Final answer:
Cruz's running speed is 10 mph, and his biking speed is 16 mph, which we found by setting up an equation representing the total distance he covered and the time spent on each activity at their respective speeds.
Explanation:
To determine Cruz's biking and running speeds, we can use the information given about the total distance and the ratio of his speeds. The information tells us that Cruz ran for 1.5 hours (from 6:00 to 7:30) and biked for 2.25 hours (from 7:30 to 9:45). If we let r represent his running speed, then his biking speed would be 1.6r because it's said to be 1.6 times his running speed.
Cruz's total running distance would then be r × 1.5 hours, and his biking distance would be 1.6r × 2.25 hours. We know that the total distance covered is 51 miles, so we can set up the following equation:
1.5r + 1.6r × 2.25 = 51
Now, solve for r:
1.5r + 3.6r = 51
5.1r = 51
r = 51 / 5.1
r = 10 miles per hour
Therefore, Cruz's running speed is 10 mph, and his biking speed is:
1.6 × 10 mph = 16 mph
Cruz's running speed is 10 mph, and his biking speed is 16 mph.
Solve for x, y = 3x + 5xz
Answer: x= y /5z+3
Step-by-step explanation:
Final answer:
To solve for x in the given equation y = 3x + 5xz, rearrange the equation to isolate x by dividing (y - 5xz) by 3.
Explanation:
Solve for x: y = 3x + 5xz
Given the equation y = 3x + 5xz, we need to isolate x. To do this, we can rearrange the equation:
x = (y - 5xz) / 3
Can someone help me with this question
There is a rule for functions:
One input(x-value) can only have one output(y-value).
If one input has more than one output, it's not a function.
(This doesn't apply to outputs, one output can have more than one input and still be a function)
Option 1: It is not a function because the inputs 9 and 10 have more than one output
Option 2: It is not a function because the input 3 has more than one output
Option 3: It is a function because each input has only one output
Option 4: It is not a function because the input 5 has more than one output
Lita has a coin with heads on one side and tails on the other side. She is going to flip it in the air three times. What is the probability of the coin landing tails up on the first flip and heads up twice on the last two flips? P(Tails, then heads, then heads) Write as a simplified fraction.
Answer:
The probability is 1/8
Step-by-step explanation:
In this question, we are tasked with calculating that if a coin is flipped three times, we have the outcome in the question; THH
Now before we go on to calculate this probability, we need to understand some technicalities. Flipping a coin can only result into two outcomes as there are only two sides of a coin. These are the head and the tail. What this means is that if a coin is flipped, we should only expect landing on the head and on the tail.
Now these opposite sides have equal probability. This means the probability of landing on the head = probability of landing on the tail. These probabilities are equal as they are the only two options we have. Hence, the probabilities are 1/2 each
Hence, P(H) = P(T) = 1/2
Now, we proceed to calculating the probability of HTT
this mathematically means P(H) * P(T) * P(T) = 1/2 * 1/2 * 1/2 = 1/8
Answer:
1/8
Step-by-step explanation:
Help! Please! I’ve got 14 Minutes left before i need to submit it!
44 boots were sold all together. To figure this out first you need to find how many of the other boots there were. 8 rugby boots and 12 hiking boots. 8 + 12 + 24 = 44.
Which is the equation of a trend line that passes through the points (7, 450) and (14, 401)?
y = negative 7 x + 499
y = negative StartFraction 1 Over 7 EndFraction x + 451
y = StartFraction 1 Over 7 EndFraction x + 449
y = 7 x + 401
Answer: a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
i got it correct on edg
have a good day :D
Find the amplitude and period of the graph y=4 sin πθ
Answer:
The amplitude is 4 and the period is 2
Step-by-step explanation:
In the equation y = A sin (B x)
A is the amplitude, where the amplitude is the height from highest to lowest points and divide the answer by 2The period is [tex]\frac{2\pi }{B}[/tex] , where the period is the distance from one peak to the next peak∵ The equation is y = 4 sin(πФ)
- Compare it with form above
∴ A = 4 and B = π
∵ A is the amplitude
∴ The amplitude is 4
∵ Period = [tex]\frac{2\pi }{B}[/tex]
∴ Period = [tex]\frac{2\pi }{\pi }[/tex]
∴ Period = 2
∴ The period is 2
The measure of central angle RST is radians. What is the area of the shaded sector? 4Pi units squared
8Pi units squared
16Pi units squared
20Pi units squared
Answer:
"[tex]8\pi[/tex] units squared"
Step-by-step explanation:
The image of the circle is attached.
The shaded area of the circle is basically HALF of the whole circle. If we can get the area of the circle, we will halve it, to get our answer for area of shaded region.
