If a cube is sliced perpendicular to its base, the resulting two dimensional cross-section will be a square. This is because each face of a cube is a square, and a perpendicular slice across the base will result in a square shape. A trapezoid or a circle would not result from a perpendicular slice of a cube.
When a cube is sliced perpendicular to its base, the shape of the resulting two-dimensional cross-section is a square.
Step-by-step explanation:
1. A cube has six faces, all of which are squares.
2. When you slice the cube perpendicular to its base, you are cutting it in a direction that is at a 90-degree angle to the base.
3. Since all the faces of a cube are squares, the resulting cross-section from a perpendicular slice will also be a square.
So, the correct answer is option 2, a square.
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Question 15
Find the area of the quadrilateral with the vertices A (-8, 6), B(-5, 8), C (-2, 6), and D (-5,0).
units²
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The area of the quadrilateral can be found by dividing it into two triangles and finding the sum of their areas. The line connecting points B and D divides the quadrilateral into two triangles ABD and BCD. The area of triangle ABD is 1/2 * base * height = 1/2 * 6 * 6 = 18 square units. The area of triangle BCD is 1/2 * base * height = 1/2 * 3 * 8 = 12 square units. Therefore, the area of the quadrilateral is 18 + 12 = 30 square units.
A ball of radius 11 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.
The volume of the resulting solid is estimated 4,128.38 cubic units.
How do we calculate?
The volume of the ball isgitten as:
V_ball = (4/3)πr^3
r is the radius of the ball. In this scenario
r = 11, so:
V_ball = (4/3)π(11)^3
V_ball = (4/3)π(1331)
V_ball = 4,396.46 cubic units
The volume of the hole is gotten as :
V_hole = (4/3)πr^3
r is the radius of the hole.
In thisscenario, r = 4, so:
V_hole = (4/3)π(4)^3
V_hole = (4/3)π(64)
V_hole = 268.08 cubic units
In conclusion, the volume of the resulting solid is:
V_resulting_solid = V_ball - V_hole
V_resulting_solid = 4,396.46 - 268.08
V_resulting_solid = 4,128.38 cubic units
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Consider the graph of function g
y4
If f(x)=x², which equation represents function g?
OA. g(z) f(27)
OB. g (2) f(42)
M
2
O C. g(z) = 2 f(z)
(2)
D. 9(2) -
Answer:
D
Step-by-step explanation:
Use logarithmic differentiation to find the derivative of the function y= x²/x y'(x)= 2 + 1 In x) x²
To use logarithmic differentiation to find the derivative of the function y = x²/x, we first take the natural logarithm of both sides:
ln(y) = ln(x²/x)
Using the properties of logarithms, we can simplify this to:
ln(y) = 2 ln(x) - ln(x)
Now we differentiate both sides with respect to x using the chain rule:
1/y * y' = 2/x - 1/x
Simplifying this expression, we get:
y' = y * (2/x - 1/x²)
Substituting back in the original expression for y, we have:
y' = x²/x * (2/x - 1/x²)
Simplifying further, we get: y' = 2x - 1/x
Therefore, the derivative of the function y = x²/x using logarithmic differentiation is y' = 2x - 1/x.
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Please Help Fast!!!!!!!!!!!!!!!!!!!!!!!!!
The number of solutions that are there for the pair of equations for lines Q and S is zero solution (no solution) because the lines are parallel with no point of intersection.
What is no solution?In Mathematics and Geometry, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
This ultimately implies that, a system of equations would have no solution when the line representing each of the equations are parallel lines and have the same slope i.e both sides of the equal sign are the same and the variables cancel out.
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The length of one diagonal of a rhombus is a geometric mean of the length of the other diagonal and the length of the side. Find angle measures of a rhombus
The angle measure of the rhombus with one diagonal of a rhombus is a geometric mean of the length of the other diagonal are measured to be 75.5° .
