The coordinates of Casper which lies exactly in the middle of Denton and Beacon are (-4, -1).
What are the Coordinates?Coordinates are defined as the set of points in a coordinate plane or space, which describes the position of that point in that plane or space.
In a coordinate plane, the midpoint of two points (x₁, y₁) and (x₂, y₂) is the point (x, y) such that their measures are,
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
First, we can write the given measures.
Coordinates of Albion = (5, 5)
Coordinates of Denton = (-7, -3)
Given that, Beacon is lying exactly in the middle of Albion and Denton.
Let the coordinates of Beacon be (x, y).
Using the formula above,
x coordinate of Beacon = (5 + -7) / 2 = -1
y coordinate of Beacon = (5 + -3) / 2 = 1
Coordinates of Beacon are thus (-1, 1).
Casper is lying exactly in the middle of Denton(-7, -3) and Beacon (-1, 1).
Let (x' , y') be the coordinates of Casper.
Using the same formula,
x' = (-7 + -1) / 2 = -4
y' = (-3 + 1) / 2 = -1
Hence the coordinates of Casper are (-4, -1).
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Four years ago, the sum of ages of father and his son was 27 years. After five years, the ratio of the ages of the son and father will be 2: 7. Find the present ages of father and his son. Ans: 30 yrs, 5 yrs
Step-by-step explanation:
x current age of the father
y current age of the son
first equation (x-4)+(y-4)=27 so x=27+4+4-y=35-y
second equation (y+5) : (x+5)= 2:7
so (y+5)*7=(x+5)*2
let's replace x we found at the first equation with the one at second equation
(y+5)*7=(35-y+5)*2
7y+35=(40-y)*2
7y+35=80-2y
7y+2y=80-35
9y=45
y=5
x=35-y=35-5=30
Ashley created 3 music playlists using a total of 48 rock and pop songs. Each playlist has 9 rock songs. Each playlist also has the same number of pop songs. Which equation could be used to determine the number of pop songs, x
, Ashley has in each playlist?
Responses
1. x(3+9)=48
2. 3(x+9)=48
3. 3x+9=48
4. 9x+3=48
Answer:
2. 3(x + 9) = 48
Step-by-step explanation:
We are given
There are a total of 3 playlistsThere are a total of 48 rock and pop songsEach playlist has 9 rock songsEach playlist has x pop songsIf each playlist has 9 rock songs and x pop songs, then each playlist has 9 + x songs.
If there are three playlists, there are three playlists which each have x + 9 songs. In other words, 3(x+9). This represents the total number of songs, which is 48. Therefore the answer is 3(x+9)=48.
Hope this helps!
Anna runs 3/4 miles in 6 minutes, or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour?
Speed of Ana = 7.5miles/hour
Step-by-step explanation:
Given,
Ana runs 3/4 mile in 6 minutes.
To find,
The speed of Ana in miles per hour
Recall the formula,
Speed = distance travelled/time taken
60 minutes = 1 hour
Solution:
Distance traveled = 3/4 mile
Time taken = 6 minutes
Since 60 minutes = 1 hour, we have
1 minute =1/60 hour
6 minutes = 6/60 hour
=1/10 hour
Hence speed = distance travelled/time taken
= 3/4 / 1/10 miles/hour
= 15/2 miles/hour
= 7.5miles/hour
∴ Speed of Ana = 7.5miles/hour
the sun is shining and a spherical snowball of volume 260 ft3 is melting at a rate of 11 cubic feet per hour. as it melts, it remains spherical. at what rate is the radius changing after 6.5 hours?
If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h .
A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.
We have to find the rate at which the radius is changing after 6.5 hours.
So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.
Volume Of Sphere is V = (4/3)πr³ and dV/dt = -11 ft³/h ;
So, dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt) ;
derivative of volume formula with respect to "r", we get:
⇒ dV/dr = 4πr² ;
Substituting the given values in chain rule equation, we get:
⇒ -11 = (4/3)πr² × dr/dt ;
⇒ dr/dt = -11/((4/3)πr²)
For rate of change of the radius when t = 6.5 hours, we find the radius at that time.
The initial volume of the snowball = 260 ft³.
