Answer:
She would earn in a week (six days) 1482 cents.
Step-by-step explanation:
Given:
Mrs. Hall went to work for the shirt factory.
She earned nineteen cents per hour.
She worked thirteen hours per day.
Now, to find the money she earn in a week (six days).
Money she earned per hour = 19 cents.
As she she worked 13 hours per day.
So, money she earned per day = [tex]19\times 13=247.[/tex]
Now, to get the total money she earned in a week (six days) we multiply 6 by money earned in per day:
[tex]6\times 247[/tex]
[tex]=1482\ cents.[/tex]
Therefore, she would earn in a week (six days) 1482 cents.
A smoothie stores sell 3 strawberry smoothies and 5 banana smoothies for a total cost of 27.50 .The strawberry smoothie cost 0.50 more than the banana smoothies
Answer:
Cost of each banana smoothies is 3.25 and Cost of each Strawberry smoothie is 3.75.
Step-by-step explanation:
Given:
Number of strawberry smoothies =3
Number of banana smoothies = 5
Total cost = 27.50
We need to find cost of strawberry cookies and cost of banana cookies.
Solution:
Let cost of each banana smoothies be 'x'.
Given:
The strawberry smoothie cost 0.50 more than the banana smoothies.
So we can say that;
Cost of each Strawberry smoothie = [tex]0.5+x[/tex]
Now we can say that Total cost is equal to sum of Number of strawberry smoothies multiplied by Cost of Strawberry smoothie and Number of banana smoothies multiplied by cost of banana smoothies.
framing in equation form we get;
[tex]3(x+0.5)+5x=27.5[/tex]
Applying distributive property we get;
[tex]3x+1.5+5x=27.5\\\\8x+1.5=27.5[/tex]
Subtracting both side by 1.5 we get;
[tex]8x+1.5-1.5=27.5-1.5\\\\8x=26[/tex]
Dividing both side by 8 we get;
[tex]\frac{8x}{8}=\frac{26}{8}\\\\x=3.25[/tex]
Cost of each banana smoothies = 3.25
Cost of each Strawberry smoothie = [tex]0.5+x=0.5+3.25=3.75[/tex]
Hence Cost of each banana smoothies is 3.25 and Cost of each Strawberry smoothie is 3.75.
Answer:
the slope is 4
Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 8 minutes to fill the swimming pool with 72 gallons of water. At what rate does the swimming pool fill, in gallons per minute?
Answer:
The rate the swimming pool is filled is 9 gallons of water per minute
Step-by-step explanation:
Let's review the information provided by Ronald to us to help him to find the answer to the question:
Time it takes to fill the swimming pool = 8 minutes
Amount of water the swimming pool can hold = 72 gallons
2. At what rate does the swimming pool fill, in gallons per minute?
Rate the swimming pool is filled = Amount of water the swimming pool can hold /Time it takes to fill the swimming pool
Replacing with the real values, we have:
Rate the swimming pool is filled = 72/8 = 9 gallons of water per minute
Compute the following products.
a. (4x + 5)(4x - 5)
b. (4x + 5)2
which of the following values for x and y satisfy the following system of the equations?
{ x + 4y = 10
{5x + 10y = 20
a. x = 3, y = 2
b. x = 2, y - 3
c. x = -2, y = 3
d. x = 3, y = -2
Answer:
The answer to your question is letter C
Step-by-step explanation:
Equations
x + 4y = 10
5x + 10y = 20
Process
1.- Substitute all the options in both equations and evaluate them
a) x = 3, y = 2 This option is incorrect
(3) + 4(2) = 10 3 + 8 = 10 11 ≠ 10
5(3) + 10(2) = 20 15 + 20 = 20 35 ≠ 20
b) x = 2, y = -3 This option is incorrect
(2) + 4(-3) = 10 2 -12 = 10 -10 ≠ 10
(2) + 10(-3) = 20 2 - 30 = 20 -28 ≠ 20
c) x = -2, y = 3 This is the right answer
(-2) + 4(3) = 10 -2 + 12 = 10 10 = 10
5(-2) + 10(3) = 20 -10 + 30 = 20 20 = 20
d) x = 3, y = -2 This option is incorrect
(3) + 4(-2) = 10 3 - 6 = 10 - 3 ≠ 10
5(3) + 10(-2) = 20 15 - 20 = 20 -10 ≠ 10
Point X is at 2/3 on a number line on the number line point why is the same distance from 0 is point X but has a numerator of 8 what is the denominator of the fraction at point why
Answer:
Denominator
x = 12
Step-by-step explanation:
Let x be the denominator of the fraction at point y.
Given:
Point X is at 2/3 on a number line from 0.
On the same line, point y is the same point from 0.
Numerator of the fraction at point y is 8.
We need to find the denominator of the fraction at point y.
Solution:
From the above statement the distance from 0 to point X and 0 to point Y is same, so point X is equal to Y.
[tex]\frac{2}{3} =\frac{8}{x}[/tex]
By cross multiplication.
[tex]x=\frac{8\times 3}{2}[/tex]
[tex]x= \frac{24}{2}[/tex]
[tex]x = 12[/tex]
Therefore, the denominator of the fraction at point y is 12.
Bianca and Meredith are sisters. Meredith's height is 23 of Bianca's height plus 32 inches. Meredith is 60 inches tall. A girl is sixty inches tall. Write an equation to find Bianca's height, x, in inches.
Answer:
Bianca's height = 42 inches
Step-by-step explanation:
Let x be the Bianca height.
Given:
Meredith height = 60 inches
We need to find the Bianca height.
Solution:
From the given statement the Meredith's height is [tex]\frac{2}{3}[/tex] of Bianca's height plus 32 inches, so the equation is.
Meredith's height = [tex]\frac{2}{3}(Bianca\ height)+32[/tex]
Substitute Meredith's height in above equation.
[tex]60=\frac{2}{3}x+32[/tex]
Now we solve the above equation for x.
[tex]\frac{2}{3}x=60-32[/tex]
[tex]\frac{2}{3}x=28[/tex]
By cross multiplication.
[tex]x=\frac{3\times 28}{2}[/tex]
28 divided by 2.
[tex]x= 3\times 14[/tex]
[tex]x=42\ in[/tex]
Therefore, the height of the Bianca is 42 inches.
When it is 2:00 p.m. in New York City, it is 9:00 PM in Athens. If you leave New York at 7:30 a.m. on Wednesday and fly to Athens over the course of 13 hours and 45 minutes, what time will it be in Athens when you land?a. 2:30 p.m. Wednesdayb. 9:15 p.m. Wednesdayc. 4:15 a.m. Thursdayd. 1:15 p.m. Thursday
Answer:
option (c) 4:15 a.m. Thursday
Step-by-step explanation:
Time difference in New York City and Athens = 7 hours
Now,
The flight leaves at 7:30 a.m on Wednesday i.e 7:30 hrs
Therefore,
the time in Athens at the time of leaving of flight = 7:30 hrs + 7 hours
= 14 : 30 hrs i.e 2 : 30 pm on Wednesday
now,
after the 13 hours and 45 minutes of flight time in Athens i.e
= 14 : 30 + 13 : 45
= 28 : 15 i.e 1 day and 4 : 15 hrs
This means Flight will land at 4 : 15 a.m on Thursday
Hence,
option (c) 4:15 a.m. Thursday
Answer:
C
Step-by-step explanation:
4:15am Thursday
Condo living room is in the shape of a rectangle has a area of three 60 ft.² the width of the living room is 58 it's what what is the length of the living room
Question is not proper, Proper question is given below;
Consuelo's living room is in the shape of a rectangle and has an area of 360 square feet. The width of the living room is [tex]\frac{5}{8}\ ft[/tex] its length. What is the length of the living room?
Answer:
Length of the living room is 24 feet.
Step-by-step explanation:
Given:
Area of the living room = [tex]360 \ ft^2[/tex]
We need to find the length of the living room.
