Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35 mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose's speed.
========================================================
Explanation:
x = Jose's speed in mph
x+35 = Kayla's speed since she drives 35 mph faster than Jose
Jose gets a 2.1 hour head start and it takes Kayla 1.2 hours to reach him. So this means Jose has been driving for 2.1+1.2 = 3.3 hours when Kayla reaches him. The distance he travels is
distance = rate*time
d = r*t
d = x*3.3
d = 3.3x
while Kayla's distance equation is
d = r*t
d = (x+35)*1.2
d = 1.2x+42
Since Kayla meets up with Jose at the 1.2 hour mark, this means the two distances they travel is the same. Set their distance expressions equal to one another. Solve for x.
3.3x = 1.2x+42
3.3x-1.2x = 42
2.1x = 42
x = 42/(2.1)
x = 20
Jose's speed is 20 mph, while Kayla's speed is x+35 = 20+35 = 55 mph.
Jose's fairly slow speed is probably due to a number of factors such as heavy traffic, icy roads, or poor visibility. Kayla probably got a bit of a break with more favorable conditions.
Since Jose travels at 20 mph and does so for 3.3 hours, he travels d = r*t = 20*3.3 = 66 miles. Kayla travels d = r*t = 55*1.2 = 66 miles as well. We get the same number each time to help confirm the answer.
LOOK AT THE PICTURE ATTACHED AND HELP QUICKLLYYYYY PLZZZ!!!!
Answer: √490
Step-by-step explanation:
How do you find the Dilation of 1.5? Also how would you write the Algebraic representation?
Answer:
Multiply each coordinate point by 1.5, y=1.5x
Step-by-step explanation:
please please help!
Answer:
Option B is the correct answer
Step-by-step explanation:
Given that
[tex]\sin \theta =\frac{-1}{\sqrt{2}}[/tex]
Value of sine function is negative in third and fourth quadrant
Hence this is true for
[tex]\theta =225^{0},315^{0}[/tex]
Option B is the correct answer
[tex]\displaystyle \text{Find the summation given that } f(x) = x^3 \text{ and } \triangle x_i = 2 + \frac{i}{4}. \\ \\\[ \sum_{i = 1}^{4} x^3 \times \triangle x[/tex]
Answer:
Click the picture and u will see the answer.
#CarryOnLearning
The summation of the given function from 1 to 4 is 10.5x³.
The given parameters:
[tex]\Sigma \ x^3 \times \Delta x, \ \ \ \Delta x = 2 + \frac{i}{4} \\\\[/tex]
The summation of the given function from i = 1, to i = 4, is calculated as follows;
[tex]\Sigma \ x^3 \times \Delta x = x ^3 (2 + \frac{1}{4} ) + x ^3 (2 + \frac{2}{4} ) + x ^3 (2 + \frac{3}{4} ) + x ^3 (2 + \frac{4}{4} )\\\\= x^3(10\frac{1}{2} )\\\\=\frac{21}{2} x^3\\\\= 10.5x^3[/tex]
Thus, the summation of the given function from 1 to 4 is 10.5x³.
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Help help math math math
Answer:
[tex]slope = \frac{20 - 16}{5 - 3} [/tex]
[tex] = \frac{4}{2} [/tex]
[tex] = 2 \: is \: the \: answer[/tex]
The slope of the equation is 2.
What is the slope of an equation?The slope of an equation shows a gradient line that measures the steepness of the line.
It can be expressed by using the formula:
[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]
[tex]\mathbf{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
From the parameters given;
The change in y distance from y2 to y1 The change in x distance from x2 to x1[tex]\mathbf{slope = \dfrac{20-16}{5-3}}[/tex]
[tex]\mathbf{slope = \dfrac{4}{2}}[/tex]
slope = 2
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Given the set of numbers, 2, 3, 4, 8, 10 with mean = 6 The Second moment about the mean for this set is?
Answer:
Given,
2,3,4,8,10
ex=2+3+4+8+10+x
=27+x
mean=6
no of data=5
now,
mean = ex/n
or,6=27+x/5
or,5×6=27+x
or,30=27+x
or,30-27=x
3=x
Mark which expressions represent the distance between 46 and-15
T is the midpoint of RS, T has coordinates (6, 4), and S has coordinates (3,-2). What are the
coordinates of R?
Answer:
help
Step-by-step explanation:
Use the following table to answer the questions below. Give your probabilities as DECIMALS rounded to the hundredths place.
Fair Hair
Dark Hair
Blue Eyes
8
5
Other
7
10
Jamie investigated hair and eye color.
One of the people is chosen. Calculate the probability of choosing
a. Someone with Blue eyes
b. Someone with fair hair and blue eyes
A person with dark hair is chosen. Calculate the probability of
1. them having blue eyes.
2. them not having blue eyes
Answer: 1 =.43, 2=.26, 3=.16 4=.33
Step-by-step explanation: So to find all these answers we have to know the total number of people in the chart 30. Then we have to find what info we need from the chart and divide it by the total number of people. I hope this helped I tried to make it simple.
Which is an advantage of using a credit card?
A. You can make purchases when you don’t have cash
B. You don’t indulge in impulse buying
C. You don’t have to pay interest
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
On a number line, point O is at -7, and point P is at 8. Point N lies between points O and P. If the ratio of ON to NP is 4:8, where does point N
lie on the number line?
Point N is at
on the number line.
Answer:
N is at -2 on the number line
Step-by-step explanation:
The location of point N can be found by writing the segment lengths as a proportion.
ON : NP = 4 : 8
8(ON) = 4(NP) . . . . . . . . "cross multiply"
2(N -O) = (P -N) . . . . . divide by 4, show lengths ON and NP
2(N -(-7)) = 8 -N . . . . . use given values of O and P
3N = -6 . . . . . . . . . . . add N-14 and simplify
N = -2 . . . . . . . . . . divide by 3
Point N is at -2 on the number line.
If the ratio of ON to NP is 4:8, point N lie on the -2 at the number line.
Point O is at -7.
Point P is at 8.
The ratio of ON to NP is 4:8.
The ratio 4:8 simplifies to 1:2. This means that ON is one-third of the total distance from O to P, and NP is two-thirds of the total distance.
The total distance from O to P is the sum of the distances between O and N, and between N and P.
As the ratio of ON to NP is 1:2, and the total distance is 15 (8 - (-7) = 15), we can set up the following equation:
ON/NP = 1/2
ON/(15 - ON) = 1/2
Now we can solve for ON:
2 × ON = 15 - ON
3 × ON = 15
ON = 5
So, ON is 5 units away from O.
Now O is at -7, point N is at -7 + 5 = -2 on the number line.
So, N is at -2.
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1/2 2/5 6/10 least to greatest
Answer:
2/5, 1/2, 6/10
Step-by-step explanation:
did problem
Answer:
1. 2/5
2. 1/2
3. 6/10
Step-by-step explanation:
Hope this helps
May I get braineist pls
(I WILL GIVE BRAINLIEST) PLEASE HELP!
Answer:
Option D
Step-by-step explanation:
Step 1: Determine the correct option
Option A, this option doesn't work because -3.46 is not greater than -2 1/3. Although the number 3 is greater than 2, these numbers are negative therefore the bigger the negative number, the smaller the number actually is.
Option B, this option doesn't work because 16/5 is not greater than 6. If we convert 16/5 into a decimal we get 3.2 and this number isn't bigger than 6.
Option C, this option doesn't work because once again it states that -3.46 is greater than -2 1/3 when in reality it's actually smaller.
Option D, this option does work because everything goes according the way it should. -3.46 is smaller than -2 1/3 and -2 1/3 is smaller than -3/4 and -3/4 is smaller than 16/5 and 16/5 is smaller than 6.
Answer: Option D
Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.
Formula for a converging infinite series. a1 is the first term and r is the common ratio.
A. 4
B. 1.33
C. 5.33
Answer:
4
Step-by-step explanation:
This is an infinite geometric series. This has a sum of
Where
a is the first term, and
r is the common ratio (one term divided by the previous term)
Let's figure out the first 2 terms by plugging in n = 1 first and then n = 2 for the series.
What is one five eights plus one two eights?
Answer:
5/8
Step-by-step explanation:
Answer: I think it's 2 7/8 lemme know if i'm wrong
Step-by-step explanation:
Identify the variation as direct, inverse, joint or combined.
V =nr2h
O direct
O inverse
O joint
combined
Answer:
Sorry po just seen your email and I
Answer:
Sorry po just seen your email and I
Roy used 1/4 of his money on 3 pens and 6 notebooks. The cost of each pen is 3 times the cost of each notebook. He bought some more pens with 2/3 of his remaining money. How many pens did Roy buy altogether?
=========================================================
Explanation:
Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.
2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.
---------------
In terms of cost,
1 pen = 3 notebooks
which is another way of saying 1 pen is the same price as 3 notebooks.
Multiply both sides by 2 to get
2 pens = 6 notebooks
Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.
---------------
In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.
Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.
--------------
Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.
Overall, he purchased 3+10 = 13 pens
Answer:
13 pens
Step-by-step explanation:
If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.
After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...
(2/3)(3/4) = 2/4
of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.
Roy bought 3 +10 = 13 pens altogether.
The graph of the function f is shown below
Find f(0)
Answer:
2
Step-by-step explanation:
Write that down before Katie deletes it. There is no work to show, only read the graph.
The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.
Enter a number answer only.
Answer:
Width = 10 inches
Step-by-step explanation:
Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.
We can establish the following values to help us solve for the width of a rectangle:
Perimeter (P) = 68 inches
Length (L) = 14 + W inches
Width (W) = unknown
Solve for the Width (W)P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.
Divide both sides by 2:
[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]
[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]
Substitute the value of the Perimeter and the length (L) into the formula:
[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]
Combine like terms on the right-hand side, and simplify the left-hand side of the equation:
[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]
Subtract 14 from both sides:
34 - 14 = 14 - 14 + 2W
20 = 2W
Divide both sides by 2 to solve for the width (W):
[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]
W = 10 inches
Therefore, the width of the rectangle is 10 inches.
Double-check:Verify whether the derived value for the width is correct:
P = 2L + 2W
68 = 2(14 + 10) + 2(10)
68 = 2(34) + 20
68 = 48 + 20
68 = 68 (True statement).
Thus, the length of the rectangle is 34 inches, and the width is 10 inches.
1. The length of each side of a square increased by 40%. By what percent does the area of the square increase?
2. The length of a rectangle increases by 20%, and the width decreases by 20%. What is the overall percent change in the area of the rectangle?
(they are two separate questions)
Answer: to number 1 :The area of the square increases by 96% to number 2: increase in width = 50%
Step-by-step explanation
The aquarium owns two research boats that will be docked next to the new building. The Delfino recently took 5 hours to cover 57.5 miles of shoreline. On its last research voyage, the Balina surveyed 54 miles in 4.5 hours. Which boat is faster?
The Delfino can travel at a rate of ______________ miles per hour (mph).
The Balina can travel at a rate of ______________ miles per hour (mph).
Answer:
The Balina is faster than the Delfino.
Step-by-step explanation:
Divide the amount of miles covered by the amount of hours it took for each one.
For the Delfino:
57.5 / 5 = 11.5
For the Balina:
54 / 4.5 = 12
You're welcome T^T
help me out with this question .?
1
Step-by-step explanation:
true ya false you say me
what is 9/blank= 4? i really don't know
Answer:
9/4
Step-by-step explanation:
Answer:
9/2.25 = 4
Step-by-step explanation:
9/x = 4
x = 9/4 or 2.25
A coin weighs 3/4 ounces. Laura picked up 6 of these coins. What is the total weight of the coins she picked up? In simplest form.
Answer:
1 1/2 pound
Step-by-step explanation:
If each coin weighs 3/4 ounces and she picked up 6 then you do 3/4 x 6/1 which equals 18/4 and since there is 16 ounces in a pound it simplifies to 1 2/4 or 1 1/2 pounds
MAX POINTS!!!! Please help me solve the problem in the picture and tell me what I’m doing also explain each step.
I know myself that the answer is 0.4
Solve. 6 Everyone at a park was either hiking or riding a bike. There were 24 more hikers than bike riders. If there were a total of 100 people at the park, how many were hiking?
b r = 178 + h;
b r + h = 676;
then, 178 + 2h = 676 => h = 498/2 = 249 => b r = 178 + 249 = 427
Answer:
676
Step-by-step explanation:
h=b+178=427
b=b=249
-------------
(b+178)+b=676
2b+178=676
2b=498
b=249
-------------
249+427=676
Kaneppeleqw and 2 more u
Mariana's office recycled a total of 9 kilograms of paper over 3 weeks. After 4 weeks,
how many kilograms of paper will Mariana's office have recycled? Solve using unit rates.
Answer:
9 kg per 3 weeks = 3 kg per week
Therefore, after 4 weeks it is (4 * 3) kilograms or 12 kilograms
Step-by-step explanation:
Kevin and Randy Muise have a jar containing 32 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $5.40. How many of each type of coin do they have?
PLSSSS AnSWER QUICKLY
Answer:
19 quarters and 13 nickles
Step-by-step explanation:
You have 32 coins in your pocket consisting of nickels and quarters with a total value of $5.40
How many nickels and quarters do you have?
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation → 0.05n + 0.25q = $5.40 where n = nickels and q = quarters
Coin Total Equation → n + q = 32
Step 2: Rearrange Coin Total Equation in terms of nickels (n)
n = 32 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for n into our Coin Value Equation:
0.05(32 - q) + 0.25q = $5.40
0.05(32) - 0.05(q) + 0.25q = $5.40
1.6 - 0.05q + 0.25q = $5.40
1.6 + (0.25 - 0.05)q = $5.40
1.6 + 0.2q = $5.40
Step 4: Subtract 1.6 from each side of the equation to isolate q
1.6 - 1.6 + 0.2q = $5.40 - 1.6
0.2q = 3.8
Step 5: Divide each side of the equation by 0.2 to isolate q
0.2q
0.2
=
3.8
0.2
q = 19
Step 6: Using our value for q, Solve for n using our Coin Total Equation:
n + 19 = 32
Subtracting 19 from both sides, we get n + 19 - 19 = 32 - 19
n = 13
Summarizing our word problem, we see that 19 quarters and 13 nickels adds up to $5.40
A pattern rule is square, triangle, circle, oval. What is the 50th shape?
Patterns are used to represent sequence of numbers.
The shape at the 50th position is a triangle
The pattern rule is given as: square, triangle, circle, oval.
The number of shapes (n) is given as:
[tex]n =4[/tex]
So, the 50th shape is calculated using the following absolute operator
[tex]Shape = 50\%4[/tex]
i.e. divide 50 by 4, and take note of the remainder.
When 50 is divided by 4, the remainder is 2
So, we have:
[tex]Shape =2[/tex]
This means that, the shape at the 50th position is the same shape at the 2nd position.
Hence, the shape is triangle
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