.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Average speed = 50 miles per hour
Time taken = 4 1/2 hours = 4.5 hours
Speed can be calculated using the formula,
Speed = Distance / Time
Distance = Speed × Time
= 50 × 4.5
= 225 miles
Detroit was 225 miles away.
Learn more about Speed here :
https://brainly.com/question/7359669
#SPJ1
Simplify the expression:
[tex]\frac{\frac{1}{a} +\frac{2}{b} }{\frac{2}{a}+ \frac{1}{b} }[/tex]
The simplified form of the given expression is 2a+b/2b+a.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is [tex]\frac{\frac{1}{a}+ \frac{2}{b} }{\frac{2}{a}+ \frac{1}{b} }[/tex].
The expression can be simplified as follows
[tex]\frac{\frac{b+2a}{ab} }{\frac{2b+a}{ab} }[/tex]
= 2a+b/2b+a
Therefore, the simplified form of the given expression is 2a+b/2b+a.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ1
don’t understand please help
Choose the method of pay that would result in the most earnings for one month on sales of $60,000.
The method of pay that would result in the most earnings for one month on sales of $60,000 would be: d. Graduated commission of 5% on the first $40,000 in sales and 9% on anything over that.
How to find the earnings?The earnings can be calculated as follows:
a. Earnings = 6% of 60000
Earnings = $3,600
b. Earnings = 1500 + .03(60000)
Earnings = 1500 + 1800
Earnings = $3,300
c. For the first $50,000: $50,000 * 4% = $2,000
For the remaining $10,000: $10,000 * 10% = $1,000
Total earnings: $2,000 + $1,000 = $3,000
d. For the first 5 % ×40,000 = 2000
For the remaining (60,000-40,000) = .09 x 20000 = 1800
Total earnings :2000 + 1800 = $3,800
Therefore the correct option is D.
Learn more about greatest earnings here:https://brainly.com/question/25631040
#SPJ1
The complete question is:
Choose the method of pay that would result in the most earnings for one month on sales of $60,000.
a. Straight commission of 6% on all sales.
b. Monthly salary of $1,500 plus 3% commission on all sales.
c. Graduated commission of 4% on the first $50,000 in sales and 10% on anything over that.
d. Graduated commission of 5% on the first $40,000 in sales and 9% on anything over that.
Temperature is an example of a variable that uses (select one):
1. the ordinal scale
2. the interval scale
3. either ordinal or ratio scale
4. the ratio scale
Temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.
What is Temperature?The physical concept of temperature indicates in numerical form how hot or cold something is.
A thermometer is used to determine temperature.
One variable that makes use of the scale interval is temperature.
Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.
The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes.
One of the seven base units in the International System of Units is the kelvin (SI). The lowest point on the thermodynamic temperature scale is absolute zero, or zero Kelvin, or 273.15 °C.
Therefore, the temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.
Know more about Temperature here:
https://brainly.com/question/24746268
#SPJ4
Find a solution to the system of equations 
Answer:
(4, 1 )
Step-by-step explanation:
the solution to a system of equations given graphically is at the point of intersection of the 2 lines.
the lines intersect at (4, 1 )
then the solution is (4, 1 )
For the diagram below, which equation is the correct use of the distance formula?
Help please guys....
The equation that portrays the correct use of the distance formula is 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² )
Which equation is the correct use of the distance formula?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
From the diagram;
Point A (5,6)
x₁ = 5y₁ = 6Point B (11,y₂)
x₂ = 11y₂ = y₂Distance d = 6.71
Plug the given values into the distance formula.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² )
Therefore, the correct use of the formula is 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² ).
Option D) 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² ) is the correct answer.
Learn more about the distance formula here: brainly.com/question/24509115
#SPJ1
Nicole measured some distances on a map of Lassen Volcanic National Park. The scale on the map is 34
inch = 2 miles. What is the actual distance from Raker Peak to Hat Mtn?
Responses
A 4 miles4 miles
B 223
miles2 2 3 miles
C 214
miles2 1 4 miles
D 212
miles2 1 2 miles
E 3 miles
Performing a change of scale we will see that the actual distance is 4 miles.
What is the actual distance from Raker Peak to Hat Mtn?We know that the scale is:
3/4 inch = 2 miles.
And the distance that Nicole found on the map is (1 + 1/2) inches.
We can rewrrite the scale as:
1 inch = (4/3)*2 miles
1 inch = (8/3) miles.
Then the actual distance will be:
distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.
The correct option is A.
Learn more about changes of scale:
https://brainly.com/question/15891755
#SPJ1
Which additional fact would prove that quadrilateral WXYZ is a parallelogram?
The additional fact that would prove that XW is a parallelogram is given as follows:
C. YZ = WX.
How to obtain the values?For a parallelogram, we have that the opposite sides are congruent, that is, they have the same side length.
The congruent pair of side lengths given in this problem is presented as follows:
XY and WZ.
Hence the missing pair of side lengths given in this problem is presented as follows:
YZ and WX.
Missing that the correct option is given by option C.
More can be learned about parallelograms at https://brainly.com/question/30532990
#SPJ1
Gavin’s gross pay is $3851. his deductions total $756.72. what percent of his gross pay is take-home pay? responses 20% 20% 24% 24% 80% 80% 82%
Answer:
80%
Step-by-step explanation:
Gross Pay = $3851
Deductions = $756.72
Take-home Pay = $3851 - $756.72 = $3,094.28
Ratio of take-home pay to gross pay = 3,094.28/3851 = 0.8035
As a percentage = 0.8035 x 100 = 80.35%
or approximately 80% to match the answer choice
according to mark cherry, in 2008, in the united states, how many patients were waiting for and organ transplant/donation and how many actually received an organ transplant?
There are many more people awaiting such a transplant than there are available organs, leading to a large backlog of patients who are not able to receive an organ transplant.
In 2008, the United States Department of Health and Human Services reported that there were approximately 113,000 patients in the United States awaiting organ transplants. Of those, only 28,535 received an organ transplant that year. This is a ratio of approximately 1 in 4. This can be expressed mathematically as 28,535/113,000 = 0.25, or one fourth. This means that for every 4 people awaiting an organ transplant in the United States in 2008, only 1 actually received one. While organ transplants are a life-saving procedure for many, the reality is that there are many more people awaiting such a transplant than there are available organs, leading to a large backlog of patients who are not able to receive an organ transplant.
Learn more about ratio here:
https://brainly.com/question/13419413
#SPJ4
Complete question:What were the numbers of patients waiting for and receiving an organ transplant/donation in the United States in 2008, according to Mark Cherry?
Fill in the missing number. % of 98 = 49
50%
since 98/2 = 49
Thats it
A store’s dressing room has a limit of 10 garments per customer. If Carol has at least 3 garments below the limit, how many garments does she have in her dressing room?
Carol has at least 7 garments in the dressing room.
How to find the number of garments in her dressing roomInformation given in the problem is
A store’s dressing room has a limit of 10 garments per customer
If Carol has at least 3 garments below the limit
the limit is 10 garments, this is the maximum number of clothes and Carol has 3 garments below the limit
we can conclude that Carol has at least
= 10 - 3
= 7
Carol has 7 garments in the dressing room.
Learn more about subtraction at:
https://brainly.com/question/13378503
sSPJ1
PLEASE HELP TIMED
What is the solution of x+4/2x-1 < 0
Answer:
x<2
Step-by-step explanation:
this is correct answer
the answer is 1.6x ............
Answer: ok njnnnnnnnnnnnnnnnnnnnnnnnn
whats fractio equivlet to 18.75%
Answer:
18 3/4
Step-by-step explanation:
Answer:
18 3/4 or 75/4
Step-by-step explanation:
a 5-card poker hand is dealt at random from a standard 52-card deck. what is the total number of possible hands?
By using the formula for permutation, we can find that there are 2,598,960 possible combinations of 5 cards that can be dealt from a standard deck of 52 cards.
Poker is a popular card game that is played with a standard deck of 52 cards.
A permutation is the arrangement of objects in a specific order. In this case, the objects are the 52 cards in a standard deck, and the order is the 5 cards that are dealt to each player.
To find the number of possible 5-card hands, we can use the formula for permutation:
P(52, 5) = 52! / (52 - 5)!
Where "52!" is the factorial of 52, meaning the product of all positive integers from 1 to 52.
52! / (52 - 5)! = 806,368,039,360 / 47! = 2598960
The final answer is that there are 2,598,960 possible 5-card hands that can be dealt from a standard deck of 52 cards.
To know more about permutation here.
https://brainly.com/question/1216161
#SPJ4
Suzanne has a 12 inch board for construction and a wooden chair. The directions say to use a board that is 29 cm long is your board long enough to cut?
Yes 12 inches converted to centimeters is around 30 cm
Provide the vertical movement for the
following absolute value function:
-4x + 5|- 3
Hint: -|x - h| + V
Move 3 units [?].
down
up
W
The vertical movement for the absolute value function in this problem is given as follows:
Move 3 units down.
What is the absolute value function?The absolute value function of vertex at coordinates (h,k) is defined as follows:
y = a|x - h| + k.
For the parent absolute value function, the y-coordinate of the vertex is given as follows:
y = 0.
For the absolute value function -4|x + 5| - 3, the y-coordinate of the vertex is given as follows:
y = -3.
Hence the subtraction by 3 means that there was a movement of 3 units down.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
consider a data set with at least three data values. suppose the highest value is increased by 10 and the lowest is decreased by 10. (a) does the mean change? explain.
If the highest value is increased by 10 and the lowest is decreased by 10 the mean doesn't change
Let us assume the data set with 10 observations:
{5, 6, 4, 3, 2, 6, 4, 9, 4, 4}.
Arranging data set in ascending order
{2, 3, 4, 4, 4, 4, 5, 6, 6, 9}
Mean of this data = Sum of all observations/Total number of observations
Mean = (2 + 3 + 4 + 4 + 4 + 4 + 5 + 6 + 6 + 9)/10
Mean = 47/10 = 4.7
Now, Increasing the highest value by 10 and decreasing the lowest value by 10
So, the new data set is {-8, 3, 4, 4, 4, 4, 5, 6, 6, 19}
Mean of this data = -8 + 3 + 4 + 4 + 4 + 4 + 5 + 6 + 6 + 19/10
Mean = 47/10 = 4.7
Hence, the mean doesn't change.
To learn more about mean here:
brainly.com/question/30090607
#SPJ4
If g(x) = 3(4)^x
what is the value of g(2) ?
Answer:
Step-by-step explanation:
g(2) = 3/2(2) + 4 = 3 + 4 = 7
Number 15 please !!50 POINTS!!
The trigonometric ratios for angle Y are given as follows:
[tex]\sin{Y} = \frac{6}{\sqrt{61}}[/tex][tex]\cos{Y} = \frac{5}{\sqrt{61}}[/tex]tan(Y) = 6/5.[tex]\csc{Y} = \frac{\sqrt{61}}{6}[/tex][tex]\sec{Y} = \frac{\sqrt{61}}{5}[/tex]cot(Y) = 5/6.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The inverse ratios are given as follows:
Cosecant: one divided by sine.Secant: one divided by cosine.Cotangent: one divided by tangent.More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
Select the best Measures of Center for the data set: 3, -26, -1, -5, 4, 1, 3
The best Measures of Center for the data set: 3, -26, -1, -5, 4, 1, 3 is median
How to determine the best measureFrom the question, we have the following parameters that can be used in our computation:
3, -26, -1, -5, 4, 1, 3
In the above dataset, the observation -26 is an outlier
This is so because -26 is relatively far from other observations
When a dataset has an outlier, the best measure of center to use is the median
Read more about median at
https://brainly.com/question/14532771
#SPJ1
when purchasing a vechicle, which of the following would initially offer the lowest monthly payment
special apr financing
ballon payment plan
cash back offer
regular apr financing
The special apr financing would initially offer the lowest monthly payment. The correct answer is the first option.
The special apr financingThe monthly payment offered by "special APR financing" is likely to be the lowest among the options given. The "special APR financing" generally refers to a promotional interest rate offered by the dealership or the manufacturer, which can result in lower monthly payments. However, the total cost of the vehicle over the life of the loan could be higher compared to the other options.
It's always best to consider the total cost of the vehicle and compare the options based on the interest rate, loan term, down payment, and any additional fees before making a final decision.
Learn more about The special apr financing here https://brainly.com/question/2772156
#SPJ1
6739 divided by 6 in long division
Answer:
1123
Step-by-step explanation:
I did 6739 / 9 = 1123.
I need answer ASAP the question is in the picture
Answer:
A. yes they both have the same solutions.
B. below...
Step-by-step explanation:
what is a linear system with fewer equations than unknowns?
Infinitely many solutions exist for a system with fewer equations than unknowns, yet there may be none. An underdetermined system is one that operates in this manner.
What in mathematics is a linear system?
A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.
Equations with unknowns or variables that have powers of one are known as linear equations. Because the variables x, y, and z are linear, for instance, 3x - 4y + 5z = 3 is a linear equation, however xy + 3z = 7 is not because the phrase xy is a product of two variables.
Learn more about linear system
brainly.com/question/26544018
#SPJ4
In ΔEFG, f = 400 inches,
m
m∠F=94° and
m
m∠G=33°. Find the length of g, to the nearest 10th of an inch.
The measurement of the side g in the Δ EFG is 218.38
What is sine rule of triangle?The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
Given that, In Δ EFG, f = 400 inches, m ∠ F = 94° and m ∠ G = 33°, we need to find, the length of g (refer to figure attached)
Using the sine rule of the triangle,
f / Sin F = g / Sin G = e / Sin E
400 / Sin 94° = g / Sin 33°
g = 400 / Sin 94° × Sin 33°
g = 218.38
Hence, the measurement of the side g in the Δ EFG is 218.38
Learn more about sine rule, click;
https://brainly.com/question/22288720
#SPJ1
Answer:
g= 218.4
Step-by-step explanation:
Draw a diagram:
Draw a diagram:
E
F
G
f = 400
g = ?
94°
33°
A.A.S.
→
Law of Sines
A.A.S.→Law of Sines
sin
=
sin
sinA
a
=
sinB
b
From reference sheet.
Find other angle:
Find other angle:
∠
=
180
−
94
−
33
=
5
3
∘
∠E=180−94−33=53
∘
E
F
G
f = 400
g = ?
94°
33°
53°
sin
33
=
400
sin
94
sin33
g
=
sin94
400
Plug in. Opposite sides go together.
=
400
sin
33
sin
94
≈
218.3876
≈
218.4
g=
sin94
400sin33
≈218.3876≈218.4
Solve for the side and evaluate.
Your Solution:
=
218.4
g=218.4
Upon graduation, Natalie had five job offers. The annual salaries for four of the jobs were: $36,000, $45,000, $28,000, and $32,000. The average of the five annual salaries was $38,000. What was the fifth annual salary?
Answer:
The fifth salary = $49,000
Step-by-step explanation:
Let x be the fifth salary
Total salary = $36,000, + $45,000 + $28,000 + $32,000 + x
= $141,000 + x
The average of 5 salaries is $38,000
Total = Average x number of elements
= 38000 x 5 = 190,000
Equating the two totals
141,000 + x = 190,000
Subtract 141, 000 from both sides
x = 190,000 - 141, 000
x = $49,000
So the fifth salary = $49,000
a worker has asked her supervisor for a letter of recommendation for a new job. she estimates that there is an 85 percent chance that she will get the job if she receives a strong recommendation, a 50 percent chance if she receives a moderately good recommendation, and a 10 percent chance if she receives a weak recommendation. she further estimates that the probabilities that the recommendation will be strong, moderate, and weak are 0.6, 0.3, and 0.1, respectively. a. how certain is she that she will receive the new job offer? b. given that she does receive the offer, how likely should she feel that she received a strong recommendation? (
Disregarding intermediate, let's assume she has access to a letter that can be powerful or weak. Let's say she receives a persuasive letter. If she receives a strong letter, her chance of being hired is then increased.
P(J|S)
If, however, she receives a subpar letter, Considering since she received a subpar cover letter, her chances of landing the job are slim.
P(J|W)
Let's assume that we have some knowledge of such two numbers. I believe
In addition, we recognize how likely it is that she will receive either one or both letters: P(J|S)=0.8 P(J|W)=0.1
Note that P(S)+P(W)=1 since there are only two possibilities: P(S)=0.7 and P(W)=0.3.
P(J)=P(J|S) P(S)+P(J|W) P(W)
This is a representation of two distinct directions that could be taken. In one, we receive a compelling letter and ponder if she'll be hired in light of that compelling letter. As a result of the weak letter from the other, we are unsure if she will be hired. We give the pathway carrying the formal letter a higher weight because there is a substantially larger chance of receiving it compared to a weak letter.
The law of probability value is used in this situation.
To know more about probability click here
brainly.com/question/15528070
#SPJ4
the standard deviation is used in conjunction with the
When describing bell-shaped distributions statistically, the standard deviation is utilised along with the mean.
What does the mean actually measure?
While the standard deviation gauges the distribution's spread, the mean gauges the distribution's centre.
What is the purpose of standard deviation?
For the aim of quantifying dispersion, or the variation that takes place in the values of a data set that is taken into consideration, the standard deviation is used. The data points are said to be close to the mean when the standard deviation number is reduced. The opposite will occur when it is higher. In this way, it gauges how widely apart data points are from the mean.
Anything's predicted value is sometimes referred to as a mean. It is the object that serves as the focal point for all data points. The standard deviation determines how widely apart all the data points are from the mean, whereas the mean is the centre of the distribution.
What is the name of standard deviation?
Because it is the square root of the means of the squared errors from the arithmetic average, standard deviation is often referred to as root-mean square deviation. Standard deviation is a word used in economics to indicate how risky an investment is.
To know more about Standard Deviation visit :
https://brainly.com/question/14554601
#SPJ4