Solution:
the length of the living room be 'l'.
Given:
Width of the living room [tex]\frac{5}{8}\ ft[/tex] of it length.
width [tex]w= \frac{5}{8}l[/tex]
It has been given that living room is in rectangular format.
So we can say that;
Area of living room is equal to length of the living room times width of the living room.
framing in equation form we get;
[tex]l\times w=360\\\\l\times\frac{5}{8}l=360\\\\\frac{5}{8}l^2=360[/tex]
Now Multiplying both side by [tex]\frac{8}{5}[/tex] we get;
[tex]\frac{5}{8}l^2\times\frac{8}{5}=360\times\frac{8}{5}\\\\l^2= 576[/tex]
Taking square root on both side we get;
[tex]\sqrt{l^2} =\sqrt{576} \\\\l=24 \ ft[/tex]
Hence Length of the living room is 24 feet.
The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of −5.65 m/s2 for 4.00 s, making straight skid marks 62.9 m long, all the way to the tree. With what speed (in m/s) does the car then strike the tree?
Answer: the speed with which the car strikes the tree is 27.025 m/s
Step-by-step explanation:
We would apply Newton's equation of motion. It is expressed as
S = ut + 1/2at²
Where
S represents the distance covered by the car
u represents the initial velocity of the car( the speed with which the car strikes the tree)
t represents the time taken to cover the distance
a represents the deceleration of the car.
From the information given,
S = 62.9 meters
a = - 5.65 m/s2
t = 4 seconds
Therefore
62.9 = u × 4 + 1/2 × - 5.65 × 4²
62.9 = 4u - 45.2
4u = 62.9 + 45.2
4u = 108.1
u = 108.1/4 = 27.025 m/s
Final answer:
The car's speed at the moment it strikes the tree, after decelerating with an acceleration of -5.65 m/s² for 4.00 seconds over a distance of 62.9 m, is calculated to be 22.6 m/s.
Explanation:
The question relates to the final speed of a car after it has been decelerating over a certain distance due to the driver applying the brakes. With an acceleration of −5.65 m/s² over a time period of 4.00 seconds, and the car making skid marks 62.9 m long, we are tasked with determining the speed at which the car eventually hits the tree.
To solve this problem, we first calculate the initial speed of the car before it started to decelerate. We use the kinematic equation: v = u + at, where 'v' is the final velocity (0 m/s, since the car eventually stops), 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time. Rearranging this equation to solve for 'u', we get u = v - at. Substituting the given values, we find that the initial velocity 'u' was 22.6 m/s.
However, to find the speed at which the car hits the tree implies we need to know the speed at a specific point before it comes to a complete stop, specifically at the end of the 62.9 m distance. For this, considering the constant deceleration, the car's speed when it strikes the tree can be considered to be the same as its speed just before deceleration, which is calculated to be 22.6 m/s.
Let A be the set of students at your school and B the set of books in the school library. Let R₁ and R₂ be the relations consisting of all ordered pairs (a, b), where student a is required to read book b in a course, and where student a has read book b, respectively. Describe the ordered pairs in each of these relations.
a) R₁ ∪ R₂
b) R₁ ∩ R₂
c) R₁ ⊕ R₂
d) R₁ − R₂
e) R₂ − R₁
Answer:a) {(a,b)[a is required to read book b or has read book b]}
b) {(a,b)[a has read book b that he was required to read)]
c) {(a,b)[a is either required to read book b or has read it but he has not read both)]
d) {(a,b)[a is required to read book b and he is yet to read book b)]
e) {(a,b)[a has read book b that was not required)]
Step-by-step explanation: The answers is a description of the explanation
The question asks about various operations with the sets R₁ and R₂, which represent the students and the books they are required to read and have read respectively. It looks at the union, intersection, symmetric difference, and difference of these two sets in relation to each other, where variables 'A' and 'B' represent a student and a book respectively.
