Starting at the same point, Tom and Juanita go biking in opposite directions. If Tom rides at a speed of 24 mph, and Juanita rides at a speed of 30 mph, how far apart will they be in 3 hours?
Tom and Juanita, starting from the same point and biking in opposite directions for 3 hours, will end up 162 miles apart.
Explanation:Starting from the same point, Tom and Juanita go biking in opposite directions for 3 hours. From what we know, Tom rides at a speed of 24 mph and Juanita rides at a speed of 30 mph.
When an object moves in one direction, its distance travelled is calculated from the formula distance = speed x time. This is because speed is described as the distance travelled per unit time. In this case, Tom travels 24 miles in 1 hour, so in 3 hours, he will cover 24 mph x 3 hours = 72 miles. Juanita will cover 30 mph x 3 hours = 90 miles.
Because they are moving in opposite directions, these distances add together. So in 3 hours, Tom and Juanita will be 72 miles + 90 miles = 162 miles apart.
Learn more about Relative Speed here:https://brainly.com/question/14362959
#SPJ12
Tom and Juanita will be 162 miles apart after 3 hours of biking in opposite directions at their respective speeds.
To solve this problem, we can use the formula for distance, which is the product of speed and time.
Since Tom and Juanita are riding in opposite directions, their distances from the starting point will add up to the total distance between them after a certain amount of time.
The correct total distance apart should be calculated as follows:
Total distance apart = Distance of Tom + Distance of Juanita Total distance apart = 72 miles + 90 miles = 162 miles Upon re-evaluating the calculation, we find that the total distance apart is indeed 162 miles, not 156 miles as initially stated.The correct final answer is:
Total distance apart = 162 miles Therefore, Tom and Juanita will be 162 miles apart after 3 hours of biking in opposite directions at their respective speeds.ABC has vertices at A(5,-1), B(9, -9), and C(4,-1). Write the equation of the line in slope-intercept form that is perpendicular to AB and passes through point C
Answer:
[tex]y=\frac{1}{2}x-3[/tex]
Step-by-step explanation:
step 1
Find the slope of AB
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
A(5,-1), B(9, -9)
substitute the values
[tex]m=\frac{-9+1}{9-5}[/tex]
[tex]m=\frac{-8}{4}[/tex]
[tex]m=-2[/tex]
step 2
Find the slope of the line that is perpendicular to AB
we know that
If two lines are perpendicular, their their slopes are opposite reciprocal (the product of their slopes is equal to -1)
we have
[tex]m_A_B=-2[/tex]
therefore
The slope of the perpendicular line is
[tex]m=\frac{1}{2}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{2}[/tex]
[tex]C(4,-1)[/tex]
substitute
[tex]y+1=\frac{1}{2}(x-4)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y+1=\frac{1}{2}x-2\\\\y=\frac{1}{2}x-2-1\\\\y=\frac{1}{2}x-3[/tex]
Danielle and her friends put their money together to buy a book of tickets for the fair that contains 50
tickets. She and her two friends each paid $5.00. What is the price per ticket?!
Step-by-step explanation:
There are 3 people in total, Danielle and w of her friends. Since they paid $5 each they paid $15 in total for the 50 tickets. To find the price per ticket simply divide the total paid by the amount of tickets.
Price per ticket = 15.0÷50 = $0.30
Answer: Each ticket cost 0,3$
Step-by-step:
You have to divide 15 by 50 (15/50)
In this way you get the answer really quickly.
Hope I helped you!
Drag numbers to show which are closest to ‐3/4 and ‐1/2 on the number line. -0.65 -1/3 -7/8 -3/5
Answer:
for -3/4 it is -0.65 and for -1/2 it is -3/5
Step-by-step explanation:
Final answer:
The numbers closest to -3/4 (-0.75) and -1/2 (-0.5) on the number line are -0.65 and -0.6 (or -3/5), respectively.
Explanation:
The question involves identifying which numbers on a list are closest to -3/4 and -1/2 on the number line. To do this, we should consider converting all the fractions and decimals to a common format (decimals) to easily compare their distances to -3/4 (which is -0.75 as a decimal) and -1/2 (which is -0.5 as a decimal).
The numbers provided are:
-0.65
-1/3 (which is approximately -0.333 as a decimal)
-7/8 (which is -0.875 as a decimal)
-3/5 (which is -0.6 as a decimal)
Now, to determine which numbers are closest to -3/4 and -1/2:
For -3/4 (-0.75), the closest number is -0.65.
