Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.
Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour.
They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles. At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour.Here, Thus, Florida Avenue is hypotenuse triangular path and the other two sides are Capitol Street and H Street. The distance of Florida Avenue is,
[tex]1^2+1.75^2=d^2\\1+3.0625=d^2\\4.0625=d^2\\d=\sqrt{4.0625}\\d=2.0156[/tex]
Thus, Jesse walks 2.0156 with 5 miles per hour. Thus, the time taken by him is
[tex]t_J=\dfrac{2.0}{5}\\t_j=0.4\rm\;hr[/tex]
Mark plans to jog back the way they came which is 2.75 miles (1+1.75) long with speed of 12 miles per hour. Thus, the time taken by him is
[tex]t_M=\dfrac{2.75}{12}\\t_M=0.23\rm\;hr[/tex]
Thus, Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.
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Does anybody know this? I followed the example and did the formula and it told me it was 11.99 but it was wrong. Find the length of the radius if the area of the sector is 361.6 and the central angle is 288 use 3.15 round your answer to the neatest whole number
Hi Student!
The first step that we need to take to solving this problem (and almost any problem), is to concentrate the important information for the problem that is provided. Looking at the problem we can see that we are trying to determine what the length of the radius is. In order to solve this problem we are provided with the area of a sector of 361.6 meters squared and a central angle of 288 degrees.
Now that we have the important information taken care of, we can move onto the part of actually solving the problem. We must first convert our degrees to radians because the equation that we will be using can only use radians for the angle and not degrees. We can simply convert our angle to radians by multiplying it by π/180.
[tex]288\ degrees\ *\ \frac{\pi }{180\ degrees}[/tex]
[tex]288\ degrees\ *\ \frac{3.14}{180\ degrees}[/tex]
[tex]\frac{288\ degrees\ *\ 3.14}{180\ degrees}[/tex]
[tex]5.024\ radians[/tex]
After completing this step, we have converted our degrees to radians and now we can move onto the step where we plug in our information into an equation and solve for our unknown.
[tex]Sector\ Area = radius^2\ *\ \frac{angle}{2}[/tex]
[tex]361.6\ m^2 = radius^2\ *\ \frac{5.024}{2}[/tex]
[tex]361.6\ m^2 = radius^2\ *\ 2.512[/tex]
[tex]\frac{361.6\ m^2}{2.512} = \frac{radius^2\ *\ 2.512}{2.512}[/tex]
[tex]143.949\ m^2 = radius^2[/tex]
[tex]\sqrt{143.949\ m^2} = \sqrt{radius^2}[/tex]
[tex]12\ m = radius[/tex]
Therefore, after solving our equation for our unknown, we can see that our radius is really close to 12 meters (so we can just round up as the problem stated).
the volume of a cube with edge lengths of 2/3 units
What is the edge length of a cube with volume 27/64 cubic units?
Pleas helppppppppppppp
Answer:
[tex]a=\sqrt[3]{\frac{27}{64}} = 0.75[/tex]
edge length = 0.75
Equation: [tex]a=\sqrt[3]{V}[/tex]
f(x)=4x-1. g(x)=-2|x+3|. what is the y value when f(x)=g(x)
..............................................................
1. How many triangles are congruent to AABC?
А.
2
В.
3
С.
4
D.
5
Answer:
Answer: 3, 3 of them are translated
Answer:
B. 3 triangles are congruent to ABC
Step-by-step explanation:
2 triangles are congruent if all corresponding side lengths are equal, or using SAS (Side-Angle-Side theorem) to confirm 2 corresponding sides & the included angle is equal those of another triangle.From the picture, triangle ABC is not a right triangle. The length of AB is graphed with a length of 4. From point C to segment AB is a height of 3. The triangle in quadrant I (top right) has both of these dimensions.
Similarly, the triangle on the x-axis (positive side) below it (between Q1 and Q4) is also congruent to ABC.
The triangle fully in quadrant III (bottom left) is congruent to ABC with a height of 3 and base length of 4.
The triangle in the bottom right corner (Q4) has a height of 4, therefore it is not congruent to ABC which has a height of 3.
The triangle on the x-axis (negative left side) is also not congruent to ABC. It may have a height of 3 and base length 4, but the angles are different which means the other side lengths don't correspond to ABC.
[+ I'm not sure if your teacher would consider this a real answer but I figured I'd mention that in proofs tri.ABC is also congruent to tri.ABC.]
One week, Alonso earned $204.40 at his job when he worked for 14 hours. If he is paid the same hourly wage, how many hours would he have to work the next week to earn $554.80
Answer:
About 30-34 hours i estamate
Step-by-step explanation:
Alonso should work for 38 hours to earn $554.80.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Alonso earned $204.40 at his job when he worked for 14 hours.
Let Alonso per hour be x,
x = 204.40 / 14
x = 14.6
Now,
Alonso works for hours to earn $554.80,
= total pay/pay of an hour
= $554.80 / 14.6
= 38
Alonso should work for 38 hours to earn $554.80.
Thus, Alonso should work for 38 hours to earn $554.80.
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HELP Sam measures the height of 7 different scoops of ice cream. The mean of the heights was 3.8 cm. Which of the following best describes the mean?
Answer:
B
Step-by-step explanation:
mean=(a+b+c+d+e+f+g)/7
Sam measures the height of 7 different scoops of ice cream. The mean height was 3.8 cm. If all the scoops are evenly distributed, they would all be 3.8 cm tall.
How to find the mean value of a data set?The mean value of the data set is the ratio of the sum of the data set's values to the number of values it has.
If the data set consists of values
x_1, x_2, ..., x_n
, then we get the mean value as:
[tex]\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}[/tex]
Sam measures the height of 7 different scoops of ice cream. The mean height was 3.8 cm.
[tex]\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}[/tex]
mean=[tex]\dfrac{(a+b+c+d+e+f+g)}{7}[/tex]
Therefore, If all the scoops are evenly distributed, they would all be 3.8 cm tall.
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If an item has a retail price = $475 and a discount of $45, what percentage discount is offered?
Answer:
A 9.47% discount was given
Step-by-step explanation:
The question is asking us to find how much percent of 475 is 45. Therefore we do the following:
[tex] \frac{45}{475} \times \frac{100}{1} = \frac{4500}{475} [/tex]
after dividing we get 9.473 which is approximately 9.47%
To check if what we got is correct we do the opposite and instead find 9.47% of 475.
[tex] \frac{475}{1} \times \frac{9.47}{100} = \frac{4498.25}{100} [/tex]
After dividing we find that is equal to 44.98 which is approximately 45.
A star with an initial radius of r=1. 0108 m and a period of 30. 0 days collapses suddenly to a radius of r=1. 0104 m
The initial angular velocity of the star will be [tex]w=2.4\times 10^{-6} \ \frac{rad}{sec}[/tex].
What is angular velocity?Angular velocity refers to how fast an object rotates or revolves relative to another point. It is a rate of change of angle.
Here for the 30 days period the angular velocity will be calculated as:
[tex]W=\dfrac{2\pi}{T}=\dfrac{2\times \pi}{30\times 24\times 3600}=2.4\times 10^{-6} \ \frac{rad}{sec}[/tex]
So the initial angular velocity of the star will be [tex]2.4\times 10^{-6} \frac{rad}{sec}[/tex]
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The square root of 83
Answer:
The answer would be 9.1104335791443.
A 10 inch long piece of string is approximately 25.4 centimeters long.
What is the length, in centimeters, of a string that is 45 inches long, rounded to the nearest tenth?
If 10 inches is equal to 25.4 centimeters. Then the 45 inches will be equal to 114.3 centimeters.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.
A 10 inches long piece of string is approximately 25.4 centimeters long.
If the length of the string is 45 inches. Then the length in cm will be
Let x be the length. Then we have
x/45 = 25.4/10
x = 114.3 cm
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PLS HELP PLS ANSWER AS SOON AS POSSIBLE
Answer:
y>1/3x-3
Step-by-step explanation:
The slope for this equation is 1/3x-3. Because the line is dashed, we know that we're dealing with either < or >. The shading goes upwards, so it's greater than. That means, we would get y>1/3x-3.
Hope this helps!
Many large cities have considered or passed proposals that ban the use of plastic grocery bags in stores. A concerned student would like to measure if residents of her hometown would consider a similar ban on plastic bags. Standing in a busy shopping area, the student approaches adults and asks, "Items made of plastics are a dangerous, growing source of pollution to our world’s oceans and threaten many animal species. Given this, would you support a ban on plastic shopping bags in our city stores?” How might the results of this survey be biased in estimating the proportion of all town residents who would support a ban on plastic bags?
The student may overestimate support for a plastic bag ban because only adults in the shopping area were chosen to participate.
The student may overestimate support for a plastic bag ban because the wording of the question may influence adults to support a ban.
The student may underestimate support for a plastic bag ban because the wording of the question may influence adults to not support a ban.
The student may underestimate support for a plastic bag ban because some adults may not want to answer questions about the environment.
Answer: The student may overestimate support for a plastic bag ban because the wording of the question may influence adults to support a ban.
Step-by-step explanation:
The work of a student to find the dimensions of a rectangle of area 8 + 16x and width 4 is shown below:
Step 1: 8 + 16x
Step 2: 4(4) + 4(12x)
Step 3: 4(4 + 12x)
Step 4: Dimensions of the rectangle are 4 and 4 + 12x
In which step did the student first make an error, and what is the correct step?
Answer:
Step 1: 8 + 16x Step 2: 4(4) + 4(12x) Step 3: 4(4 + 12x) Step 4: Dimensions of the rectangle are 4 and 4 + 12x In which step did the student first make an error and what is the correct step? Step 3; 4 + (4 + 12x) Step 3; 4 + (4 ⋅ 12x) Step 2; 4(2) + 4(4x) Step 2; 4(2) + 4x(2)
Jennifer has a job that pays her $5200 per month. She also has to pay
12% per month in Federal Taxes and 3.5 % per month in State Taxes. If
these are her only deductions, then what is her net pay for the year?
O A. $4,394
B. $26,364
C. $52,728
D. $63,872
Answer:
4394
5200 X 0.12 = 624 --> 5200 - 624 = 4576
5200 X 0.035 = 182
4576 - 182 = 4394
helpppppppp asappppppppppp pleaseeee
Length of sides:
A = 4 ftB = 8 ftC = 6 ftD = 10 ftSurface Area:
(perimeter of base)(length) + (base)(height)
(8+10+6)(4)+(8)(6)
(24)(4)+48
96+48
144 ft²
please help me Find the slope
Answer:
-1/2
Step-by-step explanation:
let's look at the change from the red point to the blue point
thus, (x₁, y₁) = red point = (-4, 1) and (x₂, y₂) = blue point = (-2, 0)
note that (x₁, y₁) and (x₂, y₂) can be interchanged
slope = change in y / change in x = (y₂-y₁)/(x₂-x₁) = (0-1) / (-2-(-4)) = -1/2 as our slope
WILL GIVE BRAINLIEST Drag the values into the boxes to classify each number as rational or irrational.
Answer:
See below ~
Step-by-step explanation:
5/4 = 1/25 ⇒ Rational√100 = 10 ⇒ Rational7.3 ⇒ Rational0.00247 ⇒ Rational√4/9 = 2/3 = 0.66666... ⇒ Rational√2/24 = 1/2√1/6 ⇒ Irrational0.01.... ⇒ RationalBetty’s Bite-Size Candies are packaged in bags. The number of candies per bag is normally distributed, with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint, a sample of bags is checked, and 12 bags contain fewer than 47 candies. How many bags were probably taken as samples?
A. 15 bags
B. 75 bags
C. 36 bags
D. 24 bags
SOMEONE HELP QUICK!!
Answer:
24
Step-by-step explanation:
47= Mean
4 bags represent 16% of samples
16%=4
100= x
X=100 x4/16
100x4=400
400/16= 25
Since the answer ask for a probablity the answer is 24.
I need help with all of these questions you see on the top. there the red squares. please someone smart. this is one of the problems I need to finish this tonight.
Answer:
49°
Step-by-step explanation:
The marked angles are "vertical" angles. They have the same measure.
∠TGF = ∠HGM = 49°
_____
You don't need to know the value of p to answer this question. It is 7.
Answer:
∠TGF = 49°
Step-by-step explanation:
From the diagram, we get that ∠TGF is equal to ∠MGH because they are vertical angles.
Hence,
⇒ ∠TGF = ∠MGH
⇒ ∠TGF = 49°
please help please :)
Answer:
Amber these are tricky
Step-by-step explanation:
plug in 0 for x to see where it intercepts, also, b/c the line goes up hill, it's a positive slope. :)
So B) is good
jake has an account that is compounded every month at a rate of 3.5%.if he invests $20,000,what will the balance be after 5 years
Nyla compared 790 and 709.her work is shown at the right. Is Nyla comparison correct ? If not, correct her mistake
Answer:
its correct so you don't need to do anything
Step-by-step explanation:
The solution is, result of subtraction = 81.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
given that,
Nyla compared 790 and 709.
so, we have,
790 - 709
=81
Hence, The solution is, result of subtraction = 81.
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HELPPPPP QUICKLYYY !!! The picture shows a cylinder of height x which has been inscribed in a sphere of radius r. Find the volume of a cylinder in terms of x.
See attached. We can draw a right triangles contained within both shapes.
The triangle has height x (same as the cylinder), base 2r (same as the diameter of the cylinder), and hypotenuse 6 (same as the diameter of the sphere).
Since it's a right triangle, the Pythagorean theorem holds and we have
x² + (2r)² = 6²
which we solve for r to get
x² + 4r² = 36
4r² = 36 - x²
r² = 9 - x²/4
r = √(9 - x²/4)
Then the volume of the cylinder, whose height is x and whose base has radius r, is
π r² x = π (9 - x²/4) x = (36x - x³) π/4
Math in My World
Example 1
Blair is arranging 18 cupcakes on a shelf. Find the
factors of 18. Use arrays to find the factors.
Answer:
445455
Step-by-step explanation:
A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 3080 seats. The students filled 1078 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answe
about 30-45 Percent.
Step-by-step explanation:
Consider z1 = 4 – 4 startroot 3 endrooti and z2 = –16i. What is z1 – z2? 4 – 12startroot 3 endroot i 4 12startroot 3 endroot i 4 – 4( startroot 3 endroot – 4)i 4 4 (startroot 3 endroot – 4)i
The answer is: [tex]z_1-z_2[/tex]= 4-4([tex]\sqrt{3i}[/tex]-4i)
The correct option is: (D)
What are Complex numbers?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).
Since we have given : [tex]z_1[/tex]==4-4[tex]\sqrt{3i}[/tex] and [tex]z_2[/tex]= -16i
The difference of z1 - z2 would be:
So,
[tex]z_1-z_2[/tex] = 4-4[tex]\sqrt{3i}[/tex] - (-16i)
[tex]z_1-z_2[/tex] =4-4[tex]\sqrt{3i}[/tex]+16i
[tex]z_1-z_2[/tex] =4-4([tex]\sqrt{3i}[/tex] -4i)
Hence, [tex]z_1-z_2[/tex]= 4-4([tex]\sqrt{3i}[/tex]-4i)
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Answer:
4 – 4( StartRoot 3 EndRoot – 4)i
it's C.
Step-by-step explanation:
took the L for yall bc my shtoopid ahh thought it was D, which is 4 + 4
The smallest angle of rotational symmetry for a regular polygon is 30°. how many sides does the regular polygon have? 9 12 20 30
The regular polygon must have 12 sides so the smallest angle of rotational symmetry is 30°
How many sides the polygon have?We know that the smallest angle of rotational symmetry is 30°, then the exterior angles must measure that.
Remember that the sum of the exterior angles of a regular polygon must be equal to 360°, then we have:
360° = n*30°
Where n is the number of sides
Solving for n we get:
n = 360°/30° = 12
We conclude that the regular polygon has 12 sides.
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Answer: B. 12
Step-by-step explanation: On Edge!!!
A letter is chosen at random from the word CALIFORNIA. Find the probability of all the letters in the word
Answer:
C - 1/10A - 2/10L - 1/10I - 2/10F - 1/10O - 1/10R - 1/10N - 1/10Do not put A and I more than once, we already measured it before.
10 letters in all
Find how many there are per letter
C - 1/10
A - 2/10
L - 1/10
I - 2/10
F - 1/10
O - 1/10
R - 1/10
N - 1/10
shows a reading which is 8% higher than the actual pressure.
what is the actual pressure when it shows up as £39.42
The actual pressure before the percentage increase is 36.5
How to calculate the Actual pressure?New pressure = £39.42Percentage increase = 8%let
x = actual pressure39.42 = x + (8% of x)
39.42 = x + (0.08x)
39.42 = 1.08x
x = 39.42 ÷ 1.08
x = 36.5
Therefore, the actual pressure before the percentage increase is 36.5
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1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves y = x2 and y = 2x – x2.
(a) The differential equation is separable, so we separate the variables and integrate:
[tex](x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx[/tex]
[tex]\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx[/tex]
[tex]\ln|y| = x - \ln|x+1| + C[/tex]
When x = 0, we have y = 2, so we solve for the constant C :
[tex]\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)[/tex]
Then the particular solution to the DE is
[tex]\ln|y| = x - \ln|x+1| + \ln(2)[/tex]
We can go on to solve explicitly for y in terms of x :
[tex]e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}[/tex]
(b) The curves y = x² and y = 2x - x² intersect for
[tex]x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1[/tex]
and the bounded region is the set
[tex]\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}[/tex]
The area of this region is
[tex]\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}[/tex]