Explanation:This is a question in set theory. We will be defining the different operations performed on the ordered pairs of two relations R₁ and R₂. Let's consider 'A' as a student studying in your school and 'B' be a book in the library, the ordered pairs (A, B) indicate the relationship between the student and the book.
R₁ ∪ R₂: Represents the union of the relations. This would contain all ordered pairs where 'A' is required to read 'B' (relation R₁) or 'A' has read 'B' (relation R₂).R₁ ∩ R₂: Represents the intersection of the relations. This would include all ordered pairs where 'A' is required to read 'B' (relation R₁) and 'A' has also read 'B' (relation R₂). In simpler terms, it's the books that students were required to read and they have read.R₁ ⊕ R₂: Represents the symmetric difference of the relations. This would contain ordered pairs where 'A' is either required to read 'B' or 'A' has read 'B', but not both.R₁ − R₂: Represents the difference of the relations. This includes all ordered pairs where a student 'A' is required to read a book 'B', but has not read it yet.R₂ − R₁: Represents the reverse difference of the relations. This set includes all ordered pairs where a student 'A' has read a book 'B' but was not required to read it for a course.Learn more about Set Theory here:
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how can you write the statement "obtuse angles have greater measures than acute angles" so that it is a good definition
Since obtuse angles are greater than 90 degrees and acute angles are less than 90 degrees, then obtuse angles have greater measures than acute angles.
Happy to help
Answer:
Step-by-step explanation:
obtuse angles >90
acute angles <90
Two physics students are doing a side competition during a game of bowling, seeing who can toss a ball with the larger momentum. The first bowler throws a 4.5 kg ball at 8.6 m/s. Part A A second bowler throws a 6.4 kg ball. What speed must she beat to win the competition?
Answer:
she should beat a speed of v₂ = 6.04 m/s in order to win the competition
Step-by-step explanation:
Since the momentum p is defined as
p = m*v
where
m= mass of the ball
v= velocity of the ball
denoting 1 and 2 as the first and second bowler , then to reach the momentum of the first bowler
p₂=p₁
therefore
m₁*v₁ = m₂*v₂
v₂ = v₁ * (m₁/m₂)
replacing values
v₂ = v₁ * (m₁/m₂) =8.6 m/s * (4.5 kg/6.4 kg ball) = 6.04 m/s
then since the momentum p = m*v increases with increasing v (at constant m) , she should beat a speed of v₂ = 6.04 m/s in order to win the competition
1.) Simplify the expression.
sin ( u + π/2 )
a.) tan u
b.) sin u
c.) csc u
d.) cos u
e.) cot u
Answer:
[tex]sin ( u +\frac{\pi}{2} ) = cos (u)[/tex]
Step-by-step explanation:
Let us use the identity
sin(A+B)= cos(A) sin(B)+cos (B) sin(A) to simplify the given expression
Then
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(u\right)[/tex]--------------------(1)
Here
[tex]cos (\frac{\pi}{2}) = 0\\[/tex]---------------------(2)
[tex]sin(\frac{\pi}{2})= 1[/tex]---------------------(3)
Substituting the values in (1)
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)(1)+(0)\sin \left(u\right)[/tex]
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right) + 0[/tex]
[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)[/tex]
1. Write the equation of the line with a slope of -5 and a y-intercept of (0,3). 2. Write the equation of the line with a slope of -1/3 and passing through the point (6, -4). 3. Write the equation of the line passing through the points (0, -4) and (-2, 2). 4. Write the equation of the line passing through the points (-6,1) and (-4,2). 5. Write the equation of the line with an undefined slope, passing through the point (2, 5). Hint: refer back to lesson 4.04 for help with this one.