Let d₁ and d₂ be the lengths of the diagonals of the rhombus and s as the side length. We have,
d₁ = s√2 (since the diagonal is the hypotenuse of a right triangle formed by two sides of length s)
d₁ = √d₂s
Combining these two equations, we get,
s√2 = √d₂s
Squaring both sides, we get,
2s² = d₂
Since the diagonals of a rhombus are perpendicular bisectors of each other, we have,
cosθ = (1/2) (where θ is one of the acute angles of the rhombus)
Using the law of cosines with sides s and d₂/2, we have,
(s² + (d₂/2)² - 2sd₂/2cosθ) = s²
Simplifying, we get,
d₂ = 4s cosθ
Substituting this expression for d₂ in 2s² = d₂, we get,
2s² = 4scosθ
Dividing both sides by 2s and simplifying, we get,
s = 2cosθ
Therefore, the angle measures of the rhombus are,
θ = arccos(s/2)
= arccos(cosθ/2)
= arccos(1/4)
= 75.5°
And the other acute angle has the same measure.
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Patty and Carol leave their homes in different cities and drive toward each other on the same highway.
• They start driving at the same time.
• The distance between the cities where they live is 300 miles.
• Patty drives an average of 70 miles per hour.
. Carol drives an average of 50 miles per hour.
Enter an equation that can be used to find the number of hours, t, it takes until Patty and Carol are at the same
location.
The equation to find the number of hours, t, until Patty and Carol are at the same location is: 70t + 50t = 300.
1. Patty and Carol start driving at the same time, towards each other on the same highway.
2. The distance between their cities is 300 miles.
3. Patty drives at an average speed of 70 mph, so in t hours she covers 70t miles.
4. Carol drives at an average speed of 50 mph, so in t hours she covers 50t miles.
5. As they drive towards each other, the sum of the distances they cover should equal the total distance between their cities.
6. Therefore, combining the distances covered by Patty and Carol, we get: 70t (Patty's distance) + 50t (Carol's distance) = 300 (total distance).
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Find (A) f'(x). (B) the partition numbers for f', and (C) the critical numbers of f. f(x) = x³ - 75x - 2 (A) f'(x)= (B) Find the partition numbers for f' Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The partition number(s) is/are x = (Use a comma to separate answers as needed) B. There are no partition numbers (C) Find the critical numbers for f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The critical number(s) is/are x = (Use a comma to separate answers as needed) B. There are no critical numbers
The critical numbers of f are x = -5 and x = 5.
(A) To find the derivative f'(x), we differentiate f(x) = x³ - 75x - 2 with respect to x:
f'(x) = 3x² - 75
(B) There are no partition numbers for f' as partition numbers are related to integer partitions, which are not applicable in this context.
(C) To find the critical numbers of f, we set f'(x) equal to 0 and solve for x:
3x² - 75 = 0
x² = 25
x = ±5
So the critical numbers of f are x = -5 and x = 5.
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The height of three basketball players is 210 cm, 220 cm and 191 cm.
What is their average height?
Answer:
Average height = 207 cmStep-by-step explanation:
It's given that, The height of three basketball players is 210 cm, 220 cm and 191 cm.
h₁ = 210 cm
h₂ = 220 cm
h₃ = 191 cm
Total number of observations = 3.
Average = Sum of all observations/Total number of observations.
↠ Average = h₁ + h₂ + h₃/3
↠ Average = 210 +220 + 191 /3
↠ Average = 430 + 191/3
↠ Average = 621/3
↠ Average = 207
Therefore, The required average height is 207 cm.
I'm board so before this gets reported what's your fav show(s) on netflix
Mine is:
Lucifer
On my block
First few seasons of flash
Choose the correct answer.
Find the quadratic equation given the points (6,0), (-1,0), and (7,4).
h(x) = 1/2(x + 1)(x − 6)
h(x) = 2(x+6)(x − 1)
h(x) = 2(x + 1)(x - 6)
h(x):1/2(x+6) (x - 1)
The quadratic equation given the points (6,0), (-1,0), and (7,4).