After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be: V = 260 - (11 × 6.5) = 188.5 ft³ ;
So , V = (4/3)πr³
⇒ 188.5 = (4/3)πr³
⇒ r³ = (188.5 × 3 / (4π)) ;
≈ 3.55ft
Now we substitute r = 3.55 feet
⇒ dr/dt = -11/[(4/3)π(3.55)²] ;
⇒ dr/dt ≈ -0.208 ft/h ;
Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing .
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To plot the point (6, -8), you would start at the origin and move
6 units to the ____ and
8 units ______
up, down, left, right
The coordinates ( 6,-8 ) are plotted by moving 6 units right and 8 units down.
What is the cartesian plane?The intersection of the x- and y-axes creates the two-dimensional coordinate plane known as the cartesian plane. The origin is the point at which the x- and y-axes cross perpendicularly.
here, we have,
Given coordinates (6,-8)
for the cartesian plane, we know that the origin has points (0, 0)
and divided into four Quadrants,
the left side of the origin is a negative x-axis and the right side is a positive x-axis.
and the upside of the origin is a positive y-axis and the downside is a negative y-axis.
here coordinates of x =6 and y = -8
6 is 6 units right from the origin
and -8 is 8 units down from the origin.
Hence for the coordinates , 6 units to the right and 8 units down , is correct.
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Please help i’ll give brainliest
Answer: 4.5
Step-by-step explanation:
The table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify the correlation of coefficient. Round your answer to three decimal places
The value of correlation cofficient between the number of people who complete successfully complete each jump, y and height of jump, x is equals to the - 0.091.
We have a table which consists height ( in feet ), x and completions, y present above figure. We have to calculate the correlation coefficient for variables x and y. Correlation coefficients are used to measure how strong the relationship is between two variables. The commonly used cofficient in linear regression is Pearson's correlation (also called Pearson's R) coefficient . Formulas return a value between -1 and 1, where,
A strong positive relationship, r = 1Strong negative relationship, r= -1A result of zero indicates no relationship at all.Formula used to determine the cofficient is r = (n∑ xy - (∑x)(∑y))/√[ n∑x² - (∑x)²][n∑y² - (∑y)²]
Here, n = 6, ∑xy = 375.8 , ∑ x =22.4, ∑y
= 102, ∑ x² = 96.5, ∑y² = 1978
so, r = 6×(375.8) - 102(22.4))/√[(6×96 - (22.4)²)(6×1978 - 102²)]
= -30/329.68
= - 0.091
Hence, required value of r is - 0.091.
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Complete question:
The above table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify the correlation of coefficient. Round your answer to three decimal places.
WILL MARK BRANLIEST!!! PLEASE HelP
The sum of the geometric sequence for this problem is given as follows:
S = 665.
How to obtain the sum?The sum of the first n terms of a geometric sequence of first term [tex]a_1[/tex] and common ratio q is given by the equation presented as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
The parameters for this problem are given as follows:
[tex]a_1 = 32, n = 6, r = 1.5[/tex]
Hence the sum is obtained as follows:
S = 32 x (1 - 1.5^6)/(1 - 1.5)
S = 665.
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write the equation for the given graphs. How do we find the "a" value?
The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11
How to determine the equations of the graphsFrom the question, we have the following parameters that can be used in our computation:
The graphs
The lines are absolute function graphs, and they can be represented as
y = a|x - h| + k
Where
Vertex = (h, k)
For the blue line, we have
(h, k) = (2, -5) and (x, y) = (0, -4)
So, we have
-4 = a|0 - 2| - 5
2a = 1
a = 1/2
So, the equation is y = 1/2|x - 2| + 5
For the red line, we have
(h, k) = (-2, 3) and (x, y) = (0, -11)
So, we have
-11 = a|0 + 2| + 3
2a = -14
a = -7
So, the equation is y = -7|x + 2| - 11
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43. given a standard deck of 52 playing cards, where half (clubs and spades) are black and half (hearts and diamonds) are red, what is the probability of picking three black cards in a row if the cards are not replaced?
The probability of picking three black cards in a row, without replacement, from a standard deck of 52 playing cards is 2/17, or approximately 0.1176 (rounded to four decimal places).
The probability of picking a black card on the first draw = 26/52 = 1/2
(since there are 26 black cards in the deck)
The probability of picking a black card on the second draw, given that a one was picked on the first draw and the card is not replaced = 25/51,
(since there are now only 25 black cards left out)
The probability of picking a black card on the third draw, given that the ones picked on the first two draws are not replaced = 24/50 = 12/25,
(since there are now only 24 black cards left out)
To pick three black cards in a row, we need to multiply the probabilities of each individual draw = (1/2) * (25/51) * (12/25) = 6/51
Simplifying this fraction, we get = 6/51 = 2/17
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to decide which thing of coffee is better value-for-money calculate the price per gram of a 250 g of coffee for 2949 stands and a 750 grams of coffee for $69.99
The second option has the better value-for-money.
Which coffe has the better value-for-money?To find the price per gram, you need to take the quotient between the cost and the mass for each case.
The first brand costs $29.49 for 250 grams, then the cost is:
c = $29.49/250g = $0.12 per gram.
The other brand costs $69.99 for 750 grams, then the cost per gram is:
C = $69.99/750g = $0.09 per gram
We can see that the second option has the better vale-for-money.
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SOMEBODY PLEASE HELP ME ASAP I WILL LOVE YOU FOREVER
By determining the value of x when y = 0, (x, 0), and the value of y when x = 0, respectively, the x-intercept and y-intercept are determined (0, y).
What is linear equation?A two-variable equation with a line-shaped graph is referred to as a linear equation. A collection of coordinate plane points that are all the solutions to the linear equation make up the graph. If all of the variables have true numerical values, the equation can be graphed by first drawing a sufficient number of points to identify a pattern, then connecting those points to include all of the points.
A linear equation is represented in standard form as
Ax+By=C,A,B≠0
The equation for y must first be solved before you may graph a linear equation in its usual form.
The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).
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QuestionIntermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the intervalATrueBFalse
The given statement about the intermediate value theorem is false
The given statement is
"Intermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"
But according to Intermediate value theorem "if a continuous function f with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"
So if we takes discontinuous function the given statement will be wrong
Therefore, the statement is false
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in hypothesis testing, the alternative hypothesis is . a. the hypothesis tentatively assumed true in the hypothesis-testing procedure b. the hypothesis concluded to be true if the null hypothesis is rejected c. the maximum probability of a type i error d. the maximum probability of a type ii error
Answer:
taking your points
Step-by-step explanation:
2. 10,175 rounded to the nearest thousand 0 is the target, aka the number place I’m rounding to
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.30 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
The total cost of the meal is $
Answer:
$82.21
Step-by-step explanation:
cost of meal: $78.30
15% discount: 15% of $78.30 = 0.15 × $78.30 = $11.75
tip: 20% of $78.30 = 0.20 × $78.30 = $15.66
total cost = $78.30 - $11.75 + 15.66 = $82.21
Answer: $82.21
Find your Average daily balance
Scenario 2: You have a credit card with 25% APR. You have a classic car/truck you
are restoring and decide to buy some things with your new credit card. At the
beginning of your You buy new wheels and tires for 1500 dollars You don't buy
anything else for 14 days. However, your battery dies and your brake calipers start
leaking so you spend another 500 dollars. You don't buy anything else for the rest
of the month. You also don't make any payments. Your billing cycle is 30 days.
Follow the steps to calculate how much interest will be charged at the end of the
billing cycle.
The Average daily balance of the given scenario is $2083.
What is the amount of a fixed period payment to be done to pay off the loan amount which is increasing compoundly?Suppose we're given that:
P_v = Present value of the loan amount
r = rate of interest (compound interest) per period of time
n = number of period of time in which loan is to be paid off
P = A fixed period payment needed to be done for paying off the loan in n number of periods.
Then, we get:
[tex]P = \dfrac{r\times P_v}{1 - (1 + r)^{-n}}[/tex]
Given;
APR= 25%
Cost of wheels and tires= $1500
Time=14days
Cost of brake calipers and leaking= $500
Time=30days
Now,
P= 25x2000/1-(1+25)^-30
P=50000/24
P=2083
Therefore, the monthly balance of loan will be $2083.
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if you want to wear 4 of your 10 bow ties next week (monday through sunday), how many ways can this be accomplished?
There are 10/4 ways ( [tex]\frac{10}{4}[/tex] ) to accomplish the given task by wearing the ties for a week according to the permutations and combinations.
Given if you wear tie for a week, where one need t wear 4 of his ties from the 10 of total. The number of ways to wear the ties will be equal to the value. So there are many ways to wear a tie of different types and also to remove the tie there are different ways. Now we will see the ways to wear a tie accordingly.
According to the permutations and combination rules the formula will be:
Number of ways: (Number of ties want to wear) / (Number of Total ties)
Therefore total number of ways to wear ties = 10/4
Number of ways this can be accomplished is 10/4
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Solve the system of equations. State the decimal solution to the nearest hundredth.
2.5x+3.75y=10.5
1.25x−8.5y=−5.25
The solution to the system of equations is (2.68, 1.01)
How to solve the system of equationsFrom the question, we have the following parameters that can be used in our computation:
2.5x+3.75y=10.5
1.25x−8.5y=−5.25
Express properly
2.5x + 3.75y = 10.5
1.25x − 8.5y = −5.25
Next, we make a plot of the system to determine the solution
The point of intersection in the plot represent the solution to the equations
In this case, the intersection has a coordinate of (2.68, 1.01)
Hence, the solution is (2.68, 1.01)
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simplify 3 to the -2 power
Answer: 0.1 decimal 1/9 fraction
Step-by-step explanation:
Answer:
0.1 or 1/9 i think so but I am sure
Solve for the value of d.
(8d+4)⁰
(6d+8)⁰
Hi there, here's your answer:
Given 2 angles:
(6d + 8)° and (8d + 4)°
Observe the figure carefully. You will notice that the two angles form a linear pair.
We know that in a linear pair, sum of the two angles = 180°.
Hence,
(8d + 4 + 6d + 8)° = 180°
(14d + 12)° = 180°
(14d)° = (180 - 12)°
= 14d = 168°
Or
d = 12
Thus, we find the value of d to be d = 12.
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Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats. Ice Cream (cups) Soda (cups) 3.5 10.5 8 24 12.5 37.5 17 ? At this rate, how much soda will Sidney use for 17 cups of ice cream? 42 cups 51 cups 54 cups 62 cups
Answer: the correct answer is 51
Step-by-step explanation: i solved this on my quiz
i hope this helps!
Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.
What is the ratio?
A ratio is a relationship between two things when it is expressed in numbers or amounts. For example, if there are ten boys and thirty girls in a room, the ratio of boys to girls is 1:3, or one to three.
We can start by noticing that the ratio of cups of ice cream to cups of soda used to make the floats is always 1:3.
To find out how much soda Sidney will use for 17 cups of ice cream, we can set up a proportion:
3.5/10.5 = 8/24 = 12.5/37.5 = 17/x
Solving for x, we can cross-multiply:
3.5x = 10.5 * 17
x = 54
Therefore, Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.
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Students at the college
answer:
Huh?
Step-by-step explanation:
students at the college what...?
3. Meenakshi bought 12 books, each costing 250.75, if she gave the shopkeeper ₹ 4000. How much money will returned?
ans
4. One crayon set costs 25. How many crayon sets can be bought for rupees 2750
ans
5. Manu goes to buy a new bicycle in an exchange offer. The price of the new bicycle is bike on exchange is he pays for his new bike?
ans
pls put the questin number and give the answer
3. The amount that should be returned to Meenaski for buying 12 books worth R250.75 each and giving the shopkeeper R4,000, using mathematical operations, is R991.
4. The number of crayon sets that can be bought for R2,750 if one set costs R25, using division operation, is 110.
5. Manu will pay R1,700, exchanging his old bike for a new bike.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
These mathematical operations are performed to solve algebraic problems using the relevant mathematical operands and rules.
Books:The number of books bought = 12
The unit cost of each book = R250.75
The total cost of the 12 books = R3,009 (R250.75 x 12)
The amount advanced to the cashier = R4,000
The balance to be returned = R991 (R4,000 - R3,009)
Crayon:The cost of a set of crayon = R25
The amount of money for the purchase = R2,750
The number of crayon sets that can be bought with R2,750 = 110 (R2,750/R25).
Bicycle:The price of the new bicycle = R2,500
The value of the old bike for exchange = R800
The amount to be paid = R1,700 (R2,500 - R800)
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Question Completion:The price of the new bicycle is R2,500. The bike on exchange is worth R800. How much does he pay for his new bike?
pins each cost £1.10
1000 pins are sold
35% of the pins are donated to charity
the rest are sold: 60% are sold for £3
40% are sold are sold £5 for 2
work out the percentage profit the company should make
The profit is £1,370. Then the percentage profit of the company will be 124.54%.
What is a profit?A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.
The profit is given as,
Profit = Selling price - Cost price
The number of pins left after the donation to charity is given as,
⇒ (1 - 0.35) x 1,000
⇒ 0.65 x 1,000
⇒ 650 pins
The selling price when 60% are sold for £3 and 40% are sold for £5 is given as,
Selling price = 0.60 x 650 x £3 + 0.40 x 650 x £5
Selling price = £1,170 + £1,300
Selling price = £2,470
The cost price is given as,
Cost price = £1.10 x 1,000
Cost price = £1,100
The profit is given as,
P = £2,470 - £1,100
P = £1,370
Then the percent of profit is given as,
P = [(£1,370) / £1,100] x 100
P = 124.54%
The profit is £1,370. Then the percentage profit of the company will be 124.54%.
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What percentage of winners driving a chevrolet won with an average speed of at least miles per hour?
The percentage of winners driving a Chevrolet who won with an average speed of at least miles per hour is fifty percent (50%).
We can infer that for a Chevrolet car,
the percentage of average speed (in miles/hour) for the range of 150-159.9 is 25%,
the percentage of average speed (in miles/hour) for the range of 160-169.9 is 18.75%,
and the percentage of average speed (in miles/hour) for the range of 170-179.9 is 6.25%.
Thereby, the percentage of winners of the race who were driving a Chevrolet and had an average speed of at least 150 miles/hour is,
50%.
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The vertex form of the function is y = (x +)2+.
The vertex form of the function is [tex]y = (x+4)^{2} - 19[/tex]
Vertex form of function:
The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.
The vertex form of the equation is written as,
[tex]y = (x+h)^{2} + k[/tex]
Given function is,
y = x² + 8x + 16 - 3 -16
It is observed that,
x² +8x + 16 = (x+4)²
So that, we can write as above function,
y = x² + 8x + 16 - 3 -16 = (x+4)² - 3 -16
or
y = (x+4)² - 19
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if we are given a right-tail probability (or area) a and want a measurement m, which function in excel should we use? assume that the mean of the distribution is mu and the standard deviation is sigma.
The function in Excel that we should use to find a measurement M given a right-tail probability (or area) A is = NORM.INV(1-A, mu, sigma)
In order to find a measurement M given a right-tail probability A in Excel, we can use the NORM.INV function. The NORM.INV function in Excel returns the inverse of the normal cumulative distribution for a given probability.
The formula for NORM.INV function is:
= NORM.INV(1-A, mu, sigma)
where:
A is the right-tail probability (or area)
mu is the mean of the distribution
sigma is the standard deviation
The function returns the measurement M such that the right-tail area from M to infinity under the normal curve is equal to A.
Note - In some versions of Excel, the function may be called NORM.INV.RT instead of NORM.INV.
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A snail moves at a speed of 2 feet per minute. How many yards will the snail have moved in one hour? The snail has moved a total of
3
yards
The snail moves a distance of 40 yards in one hour as it moves at a speed of 2 feet per minute.
We can start by converting the speed of the snail from feet per minute to yards per hour, since the distance moved is given in yards per hour.
There are 60 minutes in an hour, so the snail's speed in yards per hour is:
2 feet per minute * 60 minutes per hour * (1/3) yards per foot = 40 yards per hour
Hence,
The snail moves a distance of 40 yards in one hour.
Since we are given that the snail has moved a total of 3 yards, we can find the amount of time it took by dividing the distance by the rate:
time = distance / rate
time = 3 yards / 40 yards per hour
time = 0.075 hours or 4.5 minutes
Therefore, the snail will move a distance of 3 yards after 4.5 minutes and distance of 40 yards in one hour.
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Please help I don't understand.
The surface area of the sphere is 113.2 ft².
Surface area of the Sphere:The area that a sphere's outer surface covers in three dimensions is known as the surface area of the Sphere. A sphere is a three-dimensional solid that resembles a circle in shape and is round.
The formula for a sphere's total surface area is given by
Surface area = 4 π r² square unitsHere we have
The formula for the radius of a sphere r = 1/2 [√S/π]
Diameter of the Moeraki boulder radius = 3 feet
=> 3 feet = 1/2 [√S/π]
=> 6 = [√S/π]
Squaring on both sides
=> 36 = [√S/π]²
=> S/π = 36
=> S = 36π
=> S = 113.2
Therefore,
The surface area of the sphere is 113.2 ft².
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