Answer:
Step-by-step explanation:
1) The equation of a line is given by y = mx + c, where m = slope or gradient and c is intercept on y - axis. Given in this question, m = -5 and c = 3. Subtituting this in the equation y = mx + c, we have y = -5x + 3, therefore, the equation of the line is y = -5x + 3 or y + 5x = 3
2) The equation of a line is given as y-y1 = m(x-x1), where x1 = 6, y1 = -4 and m = -1/3. The equation of the line is y - -4 = -1/3(x - 6)
y+4 =-1/3(x-6)
3(y+4)= -1(x-6)
3y + 12 = -x+6
x+3y=6-12
x+3y= -6, therefore the equation of the line is x+3y = -6
3) The equation is y-y1=m(x-x1), where m=(y2-y1)/(x2-x1)=
(2- -4)/(-2-0)=6/-2=-3
y- -4= -3(x-0)= -3x
y+4= -3x
y+3x= -4
4) y-y1=m(x-x1)
m=(2-1) /(-4- -6)=1/2
y-1=1/2(x- -6)
y-1=1/2(x+6)
2(y-1) = x+6
2y-2=x+6
2y-x =6+2=8 2y-x=8
5) The equation is with undefined slope passing through (2, 5) is
x-2=0
x=2
You go out to pick blueberries and black berries. You know that to make a black and blue pie, you need to have 5 blueberries for every 2 blackberries you pick. If an entire pie has 140 berries, the pie contains_____ blueberries and ______ blackberries.
Answer:
100 blueberries and 40 blackberries
Step-by-step explanation:
Multiply each by 20 and you have 5 x 20 = 100 and 2 x 20 = 40
In the figure, . Find x and y.
Question 3 options:
a. x = 32, y = 137
b. x = 38, y = 151
c. x = 52, y = 137
d. x = 137, y = 52
Answer:
The answer to your question is x = 52° and y = 137°
Step-by-step explanation:
Process
1.- Find the value of x using the large right triangle, remember that the sum of the internal angles in a triangle equals 180°.
x + 38 + 90 = 180
x = 180 - 90 - 38
x = 52°
2.- To find y, we notice that x and y -9 are supplementary angles so their sum gives 180°.
x + y - 9 = 180
Substitution
52 + y - 9 = 180
y = 180 + 9 - 52
y = 137°
Luke's basketball team went to an amusement park at the end of the season. The cost of the admission for 5 coaches and 12 players was 407.50. The admission cost for each coach was 27.50. What was the admission cost for each player?
Answer:the admission cost for each player is $22.5
Step-by-step explanation:
Let x represent the admission cost for each player.
Luke's basketball team went to an amusement park at the end of the season. The cost of the admission for 5 coaches and 12 players was 407.50. The admission cost for each coach was 27.50. This means that
5 × 27.50 + 12x = 407.5
137.5 + 12x = 407.5
Subtracting 137.5 from the left hand side and the right hand side of the equation, it becomes
12x + 137.5 - 137.5= 407.5 - 137.5
12x = 270
Dividing the left hand side and the right hand side of the equation by 12, it becomes
12x/12 = 270/12
x = 270/12 = 22.5
Answer:
$22.5
Step-by-step explanation:
To find the cost for each player, first, let us find the cost of all coaches, then the rest will be for the players
Step 1: Multiply the cost for 1 coach by 5
[tex]27.50 \times 5 = 137.5[/tex]
Step 2: Subtract the result from the total amount of both players and coaches
[tex]407.50 - 137.5 = 270[/tex]
Now we have found the total cost of all 12 players. Next up, we need to find the cost of just one player
Step 3: Divide the result by the number of players
[tex]270 \div 5[/tex]
[tex]= \frac{270}{5}[/tex]
[tex]= 22.5[/tex]
The admission cost for each player was 22.5 dollars.
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.793. How confident can you be that your predicted value will be reasonably close to the actual value? A. I can’t be confident at all; this is about as close to a random guess as you can get. B. I can be a little confident; it might be close, or it might be way off. C. I can be very confident; it will be close, but it probably won’t be exact. D. I can be certain that my predicted value will match the actual value exactly.
Answer:
The correct option is c.
can be very confident; it will be close, but it probably won’t be exact.