The correct answer is h(x) = 1/2(x + 1)(x - 6).
To find the quadratic equation given the points (6,0), (-1,0), and (7,4), we can use the general form of a quadratic equation, which is [tex]h(x) = ax^2 + bx + c.[/tex]
First, let's substitute the coordinates of the given points into the equation to create a system of equations:
For the point (6,0):
[tex]0 = a(6)^2 + b(6) + c ---- (1)[/tex]
For the point (-1,0):
[tex]0 = a(-1)^2 + b(-1) + c ---- (2)[/tex]
For the point (7,4):
[tex]4 = a(7)^2 + b(7) + c ---- (3)[/tex]
We now have a system of three equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.
Solving the system of equations (1), (2), and (3), we find:
a = 1/2
b = -3/2
c = 0
Thus, the quadratic equation that satisfies the given points is:
h(x) = 1/2(x + 1)(x - 6).
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The length of one diagonal in a rhombus is 26. 4 cm and the area of the rhombus is 204. 6 cm squared. How long is the second diagonal?
A rhombus with a diagonal of 26.4 cm and an area of 204.6 square cm has another diagonal of length 15.5 cm
Rhombus is a 2-Dimensional shape. It is a quadrilateral. It is a specialized form of a parallelogram. All sides of a rhombus are equal in length.
Similar to a parallelogram, it has opposite sides parallel to each other and opposite angles of equal magnitude.
The area of a rhombus is expressed as half of the product of diagonals.
A = 0.5pq
A is the area
p is the length of one diagonal
q is the length of another diagonal
A = 204.6 square cm
p = 26.4 cm
204.6 = 0.5 * 26.4 * q
q = 15.5 cm
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Box and whisker plots
Answer: Box and whisker plots are plots on number lines with a box and two lines off the edges, called whiskers. The box has a line at the upper quartile(1), one at the lower quartile(2), and one in the center of the box at the median(3). The two lines go to the ends of the data, one at the minimum(4) and one at the maximum(5).
4 2 3 1 5
|-----[___|____]-----------|
₀__₁__₂__₃__₄__₅__₆__₇__₈
I hope this helps.
The area of the shaded region under the curve of a function f(x) = ax + b on the interval [ 0, 4 ] is 16 square units.
The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units. So, all the options satisfy the value of a and b except (7, -9).
How to find the area of a region?The area of the given region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.
f(x) is a linear function, the area under the curve on the interval [0,4] is a trapezoid with a height of 4 and bases of lengths f(0) and f(4).
The area of a trapezoid is the height times the average of the bases.
a. f(x)=-2x+8 f(0)=8, f(4)=0;
area = 4(8/2) = 16
b. f(x)=x+2; f(0)=2, f(4)=6;
area = 4(8/2) = 16
c. f(x)=3x-2; f(0)=-2, f(4)=10;
area = 4(8/2) = 16
d. f(x)=5x-6; f(0)=-6, f(4)=14;
area = 4(8/2) = 16
e. f(x)=7x-9; f(0)=-9, f(4)=19;
area = 4(10/2) = 20
Thus, The area is NOT 16 for choice e.
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Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model, (y) hat = (b) with subscript (1)x+ (b) with subscript (0). Using the method of least-squares regression, the faculty group obtained the following prediction equation, (y) hat=2,000x+ 14,000.
Interpret the estimated y-intercept of the line.
A)There is no practical interpretation, since rating of 0 is not likely and outside the range of the sample data.
B)For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.
C) The base administrator raise at State University is $14,000.
D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000
Yes, there is a relationship like a straight line between the raises administrators at State University receive and their performance on the job
The estimated y-intercept of the line in the given straight-line regression model is $14,000.The interpretation of this value is that for an administrator who receives a rating of zero, we estimate his or her raise to be $14,000. This value represents the base raise amount for the administrators at State University, regardless of their job performance rating.To obtain this interpretation, we consider the equation of the regression line, which relates the predicted raise amount (y hat) to the job performance rating (x). The y-intercept term in this equation is the value of y hat when x equals zero. Therefore, the estimated y-intercept of $14,000 represents the predicted raise amount for an administrator whose job performance rating is zero, which corresponds to the base raise amount at State University.