For -1/2 (-0.5), the closest number is -0.6 (or -3/5).
Natalie can send or receive a text message for $0.15 or get an unlimited number for $5. Write and solve the inequality to find how many messages she can send and receive so the unlimited plan is cheaper than paying for each message
[tex]33\frac{1}{3}[/tex] number of messages she can send and receive so the unlimited plan is cheaper than paying for each message
Solution:
Natalie can send or receive a text message for $0.15
Natalie can get an unlimited number for $5
To find: Number of messages she can send and receive so the unlimited plan is cheaper than paying for each message
Let "x" be the number of messages
Cost for sending and receiving message = $ 0.15
Cost for unlimited plan = $ 5
Then, according to given, we frame a inequality as:
The condition is: unlimited plan is cheaper than paying for each message
Therefore,
(number of messages)(Cost for sending and receiving message) is greater than or equal to Cost for unlimited plan
[tex]x \times 0.15\geq 5\\\\0.15x\geq 5\\\\\text{Solve for "x" }\\\\\text{Divide both sides of equation by 0.15 }\\\\\frac{0.15x}{0.15}\geq \frac{5}{0.15}\\\\x\geq 33.33\\\\x\geq 33\frac{1}{3}[/tex]
Thus for [tex]33\frac{1}{3}[/tex] messages ,the unlimited plan is cheaper than paying for each message
a pitcher throws a fastball to strike out the batter. his pitch takes only 0.63 seconds to reach the catchers mitt. how fast did the ball travel the 60ft to the plate?
A residual plot for a set of data with a linear regression equation is shown. Which statement is correct?
A) The least squares regression line is a good fit since there is a definite pattern in the residual plot.
B) The least squares regression line is not a good fit as there is a definite pattern in the residual plot.
C) The least squares regression line is a good fit as you have about the same number of points above and below the line.
Eliminate
D) The least squares regression line is not a good fit since there is about the same number of data points above and below the line.
Answer:
It’s B
Step-by-step explanation:
Final answer:
The correct statement is that if there is a definite pattern in the residual plot, the least squares regression line is not a good fit. It indicates that potentially another model might better capture the variability in the data. So the correct option is B.
Explanation:
The correct statement about the residual plot for a set of data with a linear regression equation is that if there is a definite pattern in the residual plot, it suggests that the least squares regression line is not a good fit for the data. A good fit would be indicated by residuals that are randomly scattered around the horizontal axis, with no apparent pattern. This is because the residuals, which represent the differences between the observed values and the values predicted by the regression line, should not correlate if the model is appropriate for the data set.
The correct option is B) The least squares regression line is not a good fit as there is a definite pattern in the residual plot. This indicates that the linear model may not be capturing all the variability in the data, and some other models might be more appropriate. Option A is incorrect because a definite pattern in the residuals is a sign of a poor fit. Options C and D are not correct because having the same number of points above and below the line does not necessarily mean the model is a good fit; it's the pattern in the points that matters.
Hello, I'm trying to solve 6x + y = 4, x - 4y = 19. I have found the y but I cant seem to find the x. Plz help and we cant use decimals.
Answer:
[tex]x=\frac{7}{5}[/tex]
[tex]y=-\frac{22}{5}[/tex]
Step-by-step explanation:
Given:
The given expressions are.
[tex]6x+y=4[/tex]
[tex]x-4y=19[/tex]
We need to find x and y values.
Solution:
Equation 1⇒ [tex]6x+y=4[/tex]
Equation 2⇒ [tex]x-4y=19[/tex]
First solve the equation 1 for y.
[tex]6x+y=4[/tex]
[tex]y = 4-6x[/tex] --------(3)
Substitute [tex]y = 4-6x[/tex] in equation 2.
[tex]x-4(4-6x)=19[/tex]
Simplify.
[tex]x-(4\times 4 - 4\times 6x)=19[/tex]
[tex]x-(16-24x)=19[/tex]
[tex]x-16+24x=19[/tex]
Add 16 both side of the equation.
[tex]25x-16+16=19+16[/tex]
[tex]25x=35[/tex]
[tex]x=\frac{35}{25}[/tex]
Divide Numerator and denominator by 5.
[tex]x=\frac{7}{5}[/tex]
Substitute x value in equation 3 and simplify.
[tex]y=4-6(\frac{7}{5})[/tex]
[tex]y=4-\frac{6\times 7}{5}[/tex]
[tex]y=4-\frac{42}{5}[/tex]
[tex]y=\frac{5\times 4-42}{5}[/tex]
[tex]y=\frac{20-42}{5}[/tex]
[tex]y=-\frac{22}{5}[/tex].