Step-by-step explanation:
Correlation coefficient r lies between -1 and +1 , if r is close to +1 the variables compared are highly positively correlated. If r is close to -1 then the variables compared are highly negatively correlated. If r is close to zero then the correlation between the variables compared is low. If r=0 then the variables compared do not correlate at all.
The closer the correlation coefficient is to +1, the better the prediction.
Therefore since r=0.793 , the correlation coefficient is close to +1 , it means there is a highly positive correlation between variables. Therefore the correct option is c. If r is exactly +1 then we can say without any shadow of doubt that the prediction will be perfect.
A categorical variable whose values are purely qualitative and unordered is called a _______ variable. Please type the correct answer in the following input field, and then select the submit answer button or press the enter key when finished. Your answer:
Answer: Nominal
Step-by-step explanation:
A categorical variable whose values are purely qualitative and unordered is called a Nominal variable. Nominal variables are qualitative variables that does not have a particular rank, order or value. An example of nominal variables are colour (red,blue etc), gender (male, female), skin and hair colour etc.
An investigator reviewed the medical records of 200 children seen for care at Boston Medical Center in the past year who were between the ages 8 and 12 and identified 40 children with asthma. He also identified 40 children of the same ages who were free of asthma. Each child and their family were interviewed to assess whether there might be an association between certain environmental factors such as exposure to second-hand smoke. This study is an example of a:_______. a. randomized controlled trial. b. case-control study. c. cohort study. d. crossover trial.
Answer:
cohort study
Step-by-step explanation:
Given that an investigator reviewed the medical records of 200 children seen for care at Boston Medical Center in the past year who were between the ages 8 and 12 and identified 40 children with asthma. He also identified 40 children of the same ages who were free of asthma. Each child and their family were interviewed to assess whether there might be an association between certain environmental factors such as exposure to second-hand smoke.
The objective of this experiment is to test the causes of the disease asthma and to find the risk factors and environment causing this disease.
So this cannot come under randomized control nor case control.
Cross over study is to put to two different environments two groups and study. But here nothing is influenced actual environments are studied
Hence this comes under cohort study
Answer:
cohort study
Step-by-step explanation:
Use the formula for the probability of the complement of an event. A coin is flipped 4 times. What is the probability of getting at least 1 tail?
Answer: 15/16
Step-by-step explanation:
There will be 16 outcomes for 4 coins=2^4
Probability of only head is : P(C)=1/16
P(C) + P(C') = 1
P(C') = 1 - P(C)
P(C') = 1 - 1/16
Take the l.c.m
P(C') = (16-1) / 16
P(C') = 15/16
So the probability of getting at least 1 tail is 15/16
Answer:
D 0.94
Step-by-step explanation:
when solved the answer is 15/16. This equals 0.9375 which rounded to the second decimal = 0.94
A number is picked randomly in the range [2,8]. If past selection indicates that the numbers picked are less than 5, what is the probability that a number picked will be (a) less than 4 (b) greater than 4. What is the probability that the number picked is 4.5
Answer:
a) P = 2/7
b) P = 4/7
c) P = 1/7
Step-by-step explanation:
In the range of [2,8], we have the following integers which are: 2, 3, 4, 5, 6, 7, 8. So this is a total of 7 integers.
a) We look for the probability that the numbers are less than 4, so we conclude that there are possible numbers 2 and 3 out of possible 7, so the required probability is equal to P = 2/7.
b) We look for the probability that the numbers are greater than 4, so we conclude that there are possible numbers 5, 6, 7, 8 out of possible 7, so the required probability is equal to P = 4/7.
c) Based on the previous two examples, we conclude that the required probability is P = 2/7· 1/2=1/7.
A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (7, 4). What is the vector joining the ship to the rock?
Answer:
SR = (6,4)
Step-by-step explanation:
The ship position is (1,0)
The rocks position is (7,4)
SR is the vector line joining ship and rock
Using triangle law of addition
OS + SR = OR
SR = OR - OS
= ( 7 - 1 , 4 - 0)
= (6,4)
The vector line joining Ship and rock is (6,4)
Let A(t) be the area of the region in the first quadrant enclosed by the coordinate axes, the curve y = e −x , and the vertical line x = t, t > 0. Let V (t) be the volume of the solid generated by revolving the region about the x-axis. Find the following limits.
Answer:
I=\frac{t^2}{2}
Step-by-step explanation:
From exercise we have that x=t, t>0. Because A(t) be the area of the region in the first quadrant, we get that x started at 0. The limits for y are the following e-x and e. We get the integral :
I=\int\limits^0_t \int\limits^{e}_{e-x} 1 dy dx
I=\int\limits^0_t [y]_{e-x}^{e} dx
I=\int\limits^0_t (e-e+x) dx
I=\int\limits^0_t {x} \, dx
I=[\frac{x^2}{2} ]_{0}^{t}
I=\frac{t^2}{2}
The length of the entire border of the Unites States is approximately 32,000 miles, 5 8 of which is coastline. How long is the coastline of the U.S., and how long are the land boundaries?
Answer:the coastline is 20000 miles.
The land boundaries are 12000 miles.
Step-by-step explanation:
The length of the entire border of the Unites States is approximately 32,000 miles.
5/8 of the entire length is the coastline. It means that the length of the coastline of the U.S would be
5/8 × 32000 = 20000 miles.
Therefore, the length of the boundaries of the US would be
32000 - 20000 = 12000 miles.
A certain car costs $11,595 before taxes are added. Taxes are $860 and license tags cost $95. What is the overall tax rate (to the nearest tenth)?
A. 0.8%
B. 7.4%
C. 8.2%
D. 12.1%
Answer:
The answer is B)7.4%
Step-by-step explanation:
Pure cost of the car is 11595$. It is stated that taxes costs 860$ for the car. To find the overall tax rate we need to simply divide tax value to car original cost.
[tex]860/11595=0.074[/tex]
Lucy's Lunch and Latte has found that customers are put off by the local tourism tax of 9% that is added to their bill. If Lucy decides to cover the tax herself, rather than adding it to the customer's bill, what percent will the customer see in savings? Write your answer as a percent rounded to the nearest tenth. (Hint: the answer is not 9%.)
Answer:
Customer will save 8.3%.
Step-by-step explanation:
Let the amount of bill paid by the customers = $x
Local tourism tax = 9%
Total amount of bill including local taxes
= (x + 9% of x)
= x + 0.09x
= 1.09x
If Lucy decides to pay the tax portion of the bill = 0.09x
Then percentage saving by the customer = [tex]\frac{\text{Taxes on bill}}{\text{Bill amount including tax}}\times 100[/tex]
= [tex]\frac{0.09x}{1.09x}\times 100[/tex]
= 8.26%
≈ 8.3%
Therefore, customer will see 8.3% saving.
Jayden has some dimes and some quarters. He has at most 25 coins worth at least $4.60 combined. If Jayden has 7 dimes, determine all possible values for the number of quarters that he could have.
Answer:
16,17,18
Step-by-step explanation:
\underline{\text{Define Variables:}}
Define Variables:
May choose any letters.
\text{Let }d=
Let d=
\,\,\text{the number of dimes}
the number of dimes
\text{Let }q=
Let q=
\,\,\text{the number of quarters}
the number of quarters
\text{\textquotedblleft at most 25 coins"}\rightarrow \text{25 or fewer coins}
“at most 25 coins"→25 or fewer coins
Use a \le≤ symbol
Therefore the total number of coins, d+qd+q, must be less than or equal to 25:25:
d+q\le 25
d+q≤25
\text{\textquotedblleft at least \$4.60"}\rightarrow \text{\$4.60 or more}
“at least $4.60"→$4.60 or more
Use a \ge≥ symbol
One dime is worth $0.10, so dd dimes are worth 0.10d.0.10d. One quarter is worth $0.25, so qq quarters are worth 0.25q.0.25q. The total 0.10d+0.25q0.10d+0.25q must be greater than or equal to \$4.60:$4.60:
0.10d+0.25q\ge 4.60
0.10d+0.25q≥4.60
\text{Plug in }\color{green}{7}\text{ for }d\text{ and solve each inequality:}
Plug in 7 for d and solve each inequality:
Jayden has 7 dimes
\begin{aligned}d+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10d+0.25q\ge 4.60 \\ \color{green}{7}+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10\left(\color{green}{7}\right)+0.25q\ge 4.60 \\ q\le 18\hspace{10px}\text{and}\hspace{10px}&0.70+0.25q\ge 4.60 \\ \hspace{10px}&0.25q\ge 3.90 \\ \hspace{10px}&q\ge 15.60 \\ \end{aligned}
d+q≤25and
7+q≤25and
q≤18and
0.10d+0.25q≥4.60
0.10(7)+0.25q≥4.60
0.70+0.25q≥4.60
0.25q≥3.90
q≥15.60
\text{The values of }q\text{ that make BOTH inequalities true are:}
The values of q that make BOTH inequalities true are:
\{16,\ 17,\ 18\}
{16, 17, 18}
Jayden must have at least 16 quarters in order to have at most 25 coins worth at least $4.60 combined.
Explanation:Let's assume Jayden has x quarters. Since Jayden has 7 dimes, he has a total of 7 + x coins. The value of a dime is $0.10, so the value of the dimes is 7 × $0.10 = $0.70.
The value of a quarter is $0.25, so the value of the quarters is x × $0.25 = $0.25x. The total value of all the coins is at least $4.60, so we have the equation:
$0.70 + $0.25x ≥ $4.60.
Simplifying the equation, we get:
$0.25x ≥ $4.60 - $0.70
$0.25x ≥ $3.90
x ≥ $3.90 / $0.25
x ≥ 15.6
Since we can't have a fraction of a coin, Jayden must have at least 16 quarters in order to have at most 25 coins worth at least $4.60 combined.
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The inverse of a cosine function is the
function ___
arcsine
secant
arccosine
cosecant
Answer:
cosecant
Step-by-step explanation:
Inverse Cosine
cos-1
Cos-1
arccos
Arccos
The inverse function of cosine.
Basic idea: To find cos-1 (½), we ask "what angle has cosine equal to ½?" The answer is 60°. As a result we say cos-1 (½) = 60°. In radians this is cos-1 (½) = π/3.
More: There are actually many angles that have cosine equal to ½. We are really asking "what is the simplest, most basic angle that has cosine equal to ½?" As before, the answer is 60°. Thus cos-1 (½) = 60° or cos-1 (½) = π/3.
Details: What is cos-1 (–½)? Do we choose 120°, –120°, 240°, or some other angle? The answer is 120°. With inverse cosine, we select the angle on the top half of the unit circle. Thus cos-1 (–½) = 120° or cos-1 (–½) = 2π/3.
In other words, the range of cos-1 is restricted to [0, 180°] or [0, π].
Note: arccos refers to "arc cosine", or the radian measure of the arc on a circle corresponding to a given value of cosine.
Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Cos or Cos-1). However, most mathematicians do not follow this practice. This website does not distinguish between capitalized and uncapitalized trig functions.

See also
Inverse trigonometry, inverse trig functions, interval notation
The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called__________
Answer:
Metaphysics
Step-by-step explanation:
Metaphysics is a system of reasoning or process that is often employed to find answers through examining fundamental nature of reality, the relationship between minds and also knowledge.
The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called philosophy.
The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called philosophy.
Philosophy is the discipline that seeks to explore and understand the fundamental aspects of existence, including the nature of reality, the principles of ethics and morality, and the limits of human knowledge. It involves the rigorous examination of concepts, arguments, and ideas to gain deeper insights into the nature of the world and our place in it.
Philosophers engage in critical thinking and analysis to address questions related to the meaning of life, the nature of truth, the basis of ethics, and the foundations of human understanding. Through philosophical inquiry, individuals seek to develop a deeper and more comprehensive understanding of the complex issues that shape our lives and society.
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