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A shipping company must design a closed rectangular shipping crate with a square base. The volume is 12288ft3. The material for the top and sides costs $2 per square foot and the material for the bottom costs $10 per square foot. Find the dimensions of the crate that will minimize the total cost of material.
Optimize crate cost by expressing material cost in terms of x and y, calculating cost of all four sides, and finding minimum cost. Optimal dimensions: x = 16 ft, y = 48 ft. Minimum cost: $8704.
To find the dimensions of the crate that will minimize the total cost of material, we need to use optimization techniques, we need to express the cost of materials in terms of x and y then calculate the cost of all four sides, then find the minimum cost.
Let's start by defining the variables we need to work with:
Let x be the length of one side of the square base (in feet), Let y be the height of the crate (in feet).
From the given volume, we know that:
V = x^2 * y = 12288 ft^3
We can use this equation to solve for one of the variables in terms of the other:
y = 12288 / (x^2)
Now we need to express the cost of materials in terms of x and y.
The area of the bottom is x^2, so the cost of the bottom is:
[tex]C_b = 10 * x^2[/tex]
The area of each side is x * y, and there are four sides, so the cost of the sides is:
[tex]C_s = 4 * 2 * x * y = 8xy[/tex]
The area of the top is also x^2, so the cost of the top is:
[tex]C_t = 2 * x^2[/tex]
The total cost of materials is the sum of these three costs:
[tex]C = C_b + C_s + C_t = 10x^2 + 8xy + 2x^2[/tex]
Now we can substitute y = 12288 / (x^2) into this equation:
[tex]C = 10x^2 + 8x * (12288 / x^2) + 2x^2[/tex]
Simplifying this expression, we get:
[tex]C = 12x^2 + 98304 / x[/tex]
To find the minimum cost, we need to find the value of x that minimizes this expression. We can do this by taking the derivative of C with respect to x and setting it equal to zero:
C' = 24x - 98304 / x^2 = 0
Solving for x, we get:
x = 16 ft
Now we can use this value of x to find y:
y = 12288 / (16^2) = 48 ft
Therefore, the dimensions of the crate that will minimize the total cost of material are:
- Length of one side of the square base = x = 16 ft
- Height of the crate = y = 48 ft
To check that this is indeed the minimum cost, we can plug these values back into the expression for C and calculate the cost:
C = 10 * 16^2 + 8 * 16 * 48 + 2 * 16^2 = 8704
Therefore, the minimum cost of material for the crate is $8704.
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Mrs. Thomas has two rolls of garden edging that are each 96 inches long.
She wants to make two new flower beds in her back yard. Each flower bed
will be bordered by one roll of the edging. One flower bed will be in the
shape of a quadrilateral. The other will be in the shape of a triangle.
Mrs. Thomas decides to make a scale drawing of each flower bed using a
scale of 1 centimeter = 5 inches. What will be the total length of each roll
of edging in her scale drawings?
The total length of each roll of edging in Mrs. Thomas's scale drawings will be 19.2 cm.
How to find the total length ?To find the total length of each roll of edging in her scale drawings, we need to convert the length from inches to centimeters using the given scale.
To convert the length to centimeters:
( Length in cm ) / ( Length in inches ) = ( 1 cm ) / ( 5 inches )
x / 96 inches = 1 cm / 5 inches
x 5 inches = 96 inches x 1 cm
5x = 96 cm
x = 96 cm / 5
x = 19.2 cm
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Directions: Write an equation for the circle shown on the graph in standard form. 15.
Answer: x(squared) + (y + 2)(squared) = 36
Step-by-step explanation:
The center of the circle is at (0 , -2), so we will eliminate the x value by just writing x(squared), and then we will write the y value as (y + 2)(squared) because the standard form for a circle is
(x - h)(squared) + (y + 2)(squared) = r(squared)
And if we count from the center to the top point of the circle, the number would be 6, so we would square 6 which would be 36.
PLEASE HELP ME ASAP
Can you please make a copy and put dots in eachone that goes where its supposed to go
Answer:
1
1
1
2
2
2
2
Step-by-step explanation:
5. A 40-kg ornamental star is suspended by two chains fastened to
horizontal beams at different heights with angles as shown.
Determine the tension in each chain.
The diagram is shown below; I also know we have to split up the triangles to make two right angle triangles but I’m not sure where to go from there
Answer:We can start by resolving the forces acting on the ornamental star in the vertical direction and in the horizontal direction. Since the star is stationary, these forces must balance each other out.
Let's call the tension in the higher chain T1 and the tension in the lower chain T2. We can use trigonometry to find the vertical and horizontal components of each tension force.
For T1:
The vertical component is T1cos(40°) and the horizontal component is T1sin(40°).
For T2:
The vertical component is T2cos(30°) and the horizontal component is T2sin(30°).
Now, resolving the forces in the vertical direction, we have:
T1cos(40°) + T2cos(30°) - mg = 0
where m is the mass of the star and g is the acceleration due to gravity.
Substituting the values:
T1cos(40°) + T2cos(30°) - (40 kg)(9.81 m/s^2) = 0
T1cos(40°) + T2cos(30°) = 392.4 N
Next, resolving the forces in the horizontal direction, we have:
T1sin(40°) = T2sin(30°)
Now we have two equations with two unknowns:
T1cos(40°) + T2cos(30°) = 392.4 N
T1sin(40°) = T2sin(30°)
Solving these equations simultaneously, we get:
T1 = 266.4 N
T2 = 205.1 N
Therefore, the tension in the higher chain (T1) is 266.4 N and the tension in the lower chain (T2) is 205.1 N.
Step-by-step explanation:
6. A football player throws a football. The function h given by h(t) = 6 + 75+ - 161
describes the football's height in feet † seconds after it is thrown.
A. The football is thrown from ground level.
B. The football is thrown from 6 feet off the ground.
C. In the function, - 167? represents the effect of gravity.
D. The outputs of h decrease then increase in value.
E. The function h has 2 zeros that make sense in this situation.
F. The vertex of the graph of h gives the maximum height of the foot
The correct options are:
The football is thrown from 6 feet off the ground. In the function, - 167? represents the effect of gravity.The vertex of the graph of h gives the maximum height of the footThe description of the football's heightOption B: The football is thrown from 6 feet off the ground.
when t = 0
h(t) = 6 * 75 * 0 + 16 * 0
= 6 feet
Option C : - 16t² represents the effect of gravity
we have
[tex]h = ut - \frac{1}{2}gt^2[/tex]
[tex]\frac{1}{2}gt^2=-16t^2[/tex]
F. The vertex of the graph of h gives the maximum height of the foot
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consider h(x)= 11x² - 6x calculate H (x) Fx 6.Xr1 유 11 6 3 (22.-6) 3 6 In(3) 11 A) 2 +1 (221 - 6)31 B) - (11r? - br)3*** In(3) 2 (3***") - 6 In(3) (221 - 63#* - (1142 – 63)3 (3***")" 2 +1 4 (221 - 63 - (1122 – 6x)3 In(3) i 1 D)
The answer is B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.
To solve this problem, we are given a function h(x) and asked to find its antiderivative or indefinite integral, which is denoted by H(x) and is defined as the function whose derivative is h(x). We are also given a specific value of H(x) at x = 6 and asked to use it to find the constant of integration, denoted by C.
The given function is h(x) = 22x - 3x² - 6/x, and we want to find H(x), which is the antiderivative of h(x). Using the power rule of integration, we can integrate each term of h(x) separately:
∫ (22x - 3x² - 6/x) dx = ∫ 22x dx - ∫ 3x² dx - ∫ 6/x dx= 11x² - x³ - 6ln|x| + Cwhere C is the constant of integration. Note that we need to include an absolute value sign around x in the natural logarithm term because the function is not defined for x = 0.
Next, we are given that H(6) = 31, which means that when x = 6, the value of H(x) is 31. Substituting x = 6 and H(x) = 31 into the above equation, we get:
31 = 11(6)² - (6)³ - 6ln|6| + CSimplifying, we get:
31 = 132 - 216 - 6ln(6) + CC = 221/3 - 6ln(6)Therefore, the antiderivative of h(x) is:
H(x) = 11x² - x³ - 6ln|x| + 221/3 - 6ln(6)We can simplify the expression by using the identity ln|a/b| = ln|a| - ln|b|:
H(x) = 11x² - x³ - 6ln(3) - 6ln(x) + 2ln(3) + Cwhere C is the constant of integration. Thus, the final answer is:
B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.To learn more about integration, here
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A baker has a small and large bag of sugar for making cakes. The large bag contains 30 cups of sugar and is 2. 5 times larger than the small bag. The small bag contains enough sugar to make 9 cakes and has 0. 75 cups of sugar remaining.
how many cakes can be made with a large bag of sugar?
After solving the word problem, the large bag contains enough sugar to make 40 cakes
Since the large bag is 2.5 times larger than the small bag, and the small bag contains enough sugar to make 9 cakes, the large bag contains enough sugar to make:
2.5 * 9 = 22.5 cakes
However, since there are only 30 cups of sugar in the large bag, and we don't know how much sugar is needed to make a single cake, we cannot determine the exact number of cakes that can be made with a large bag of sugar.
As for the small bag, if it had enough sugar to make 9 cakes and there are 0.75 cups of sugar remaining, then each cake requires:
(sugar in bag - remaining sugar) / number of cakes
= (9 - 0.75) / 9
= 0.75 cups of sugar
Therefore, the large bag contains enough sugar to make:
30 cups / 0.75 cups per cake
= 40 cakes
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Find the following limit. Is the function continuous at the point being approached? lim sec (ysec²y- tan²y-1) y→ 1 lim sec (y sec²y-tan ²y-1)- (Simplify your answer.) y→ 1
The limit of sec(y sec²y - tan²y - 1) as y approaches 1 is undefined. The function is not continuous at the point being approached.
Explanation: To evaluate the limit, we can first simplify the expression inside the secant function using the trigonometric identity:sec²θ - tan²θ = 1/cos²θ - sin²θ/cos²θ = (1 - sin²θ)/cos²θ = cos²θ / cos²θ = 1Substituting this expression back into the limit, we get:lim sec(y sec²y - tan²y - 1)y→1= lim sec(y - 1)y→1As y approaches 1, the argument of the secant function approaches 0, which means that the secant function approaches infinity. Therefore, the limit is undefined.Since the limit is not defined, the function is not continuous at the point being approached. A function is continuous at a point if and only if the limit of the function as x approaches that point exists and is equal to the value of the function at that point. In this case, since the limit does not exist, the function is not continuous at y = 1.
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Chase was on his school’s track team and ran the 2400m race. He has been working on his pace and can run 1600m in 5. 5 minutes. If he keeps this pace through the entire race, how long will it take him to finish the 2400m race?
A. 8. 25 minutes
B. 7. 75 minutes
C. 8. 5 minutes
D. 8. 42 minutes
Please help. The problem is found in the photo below, just please help.