Area of circle is given as:
[tex]A=\pi r^2[/tex]
Where
A is area
r is the radius
Looking at the pic, the radius is "4", so we substitute and find area of circle:
[tex]A=\pi r^2\\A=\pi (4)^2\\A=\pi (16)\\A=16\pi[/tex]
THe shaded area is HALF of that, so:
Area of Shaded = [tex]\frac{16\pi}{2}=8\pi[/tex] sq. units.
Answer is "[tex]8\pi[/tex] units squared"
Plz I need your help! Question in picture!
Answer:
This may be incorrect but $4
Step-by-step explanation:
Find the mean and the median of the data set: 9, 7, 7, 4, 18 , 8, 5, 2,
f(x)=3x-2 and g(x)=2x-4
Find the f(g(x))
Answer:
6x-14
Step-by-step explanation:
its f of g of x so insert the g function when x appears in the f function
3(2x-4) -2
6x - 12 -2
6x-14
what is the area of a square if the side is 2cm
Answer:
The area of the square if the side is 2cm, It would be 4cm, because 2 times 2 is 4. Hope this helps!
Step-by-step explanation:
You would do 2 times 2 to get 4cm.
Answer:
[tex]4cm^{2}[/tex]
Step-by-step explanation:
The formula for working out the area of a square/rectangle is Length multiplied by the width. To work this out you would simply multiply 2 by 2, which gives you 4. This is because a square would have 4 identical sides and that the formula is length multiplied by the width.
1) Multiply 2 by 2.
[tex]2*2=4cm^{2}[/tex]
In a box the number of blue counters and the number green counters are in the ratio 7:4. The number of green counters and the number of red counters are in the ratio 3:1. The total number of counters in the bag is 444. How many green counters are in the bag?
Answer:
Number of green counters is 144
Step-by-step explanation:
Please refer to the attached image for explanations
Calculate the total number of parts in the ratio. Determine the total number of green and red counters, which are 4 parts out of a total of 11. Multiply this fraction by the total number of counters (444) to get the total number of green and red counters. The number of green counters is 3 parts out of this total, so a similar multiplication gives the number of green counters.
Explanation:The problem involves the concept of ratios and arithmetic. We need to solve the question in two stages:
Firstly, the question tells us that the number of blue counters and green counters are in the ratio 7:4. This implies, for every 7 blue counters, there are 4 green ones. Therefore, the total number of blue and green counters together can be thought of as 7+4 which equals 11 parts. Secondly, the number of green counters and red counters are in the ratio 3:1. Therefore, the total number of green and red counters together equals 3+1, which is equal to 4 parts. We're given that the total number of green, red, and blue counters is 444. Now, going back to the first step the blue counters are 7 parts out of 11. The green and red counters combined are 4 parts out of 11. So, the total of green and red counters is 4/11 * 444 = 161.04. But since we can't have 0.04 of a counter, it rounds to 161. Now, given that the green counters and red counters are in the ratio 3:1, so out of the total 161, the green counters are 3/4 * 161 = 120.75, which rounds to 121. So there are 121 green counters in the bag.Learn more about Ratios here:
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Which of these best describes π?
A>The ratio of the radius of a circle to its diameter
b>The ratio of the circumference of a circle to its diameter
c>The square root of the area of a circle
D>The radius of a circle times 3.14
Answer:
B-The ratio of the circumference of a circle to it's diameter
The solution is Option B.
The ratio of the circumference of a circle to its diameter is called π
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
Let the radius of the circle be represented as r
So , the diameter of the circle d = 2r
Now , the circumference of the circle C = 2πr
And , ratio of the circumference of a circle to its diameter is
Substituting the values in the equation , we get
C / d = 2πr / 2r
On simplifying the equation , we get
C / d = π
Therefore , the ratio of circumference to diameter is π
Hence , the equation is solved
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PLZ HELP SOS!!!!!!!!
solve for x
thank you!!!!!!!!!!
Answer:
23. x = 11.1 // 24. x = 21.4
Step-by-step explanation:
23.
Observe which sides are known and needed. 15 is the hypotenuse and x is the adjacent side. The trigonometric function that connects both the hypotenuse and the adjacent side is cosine. Using the degree, set up the equation as so: cos(42) = x/15. (Because cosine is adjacent over hypotenuse, x is over 15). Isolate x to solve for it by multiplying both sides by 15. cos(42) * 15 is 11.1
24.
Observe which sides are known and needed. x is the hypotenuse and 11 is the opposite side. The trigonometric function that connects both the hypotenuse and the opposite side is sine. Using the degree, set up the equation as so: sin(31) = 11/x. (Because sine is opposite over hypotenuse, 11 is over x). Isolate x to solve for it by multiplying both sides by x and then dividing both sides by sin(31). 11 divided by sin(31) is 21.4
A group of adults plus one child attend a movie at Cineplex 15. Tickets cost $9 for adults and $6 for children. The total cost for the movie is $78. Write an equation to find the number of adults in the group.
A teen magazine began its circulation of 500,000 in its first year. Since then, the circulation has increased an average of 33,388 per year. Suppose that the magazine began in 1944, and the trend continues. In what year will the circulation reach 3,000,000? Suppose that the magazine began in 2000, and the trend continues. What is the circulation in 2006? Show work. PLEASE HELP! NOBODY IS ANSWERING MY QUESTIONS!
Answer:
Step-by-step explanation:
First subtract 3000000 and 50000, which equals 2500000.
Then divide 2500000 and 33388, in order to find the number of years, which equals: 74.877201.
Add 74.877201 to 1944, to find out what year the circulation will reach 3 million, the answer is 2018.877. Round up to the nearest year, so 2019.
In order to find the circulation in 2006, first subtract 2006 and 1944, which equals 62 years, then multiply 62 years by 33388 , which equals 2070056. Add 500000 to 2070056. The answer is 2570056.
Does the rule y= -3(3)x represent a linear or an exponential function?
Answer:
There's no exponent, so this is a linear function.
Step-by-step explanation:
We can simplify:
y = -3(3)x
y = -9x
Here we can see this is simply linear: there is just an x^1, and no other exponent.
x+4y=16
5x+4y=0
need to solve systems of equations by graphing
Answer:
Step-by-step explanation:
(-4,5)
x= -4 y=5
In a survey of 20 college students, it was found that 9 were taking an English class, 3 were taking a math class, and 2 were taking both English and Math. How many students were taking a math class only? Please show work.
A) 10
B) 1
C) 13
D) 11
Answer:
1
Step-by-step explanation:
3-2=1
Answer:
The answer is B) 1.
Step-by-step explanation:
Let’s use a Venn diagram to solve this problem.
We know that 9 students are taking an English class and 3 are taking a math class. We also know that 2 students are taking both classes. Therefore, we can fill in the Venn diagram as shown above.
To find the number of students taking a math class only, we need to subtract the number of students taking both classes from the total number of students taking a math class. That is:
Math only = Total Math - Both
Math only = 3 - 2
Math only = 1
Therefore, 1 student is taking a math class only.
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I had 1 apple and then I ate it. How many do I have now?
0
1-1=0
So u have 1 then you take one away so it will get u 0 apples left
Answer:
0 apples in total,
Step-by-step explanation:
You ate the apple, so most would consider that you have 0 apples left.
one minus one is equal to zero in this case.
The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.83, the probability that a car brought into the shop requires brake repair is 0.17, and the probability that a car requires both an oil change and brake repair is 0.15. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair.
Answer:
0.85
Step-by-step explanation:
Given two events A and B, the probability that either A or B occurs is given by:
[tex]p(A\cup B) = p(A)+p(B)-p(A\cap B)[/tex]
where
[tex]p(A)[/tex] the probability that A occurs
[tex]p(B)[/tex] is the probability that B occurs
[tex]p(A\cap B)[/tex] is the probability that both A and B occur at the same time
In this problem, we know the following facts:
[tex]p(o) = 0.83[/tex] is the probability that the car requires an oil change
[tex]p(b)=0.17[/tex] is the probability that the car requires a brake repair
[tex]p(o\cap b) = 0.15[/tex] is the probability that the car requires both an oil change and brake repair
Therefore, the probability that either o (car requiring oil change) or b (car requiring brake repait) occur is:
[tex]p(o\cup b)=p(o)+p(b)-p(o\cap b)=0.83+0.17-0.15 = 0.85[/tex]
A living room wall is 13 feet long. How far from the corner would you have
to put the edge of a 3ft 8in shelf for it to be centered on the wall? *
A-56 inches
B-46 inches
C-51 inches
D-48 inches
Answer:
You start the shelf 4 ft. 9 in. from the wall
Step-by-step explanation:
The game plan is to take the length of the shelf away from the length of the wall, and then divide the remaining part into two equal pieces.
13 ft.
- 3 ft. 6 in.
12 ft 12 in,
- 3ft 6 in
9 ft 6 in.
9 ft. 6 inches divided by 2 equals 4.5 ft, 3 in.
.5 ft * 12 inches = 6 inches
Answer:
56 inches.
Step-by-step explanation:
What is the solution to (x + 8) > (2x + 10)?
Answer:
C.
Step-by-step explanation:
A rectangular container 100cm long,60cm wide and 80cm high is filled with water up to the level of 50cm.What is the volume of the empty space
A.480,000cm
B.180,000cm
C.300,000cm
D.240,000cm
Answer:
D) 240 000 cm³
Step-by-step explanation:
V = 100cm×80cm×(80-50)cm
= 8000cm²×30cm
= 240 000 cm³
At a party, the hosts are giving out door prizes. Each guest receives a numbered ticket and a random drawing will be held for the prizes. There are 14 prizes and 22 guests. What is the probability of winning the last prize if multiple winning is not allowed
Answer:
The probability of winning the last prize is [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Total Number of guests = 22
Total Number of prizes = 14
We have to find the probability of winning the last prize. When its turn to announce the last prize, the previous all prizes would have been already distributed. This means, 13 of the prizes would have been already distributed. Since multiple winning is not allowed, the last prize would be distributed in the remaining guests.
After distributing 13 prizes, the number of guests who can win the last prize will be = 22 - 13 = 9
We have only 1 last prize and 9 people among which only 1 will win the prize. Probability is defined as the ratio of favorable outcomes to total number of outcomes.
In this case the favorable outcome is the person with numbered ticket who is going to win a prize. This means favorable outcome is only 1. Total number of outcomes is total number of people remaining, which is 9.
Therefore, the probability of winning the last prize is 1 in 9 i.e. [tex]\frac{1}{9}[/tex]
Jason is entering a weight lifting contest. Gurrently, his maximum bench press weight is 105 pounds. If he increases the weight by 7 pounds each week, What is the maximum weight he be able to bench press after 13 weeks?
Answer:
196 lbs is the maximum weight.
Step-by-step explanation:
7 × 13 = 91 lbs (this is the amount he added by the 13th week)
91 + 105 = 196 lbs (this is the amount he added and the amount he had. giving us the finished product.)
Calculate Jason's maximum bench press weight after 13 weeks with a weekly increase of 7 pounds. Jason will be able to bench press a maximum weight of 196 pounds.
Jason's maximum bench press weight: 105 pounds
Weekly increase: 7 pounds
Number of weeks: 13
To calculate the maximum weight after 13 weeks:
First week: 105 + 7 = 112 pounds
Second week: 112 + 7 = 119 pounds
Continue this pattern for 13 weeks.
Result: After 13 weeks, Jason will be able to bench press a maximum weight of 196 pounds.
A Furniture Company currently produces5000600 chairs per month if production increases 7% find the increase in the new number of chairs produce each month
Answer:
350042 chairs
Step-by-step explanation:
Given: Number of chairs produced by a furniture company each month = [tex]5000600[/tex]
Percentage increase in chairs = [tex]7\%[/tex]
To find: an increase in the new number of chairs produce each month
Solution:
As 5000600 chairs are produced by a furniture company each month percentage increase in chairs is [tex]7\%[/tex]
So, increase in the new number of chairs produce each month = [tex]7\% \,\, of \,\, 5000600=\frac{7}{100} (5000600)=350042[/tex]
A concert last 567 hour the band performs three concerts on the weekend how long does the band perform in total on the weekend why are you answer as a mixed number
Answer:
[tex]17\dfrac{4}{7} \:hours[/tex]
Step-by-step explanation:
A concert lasts [tex]5\dfrac{6}{7}[/tex] hours.
The band performs three concerts on the weekend.
Total length of time performed by the band is given as:
Hour Per Concert X Number of Concerts
[tex]5\dfrac{6}{7} X 3\\=\dfrac{41}{7} X 3\\=\dfrac{123}{7}\\=17\dfrac{4}{7} hours[/tex]
The band performs a total of [tex]17\dfrac{4}{7} hours[/tex].
. Lola sells jewelry. She sold 6 necklaces.She sells each necklace for $9.She spent $14 on supplies to make the necklaces. Write an expression that shows the amount of money Lola earned after paying for the supplies? *
Answer:
(6 necklaces x $9 per necklace) - $14 spent on supplies = profit for Lola
or (6 x 9) - 14 = profit for Lola
The actual profit is $40.
Step-by-step explanation:
First, you need to calculate how much money Lola made from selling jewelry. She sold 6 necklaces, and each one was sold for $9, so you can calculate the total sale proceeds by multiplying 6 x $9 = $54.
However, you then have to subtract the cost of supplies that Lola had to buy to make the necklaces, in order to find out how much money Lola actually made. Therefore, subtract $14 from the calculation above.
Therefore the final expression is: (6 x 9) - 14 = profit
Make sure to take into account order of operations when solving the equation (it's important to multiply 6x9 before you subtract out the 14). The actual profit for Lola comes out to $40.
Write the equation of a line in slope-intercept form that goes through the points (4, -2) and (-4, -4).
A. y = 4x - 3
B. y = 4x - 2
C. y = 1/4x - 3
D. y = 1/4x - 2
Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 2) and (x₂, y₂ ) = (- 4, - 4)
m = [tex]\frac{-4+2}{-4-4}[/tex] = [tex]\frac{-2}{-8}[/tex] = [tex]\frac{1}{4}[/tex] , thus
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation.
Using (- 4, - 4), then
- 4 = - 1 + c ⇒ c = - 4 + 1 = - 3
y = [tex]\frac{1}{4}[/tex] x - 3 → C