The distance between Martin's house and the school is 5 kilometers.
How to solve for distanceTo find the distance between Martin's house and the school, we can use the Pythagorean theorem.
Let's represent the distance between Martin's house and the school as x kilometers.
According to the given information:
Distance between Martin's house and Hayley's house (hypotenuse) = 13 kilometers
Distance between the school and Hayley's house (one side of the right triangle) = 12 kilometers
Using the Pythagorean theorem, we have:
x[tex]x^2 + 12^2 = 13^2[/tex]
Simplifying the equation:
[tex]x^2 + 144 = 169x^2 = 169 - 144x^2 = 25[/tex]
Taking the square root of both sides:
x = √25
x = 5
Therefore, the distance between Martin's house and the school is 5 kilometers.
Read more on distance here:https://brainly.com/question/7243416
#SPJ1
A native wolf species has been reintroduced into a national forest. Originally, 46 wolves were transplanted. Assuming that the population is growing exponentially at a rate of 5.6%, how long will it take for the population to reach 150 wolves? Round your answer to the first decimal place.
7. These triangles are similar. Find the area of the smaller
triangle to the nearest whole number.
105 ft²
16 ft
12 ft
Answer
79 ft²
59 ft²
49 ft²
89 ft²
The area of smaller triangle is 59 square feet.
The area of the larger triangle is 105 square feet.
And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.
Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.
Since, the corresponding edges of similar triangles are proportional.
Therefore, y/x=16/12
y=4/3x
Also, the area of larger triangle is 105 square feet.
1/2×4/3x×16=105
The above equation can be written as
1/2×4/3x×4/3×12=105
1/2×x×12=59
Area of smaller triangle = 59 square feet
Hence, the area of smaller triangle is 59 square feet.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
Find the values of x with the answers in simplest radical form
The value of x with the answers in simplest radical form is 18.
We are given that;
The right triangles with dimension
Now,
The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
1. 14^2+14^2=x^2
196+196=x^2
x^2=392
x=19.7
2. x^2+X^2=12^2
2x^2=144
x^2=72
x=8.48
3. 9[tex](\sqrt{2} )^2[/tex]+9[tex]\sqrt{2})^2[/tex]=x^2
162+162=x^2
324=x^2
x=18
Therefore, by pythagoras theorem the answer will be 18.
Learn more about Pythagoras theorem;
https://brainly.com/question/343682
#SPJ1
Direction: Read each item carefully. Encircle the best answer from the given
choices.
1. What is A U B; if A = {<, +, =, x) and B = {=, +, /, >}
A. {<, +, =, X}
C. {<, +, =, x, /, >}
B. (=, +, /, >}
D. {<, +, =, x, =, +, /, >}
2. What is An M; if A = {1, 2, 4) and M = {2, 3, 5}?
A. {1}
C. (3)
B. (2)
D. (4)
3. What is Bn C; if B = {C, O, U, G, H) and C = {F, E, V, E, R)
C. (F, E, V, E, R}
A. {}
B. (C,O,U,G,H}
D. (C, O, U, G, H, F, E, V, E, R}
4. What is M - J; if M = {soap, alcohol, sanitizer, mask) and J = {alcohol,
sanitizer, mask, gloves}?
A. {alcohol)
C. {mask}
B. (gloves)
D. (soap}
5. What is complement of set A if U = {Frontliners, sacrifice, their, lives, to,
combat, coronavirus) and B = {Frontliners, sacrifice, their, lives)
A. (Frontliners)
C. (to, combat, coronavirus}
1) The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) The value of A ∩ M is,
A ∩ B = {2}
3) The value of B ∩ C is,
B ∩ C = { }
4) The value of M - J is,
M - J = {soap}
5) The complement of set A is,
A' = (to, combat, coronavirus}
Now, WE can simplify as;
1) We have;
A = {<, +, =, x) and B = {=, +, /, >}
Hence, We get;
The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) Given that,
A = {1, 2, 4) and M = {2, 3, 5}
Hence, The value of A ∩ M is,
A ∩ B = {2}
3) Given that;
B = {C, O, U, G, H) and C = {F, E, V, E, R)
Hence, The value of B ∩ C is,
B ∩ C = { }
4) Given that;
M = {soap, alcohol, sanitizer, mask) and J = {alcohol, sanitizer, mask, gloves}
Hence, The value of M - J is,
M - J = {soap}
5) Given that;
U = {Frontliners, sacrifice, their, lives, to, combat, coronavirus) and A = {Frontliners, sacrifice, their, lives)
Hence The complement of set A is,
A' = U - A
A' = (to, combat, coronavirus}
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
Susan borrowed $18,500 at 5.00% p.a. from her parents to start a business. In 4 months, she repaid $5,300 towards the loan, and in 10 months she repaid $3,800. How much would she have to repay her parents at the end of 13 months to clear the outstanding balance? Use the declining balance method to calculate the last payment.
Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.
To calculate the outstanding balance at the end of 13 months, we need to use the declining balance method. This method involves applying the interest rate to the remaining balance after each repayment.
First, let's calculate the interest for the first 4 months. The interest for this period can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the principal is $18,500, the rate is 5.00% per year (or 0.05), and the time is 4 months (or 4/12 years). Thus, the interest for the first 4 months is $18,500 × 0.05 × (4/12) = $308.33.
Next, we subtract the repayment made after 4 months ($5,300) from the outstanding balance ($18,500) and add the interest for the first 4 months ($308.33). This gives us a new outstanding balance of $18,500 - $5,300 + $308.33 = $13,508.33.
Now, let's calculate the interest for the period between 4 and 10 months. The principal remains the same ($13,508.33), the rate is still 5.00% per year (or 0.05), and the time is 6 months (or 6/12 years). Therefore, the interest for this period is $13,508.33 × 0.05 × (6/12) = $337.71.
Subtracting the repayment made after 10 months ($3,800) from the outstanding balance ($13,508.33) and adding the interest for the period gives us a new outstanding balance of $13,508.33 - $3,800 + $337.71 = $10,045.04.
Finally, to determine the last payment required to clear the outstanding balance at the end of 13 months, we subtract the new outstanding balance ($10,045.04) from the principal ($18,500). The last payment is therefore $18,500 - $10,045.04 = $8,454.96.
Therefore, Susan would have to repay her parents $8,454.96 at the end of 13 months to clear the outstanding balance using the declining balance method.
For more question on balance visit:
https://brainly.com/question/23447356
#SPJ8
Michelle was fishing in her canoe at point A in the lake depicted
above. After trying to fish there, she decided to paddle due east
at a steady speed of 10 miles per hour. As she paddled, a wind
blowing due south at 5 miles per hour caused a change in her
direction. To the nearest tenth of a mile, what is the velocity,
represented by vector AC, of her canoe?
A 8.6 miles per hour
B 10 miles per hour
11.2 miles per hour
D 17.2 miles per hour
The velocity represented by vector AC of Michelle's canoe is approximately option C. 11.2 miles per hour.
How did we get the value?To determine the velocity, represented by vector AC, of Michelle's canoe, use the concept of vector addition.
Break down the motion into its components:
1. Paddling due east at 10 miles per hour: This motion can be represented by a vector pointing in the positive x-direction with a magnitude of 10 mph.
2. Wind blowing due south at 5 miles per hour: This motion can be represented by a vector pointing in the negative y-direction with a magnitude of 5 mph.
To find the resultant velocity, add these two vectors. Using the Pythagorean theorem, calculate the magnitude of the resultant velocity:
AC² = AB² + BC²
AB (paddling east) = 10 mph
BC (wind blowing south) = -5 mph (negative sign due to opposite direction)
AC² = (10 mph)² + (-5 mph)²
AC² = 100 mph² + 25 mph²
AC² = 125 mph²
Taking the square root of both sides:
AC ≈ √(125) mph
AC ≈ 11.2 mph (rounded to the nearest tenth)
Therefore, the velocity represented by vector AC of Michelle's canoe is approximately 11.2 miles per hour.
The correct answer is option C: 11.2 miles per hour.
learn more about velocity: https://brainly.com/question/80295
#SPJ1
Let f(x)
(4-x-x²
2x - 1
lim
2+1
Use a graph to determine the following limits. Enter DNE if the limit does not exist.
lim
2-1
f(x) =
f(x)
if x ≤ 1
if x > 1
lim f(x)
z 1
Answer:
See below for answers and explanations
Step-by-step explanation:
[tex]\displaystyle \lim_{x\rightarrow1^{-}}f(x) = 4-(1)-(1)^2=4-1-1=3-1=2\\\\\lim_{x\rightarrow1^{+}}f(x) = 2(1)-1=2-1=1\\\\\lim_{x\rightarrow1}f(x) = DNE[/tex]
Note that [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)[/tex] represents the left-side limit (so the limit of f(x) as x approaches 1 from the left), and [tex]\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex] represents the right-side limit (so the limit of f(x) as x approaches 1 from the right)
Because [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)\neq\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex], then [tex]\displaystyle \lim_{x\rightarrow1}f(x)=DNE[/tex]
I hope this helped!
1-56.
The owner of Universal Widgets has two teams of employees and
wants to know which team is working the "best." The assistant
manager gathered data for the number of widgets made per team
member on various days. He presented the data to the owner as
two boxplots, shown at right. The owner is confused.
a. Help the owner decide which team is working the "best"
by comparing center, shape, spread, and outliers.
b. Which team had a smaller standard deviation? Explain.
200
150
100
30
Team I
A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
The work done in stretching the spring from 10 centimeters to 40 centimeters is 9000 joules.
To determine the work done in stretching the spring from 10 centimeters to 40 centimeters, we need to understand the relationship between force, displacement, and work.
In this case, we are given that a force of 450 newtons stretches the spring by 30 centimeters.
We can use this information to calculate the spring constant (k) using Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement it undergoes.
Hooke's Law: F = kx
Where:
F is the force applied,
k is the spring constant, and
x is the displacement of the spring.
We can rearrange the equation to solve for k:
k = F / x
k = 450 N / 30 cm
k = 15 N/cm
Now that we have the spring constant, we can calculate the work done in stretching the spring from 10 cm to 40 cm using the formula for work:
Work [tex]= (1/2)k(x2^2 - x1^2)[/tex]
Where:
k is the spring constant,
x1 is the initial displacement, and
x2 is the final displacement.
Plugging in the values:
Work [tex]= (1/2)(15 N/cm)(40 cm^2 - 10 cm^2)[/tex]
Work [tex]= (1/2)(15 N/cm)(1200 cm^2)[/tex]
Work [tex]= (1/2)(15 N/cm)(1200 cm^2)[/tex]
Work = 9000 N·cm or 9000 joules (since 1 N·cm = 1 joule)
For similar question on spring.
https://brainly.com/question/28203351
#SPJ8
Applying the General Multiplication Rule A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event B be choosing a black ball first and event R be choosing a red ball second. What are the following probabilities? P(B) = P(R | B) = P(B ∩ R) = The probability that the first ball chosen is black and the second ball chosen is red is about percent.
The probability that the first ball chosen is black and the second ball chosen is red is 24.24%
How do i determine the probability?First, we shall obtain the total balls present in the box. Details below:
Red ball (R) = 4Black ball (B) = 8Total ball =?Total ball = 4 + 8
Total ball = 12 balls
Next, we shall obtain the probability of chosen a black ball first. Details below:
Black ball (B) = 8Total ball = 12 ballsProbability of chosen a black ball first, P(B) =?P(B) = n(B) / n(T)
P(B) = 8 / 12
Next, we shall obtain the probability of chosen red as the 2nd ball. Details below:
Red ball (R) = 4Total pen = 11Probability of chosen red as the 2nd ball, P(R | B) =?P(R | B)= n(R) / n(T)
P(R | B) = 4 / 11
Finally, we shall obtain the probability that the first ball chosen is black and the second ball chosen is red. Details below:
Probability of chosen a black ball first, P(B) = 8 / 12Probability of chosen red as the 2nd ball, P(R | B) = 3 / 11Probability that the 1st ball is black and the 2nd is red, P(B ∩ R) =?P(B ∩ R) = [P(B) × P(R | B)] × 100
P(B ∩ R) = [(8 / 12) × (3 / 11)] × 100
P(B ∩ R) = 0.2424 × 100
P(B ∩ R) = 24.24%
Thus, the probability that the first ball chosen is black and the second ball chosen is red is 24.24%
Learn more about probability:
https://brainly.com/question/17142351
#SPJ1
Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4.4 in. Each of the triangular faces has a base of 4.4 in and a height of 3.8 in. How much paper would it take to cover the entire pyramid?
52.8 square inches of paper to cover the entire Pyramid.
The amount of paper needed to cover the entire pyramid, we need to determine the total surface area of the pyramid.
The pyramid consists of a square base and four triangular faces.
1. Base Surface Area:
The surface area of the square base can be calculated by finding the area of a square with sides measuring 4.4 inches. The formula for the area of a square is side length squared:
Base Surface Area = (4.4 in)² = 19.36 in²
2. Triangular Faces Surface Area:
Each triangular face of the pyramid has a base of 4.4 inches and a height of 3.8 inches. The formula for the area of a triangle is 1/2 times the base times the height:
Triangular Face Surface Area = 1/2 * (4.4 in) * (3.8 in) = 8.36 in²
Since the pyramid has four triangular faces, the total surface area of the triangular faces is:
Total Triangular Faces Surface Area = 4 * (8.36 in²) = 33.44 in²
3. Total Surface Area:
To calculate the total surface area of the pyramid, we add the base surface area to the total triangular faces surface area:
Total Surface Area = Base Surface Area + Total Triangular Faces Surface Area
= 19.36 in² + 33.44 in²
= 52.8 in²
Therefore, it would take approximately 52.8 square inches of paper to cover the entire pyramid.
To know more about Pyramid.
https://brainly.com/question/30615121
#SPJ8
the region in the first quadrant enclosed by the curves y=0, x=2, x=5 and y=1/sqrt(1+x) is rotated about the x-axis. The volume of the solid generated is A. πIn(2) B. πIn(3/4) C. πIn(10) D. πIn(5) E. πIn(4/3)
The volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and [tex]y=1/\sqrt(1+x)[/tex] about the x-axis is πln(2),
(option A).
To find the volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and[tex]y=1/\sqrt(1+x)[/tex] about the x-axis, we need to use the formula for the volume of a solid of revolution.
The formula is ∫[a,b] [tex]π(f(x))^2dx[/tex], where a and b are the limits of integration and f(x) is the function that describes the distance between the axis of revolution and the curve being rotated.
In this case, we need to use the function f(x) = 1/sqrt(1+x), since this function describes the distance between the x-axis and the curve being rotated. The limits of integration are from x=2 to x=5, since these are the values of x that define the region being rotated.
Using the formula, we can set up the integral as follows:
[tex]∫[2,5] π(1/\sqrt(1+x))^2dx[/tex]
= π∫[2,5] 1/(1+x) dx
= π[ln(1+x)]|[2,5]
= π[ln(6) - ln(3)]
= πln(2) (option-A)
For such more questions on volume
https://brainly.com/question/463363
#SPJ8
Cold Beans wants to make a blend of their two best coffees, Guatemalan and Jamaican coffee. The pound of Guatemalan Coffee costs $11/lb and the other one costs $5/lb. If they want the cost of a 6 pound bag of blend to be $8/lb, how much Guatemalan coffee should they use per pound of the blend?
For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use [tex]3 \times 6 = 18[/tex]pounds of Guatemalan coffee.
Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.
Given information:
Cost of Guatemalan coffee = $11/lb
Cost of the other coffee = $5/lb
Desired cost of the blend = $8/lb
Total weight of the blend = 6 pounds
To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:
[tex](x \times 11 + (6 - x) \times 5) / 6 = 8[/tex]
In this equation, [tex](x \times 11)[/tex] represents the cost of the Guatemalan coffee in the blend, and[tex]((6 - x) \times 5)[/tex] represents the cost of the other coffee in the blend.
The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.
Now, let's solve the equation for x:
(11x + 30 - 5x) / 6 = 8
6x + 30 = 48
6x = 48 - 30
6x = 18
x = 18/6
x = 3
Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.
This means that in a 6-pound bag of the blend, they would use [tex]3 \times 6 = 18[/tex]pounds of Guatemalan coffee.
To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.
For similar question on cost.
https://brainly.com/question/2292799
#SPJ8
Which country is directly east of the Atlantic Ocean?
A conveyor belt carries supplies from the first floor to the second floor which is 23 feet higher. The belt makes a 60-degree angle with the ground.
How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot.
PLEASE no spam!!
Answer:
caculations below
Step-by-step explanation:
A conveyor belt carries supplies from the first floor to the second floor which is 23 feet higher. The belt makes a 60-degree angle with the ground.
To calculate the distance traveled by the supplies from one end of the conveyor belt to the other, we can use the trigonometric function of sine.
sin(60) = opposite / hypotenuse
Here, the opposite side is the height difference between the two floors, which is 23 feet.
sin(60) = 23 / hypotenuse
To find the hypotenuse, we can rearrange the above equation:
hypotenuse = 23 / sin(60)
Using a calculator, we get:
hypotenuse = 26.5 feet
Therefore, the supplies travel approximately 26.5 feet from one end of the conveyor belt to the other.
Rounding the answer to the nearest foot, we get:
The supplies travel approximately 27 feet from one end of the conveyor belt to the other.
Match the point in slope, given to the corresponding equation of a line
(3,6) and slope =1/2
(2,1) and slope =1/3
(4,-2) and slope = -2
(-2,8) and slope = 1
(-4,3) and slope = -1/2
Using the slope-intercept form, the equation of the lines are
a. 2y = x + 9
b. 3y = x + 1
c. y = x - 6
d. y = x + 10
e. y = -1/2x + 1
What are the equation of line?In the given question, we have the coordinate of a point and the slope of the line.
To determine the equation of the straight line, we have to use the formula of slope-intercept which is given as; y = mx + c.
Plugging the values into the formula.
a. (3, 6) and slope = 1/2
equation of line = y = mx + c = 6 = 1/2(3) + c
6 = 3/2 + c
c = 9/2
The equation of line is y = 1/2x + 9/2 ; 2y = x + 9
b. The point is (2,1) and slope is 1/3
Equation of line is;
y = mx + c
1 = 1/3(2) + c
c = 1 - 2/3
c = 1/3
Equation of line is y = 1/3x + 1/3; 3y = x + 1
c. The point is (4, -2) and slope is 1
y = mx + c
-2 = 1(4) + c
c = -2 - 4 = -6
y = x - 6
d. The point is (-2, 8) and slope is 1
y = mx + c
8 = 1(-2) + c
c = 10
y = x + 10
e. The point is (-4, 3) and slope is -1/2
y = mx + c
3 = -1/2(-4) + c
3 = 2 + c
c = 1
y = -1/2x + 1
Learn more on equation of straight line here;
https://brainly.com/question/18831322
#SPJ1
The frequency table shows the results of a survey about favorite exhibits. Find the relative frequency that a randomly selected student's favourite exhibit was either dinosaurs, or planets, express your answer as a decimal.
Butterfly: 12
Dinosaurs: 25
Planets: 17
Trains: 6
The relative frequency that a randomly selected student's favorite exhibit was either dinosaurs, or planets is 0.7.
How do we find the relative frequency?To find the relative frequency, we will divide the number of students who chose dinosaurs or planets by the total number of students surveyed.
The total number of students surveyed is 12 + 25 + 17 + 6 = 60.
The number of students who chose dinosaurs or planets is 25 + 17 = 42.
Therefore, the relative frequency will then be 42 / 60 = 0.7.
Find more exercises on relative frequency;
https://brainly.com/question/28343487
#SPJ1
you have two rocks made of the same material the same temperature. The first rock has twice the mass of the second rock. How does the thermal energy of the two rocks comare
The thermal energy of the first rock is twice the Thermal energy of the second rock.
The thermal energy of an object is directly proportional to its mass. Therefore, if the first rock has twice the mass of the second rock, it will also have twice the thermal energy.
Thermal energy is a measure of the internal energy of an object, which includes the kinetic energy of its particles. In this case, since both rocks are made of the same material and are at the same temperature, we can assume that their particles have the same average kinetic energy per particle.
The thermal energy of an object can be calculated using the formula:
Thermal energy = Mass * Specific heat capacity * Change in temperature
Since the specific heat capacity and the change in temperature are the same for both rocks (as they are made of the same material and are at the same temperature), we can simplify the comparison of their thermal energies based on mass alone.
Let's denote the mass of the second rock as "m" (arbitrary unit). Since the first rock has twice the mass, its mass can be represented as "2m".
Therefore, the thermal energy of the first rock is:
Thermal energy of the first rock = (2m) * Specific heat capacity * Change in temperature
And the thermal energy of the second rock is:
Thermal energy of the second rock = m * Specific heat capacity * Change in temperature
Comparing the thermal energies:
Thermal energy of the first rock / Thermal energy of the second rock = (2m) * Specific heat capacity * Change in temperature / (m) * Specific heat capacity * Change in temperature
The specific heat capacity and the change in temperature cancel out, leaving us with:
Thermal energy of the first rock / Thermal energy of the second rock = 2m / m = 2
Therefore, the thermal energy of the first rock is twice the thermal energy of the second rock.
To know more about Thermal energy.
https://brainly.com/question/28944987
#SPJ8
NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
Consecutive Interior Angles.
They are on the same side of a line that cuts through two other lines.
A missile is moving 1810 m/s at a 20.0° angle. It needs to hit a target 19,500 m away in a 32.0° direction in 9.20 s. What is the magnitude of the acceleration that the engine must produce?
Answer:
Aprox: 465.4 ms/2
Step-by-step explanation:
To find the magnitude of the acceleration the engine must produce, we'll break down the missile's motion into its horizontal and vertical components.
Given:
Initial velocity (V₀) = 1810 m/s
Launch angle (θ) = 20.0°
Target distance (d) = 19,500 m
Target direction (φ) = 32.0°
Time of flight (t) = 9.20 s
First, let's find the horizontal and vertical components of the missile's initial velocity (V₀x and V₀y).
V₀x = V₀ * cos(θ)
V₀y = V₀ * sin(θ)
V₀x = 1810 m/s * cos(20.0°) ≈ 1712.4 m/s
V₀y = 1810 m/s * sin(20.0°) ≈ 618.8 m/s
Now, let's find the horizontal and vertical displacements (dx and dy) of the missile using the time of flight (t) and the target distance (d).
dx = d * cos(φ)
dy = d * sin(φ)
dx = 19,500 m * cos(32.0°) ≈ 16,402.8 m
dy = 19,500 m * sin(32.0°) ≈ 10,236.8 m
Next, let's calculate the acceleration needed in the x-direction (ax) and y-direction (ay) to cover the horizontal and vertical displacements in the given time.
ax = (2 * dx) / t²
ay = (2 * dy) / t²
ax = (2 * 16,402.8 m) / (9.20 s)² ≈ 391.7 m/s²
ay = (2 * 10,236.8 m) / (9.20 s)² ≈ 257.7 m/s²
Finally, to find the magnitude of the acceleration, we can use the Pythagorean theorem:
acceleration magnitude (a) = √(ax² + ay²)
a = √(391.7 m/s²)² + (257.7 m/s²)² ≈ 465.4 m/s²
Therefore, the magnitude of the acceleration that the engine must produce is approximately 465.4 m/s².
93°
65°
m
X
finding the angle of x
The measure of angle C is,
⇒ x = 22°
We have to given that,
In a triangle ABC,
Angle A = 65 degree,
Angle B = 93 degree.
Now, Let us assume that,
Measure of angle C = x
Hence, We get;
⇒ ∠A + ∠B + ∠C = 180°
Substitute all the values,
⇒ 65 + 93 + x = 180
⇒ 158 + x = 180
⇒ x = 180 - 158
⇒ x = 22
Therefore, The measure of angle C is,
⇒ x = 22°
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
Complete question is,
In Triangle ABC, Angle A = 65 degree, B=93 degree. Find Angle C?
Need help asap
Robin's teacher asked her to find a box that would hold some small
1 inch cubes that the kindergartners used for counting. Robin
found three boxes with the following dimensions: Box A: 4" x 6" x
8" Box B: 6" x 3" x 12" Box C: 6" x 6" x 4" Which box would be
able to hold all the cubes if Robin's teacher had 200 cubes? Box
Volume of Box A =
cu.in.
Volume of Box C =
cu.in. Volume of Box B =
30 pts
cu.in.
The box that would be able to hold all the cubes if Robin's teacher had 200 cubes is given as follows:
Box B.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:
Volume = length x width x height.
Hence the volumes for each box in this problem are given as follows:
Box A: 4 x 6 x 8 = 192 cubic inches.Box B: 6 x 3 x 12 = 216 cubic inches.Box C: 6 x 6 x 4 = 144 cubic inches.As 216 > 144, Box B is the box that could hold all of the 200 cubes.
A similar problem about the volume of rectangular prisms is presented at brainly.com/question/22070273
#SPJ1
HELPP PLEASEE I REALLY NEEED THIS 7 cm
What is the volume of the figure?
3 cm
5 cm
Answer:
Volume = 105 cm³
Step-by-step explanation:
Volume of a cuboid = l × b × h (l = length. b = breadth. h = height)
Volume = 7 × 5 × 3
Volume = 35 × 3
Volume = 105 cm³
Brian cut of 25% of a stick which was 1.6 meters long what percent of the stick is remaining
Answer:
The remaining is 75%, the length of the stick would be 1.2
Step-by-step explanation:
According to the information given,
We know that Brian cut off 25% of a stick which was 1.6 meters long
and 1.6 is the 100% of the stick:
It is fairly easy to calculate this, subtract 25 from 100 ( 100 - 25 ), which is equal to 75.
Hence, the answer is 75% and 1.2 for the remaining length of the stick
For more information about percentages, go to: https://brainly.com/app/ask?q=how+to+find+the+percentage
HELP ME ASAPPPPPPPP WILL MARK BRAINLIEST PLEASEEEEEEEEEE SHOW WORK THANK YOUUUUUUU
A scientist has carbon-dated a piece of fossilized tree bark that is thought to be over 5,000 years old. The scientist determines that the sample contains 75% of the original amount of carbon-14. The half-life of carbon-14 is 5730 years. Is the scientist's hypothesis of the tree bark being over 5,000 years old correct?
The calculated age of the sample is 2865 years. Since this is less than 5,000 years, the scientist's hypothesis that the tree bark is over 5,000 years old is incorrect.
To determine if the scientist's hypothesis is correct, we can use the concept of half-life and the given information.
The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the original amount of carbon-14 in a sample would have decayed.
In this case, the fossilized tree bark is thought to be over 5,000 years old. If the sample contains 75% of the original amount of carbon-14, it means that 25% of the carbon-14 has decayed.
Let's calculate the number of half-lives that have passed:
(100% - 75%) / 50% = 0.25 / 0.5 = 0.5
So, 0.5 half-lives have passed.
Since each half-life is 5730 years, we can calculate the approximate age of the sample:
0.5 half-lives × 5730 years per half-life = 2865 years
The calculated age of the sample is 2865 years. Since this is less than 5,000 years, the scientist's hypothesis that the tree bark is over 5,000 years old is incorrect.
for such more question on scientist's hypothesis
https://brainly.com/question/24029881
#SPJ8
NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
Determine the voltage dropped on R3, given:
ET = 1325 V, R1 = 76 Ω, R2 = 61 Ω, R3 = 30 Ω, and R4 = 30 Ω
The voltage drop across resistor R₃ is determined as 237.9 V.
What is the total current flowing in the circuit?
The total current flowing in the circuit is calculated by applying Ohm's law as shown below.
V = IR
I = V / R
where;
V is the total voltage in the circuitR is the total resistance of the circuitSince the circuit is in series connection, the total resistance is calculated as follows;
R = R₁ + R₂ + R₃
R = 76 ohms + 61 ohms + 30 ohms
R = 167 ohms
The current flowing in each circuit component is calculated as;
I = V/R
I = 1325 V / 167Ω
I = 7.93 A
The voltage drop across R₃ is calculated as follows;
V₃ = IR₃
V₃ = 7.93 x 30
V₃ = 237.9 V
Learn more about voltage drop here: https://brainly.com/question/2491461
#SPJ1
The complete question is below:
This cirucit is in series. Determine the voltage dropped on R3, given:
ET = 1325 V, R1 = 76 Ω, R2 = 61 Ω, R3 = 30 Ω, and R4 = 30 Ω
2. The table includes results from polygraph experiments. In each case, it was known if the
subject lied or did not lie, so the table indicates when the polygraph test was correct. Find the
test statistic needed to test the claim that whether a subject lies or does not lie is independent of
the polygraph test indication.
Polygraph test indicated
that the subject lied.
Polygraph test indicated
that the subject did not lie.
025.571
Did the Subject Actually Lie?
No (did not lie) Yes (lied)
15
32
42
9
(1 poir
We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
How to explain the hypothesisThe test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.
In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:
The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.
Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
Learn more about hypothesis on
https://brainly.com/question/11555274
#SPJ1
Helpppolll ILL GIVE BRSINLYIST ANYTHIBG.
17 in.
8 in.
7
17 in.
30 in.
What is the volume of this figure?
15 in.
The volume of the given figure is 750 in.
Given
Base =30in
Height = 8in
Side = 15
Side = 17
Required to calculate the volume of the given figure
Volume = Base x Height + 2 side x side (there are two rectangle)
= 30 x 8 + 2 x 15 x 17
= 750
The region that a 2D shape covers in an area versus the space a 3D shape occupies is the main distinction between area and volume. Geometry is filled with a wide variety of shapes and sizes.
A mass is a solid body or an assortment of distinguishable visual components that together make a solid form, such as lines, colors, textures, etc. Length, width, and depth make up the three dimensions of volume.
Thus, the volume of the given figure is 750.
Learn more about Volume here:
https://brainly.com/question/24086520
#SPJ1
Robert is baking a cake. He
needs 5 cups of milk, but notices that
his measuring device is only marked in
pints.
How many pints of milk will Robert
need?