The answer is:
The distance to over by Adam to get to the park is 108 miles.
Why?To solve the problem, we need to write two equations using he given information about the times and his speed.
So,
For the first equation we have: Travel to Disney Park
[tex]time=4hours[/tex]
[tex]Distance=v*4hours[/tex]
For the second equation we have: Travel back from Disnery Park
[tex]time=4hours-2.5hours=1.5hours[/tex]
[tex]Speed=v+45mph[/tex]
[tex]Distance=(v+45mph)*1.5hours[/tex]
Then, if Adam covered the same distance going and coming back, we have:
[tex]v*4hours=(v+45mph)*1.5hours[/tex]
[tex]v*4hours=v*1.5hours+45mph*1.5hours[/tex]
[tex]v*4hours-v*1.5hours=45mph*1.5hours[/tex]
[tex]v*2.5hours=67.5miles[/tex]
[tex]v=\frac{67.5miles}{2.5hours}=27\frac{miles}{hour}=27mph[/tex]
We have that the speed when he was going to Disney Park was 27 mph.
Now, to calculate the distance, we need to substitute the obtained speed in any of the two first equations.
Therefore, substituting the speed into the second equation, we have:
[tex]Distance=(v+45mph)*1.5hours[/tex]
[tex]Distance=(27mph+45mph)*1.5hours=72mph*1.5hours=108miles[/tex]
Hence, we have that the distance that Adam should cover to get to the park is 108 miles.
Havea nice day!
An orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 5.2 centimeters in diameter. The company wants to sell a larger can of juice. The height of the can is kept at 9.4 cm, but the diameter is increased to 8.5 cm. About how many times more juice will the new can hold?
Image is the same question w/ a model.
The answer is:
The third option:
2.7 times as much.
Why?To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.
So, calculating we have:
Old can:
Since the cans have a right cylinder shape, we can calculate their volume using the following formula:
[tex]Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h[/tex]
Where,
[tex]r=radius=\frac{diameter}{2}\\h=height[/tex]
We are given the old can dimensions:
[tex]radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm[/tex]
So, calculating the volume, we have:
[tex]Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}[/tex]
We have that the volume of the old can is:
[tex]Volume_{Can}=199.7cm^{2}[/tex]
New can:
We are given the new can dimensions, the diameter is increased but the height is the same, so:
[tex]radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm[/tex]
Calculating we have:
[tex]Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}[/tex]
Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:
[tex]\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7[/tex]
Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:
2.7 times as much.
Have a nice day!
What is the shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex?
A a parallelogram that is not a rectangle
B a rectangle
C a triangle
D a trapezoid
Answer:
I'm pretty sure its a Trapezoid but don't quote me
Step-by-step explanation:
I don't really know
The shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex is a rectangle.
What is a rectangle?A rectangle is a quadrilateral (having four sides and four angles) in which opposite sides are equal and parallel. The diagonals bisect each other, and each angle measures 90 degrees.
The shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex is a rectangle.
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What is the second term of the sequence defined by the recursive rule f(1)=3,f(n)=f(n-1)+5
Answer:
8
Step-by-step explanation:
To obtain the second term substitute n = 2 into the recursive rule, that is
f(2) = f(2 - 1) + 5 = f(1) + 5 = 3 + 5 = 8
Find the volume of the cylinder.
Enter the exact answer.
The formula for volume of a cylinder is:
V = π r^2 h
r = 3 and h = 6
V = π * 3^2 * 6
V = π * 9 * 6
V = 54π units^3
Answer: I’m gonna say 169... this one confused me a little bit
What is the general form of the equation of the line shown?
Answer:
The desired equation is y = (-8/3)x + 3.
Step-by-step explanation:
There's no one general form; several different forms apply here.
Seeing that the y-intercept is (0, 3) and that another point on the line is (3, -5), I'd use the slope-intercept form here: y = mx + b
As we move from the first point to the second, x increases by 3 and y decreases by 8. Thus, the slope of the line through the two points is
m = rise / run = -8/3. As before, the y-intercept is (0, 3), so b = 3.
The desired equation is y = (-8/3)x + 3.
The answer is:
The first option:
[tex]3x+y-3=0[/tex]
Why?To find which is the equation of the line shown, we need to find a line that intercepts the y-axis at 3 and the x-axis and 1.
So, discarding we have:
First equation:[tex]3x+y-3=0[/tex]
Making "x" equal to 0 in order to find the y-axis intercept, we have:
[tex]3(0)+y-3=0[/tex]
[tex]y=3[/tex]
Making "y" equal to 0 in order to find the x-axis intercept, we have:
[tex]3x+0-3=0[/tex]
[tex]3x=3[/tex]
[tex]x=\frac{3}{3}=1[/tex]
So, we have found that the x-axis and y-axis intercept of the equation, are the shown in the picture.
