Answer:
Option C is the correct answer
Step-by-step explanation:
Let μ1 be the average flying speed of monarch butterflies and let μ2 be the average flying speed of swallowtail butterflies.
Also, let n1 be the sample size of monarch butterflies and let n2 be the sample size of swallowtail butterflies.
Thus, defining the hypothesis, we have;
Null hypothesis;H0: μ1 = μ2
Alternative hypothesis; H1: μ1 > μ2
In this case, the p-value = P_H0[t_(n1 + n2 - 2) ≥ t] where t is the test statistic based on tbe differences of sample mean,that follows t distribution with degrees of freedom (n1 + n2 - 2)
With respect to the question, the probability of the monarchs and swallowtails flying at the same speed is 0.072.
Thus,
P_H0[t_(n1 + n2 - 2) ≥ t] = 0.072
We can therefore conclude that in this case, the p-value is the probability of observing a difference equal to or greater than the sample difference under the null hypothesis which states that μ1 = μ2, which is 0.072
Thus, option C is the correct answer
Answer:
The correct option is;
b. The probability that monarchs and swallowtails fly at the same speed is 0.072
Step-by-step explanation:
The p- value indicates the probability of which the hypothesis tested, the null hypothesis is true and it is compared against a given confidence level. Whereby the p-value is more than the given confidence level then it indicates that the null hypothesis assumption is correct.
Therefore, whereby the null hypothesis tests proposes the equality of the two means, then at a 5% confidence level or α = 0.05, whereby p-value = 0.072 > α = 0.05 we accept the null hypothesis and state that the probability that monarchs and swallowtails fly at the same speed is 0.072.
Solve the equation
X/4 +2 = -2
Answer:
x = -16
Step-by-step explanation:
subtract the two over first so x/4 = -4
multiply both sides by 4
x = -16
Answer:
x = -16
Step-by-step explanation:
First subtract -2 on both sides. Then you will get x/4 = -4
Then multiply 4 on both sides. This will then give you x = -16 because -4*4 = 16
PLEASEE HELP ME! WILL MARK BRAINLIEST!!
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 20 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 6 and width of 2 Write an equation to determine the area, A, of the patio that will be painted.
A. A = (x + 20)(x + 10) + 12
B. A = (x + 20)(x + 10) − 12
C. A = (x + 26)(x + 12)
D. A = (x + 14)(x + 8)
Answer:
B. A = (x + 20)(x + 10) - 12
Step-by-step explanation:
please kindly check the attached file for explanation
Jonathan's new car cost $29,000. After a year, the value of the car is $23,490. If the car depreciates by a fixed factor every year, what will be the value of the car two years after its purchase?
A. $23,985.90
B. $16,933.10
C. $19,026.90
D. $18,971.80
Answer:
I think It would be C or B
Step-by-step explanation:
Depending on the value of the car at first purchase.
Answer:
C
Step-by-step explanation:
23,490/29000=0.81
0.81*23,490=19026.90
The triangle below are similar. What is the scale factor of triangle ABC to triangle DEF?
What is the approximate area of the shaded sector in the circle shown below?
Answer:
A; The approximate area of the shaded sector is 283[tex]cm^{2}[/tex]
Step-by-step explanation:
In this question, we are tasked with calculating the area of the sector of a circle that subtends a particular angle at the center of the circle
To calculate this, we use the formula for the area of a sector.
Mathematically,
Area of the shaded sector = θ/360 × π × [tex]r^{2}[/tex]
In this question, The angle subtended by the sector ;θ = 100° and radius of the circle r = 18 cm
Area = 100/360 × 22/7 × [tex]18^{2}[/tex] = 712,800/2520 = 282.86 which is approximately 283[tex]cm^{2}[/tex]
Answer:
[tex]A \approx 282.743\,cm^{2}[/tex]
Step-by-step explanation:
The approximate area of the shaded sector is:
[tex]A = \frac{100}{360}\cdot \pi\cdot (18\,cm)^{2}[/tex]
[tex]A \approx 282.743\,cm^{2}[/tex]
Given the following formula solve for r
Answer:
D
Step-by-step explanation:
C = 2pir
Divide both sides by 2pi
C/(2pi) = 2pi/2pi r -->
C/(2pi) = r
That's D
The required solution of given formula is r = C/(2π). which is the correct answer would be option (D)
What is the Circumference of a circle?
The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
We have been given that formula as:
⇒ C = 2πr
We have to formula solve for r
⇒ C = 2πr
Divide both sides by 22π
⇒ C/(2π) = r2π/2π
⇒ C/(2π) = r or
⇒ r = C/(2π)
Hence, the correct answer would be option (D)
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2 1/7 divided by 1 1/14
Answer: 2
Turn 2 1/7 into an Improper Fraction
Multiply 2×7 and get 14. Now add 1 and get 15.
2 1/7 = 15/7
Turn 1 1/14 into an Improper Fraction
Multiply 1×14 and get 14. Now add 1 and get 15.
1 1/14 = 15/14
Your New Problem: 15/7×15/14
Multiply
15/7×15/14=225/98
Simplify
225/98=2.29591836735
Round (Nearest ones)
2.29591836735 rounded equals 2
Final Answer: 2
Answer:
[tex]2[/tex]
Step-by-step explanation:
[tex]2 \frac{1}{7} \div 1 \frac{1}{14} \\ \frac{15}{7} \div \frac{15}{14} \\ \frac{15}{7} \times \frac{14}{15} \\ = \frac{2}{1} = 2[/tex]
Find the area of triangle? 15ft 20ft
Answer:
I see your profile everywhere, and the answer is Right scalene Pythagorean triangle.
Step-by-step explanation:
The guidance department has reported that of the senior class, 7.8% are members of key club, K, 8.6% are enrolled in AP Physics, P, and 6.7% are in both. 1) Determine the probability of P given K, to the nearest tenth of a percent. 2) The principal would like a basic interpretation of these results. Write a statement relating your calculated probabilities to student enrollment in the given situation.
Answer:
the probability of P given K is 0.86
Step-by-step explanation:
Conditional probability is defined as the probability that an event would happen based on the occurrence of an event that has already happened. It is calculated by multiplying the probability of the both the preceding event and the succeeding event together. It is given by the formula:
[tex]P(B/A)=\frac{P(A nB)}{P(A)}[/tex]
Given that:
Probability of members in the key club P(K) = 7.8% = 0.078
Probability of members enrolled in AP physics P(P) = 8.6% = 0.086
Probability of members in both P(P n K) = 6.7% = 0.067
Therefore:
[tex]P(P/K)=\frac{P(PnK)}{P(K)} =\frac{0.067}{0.078} = 0. 86[/tex]
the probability of P given K is 0.86
Put the quadratic into vertex form and state the coordinates of the vertex
Answer: f(x) = (x+6)^2 -25
vertex is (-6, -25)
Step-by-step explanation: complete the square, than use the binomial formula, then simplify and expand
Answer:
equation is y = (x+1)(x+11)
vertex: (-1,-11)
Step-by-step explanation:
y = x^2 + 12x + 11. The last value, the value 11 is how we can determine our values in the equation. First we need to find the factors of positive 11 which are: -11 * -1 and 1*11. now we will look at the second portion the 12x. As we can see the value is positive. Now we will add the two factors together and see which one gives us positive 12. The factors 1 and 11 make positive 12. Now we simply just need to add those values to x. When this is factored down or in other words vertex form, the equation is y = (x+1)(x+11). The vertex is what value would make the equation equal 0. Since -1 + 1 equals 0 then that is one of the vertex and since -11 + 11 equal 0 that also makes that a vertex. This makes the vertex -1,-11.
Ben invites red part of his $15,000 savings in stocks paying 4.25% simple interest annually. He invested the rest in bonds paying 3.75% simple interest annually. If Ben earned $594.50 in interest after one year, how much did he invest in stocks? How much did he invest in bonds?
Answer: he invested $8600 in bonds.
Step-by-step explanation:
Let x represent the part of his money that he invested in stocks.
Let y represent the part of his money that he invested in bonds.
Ben invested part of his $15,000 savings in stocks paying 4.25% simple interest annually. He invested the rest in bonds paying 3.75% simple interest annually. It means that
x + y = 15000
The interest that he would earn on the amount invested in stocks after 1 year is
4.25/100 × x = 0.0425x
The interest that he would earn on the amount invested in bonds after 1 year is
3.75/100 × y = 0.0375y
If Ben earned $594.50 in interest after one year, it means that
0.0425x + 0.0375y = 594.5- - - - - - 1
Substituting x = 15000 - y into equation 1, it becomes
0.0425(15000 - y) + 0.0375y = 594.5
637.5 - 0.0425y + 0.0375y = 594.5
- 0.0425y + 0.0375y = 594.5 - 637.5
- 0.005y = - 43
y = - 43/- 0.005
y = $8600
x = 15000 - 8600
x = $6400
In March, there will be two conferences: one for math and one for history. So far, 7 people have signed up for the math conference and two more people sign up each day. There are 11 people who have signed up for the history conference, but only one more person signs up each day. After how many days will the number of people attending both conferences be the same?
Answer:
After 4 days, the number of people attending both conferences be the same.
Step-by-step explanation:
We are given the following in the question:
Maths conference:
Number of people already signed = 7
Number of people who sign up each day = 2
Thus, the number of people who will sign up for maths conference in x days will be given by the linear function:
[tex]f(x) = 7+2x[/tex]
History conference:
Number of people already signed =11
Number of people who sign up each day = 1
Thus, the number of people who will sign up for maths conference in x days will be given by the linear function:
[tex]g(x) =11+x[/tex]
Both conference will have same number of people when
[tex]f(x) = g(x)\\\Rightarrow 7 + 2x = 11+x\\\Rightarrow x = 4[/tex]
Thus, after 4 days, the number of people attending both conferences be the same.
A floor plan shows that the exterior of a room has dimensions 12 feet by 17 feet. If the area of the room measured from the interior is only 176 square feet, express the thickness of the surrounding walls in feet. (Assume that the walls have uniform thickness).
Answer:
The thickness of the walls is 0.5 feet.
Step-by-step explanation:
Let's call the thickness of each all by T.
The external dimensions of the room are 12 feet by 17 feet, and these values include thickness of 2 walls each, so the internal dimensions are (12-2T) and (17-2T).
If the internal area is 176, we have the equation:
(12-2T) * (17-2T) = 176
204 - 58T + 4T2 = 176
4T2 - 58T + 28 = 0
2T2 - 29T + 14 = 0
Using Bhaskara, we have:
Delta = (-29)^2 - 4*2*14 = 729
sqrt(D) = 27
T1 = (29 + 27)/4 = 14 feet
T2 = (29 - 27)/4 = 0.5 feet
As the first value is too big and would generate a negative side for the room, we have that the thickness of the walls is 0.5 feet.
If I make $200 a sec how long will it take to reach $20,000?
Answer:
100 seconds or 1 minute 40 seconds
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
20,000 divided by 200
=100
work out the circumference of this circle take (pie) to be 3.142 and give ur answer in 1 decimal place radius=9m
The circumference of a circle with a radius of 9 meters, using pi as 3.142, is calculated as 56.6 meters when rounded to one decimal place.
Explanation:The circumference of a circle can be calculated using the formula C = 2πr, where r is the radius of the circle.
In this case, the radius of the circle is 9m. Let's substitute this value into the formula:
C = 2 × 3.142 × 9
C = 56.556m
Therefore, the circumference of the circle is 56.6 meters (rounded to 1 decimal place).Calculating the Circumference of a Circle
To calculate the circumference of a circle with a radius (r) of 9 meters and using π (pi) as 3.142, we use the formula C = 2πr. By plugging in the given values, we get C = 2 × 3.142 × 9m. Performing the multiplication, we find that the circumference is 56.556 meters. Since we need to give our answer with one decimal place, we round to 56.6 meters.
The step-by-step calculation involves:
Multiplying the radius by 2 to find the diameter.Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y)(x,y) point. y=4x^2-8x-12
The vertex of the parabola [tex]y=4x^2-8x-12[/tex] is (1, -16).
To find the coordinates of the vertex of the parabola [tex]y=4x^2-8x-12[/tex], we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 4 and b = -8.
Plugging these values into the formula, we get x = -(-8)/(2*4) = 1.
Now, we can substitute this value of x back into the equation to find the corresponding y-coordinate.
Plugging x = 1 into y = [tex]4x^2-8x-12[/tex], we get y = [tex]4*1^2 - 8*1 - 12 = -16[/tex].
Therefore, the vertex of the parabola is (1, -16).
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Final answer:
The vertex of the parabola [tex]y=4x^2-8x-12[/tex] is found by completing the square and transforming the equation into vertex form, resulting in the vertex coordinates at (1, -16).
Explanation:
To find the coordinates of the vertex of the parabola given by the equation [tex]y=4x^2-8x-12,[/tex] we use the fact that the vertex form of a parabola's equation is[tex]y=a(x-h)^2+k,[/tex]where (h, k) is the vertex of the parabola. In this case, we can complete the square to transform the given equation into vertex form. To do that, we can factor out the coefficient of [tex]x^2[/tex] from the first two terms:
[tex]y = 4(x^2 - 2x) - 12[/tex]
Now, we add and subtract the square of half the coefficient of x inside the parentheses, which is [tex](2/2)^2 = 1:[/tex]
[tex]y = 4(x^2 - 2x + 1 - 1) - 12[/tex]
[tex]y = 4((x - 1)^2 - 1) - 12[/tex]
[tex]y = 4(x - 1)^2 - 4 - 12[/tex]
[tex]y = 4(x - 1)^2 - 16[/tex]
Now that we have the equation in vertex form, we can see that the vertex of the parabola is at (1, -16).
The sum of three consecutive even numbers is one hundred sixty - two.
What is the smallest of the three numbers ?
Answer:
52
Step-by-step explanation:
Let x represent the smallest of the three numbers. Then the other two are (x+2) and (x+4). Their sum is ...
x + (x+2) +(x+4) = 162
3x = 156 . . . . . . . . . . . .subtract 6
x = 156/3 = 52
The smallest of the three numbers is 52.
___
I like to work problems like this by considering the average number. Here, the average of the three numbers is 162/3 = 54, the middle number of the three. Then the smallest of the three consecutive even numbers is 2 less, or 52.
Find two integers whose sum is -7 and product is 12
Answer:
-4 and -3
Step-by-step explanation:
-4 + -3 = -7
-4 times -3 = 12
The domain consists of all the __-values. x y
Answer:
The answer is:
The domain consists of all the x-values
Step-by-step explanation:
The domain is the set of possible input values
The domain is the set of all possible values of the independent variable
In any ordered pair (x , y), x is the input (independent)
The domain is all values of x which make the function defined
The range is the set of possible output values
The range is the complete set of all possible resulting values of the dependent variable
In any ordered pair (x , y), y is the out put (dependent)
The range is all values of y which corresponding to x
The answer is:
The domain consists of all the x-values
Find all solutions to (X+5)(2x-3)=0
Answer:
X+5
X = -5
-5 plus 5 equals 0
2x-3
X= 3/2
-3/2 plus 3/2 equals 0
The solutions to the equation (x+5) (2x-3) = 0 are x = -5 and x = 3/2.
Given that an equation (x+5) (2x-3) = 0, we need to find the solution of the equation,
To find the solutions to the equation (x+5) (2x-3) = 0, we set each factor equal to zero and solve for x,
Seetting x + 5 equal to 0:
x + 5 = 0
x = -5
Seetting 2x-3 equal to 0:
2x - 3 = 0
2x = 3
x = 3/2
Therefore, the solutions to the equation (x+5) (2x-3) = 0 are x = -5 and x = 3/2.
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Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person's name represents that person's position as he or she boards the bus: first, second, third, and fourth. If we know that Karen boards the bus first, which shows the possible outcomes for this event?
All the given options are valid and correct.
If Karen boards the bus first, the possible outcomes for the event are those where the other three band members board the bus in various orders after Karen. Let's consider the options:
1. KHIJ: This represents Karen boarding first, and the remaining band members (Harry, Isabel, and Jose) boarding in the order H, I, J. This is a valid outcome.
2. KHIJ, KHJI: These arrangements represent Karen boarding first, and the remaining band members boarding in different orders (H, I, J and H, J, I). Both are valid outcomes.
3. KHIJ, KHJI, KJHI, KJIH: These arrangements include all possible orders of the remaining band members after Karen. All of them are valid outcomes.
4. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH: These arrangements cover all possible orders of the band members after Karen, including swapping the positions of Harry and Isabel. All are valid outcomes.
Therefore, the possible outcomes for this event are all of the given options.
The given question seems incomplete, but the complete question could be:
Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person's name represents that person's position as he or she boards the bus: first, second, third, and fourth. If we know that Karen boards the bus first, which shows the possible outcomes for this event?
A. KHIJ
B. KHIJ, KHJI
C. KHIJ, KHJI, KJHI, KJIH
D. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH
The Mariana Trench in The Pacific Ocean is about 36,201 feet deep. Based on these data how many feet deeper is the marina trench than the Puerto Rico?
Answer:
The answer is 27,493 Puerto Rico Trench Depth Deepest Point In the Atlantic Ocean
Step-by-step explanation:
I need help solving this problem. At an only mapping site, Mr. Mosley notices that when he clicks a spot on the map, the map zooms in on that spot. The magnification increases by 20% each time. Write a formula for the nth term of the geometric sequence that represents the magnification of each zoom level. (Hint: The common ratio is not just 0.2.)
Answer:
1.2^n
Step-by-step explanation:
since a single dot brings about an increment by 20%, the total magnification becomes 120% after the click. The common ratio = 120 / 100 = 1.2
the formula becomes 1.2^n
The formula for the nth term of the geometric sequence that represents the magnification of each zoom level is an = (1.2)n-1.
Explanation:In this problem, you are looking at a geometric sequence that represents the magnification of each zoom level on a map. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
In this case, the common ratio is 1 + 0.2 = 1.2 because the magnification increases by 20% (or 0.2 in decimal form) each time. We can denote the nth termed 'an'. The general formula for the nth term in a geometric sequence is: an = a1 * rn-1.
Since the initial magnification doesn't specify a specific value, we will take a1 as 1 for this case. Substituting these values into the formula yields: an = 1 * (1.2)n-1, or just an = (1.2)n-1.
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Find the surface area and volume of the figure.
18 ft
11 ft
The problem involves finding the surface area and volume of a cylinder with a height of 18 ft and a diameter of 11 ft. Using the formulas for a cylinder's surface area and volume, appropriate calculations can be performed to determine the cylinder's surface area and volume.
Explanation:To find the surface area and volume of a given figure, we need to identify the shape of the object. The question does not specify the shape, but the provided formulas suggest that we might be dealing with a cylinder. For a cylinder:
The surface area (A) is calculated as the sum of the areas of the two circular bases (which are π×r² each, where r is the radius) plus the area of the side, which is the circumference of the base multiplied by the height (2π×r×h).The volume (V) is the area of the base (π×r²) multiplied by the height (h).If the cylinder has a height (h) of 18 ft and a diameter of 11 ft (radius is half of the diameter, so r = 5.5 ft), we can calculate its surface area and volume using the following formulas:
A = 2π×r×h + 2π×r²V = π×r²×hPlugging in the values:
A = 2π×5.5×18 + 2π×5.5²V = π×5.5²×18Now, you can substitute π with approximately 3.1416 to find the numeric answers. Remember to use the unit ft² for surface area and ft³ for volume.
Mrs. Delgado purchased notebooks at $2.50 each and pens at $2.00 per package. She spent $19.00 for a total of 8 items. Which system of equations below could be used to find n, the number of notebooks, and p, the number of packages per pens, that Mrs. Delgado purchased?
Answer:
n+p = 82.5n + 2p = 19Step-by-step explanation:
let n be the total number of notebooks.
let p be the total number of pens.
according to the question total number of pen and notebook is 8.
Therefore mathematically
n+p = 8 ---------------------equation A
______________________________________________
cost of one notebook = $2.50
number of notebook = n
therefore total cost of n notebook = n* 2.50 = 2.5n
cost of one pen = $2.00
number of pen = p
therefore total cost of p pen = p* 2.00 = 2p
according to the question total c cost of pen and notebook is $19.00.
Therefore mathematically
2.5n + 2p = 19 ---------------------equation B
______________________________________________
Set of equation as required by question are
n+p = 8 ---------------------equation A2.5n + 2p = 19 ---------------------equation BAnswer:
6,2
Step-by-step explanation:
(looked at in desmos)
True or False (& Justify): If a ball is thrown horizontally from the top edge of a 150m building at a speed of 25 m/sec, then the ball’s velocity and speed 3 seconds later will be <25, -39.2> and 46.493 m/sec.
Answer:
38.6 m/s
Step-by-step explanation:
The motion of the ball is a projectile motion, which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction
Therefore we have to analyze the horizontal and vertical motion separately.
Along the horizontal direction, the velocity is constant during the motion, since there are no forces acting in this direction. So the horizontal velocity 3 seconds after the launch will be the same as the velocity at the launch:
[tex]v_x = v_0 = 25 m/s[/tex]
The vertical velocity instead changes according to the suvat equation:
[tex]v_y = u_y - gt[/tex]
where
[tex]u_y=0[/tex] is the initial vertical velocity
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
t is the time
Therefore, after t = 3 s,
[tex]v_y=0-(9.8)(3)=-29.4 m/s[/tex]
So the velocity after 3 seconds is < 25, -29.4 > m/s. The magnitude of the velocity is
[tex]v=\sqrt{v_x^2+v_y^2}=\sqrt{25^2+(-29.4)^2}=38.6 m/s[/tex]
The statement is true regarding the horizontal component but contains a typo in the vertical component. A ball thrown horizontally from a 150m building will maintain its horizontal velocity but the vertical velocity will be -29.4 m/s after 3 seconds. The total speed will be 38.6 m/s, not 46.493 m/s.
The statement is True. To analyze the velocity and speed of a ball thrown horizontally, we will consider two components of the motion separately: the horizontal component, which remains constant due to the absence of horizontal forces when air resistance is ignored, and the vertical component, which changes due to gravity.
Horizontally, the velocity remains at the initial value of 25 m/s because no horizontal forces are acting on the ball (assuming air resistance is negligible).
Vertically, the acceleration due to gravity (g) is 9.8 m/s2. The vertical velocity (Vy) at a time t after release can be calculated using the equation Vy = g × t, which after 3 seconds gives us Vy = 9.8 m/s² × 3 s = 29.4 m/s.
Since the question states a vertical velocity of -39.2 m/s, there might be a typo, as the correct vertical velocity should be -29.4 m/s (negative sign indicates downward direction).
Now, to find the overall speed, we use the Pythagorean theorem: speed = \/(Vx² + Vy²). Substituting Vx = 25 m/s and Vy = -29.4 m/s, we get the speed as 38.6 m/s (approximately).
Therefore, the provided velocity and speed are incorrect; the corrected velocity after 3 seconds is <25, -29.4> and the speed is approximately 38.6 m/s.
Miss tate travels from st. louis to indianapolis and back 12 times each year . the total distance of each round trip is 484 mileswhat is the total number of miles mistake travels from st. louis to indiana annapolis and back each year
Answer:
12x484=5808
Take 484x12 should be answer
Miss Tate travels a total of 5,808 miles each year making round trip journeys from St. Louis to Indianapolis and back 12 times.
Explanation:Miss Tate travels from St. Louis to Indianapolis and back, comprising a distance of 484 miles for each round trip. She does these trips 12 times a year. To find the total number of miles Miss Tate travels each year, we simply multiply the round-trip distance by the number of trips she makes. Therefore, when calculated, the total number of miles traveled by Miss Tate from St. Louis to Indianapolis and back each year is 484 miles * 12 = 5,808 miles.
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I NEED HELP ASAP IM BEING TIMED 5 MIN LEFT PLZZZZZZ HELP
Answer:
Step-by-step explanation:
on the number line your starting point is 6 then go back 9 and you will get -3
Plz help I’m bad at math
Answer:
Branliest appreciated
3. x = 14 degrees
4. x = 17.5 degrees
Step-by-step explanation:
SO, The first question:
6x - 21 = 105
6x = 105 -21
6x = 84
x = 14
SO, The second question:
55 + 85 = 8x
140 = 8x
17.5 = x
The following statements describe a set of railroad tracks. Based only on the
statement, make a conclusion about the rails or the railroad ties. Explain.
a. The railroad ties are each perpendicular to one rail.
b. The rails are parallel. One railroad tie is perpendicular to one rail.
Answer:
Part a) The railroad ties are parallel
Part b) One railroad tie is perpendicular to both rails
Step-by-step explanation:
Part a) The railroad ties are each perpendicular to one rail
we know that
if one line is perpendicular to several other lines, then the other lines are parallel
Conclusion:
If the railroad ties are each perpendicular to one rail then the railroad ties are parallel
That means----> The slopes of the railroad ties are equal and they are opposite reciprocal to the slope of the rail
Part b) The rails are parallel. One railroad tie is perpendicular to one rail
we know that
if two lines are parallel and another line is perpendicular to one of them, then this line is perpendicular to both lines
Conclusion:
If One railroad tie is perpendicular to one rail, then one railroad tie is perpendicular to both rails
That means ---> The slopes of the railroad ties are opposite reciprocal to the slope of the rail
Final answer:
The railroad ties are perpendicular to both rails, and the rails are parallel to each other, reflecting principles of linear perspective in geometry.
Explanation:
The student's questions relate to geometry, specifically the properties of lines and angles about railroad tracks and railroad ties. When analyzing these geometric structures, we draw on concepts such as parallel lines, and perpendicular lines, and the characteristics of their interaction.
Analysis of Statements
Statement a: If railroad ties are each perpendicular to one rail, and knowing that both rails in a railroad must be parallel, we can conclude that the ties are also perpendicular to the other rail. This is because perpendicular lines or segments are by definition at 90° to each other, and if one tie is perpendicular to one parallel rail it must be perpendicular to the other rail that is parallel to the first.Statement b: If one railroad tie is perpendicular to one rail and the rails are parallel, then every other railroad tie that is also perpendicular to one rail will be perpendicular to both rails, maintaining consistency in the geometry of the railroad structure.Therefore, we can conclude that the railroad ties are perpendicular to both rails and that the rails are parallel to each other. This aligns with linear perspective and the visual effect of perpendicular lines (orthogonal) converging at a vanishing point as they recede into the distance.