Answer:
-4 = 5
0 = -1
2 = -4
4 = -7
(-4, 5)
(0, -1)
(2, -4)
(4, -7)
Step-by-step explanation:
First, let's identify what each term represents.
y-intercept: -1
slope: 3/2
Then, fill out the table.
x = -4
-1 - (3/2 · -4)
-1 - (-12/2)
-1 - (-6)
-1 + 6
y = 5
x = 0
-1 - (3/2 · 0)
-1 - 0
y = -1
x = 2
-1 - (3/2 · 2)
-1 - (6/2)
-1 - (3)
y = -4
x = 4
-1 - (3/2 · 4)
-1 - (12/2)
-1 - (6)
y = -7
Then, plot the points in the function on the graph.
(-4, 5)
(0, -1)
(2, -4)
(4, -7)
HELP
I need all the help to figure this annoying thing out
Answer:
x = 30 , y = 54
Step-by-step explanation:
the figure is a trapezium
each lower base angle is supplementary to the upper base angle on the same side, then
4x + y + 6 = 180 ( subtract 6 from both sides )
4x + y = 174 ( subtract 4x from both sides )
y = 174 - 4x → (1)
and
2x + 12 + 2y = 180 → (2)
substitute y = 174 - 4x into (2)
2x + 12 + 2(174 - 4x) = 180
2x + 12 + 348 - 8x = 180
- 6x + 360 = 180 ( subtract 360 from both sides )
- 6x = - 180 ( divide both sides by - 6 )
x = 30
substitute x = 30 into (1)
y = 174 - 4(30) = 174 - 120 = 54
thus x = 30 and y = 54
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 300 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11. 3 seats and the sample standard deviation is 4. 3 seats.
Required:
Construct a 92% confidence interval for the population mean number of unoccupied seats per flight
If a large airline wants to estimate its average number of unoccupied seats per flight over the past year Then a 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats.
To construct a confidence interval for the population mean number of unoccupied seats per flight, we will use the following formula CI = X ± z*(σ/√n)
Where:
X = sample mean = 11.3 seats
σ = sample standard deviation = 4.3 seats
n = sample size = 300
z = z-score corresponding to the desired confidence level of 92%, which we can look up in a standard normal distribution table or use a calculator. For a 92% confidence level, the z-score is 1.75.
Plugging in the values, we get:
CI = 11.3 ± 1.75*(4.3/√300)
CI = 11.3 ± 0.966
Therefore, the 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats. This means we can be 92% confident that the true population means a number of unoccupied seats per flight falls within this interval.
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The profit from selling tickets to a musical can be modeled by the function P(x) = -100x2 + 2,400x - 8,000, where x is the price per ticket, in dollars. What ticket price will maximize the profit?
The profit is maximized at $16,400 when the ticket price is $12.
To find the ticket price that maximizes the profit, we used the fact that the maximum or minimum value of a quadratic function occurs at its vertex. For a quadratic function in the form of P(x) = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b / 2a.
In this case, we were given the function [tex]P(x) = -100x^2 + 2400x - 8000,[/tex]where x represents the price per ticket. The coefficient of [tex]x^2[/tex] is negative, which tells us that the graph of this function is a downward-facing parabola. The vertex of this parabola represents the maximum value of the function.
Using the formula x = -b / 2a, we found the x-coordinate of the vertex to be x = -2400 / 2(-100) = 12. This means that a ticket price of $12 will maximize the profit.
To verify that this is indeed the maximum profit, we substituted x = 12 into the profit function P(x):
[tex]P(12) = -100(12)^2 + 2400(12) - 8000 = 16,400[/tex]
We can see that the profit is maximized at $16,400 when the ticket price is $12.
In summary, to find the ticket price that maximizes the profit, we used the formula x = -b / 2a to find the x-coordinate of the vertex of the quadratic function representing the profit from selling tickets to a musical. The maximum profit occurs at the ticket price that corresponds to the x-coordinate of the vertex.
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1. p(x)= f(x)+g(x)
Write the equation of p(x)
Answer:p(x)=3x+5
Step-by-step explanation:
f(x)=2x+3
g(x)=x+2
p(x)=(2x+2)+(x+2)= 3x+5
Answer:
p(x)=ax + b
Step-by-step explanation: