The total displacement east is:
15 cos(45) + 15
= 25.607 m
The total displacement north is:
15 sin(45)
= 10.607 m
The magnitude of the total displacement is:
sqrt(25.607^2 + 10.607^2)
= 27.717 m = 27.7 m
Its direction is N x E where:
tan(x) = 25.607 / 10.607
x = 67.5 deg
The return displacement is therefore of the same magnitude
but in the opposite direction.
Displacement 27.7 m, direction S 67.5 deg W
SHOW STEPS PLEASE
-2= -√x-3) +5
Which is a decimal expansion of 7/22?
A.
B.
C.
D.
what's the area of the Square 28in• 28in
Corey needs 24 boards that ate 47 1/ 2 inches long. How many feet of boards should he buy. Explain
Tamara’s dosage of medication has recently decreased 20 milligrams per day. What is the total decrease in Tamara’s medication at the end of the week? Show your work.
Type answer here
The scale on a map is ½ inch = 15 miles. How far apart are two towns that are 2 inches apart on the map? Someone help me please!
y = 4
y = 1/4 x +2
What is the x coordinate of the solution to the system of the linear equations?
A. 0
B. 2
C. 4
D. 8
What is 26.99 round to the nearest tenth
To round 26.99 to the nearest tenth, we increase the tenths place by 1 because the hundredths place is 9, resulting in 27.0.
When rounding 26.99 to the nearest tenth, we need to look at the hundredths place, which is 9. Since 9 is greater than 5, we round up the digit in the tenths place by 1. Therefore, the number rounded to the nearest tenth is 27.0.
Amy was asked to multiply and number by 8 and then add 5. Instead, she added 8 to the number and then multiplied the result by 5. This gave her 2015. What would the answer have been if Amy had followed the instructions correctly?
she did (x+8)*5
2015 = (x+8)*5
divide both sides by 5
403=x+8
x = 403-8 = 395
using same number if she followed instructions it would be
395*8 =3160+5 = 3165
what us the average rate of change
the rate of change is -2 for every set shown in the chart on the right
so 6 to 7 would be -11 -2 = -13
7 to 8 would be -13-2 = -15
8 to 9 = -15-2 = -17
B is the answer
0.22m+7.20=0.1m+8.40
Ms. Sims is putting away 22 books. She can put them on the table in stacks of 10 or as single books. What are the different ways Ms. Sims can put away the books?
Answer:
1)[tex]10+10+1+1=22[/tex]
2)[tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]
Step-by-step explanation:
Mrs. Sims has to put 22 books.
She can either put them in stacks of 10 or arrange them as single book(single stack).
There could be two ways in which she could arrange the books.
First way:
She could arrange the books in two stacks of 10 books ([tex]2\times10=20[/tex] and the remaining two books can be arranged as single books.
So, the arrangement is [tex]10+10+1+1=22[/tex]
Second way:
She could arrange books in one stack of 10 books and and remaining twelve books can be arranged as single books.
So, the arrangement is [tex]10+1+1+1+1+1+1+1+1+1+1+1+1=22[/tex]
A produce store sold 63 red apples. If the ratio of red apples to green apples sold was 7:2, what is the combined amount of red and green apples sold?
The total number of apples sold if, A produce store sold 63 red apples, The ratio of red apples to green apples sold was 7:2, which is 81.
What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.
Given:
A produce store sold 63 red apples,
The ratio of red apples to green apples sold was 7:2,
Assume the total number of apples sold is x then,
Total number of apple sold = 7x + 2x
But the number of red apples sold is given so,
7x = 63
x = 63 / 7
x = 9
Put the value of x in the above equation,
Total number of apple sold = 7 × 9 + 2 × 9
Total number of apple sold = 63 + 18
Total number of apples sold = 81
To know more about Ratios:
https://brainly.com/question/13419413
#SPJ5
if someone tells you that the U.S. public debt is 1.258 x 10^13 dollars, how much money is that?
Benjamin threw a rock straight up from a cliff that was 40 feet above the water. If the height of the rock h, in feet, after t seconds is given by the equation h=-16t^2+12t+40, how long will it take for the rock to hit the water?
The rock will hit the water after approximately 2 seconds.
The time it takes for the rock to hit the water, we need to set the height h equal to zero and solve for t . The equation representing the height of the rock is given by:
[tex]\[ h = -16t^2 + 12t + 40 \][/tex]
Setting h to zero:
[tex]\[ 0 = -16t^2 + 12t + 40 \][/tex]
Now, we have a quadratic equation.
To solve for t , we can use the quadratic formula:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
In this equation, [tex]\( a \), \( b \), and \( c \)[/tex] are the coefficients from the quadratic equation [tex]\( at^2 + bt + c = 0 \).[/tex]In our case:
[tex]\[ a = -16, \quad b = 12, \quad c = 40 \][/tex]
Substitute these values into the quadratic formula:
[tex]\[ t = \frac{-12 \pm \sqrt{12^2 - 4(-16)(40)}}{2(-16)} \]\\[/tex]
Now, calculate the values under the square root:
[tex]\[ t = \frac{-12 \pm \sqrt{144 + 2560}}{-32} \][/tex]
[tex]\[ t = \frac{-12 \pm \sqrt{2704}}{-32} \][/tex]
[tex]\[ t = \frac{-12 \pm 52}{-32} \][/tex]
Now, consider both the positive and negative roots:
1. For the positive root:
[tex]\[ t_1 = \frac{-12 + 52}{-32} = \frac{40}{-32} = -\frac{5}{4} \][/tex]
2. For the negative root:
[tex]\[ t_2 = \frac{-12 - 52}{-32} = \frac{-64}{-32} = 2 \][/tex]
Since time cannot be negative in this context, we discard the negative root.
Therefore, the rock will hit the water after approximately t = 2 seconds.
A ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth
The length of the ladder is 11.66 ft.
What is the Pythagoras theorem?The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
a² + b² = c²
Given that a ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house.
Let the length of the ladder be x
Therefore, using Pythagoras theorem
x² = 10² + 6²
x² = 100 + 36
x = [tex]\sqrt{136[/tex]
x = 11.66 ft
Hence, the length of the ladder is 11.66 ft.
For more references on Pythagoras theorem, click;
https://brainly.com/question/343682
#SPJ2
You are choosing between two health clubs. Club A offers membership for a fee of $ 11 $11 plus a monthly fee of $ 20. $20. Club B offers membership for a fee of $ 15 $15 plus a monthly fee of $ 18. $18. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Simplify. −2i ⋅ (−3i)
a.−6i
b. 6
c. −6
d. 6i
HURRY!
To simplify -2i * -3i, multiply -2 by -3 to get 6, then multiply i by i to get i². Because i² is equivalent to -1 in the complex number system, multiply 6 by -1 to get your answer, which is -6.
Explanation:When multiplying two complex numbers like −2i and (−3i), the 'i' terms get multiplied together separately to the numerical terms. This is due to the distributive property of multiplication.
So, if we apply the multiplication, we would have −2 multiplied by −3 which gives us 6. Then, i multiplied by i gives us i². The term i² is defined as -1 in the realm of complex numbers.
Putting these together we get 6 x -1, that results in −6.
Therefore, the simplified value of the expression is -6, which corresponds with option c.
Learn more about Complex Numbers here:https://brainly.com/question/20566728
#SPJ11
He burj khalifa is 828,000,000 micrometers tall. how is this value written in scientific notation in the gizmo™?
To write this in scientific notation, we have to move the decimal place to the left. Moving the decimal place to the left indicate a positive movement, therefore the correct scientific notation in this case is:
8.28 x 10^8 micrometers
Multiply 16.852 × 0.86
if alisson worked the times in the table and makes $9.32 an hour, how much was her gross pay this week
The gross pay for Alisson this week is $432.22. So option (d) is correct.
To calculate her gross pay, we first need to find the total number of hours worked during the week. We add up the hours worked each day:
1. Monday: 8:03 am to 5:13 pm = 9 hours and 10 minutes
2. Tuesday: 7:58 am to 4:49 pm = 8 hours and 51 minutes
3. Wednesday: 7:46 am to 4:41 pm = 8 hours and 55 minutes
4. Thursday: 8:32 am to 4:50 pm = 8 hours and 18 minutes
5. Friday: 7:31 am to 4:32 pm = 9 hours and 1 minute
Total hours worked = 43 hours and 15 minutes.
Since Alisson worked more than 40 hours this week, any hours beyond 40 are paid at time and a half. So, she worked 40 regular hours and 3 hours and 15 minutes of overtime.
Her regular pay = 40 hours * $9.32/hour = $372.80
Her overtime pay = 3.25 hours * ($9.32/hour * 1.5) = $59.42
Therefore, her total gross pay for the week is $372.80 + $59.42 = $432.22.
Complete Question;
If Alisson worked the times in the table and makes $9.32 an hour, how much was her gross pay this week?
8:03 am 5:13 pm
7:58 am 4:49 pm
7:46 am 4:41 pm
8:32 am 4:50 pm
7:31 am 4:32 pm
Remember that any time worked over 40 hours is paid at time and a half.
(a) $372.80
(b) $410.08
(c) $412.41
(d) $432.22
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 10 fl oz per hour. How fast was the pipe leaking in gallons per day?
Answer:
The pipe is leaking at the rate of 1.875 gallons of water per day.
Step-by-step explanation:
In this question we will find the leakage per day first, then convert it into gallons.
The janitor discovered a leak, leaking with a rate = 10 oz per hour
And we know that there are 24 hours in a day therefore, pipe leaking per day will be = 24×10 = 240 oz.
Since 1 oz = 0.0078125 gallons
Therefore, 240 oz = 240×0.0078125
= 1.875 gallons
The pipe is leaking at the rate of 1.875 gallons of water per day.
Zach deposits $15,000 into his savings. His savings account has an annual interest rate of 1.4%. How much money in interest will zach earn if he keeps the money in his savings for 3 years?
A line with a slope of -2 crosses the y-axis at (0, 3). The equation of the line is
the average person loses about 8 x 10^1 strands of hair each day. about how many strands of hair would the average person lose in 9 days?
there are 18 Bulls and 45 Cows on a ranch if 4 more cows and 4 more Bulls are added will the ratio of the bull to cows remain the same?
The ratio of bulls to cows does not remain the same after adding 4 more cows and 4 more bulls.
Explanation:To determine if the ratio of bulls to cows remains the same after adding 4 more cows and 4 more bulls, we need to compare the new ratio to the original ratio.
Initial ratio of bulls to cows: 18/45 = 2/5
After adding 4 more cows and 4 more bulls, the new ratio becomes (18+4)/(45+4) = 22/49.
Since the new ratio is different from the original ratio, the ratio of bulls to cows does not remain the same after adding 4 more cows and 4 more bulls.
Learn more about Ratio comparison here:https://brainly.com/question/31815139
#SPJ12
How long does it take $450 to double at simple interest rate of 100%
Final answer:
It will take 1 year for $450 to double at a simple interest rate of 100%, as the simple interest formula shows that the interest equals the principal when the rate is 100% and time is one year.
Explanation:
To calculate how long it takes for $450 to double at a simple interest rate of 100%, we can use the formula for simple interest: Interest = Principal × Rate × Time. Since the goal is to double the principal, the interest earned should be equal to the principal of $450.
The simple interest formula in this shape becomes:
$450 = $450 × 1 × Time
When we simplify this, we find that Time equals 1.
Therefore, it will take 1 year for $450 to double at a simple interest rate of 100%.
Suppose a and b are integers. How many solutions are there to the equation ab = 2a + 3b?
Evaluate 37/100+3/10
A student earned grades of C,A,B, and A. Those courses had these corresponding credit hours: 4,6,1, and 6. The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1, and F=0. Compute the grade point average (GPA) and round the result to two decimal places.
To calculate GPA we will find the total points of the student and the total credit hours of the student.
The grades point average (GPA) of the student is 3.47.
Given to us
A student earned grades of C, A, B, and A. and the corresponding credit hours: 4,6,1, and 6.The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1, and F=0. Total points of the studentsPoints of the students = earned grades x corresponding credit hours
For C = 4 x 2 = 8 pointsFor A = 6 x 4 = 24 pointsFor B = 1 x 3 = 3 pointsFor A = 6 x 4 = 24 pointsTotal points = 8 +24 + 3 + 24 = 59
Total Credit hoursTotal Credit hours = 4 + 6 + 1 + 6 = 17 hours
Grade point Average (GPA)[tex]\rm{Grade\ point\ average\ (GPA) = \dfrac{Total\ points\ of\ the\ students}{Total\ Credit\ hours}[/tex][tex]\rm{Grade\ point\ average\ (GPA) = \dfrac{59\ points}{17\ hours} = 3.47[/tex]
Hence, the grade point average (GPA) of the student is 3.47.
Learn more about Average:
https://brainly.com/question/897199