Therefore, the value of [tex]x=\frac{7}{5}[/tex] and [tex]y=-\frac{22}{5}[/tex].
2 fields are 1,200 meters from each other. On a map the 2 fields are 8 centimeters apart. What scale is the map using.
Answer:
The scale 150 metres : 1 centimeters is the map using.
Step-by-step explanation:
Given:
2 fields are 1,200 meters from each other.
On a map the 2 fields are 8 centimeters apart.
Now, to find the scale map is using.
Actual distance between the 2 fields = 1200 meters.
Distance in the map between the 2 fields = 8 centimeters.
So, to get the scale map is using we find the ratio:
[tex]Actual\ distance\ between\ the\ 2 fields/ Distance\ in\ the\ map\ between\ the\ 2 fields[/tex].
[tex]=\frac{1200}{8}[/tex]
[tex]=\frac{150}{1}[/tex]
[tex]=150\ meters:1\ centimeters[/tex]
Therefore, the scale 150 metres : 1 centimeters is the map using.
what is 5x to the third times 6
Answer:
The answer is that 5x to the third times 6 is 30x³
Step-by-step explanation:
Let's answer the question, this way:
5x to the third = 5x³
5x³ times 6 = 5x³ * 6 = 30x³
The answer is that 5x to the third times 6 is 30x³
Lincoln is measuring the angles of quadrilateral WXYZ to determine whether it is congruent to the quadrilateral below. Quadrilateral R S T Q. Angle R is 140 degrees, angle S is 94 degrees, angle T is 79 degrees, and angle Q is 47 degrees. Which pair of measurements are possible if they are congruent figures? Measure of angle W = 47 degrees and Measure of angle X = 94 degrees Measure of angle X = 94 degrees and Measure of angle Z = 79 degrees Measure of angle W = 47 degrees and Measure of angle Y = 140 degrees Measure of angle X = 140 degrees and Measure of angle Y = 94 degrees
Answer:
Hello! I'm currently doing the test right now on e d g e n u i t y 2/28/2022 and I believe that the right answer is: m<X = 140 and m<Y = 94
Step-by-step explanation: Sorry if I'm wrong.
:)
The pair of measurements that are possible in congruent quadrilaterals are Measure of angle X = 94 degrees and Measure of angle Z = 79 degrees.
Explanation:Quadrilateral WXYZ is congruent to quadrilateral RSTQ if their corresponding angles are congruent. Let's compare the measurements of the angles in both quadrilaterals:
Angle R in RSTQ = 140 degrees, Angle W in WXYZ = 47 degreesAngle S in RSTQ = 94 degrees, Angle X in WXYZ = 94 degreesAngle T in RSTQ = 79 degrees, Angle Z in WXYZ = 79 degreesAngle Q in RSTQ = 47 degrees, Angle Y in WXYZ = 140 degreesTherefore, the pair of measurements that are possible in congruent figures are:
Measure of angle X = 94 degrees and Measure of angle Z = 79 degreestessa wants to make a bandana for her dog by folding a square cloth into a 45-45-90 triangle. her dog's neck has a circumference of about 32cm. the folded bandana needs to be an extra 16cm long so tessa can tie it around her dog's neck. what should the side length of the square be to the nearest centimeter?
Answer:
The side length of the square will be 11 cm.
Step-by-step explanation:
Tessa wants to make a bandana for her dog by folding a square cloth into a 45-45-90 triangle.
Her dog's neck has a circumference of about 32 cm. the folded bandana needs to be an extra 16 cm long so Tessa can tie it around her dog's neck.
So, the hypotenuse of the 45-45-90 triangle has a length of (32 - 16) = 16 cm.
As a 45-45-90 triangle is an isosceles right triangle with side length a cm (say), then
[tex]\sqrt{a^{2} + a^{2}} = 16[/tex]
⇒ 2a² = 16² = 256
⇒ a² = 128
⇒ a = 8√2 cm.
Therefore, the side length of the square will be 8√2 cm ≈ 11 cm. (Answer)
The side length of the square should be [tex]34cm[/tex] (to the nearest cm)
After folding the square cloth into a bandana, the diagonal has to be [tex]32cm+16cm=48cm[/tex] so that it can tie around the dog's neck.
Using Pythagoras' theorem, the relationship between the sides of the square cloth and the diagonal will be
[tex]diagonal=\sqrt{side^2+side^2}\\diagonal=side\sqrt{2}[/tex]
substituting and solving for the required side length, we get
[tex]48=side\sqrt{2}\\side=24\sqrt{2}\approx 34cm[/tex]
So, the required side length of the square is [tex]34cm[/tex] (to the nearest cm)
Learn more here: https://brainly.com/question/6648302
What is the equation of a line that contains the following two points?
20 points
(3,-1) , (4,4)
A) y = -5x + 8
B) y = 3x + 5
C) y = 5x -16
D) y = -3x + 6
Answer:
the equation that contains the following 2 points is y=5x-16 which is C.
40 points for this! I NEED THE ANSWERS NOWWWWWWWWWWW
Liana's class was going on a very exciting school trip, but when Liana got to school, the school bus had already left! Frantic, Liana begged her mom to drive her to catch up with the bus. Liana's mother has to decide quickly whether she can do it. These are the facts to consider: The bus left at 8:00 AM and is moving with an average speed of 45 mph. Liana and her mom can leave no earlier than at 8:40. If Liana's mother drives with the average speed 60 mph, when can they catch up with the bus?
The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and length of this rectangle?
Liam's parents are driving three times as fast as Liam is biking, but they left later than he did. If his parents caught up with him two hours after he left, how much later than Liam did they leave?
Find the number y, if 3 1/3 of y is 60.
Find the number x, if 11/5 of x is 55.
Find the number y, if 3 1/3 of y is 60. y is 18
Find the number x, if 11/5 of x is 55. x is 25
Answer:
10;40
Step-by-step explanation:
Which number expresses 6.72 as a fraction in simplest form?
Answer: 168/25
Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over 100
. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.
168/25
Answer:168/25
Step-by-step explanation: The answer for 6.72 as a fraction in simplest form is 168/25. You can solve this using long division method. There are six 25s in 168 which is 150 and the remaining 18 can become the decimal which is 0.72. Or for simplicity, you can use a scientific calculator to evaluate the result of 168/25.
A customer/member owes $11.02 and pays $100.00 in cash. The change due is $88.98. Provide the amount owed using the smallest number of bills and coins possible.
Answer: subtract
Step-by-step explanation: you’ll see
The smallest number of bills and coins to make up $88.98 is: 4 $20, 1 $5, 3 $1, 3 quarters, 2 dimes, 3 pennies.
Explanation:The change due back to the customer is $88.98. The smallest number of bills and coins that equals this amount can be broken down as follows:
Four $20 bills, giving us $80.00,One $5 bill, adding $5.00, making the total now $85.00,Three $1 bills, adding $3.00, making the total now $88.00,Three quarters (25 cents), adding $0.75, making the total $88.75,Two dimes (10 cents), adding $0.20, puts the total at $88.95,Lastly, three pennies (1 cent), adding $0.03, gives the final total of $88.98.So, the smallest amount of bills and coins possible to make up $88.98 is: 4 $20, 1 $5, 3 $1, 3 quarters, 2 dimes, 3 pennies.
Learn more about Change Calculation here:https://brainly.com/question/31055625
#SPJ3
What is 2 3/4 * 2 1/2
Answer:
6.875
Step-by-step explanation:
Used a calculator to solve this one, it might be incorrect, i suggest doing some extra research on how to solve to see if you get this answer ;)
A highway had a landslide, where 3,000 cubic yards of material fell on the road, requiring 200 dump truck loads to clear. On another highway, a slide left 40,000 cubic yards on the road. How many dump truck loads would be needed to clear this slide?
The number of dump truck needed to clear the 40,000 cubic yards is determined as 2,667 trucks.
Rate of dump clearing by the truckThe rate of dump clearing is determined as follows;
R = 3000 dumps/200 truck
R = 15 dumps/truck
When the dump is 40,000 cubic yardsThe number of dump truck needed to clear the 40,000 cubic yards is calculated as follows;
N = 40,000/15
N = 2,666.67 trucks
N ≅2,667 trucks
Thus, the number of dump truck needed to clear the 40,000 cubic yards is determined as 2,667 trucks.
Learn more about rate here: https://brainly.com/question/25537936
To clear the slide that left 40,000 cubic yards of material on the road, approximately 2,666.67 dump truck loads would be needed.
In the first scenario, a landslide resulted in 3,000 cubic yards of material obstructing the highway. This volume of material requires 200 dump truck loads for removal.
By dividing the total volume (3,000 cubic yards) by the number of loads (200), we can calculate that each dump truck load can carry 15 cubic yards of material.