The interception points of the equation and the line are:
For x-axis:
[tex](1,0)[/tex]
For y-axis:
[tex](0,3)[/tex]
Hence, the answer is the first option.
[tex]3x+y-3=0[/tex]
Have a nice day!
Joshua eat 3/8 of a pizza trevor eats 1/2 of a pizza how much of the pizza did they eat?
Answer:
7/8ths of a pizza.
Step-by-step explanation:
3/8 + 1/2
Find the LCD and then combine.
7/8 in exact form, and 0.875 as a decimal.
What is true about the number 480,516? Check all that apply.
The 8 is in the thousands place.
The 5 is in the hundreds place.
The number is read as "four hundred eight thousand, five hundred sixteen."
480,516 is equivalent to 400,000 + 8,000 + 500 + 10 + 6
480,516 is equivalent to 400,000 + 80,000 + 500 + 10 + 6
It’s the second answer and the last answer :)
Answer:
The 5 is in the hundreds place.
480,516 is equivalent to 400,000 + 80,000 + 500 + 10 + 6
Step-by-step explanation:
An opaque bag contains 5 green marbles 3 blue marbles and 2 red marbles. What is the probability of randomly picking out a marble and the marble being red?
Answer= .2 probability
Explanation: Since there is a total of 10 marbles, and 2 are red, you would divide the red marbles (2) out of the total marbles (10) which would get u .2. Since it’s asking for probability, we would keep .2 a decimal.
The probability of randomly picking a red marble from the bag is 2 out of 10, or 0.2 when expressed as a decimal, which equates to a 20% chance.
Explanation:The subject of the question you asked is mathematics, specifically probability. In order to calculate the probability of an event happening, you divide the number of successful outcomes by the total number of outcomes. In this case, the successful outcome would be picking a red marble.
The total number of marbles in the bag is 5 (green) + 3 (blue) + 2 (red) = 10. The successful outcomes are 2 (the red marbles). Therefore, the probability of picking a red marble is 2/10 or 0.2.
To put this as a percentage, you multiply by 100, so the probability is 20%. This means that if you pick a marble out at random, there is a 20% chance that it will be red. This is assuming that after each pick, you put the marble back in the bag, also known as picking 'with replacement'.
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The x-axis and y-axis are lines of symmetry for a square. If one of its vertices has coordinates ( a, b), then the vertice opposite it is
Answer:
(-a, -b)
Step-by-step explanation:
It's a square that has both X-axis and Y-axis as lines of symmetry. We can then conclude the center of the square is at the origin (0,0).
It doesn't matter if the square is straight up (both axis being the mid-points symmetry lines, and one corner in each quadrant) or if it is turned (both axis being the diagonals and the corners are on the axis), in any case if a summit (corner) is defined as (a,b), the opposite corner will be at (-a,-b).
(a,b) could be (2,2), then opposite would be (-2,-2).
(a,b) could be (3,0), then the opposite would be (-3,0).
pleas help show work
Step by step answer.
g / -1 + 10 < 7
-g + 10 < 7
-g + 10 - 10 < 7 - 10
-g < -3
-g / -1 < -3 / -1
g > 3 --) answer
The reason why the sign is filpped is that because of g is the opposite of -g and if -g was less than 3 then g is greater than 3.
Answer:
[tex]\large\boxed{g>3\to g\in(3,\ \infty)}[/tex]
Step-by-step explanation:
[tex]\dfrac{g}{-1}+10<7\qquad\text{subtract 10 from both sides}\\\\-g<-3\qquad\text{change the signs}\\\\g>3[/tex]
If k is parallel to l find the value of a and the value of b.
Answer:
a = 30
b = 40
C
Step-by-step explanation:
This requires that you use a proportion.
a / (a + 15) = 40 / 60
The small triangle's sides are in proportion to the large triangles sides.
Reduce the right. Divide top and bottom by 20
a/(a + 15) = 40/20 // 60/20
a/(a + 15) = 2/3
Cross multiply
3a = 2(a + 15) Remove the brackets on the right.
3a = 2a + 30
Subtract 2a from both sides
3a-2a = 30
a = 30
Find B
b is done exactly the same way.
b/(b+20) = 2/3
3b = 2b + 40
3b - 2b = 40
b = 40
Can someone check over my answers? Thanks!
Answer:
Yes, I just checked it. All of it is right!
Step-by-step explanation:
Good Job!!
if the radius of a circle is 4.25 feet, what is the diameter? and if x= -5 and y=2x^2, then y=
The diameter is 8.5 feet
The Y is 100
Which statements about the graph are true? Check all that apply. The vertices are at (–3, 0) and (1, 0). The distance between the center and each covertex is 2. The distance between the center and each focus is about 2.2 units. The directrices are about 4 units from the center. Both directrices are vertical lines.
Answer:
2, 3, and 4
Step-by-step explanation:
Cᴀɴ sᴏᴍᴇᴏɴᴇ ᴇxᴘʟᴀɪɴ ʜᴏᴡ ᴛᴏ ᴅᴏ 1 ᴀɴᴅ 2
Answer:
1.
Experimental : [tex]\frac{14}{25}[/tex] or 56%
Theoretical : [tex]\frac{1}{2}[/tex] or 50%
2.
22 customers
Step-by-step explanation:
Theoretical is how many times you'd expect it to land. So for coin flipping it would be either heads or tails. The probability it would land on heads would be 50% because it's either one or the other.
Experimental is how many times you actually landed it. You flipped a coin and it landed on heads 28 times, so you can put that over 50.
Since [tex]\frac{28}{50}[/tex] can be simplified to [tex]\frac{14}{25}[/tex] or 56%, that is the experimental probability.
For the second variation, we can assume that it is direct variation.
[tex]y=kx[/tex]
When [tex]y[/tex] increases, [tex]x[/tex] increases.
Let's solve for [tex]k[/tex].
[tex]11=50k \\ \\ k=\frac{11}{50}[/tex]
We can plug that in to the second equation since we already know how many customers there will be.
[tex]y=0.22k \\ \\ y=0.22(100) \\ \\ y=22[/tex]
Identify the graphed linear equation.
A) y = 2/3x + 3/2
B) y = 2/3x - 3/2
C) y = - 2/3x + 3/2
D) y = -2/3x - 3/2
Answer:
D) [tex]y=\frac{2}{3}x+\frac{3}{2}[/tex]
Step-by-step explanation:
The given equations are in the form;
[tex]y=mx+b[/tex]
We can observe from the graph that the line is sloping forward.
This means that the slope must be positive.
[tex]\implies m=\frac{2}{3}[/tex]
Also the y-intercept is positive
This implies that;
[tex]b=\frac{3}{2}[/tex]
Hence the equation is [tex]y=\frac{2}{3}x+\frac{3}{2}[/tex]
Answer:
A
Step-by-step explanation:
Plz help me with this
Answer: [tex]\bold{d)\quad y = 3 cos (\dfrac{4}{3}x-2\pi) + 2}[/tex]
Step-by-step explanation:
[tex]\text{Period = }\dfrac{2\pi}{B}\\\\\\\dfrac{1}{2}\text{Period = }\dfrac{1}{2}\cdot \dfrac{2\pi}{B}\quad =\dfrac{2\pi}{2B}\\\\\\\text{In the given equation, B = }\dfrac{2}{3}\implies 2B=\dfrac{2\cdot 2}{3}\quad =\dfrac{4}{3}\\[/tex]
The only option that has B = 4/3 is the last one.
find the area of this figure
Answer: 125 squared ft
Area of the big rectangle ⬜️, 15ft x 10ft = 150 square ft
Area of the small square(which is spaced), 5ft x 5ft = 25 squared ft
Area of the give figure, 150squared ft- 25squared ft = 125 squared ft
Answer:
The answer is 125ft
determine the domain of the function in the correct set notation. f(x)=1 /2×+6
Answer:
First one.
Step-by-step explanation:
The domain of the function in the correct set notation is {x|x∈R x≠-3}.
What is a domain?The domain of a function is the set of all possible inputs that the function can have.
We can find the domain as follows:The function is given to be f(x)=1 /(2x+6).
Here, we can see that the function would become not be defined if the denominator becomes zero.
Therefore, the domain should not contain the values which make it not defined.
The value of x for which it becomes zero can be determined below:
2x+6=0
2x=-6
x=-3
Therefore, the domain must contain all values of real numbers except -3.
The domain of the function is found. The domain of the function is the set of all real numbers except -3. It can be written as {x|x∈R x≠-3}.
Therefore, we have found the domain of the function in the correct set notation is {x|x∈R x≠-3}.
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how many solutions does the equation - 8x + 5 = - 8x + 4 have
Answer:
None
Step-by-step explanation:
They are parallel and have the same slope
What is the area of a triangle with a=2, b=7, and c=8?
Answer:
6.44
Step-by-step explanation:
A=1/ 4 divided by﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4 =1/ 4· divided by﹣24+2·(2·7)2+2·(2·8)2﹣74+2·(7·8)2﹣84 ≈6.4372
Sorry if it's a little complicated but that's how I learned it
Answer:
c.
6.4 units
Step-by-step explanation:
What does F equal???
Answer:
F=10
Step-by-step explanation:
Need a GED Math test tutor. Comment if I can give you my number to help
Answer:
sure I'll help, 59.99 per hour. it's a pretty solid deal.
Step-by-step explanation:
BRAINLIEST + POINTS!
A spring has spring constant 0.3 m/newton. What force is necessary to stretch the spring by 1.5 meters?
If 1 newton pushes it 0.3 meters, it would take 1.5 / 0.3 newtons, or 5 newtons to push it 1.5 meters
Answer: 5 Newton
Step-by-step explanation:
We know that the Hooke's law states that the force 'F' needed to stretch or compress a spring by some distance 'a' is proportional to that distance .
[tex]F=\dfrac{a}{c}[/tex], where c is the spring constant.
Given: A spring has spring constant 0.3 m/newton.
The force is necessary to stretch the spring by 1.5 meters is given by :-
[tex]\Rightarrow\ F=\dfrac{1.5}{0.3}\\\\\Rightarrow\ F=5[/tex]
Hence, the force is necessary to stretch the spring by 1.5 meters = 5 Newton .
Mr. Pham mowed 2\7 of his lawn. his son mowed 1\4 of it. Who mowed the most. How much of his lawn still needs to be mowed.
Answer:
The father did more.
13/28 needs to be mowed which is 0.4643 of the lawn needs to be mowed.
Step-by-step explanation:
The best way to compare the two is to change them to decimals. That will at least answer who mowed the most.
Father: 2/7 = 0.2857
Son: 1/4 = 0.25
Since the father mowed 2/7 of the lawn, he mowed the most.
You can use the decimals to get the second part.
Together they did 0.25 + 0.2857 = 0.5357
The amount of the lawn left is 1 - 0.5357 = 0.4643
================
If you must have this in fractions then
1/4 + 2/7 = 7/28 + 2*4/28 = 7/28 + 8/28 = 15/28
15/28 = 0.5357 which is just what we got above.
Amount left to do = 1- 15/28 = 13/28
13/28 = 0.4643 which is what we got about.
What is the area of the trapezoid below?
Answer:
684
Step-by-step explanation:
A=a+b
2h=26+46
2·19=684
Answer:
684 m²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h (a + b)
where h is the perpendicular height and a, b the parallel bases
here h = 19, a = 46 and b = 26
A = [tex]\frac{1}{2}[/tex] × 19 × (46 + 26)
= 9.5 × 72 = 684 m²
Need help ASAP !!!!
Which odd number have 3 as a factor
Answer: 3, 21, 9, 15, ... any thing you can divide three with
Step-by-step explanation:
Step-by-step explanation:
The odd number whose a factor is the number 3 is a positive odd multiple of 3:
3, 9, 15, 21, 27, 33, 39, 45, 51, 57, ...
Which of the following is 6(x+4)(x+3)/24(x-3)(x+4) simplified
Answer:
[tex]\frac{6\left(x+4\right)\left(x+3\right)}{24\left(x-3\right)\left(x+4\right)}=\frac{x+3}{4\left(x-3\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:6\\=\frac{\left(x+4\right)\left(x+3\right)}{4\left(x-3\right)\left(x+4\right)}\\\mathrm{Cancel\:the\:common\:factor:}\:x+4[/tex]
Hope this helps!!!
[tex]Sofia[/tex]
betsy's bakery sells world famous cherry pies. each pie is measured by its diameter. what is the distance around a 10-inch pie? use 3.1 for pi
Answer:
31
Step-by-step explanation:
Distance around Pie = Pi*Diameter
Final answer:
The circumference of a 10-inch diameter cherry pie, using the value 3.1 for Pi, is 31 inches, which is the distance around the pie.
Explanation:
The distance around a circle is known as the circumference. To calculate the circumference of a 10-inch diameter cherry pie, we will use the relationship between the diameter and circumference, which involves Pi (π). The formula for the circumference C is C = π × d, where d is the diameter.
Using 3.1 as the approximate value for π, and with a diameter of 10 inches, we can calculate the circumference as follows:
C = π × d = 3.1 × 10 = 31 inches.
Therefore, the distance around a 10-inch cherry pie from Betsy's Bakery is approximately 31 inches.