3,000 / 200 = 15 cubic yards of material.
Now, applying this knowledge to the second scenario, where a landslide left 40,000 cubic yards of material on the road, we can determine the number of dump truck loads needed to clear it.
By dividing the total volume of material (40,000 cubic yards) by the volume each truck load can carry (15 cubic yards), we get the number of dump truck loads required for cleanup.
=> 40,000 / 15 = 2,666.67
To know more about volume here
https://brainly.com/question/11168779
#SPJ3
Anyone knows what the slope of this is?
Answer:
The slope is 0
Step-by-step explanation:
This is a horizontal line, and all horizontal lines have a slope of 0.
(to see why, just pick any two points, and work out the change in x over the change in y. i.e. rise/run. Since the y coordinates are all equal to 2, the numerator will be 2 -2, meaning the fraction is 0).
The slope is 0. This is because the line is horizontal. Any horizontal line has a slope of 0. Please tell me if you understand! I hope this helps!
1/12 divided by 4 =
Use transformation (-2pie,2pie) with Y=2cos(x)-1
Answer:
See attachment
Step-by-step explanation:
We want to graph
[tex]y = 2 \cos(x) - 1[/tex]
on the interval (-2π, 2π)
First we graph
[tex]y = \cos(x)[/tex]
Then we stretch vertically by a factor of 2 and shift down 1 unit.
Since the amplitude is 2 and the graph is shifted down 1 unit, the range of the transformed graph is
[tex] - 3 \leqslant y \leqslant 1[/tex]
The graph is shown in the attachment
Which of the following is the solution to the equation 2/3 over 3x = 12?
x=4
x=8
x=18
x=24
Answer:
x = 54 and none of the alternatives given is correct
Step-by-step explanation:
Let's solve for x in the equation given, this way:
2/3 ÷ 3x = 12
2/3 * x/3 = 12
2x/9 = 12
2x = 108
x = 108/2 = 54
Proof of x = 54
2/3 * 54/3 = 108/9 = 12
x = 54 and none of the alternatives given is correct
what’s the slope of -1,-10 and -1,-2
Answer:
slope = undefined
Step-by-step explanation:
for two points (x1,y1) (x2, y2)
slope, m = (y2 - y1)/(x2 - x1)
so, for (-1,-10) (-1,-2)
slope = (-2 - (-10))/(-1 -(-1)) = 8/0
slope = undefined
g(5x + 9) = g(9x + 2)
Answer:
x = 7/4 or x = 1.75 or x = 1 and 3/4
they all mean the same thing but there just in different forms (decimal form, fraction form, and mixed number form)
Which composition of similarity transformations would
map polygon ABDC to polygon A'B'D'O'?
a dilation with a scale factor greater than 1 and then
a translation
a dilation with a scale factor greater than 1 and then
a rotation
a dilation with a scale factor less than 1 and then a
reflection
a dilation with a scale factor less than 1 and then a
transation
Answer:
A dilation with a scale factor greater than 1 and then a translation.
Answer:
A
Step-by-step explanation:
In a class of 40 students, 15 offer physics, 20 offer history and 3 offer both physics and history. How many student offer neither physics nor history?
Answer:
2 students.
Step-by-step explanation:
add together all of the students and then subtract that from 40.
20+15+3 = 38
40-38 = 2
Answer:
3 athdwnts it says
Step-by-step explanation:
Here's another, Thanks. (3/5)
You are correct. The scale factor is 1/5 = 0.2
Nice work.
5 x 680 using distributive property
I believe it would be (5 x 600)+(5x80) = 3400
A 10ounce container of milk contains 200 claories how many calories does each ounce of milk have
Each ounce of milk contains 20 calories, because 200/10 = 20.
Jerry collected 45000. Kramer collected 5 times more than jerry. Elaine collected 9 times less than jerry. Newman collects the same as jerry. Kramer and Elaine collected together. How much have the collectors each collected
Kramer collected = 225000
Elaine collected = 5000
Newman collected = 45000
Solution:
Given Jerry collected 45000.
Kramer collected = 5 times more than Jerry collected
= 45000 × 5
= 225000
Kramer collected = 225000
Elaine collected = 9 times less than Jerry collected
= 45000 ÷ 9
= 5000
Elaine collected = 5000
Newman collected = same as Jerry collected
= 45000
Newman collected = 45000
Hence, Kramer collected = 225000
Elaine collected = 5000
Newman collected = 45000
Answer:
2025000 kramers collected
Step-by-step explanation: