Jensen stopped at rest area A along the side of the highway. His map shown below has a scale of 1 inch to 35 miles. Jensen planned to stop at rest stop B next.what is the actual distance in miles between the two rest areas
Jensen stopped at A and planned to stop at B next. He has a map with a scale of 1 inch to 35 miles.
It is clear that 1 inch on map corresponds to 35 miles in actual.
From the map he has, we can see that both places A and B are 2.5 inches apart on map.
Let's assume those are "X" miles away in actual. Then we can use proportions to solve this problem.
1 inch to 35 miles would be same as 2.5 inches to X miles. Mathematically, we can write it as follows :-
[tex] \frac{1 \;inch}{35 \;miles} =\frac{2.5 \;inches}{X \;miles} \\\\
\frac{X \;miles}{35 \;miles} =\frac{2.5 \;inches}{1 \; inch} \\\\
\frac{X}{35} =\frac{2.5}{1} \\\\
Cross \;\;multiplying \\\\
X = 35*2.5=87.5 \;miles [/tex]
Hence, actual distance between A and B is 87.5 miles.
If A ⊂ B, then A ∩ B = A ∪ B.
The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true; it holds only if A = B.
The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true.
If [tex]\( A \subset B \)[/tex], it means that every element in set A is also in set B.
Now, consider the intersection of A and B [tex](\( A \cap B \))[/tex]. This intersection contains all elements that are common to both sets A and B.
On the other hand, the union of A and B [tex](\( A \cup B \))[/tex] contains all elements that are in either set A or set B, or both.
Since A is a subset of B, all elements in A are already in B, which means [tex]\( A \cap B = A \)[/tex]. However, [tex]\( A \cup B \)[/tex] would just be B, because all elements in A are also in B, so [tex]\( A \cup B \)[/tex] is simply B.
Therefore, the statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not true in general; it is true only if A = B .
The formula to convert Celsius to Fahrenheit is F=9/5+32 convert 87 F to Celsius
A) 16c
B) 55c
C)31c
D)99c
The equation below shows the total volume (V), in cubic units, of 4 identical boxes with each side equal to s units:
V = 4s3
If s = 2.5 units, what is the value of V?
25 cubic units
30 cubic units
62.50 cubic units
156.25 cubic units
HELP FAST
Answer:
62.50
Step-by-step explanation: im smart
Most sample surveys use random digit dialing equipment to call residential telephone numbers at random. the telephone polling firm zogby international reports that the probability that a call reaches a live person is 0.15. calls are independent. (a) a polling firm places 7 calls. what is the probability that none of them reaches a person?
The probability that none of the 7 calls reaches a person is approximately 0.1967.
Explanation:To find the probability that none of the 7 calls reaches a person, we need to calculate the probability that each individual call does not reach a person and then multiply those probabilities together.
The probability that a call reaches a live person is 0.15, so the probability that a call does not reach a live person is 1 - 0.15 = 0.85.
Therefore, the probability that none of the 7 calls reaches a person is 0.857 ≈ 0.1967.
is the statement [x]=[x+1] true for all real numbers? explain
Answer:
The Edg answer is as follows -
The statement is not true for all real numbers. It is only true for decimal or fractional values of x .
If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.
Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.
Step-by-step explanation:
Real numbers are set of numbers that include rational and irrational numbers.
[x]=[x+1] is not true for all real numbers
Assume that: x is an integer
And x = 5
So, the equation becomes
[tex]5 = 5 + 1[/tex]
[tex]5 = 6[/tex]
The above equation is not true, because:
[tex]5 \ne 6[/tex]
Hence, [x]=[x+1] is not true for all real numbers
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the midpoint of PQ is R. R has coordinates (-3,2,-1) and P has coordinates (4,-6,-6). What are coordinates of Q?
The coordinates of point Q are (-10, 10, 4).
Explanation:To find the coordinates of point Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points P(x1, y1, z1) and Q(x2, y2, z2) are given by the average of the coordinates:
R = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2)
In this case, we are given that the midpoint R has coordinates (-3, 2, -1) and one of the points P has coordinates (4, -6, -6). Plugging in these values into the midpoint formula, we can solve for the coordinates of point Q:
Q = (2 * R - P)
Q = (2 * (-3, 2, -1) - (4, -6, -6))
Q = (-6, 4, -2) - (4, -6, -6)
Q = (-10, 10, 4)
The diagonal of rectangle ABCD measures 2 inches in length What is the length of line segment AB?
Answer:
Step-by-step explanation:
B on edge
Which statements are true regarding the regular dodecagon? Check all that apply.
The smallest angle of rotational symmetry for the dodecagon is 30°.
The dodecagon has a rotational symmetry of 180°.
The order of rotational symmetry for the dodecagon is 10.
The dodecagon has a rotational symmetry of 135°.
The angles of rotational symmetry for the dodecagon are multiples of 30°.
The statements that can be inferred to be true regarding the regular dodecagon include:
The smallest angle of rotational symmetry for the dodecagon is 30°.The dodecagon has a rotational symmetry of 180°.The angles of rotational symmetry for the dodecagon are multiples of 30°.A dodecagon simply means a twelve-sided star polygon that encloses space. It can be regular when all the interior angles and sides are equal.
It should be noted that the smallest angle of rotational symmetry for the dodecagon is 30° and it has a rotational symmetry of 180.
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Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.
Answer:
sample response: None of the roots can have multiplicity because the polynomial is cubic and 3 roots are given. Write each root as a linear factor, then multiply the three factors to get the expression for the function.
Step-by-step explanation:
Eric's father Works two part-time jobs one in the morning and one in the afternoon and works a total of 40 hours each 5-day work week. if his schedule is the same each day, and he works 3 hours each morning, how many hours does Eric's father work each afternoon
The number of hours does Eric's father work each afternoon is 5 hours.
Given that,
A total of 40 hours each 5-day work week. And, his schedule is the same each day, and he works 3 hours each morning.Based on the above information, the calculation is as follows:
[tex]= (40 - (3\times 5)) / div 5\\\\= (40 - 15) \div 5\\\\= 25 \div 5[/tex]
= 5
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PLEASE HELP!! 30 POINTS
Match the graph with the correct equation.
A) y + 3 = –(x + 5)
B) y – 3 = –(x + 5)
C) y – 3 = (x + 5)
D) y – 5= –(x + 3)
The classroom encyclopedia set seems to fill a shelf that is 24 in long each book is 3/4 in thick how many books are in the classroom set
a gardener makes a new circular flower bed. the bed is fourteen feet in diameter. Calculate the circumference and the area of the circular flower bed.
The circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.
How is the circumference of a circle calculated?The circumference is the total length covered by the boundary of an object.
To calculate the circumference of a circle with radius r units, we use the formula: Circumference = 2πr units.
How is the area of a circle calculated?The area of an object is the space its planar face or two-dimensional face covers.
To calculate the area of a circle of radius r units, we use the formula: Area = πr² sq. units.
How to solve the question?In the question, we are asked to find the circumference and the area of the circular flower bed that a gardener makes, having a diameter of fourteen feet.
We know that radius = diameter/2 = 14/2 = 7 feet.
To calculate the circumference of the circular bed, we will use the formula 2πr, where r is the radius.
Substituting the radius, r = 7 feet in the above formula, we get:
Circumference = 2(π)(7) feet = 14π feet = 43.9823 feet.
To calculate the area of the circular bed, we will use the formula πr², where r is the radius.
Substituting the radius, r = 7 feet in the above formula, we get:
Area = (π)(7)² feet² = 49π feet² = 153.9380 feet².
Thus, the circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.
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C=
5\9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I.) A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5\9 degree Celsius.
II.) A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III.) A temperature increase of 5\9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
find the measure of DBE if abc is 145
answers
30
60
90
145
Mowing the lawn is one of Jeremy's jobs at home. But, Jeremy's dad offered to help him this week. His dad drew the following diagram of the lawn and told Jeremy to choose one of the parts to mow. If Jeremy wants to mow the rectangle with the smaller area, which one should he choose?
Let's find out the area of the two parts separately to see which part is smaller.
Area of rectangle is given by Length * Width
Area of Part 1
Width of Part 1 is 16'
Length of Part 1 is 16-12 = 4'
So area of Part 1 is 16*4 = 64' square
Area of Part 2
Width of Part 2 is 8'
Length of Part 2 is 8'
So area of Part 2 is 8*8 = 64' square
So area of both the parts is same . Hence Jeremy may choose any of the parts.
Hope it helps ..!!
For what value of xis the square of the binomial 3x+1 is 9 times greater than the square of the binomial x–2?
Final answer:
The value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2 is obtained by equating (3x + 1)² to 9(x − 2)², which simplifies and solves to x = 5/6.
Explanation:
To find the value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2, we need to formulate and solve an equation based on the given conditions:
(3x + 1)² = 9(x − 2)²
Expanding both sides gives us:
9x² + 6x + 1 = 9x² − 36x + 36
Now, by simplifying and solving for x, we find:
42x = 35
x = 35 / 42
x = 5 / 6
Therefore, the value of x is 5/6.
The Heller family is having a cookout. To be sure that they have enough food, they plan to have 0.5 pound of hamburger for each adult and 0.25 pound for each child. There will be 15 children at the cookout. If they buy 10 pounds of hamburger, what is the maximum number of adults they expect?
Answer:
12
Step-by-step explanation:
Can you please help me out ??
a cube has a width of 20 ft what is the surface area of the cube
The surface area of the cube is 2,400 square feet.
To find the surface area of a cube, one must use the formula:
[tex]\[ \text{Surface Area} = 6 \times (\text{side length})^2 \][/tex]
Given that the width of the cube is 20 feet, we can assume that all sides of the cube are equal, since a cube has all sides of equal length. Therefore, the side length of the cube is 20 feet.
Now, we can substitute the side length into the formula:
[tex]\[ \text{Surface Area} = 6 \times (20 \text{ ft})^2 \] \[ \text{Surface Area} = 6 \times 400 \text{ ft}^2 \] \[ \text{Surface Area} = 2,400 \text{ ft}^2 \][/tex]
Thus, the surface area of the cube is 2,400 square feet.
Choose yes or no to tell if the fraction 3/8 will make each equation true
It says to check if [tex] \frac{3}{8} [/tex] satisfy each equation or not.
Checking first equation :-
96 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{96 * 3}{8} [/tex]
⇒ [tex] \frac{288}{8} [/tex] = 36
⇒ 36 = 36. First equation is "YES".
Checking second equation :-
38 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{38 * 3}{8} [/tex]
⇒ [tex] \frac{114}{8} [/tex] = [tex] \frac{57}{4} [/tex]
⇒ [tex] \frac{57}{4} [/tex] ≠ 14. Second equation is "NO".
Checking third equation :-
16 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{16 * 3}{8} [/tex]
⇒ [tex] \frac{48}{8} [/tex] = 6
⇒ 6 = 6. Third equation is "YES".
Checking fourth equation :-
56 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{56 * 3}{8} [/tex]
⇒ [tex] \frac{168}{8} [/tex] = 21
⇒ 21 = 21. Fourth equation is "YES".
Find an equation of the plane. the plane through the point (3, −8, −2) and parallel to the plane 9x − y − z = 7
Final answer:
The equation of the plane parallel to the given plane 9x - y - z = 7 and passing through the point (3, -8, -2) is 9x - y - z = 37.
Explanation:
The question involves finding an equation for a plane that is parallel to a given plane and passes through a specific point. Since the planes are parallel, they will have the same normal vector, and thus the same coefficients for x, y, and z. The given plane's equation is 9x - y - z = 7, so the normal vector is (9, -1, -1). Our plane must also have this normal vector, meaning our plane's equation will have the form 9x - y - z = D, where D is a constant we need to find such that the plane passes through the point (3, -8, -2).
Substituting this point into the equation gives us 9(3) - (-8) - (-2) = D, which simplifies to 27 + 8 + 2 = D. Therefore, D = 37 and the equation of our plane is 9x - y - z = 37.
Which measurement statement is correct?
A. There are 2 cups in a pint
B. There are pints in a cup
C. There are 4 quarts in a pint
D. There are 4 pints in quart
Find the perimeter of an isosceles trapezoid whose two bases have lengths of 10cm and 16 cm and a side length of 5cm
The perimeter of the isosceles trapezoid is 36cm.
Explanation:An isosceles trapezoid is a quadrilateral with two parallel sides of unequal length. To find the perimeter of an isosceles trapezoid, we need to add the lengths of all its sides. In this case, the two bases have lengths of 10cm and 16 cm, and one of the side lengths is 5cm. Since the two bases are parallel, the other side length is also 5cm.
The perimeter is calculated by adding the lengths of the bases and the two side lengths: 10cm + 16cm + 5cm + 5cm = 36cm.
I really neeed help!! 20 points!!,
The arena would like to estimate its annual running costs for the next twelve months. Use the following first 4 months' figures to estimate the running costs for 12 months. Month Costs January £14,889.51 February £22,936 March £9,856.88 April £6,777.77 The estimated running costs for 12 months is
Answer:
163,380.48
Step-by-step explanation:
First find the average of the first 4 months' figures.
To do this, find the sum of the first 4 values and then divide by 4, the number of data points:
(14889.51+22936+9856.88+6777.77)/4 = 54460.16/4 = 13615.04
It costs on average £13615.04 per month to run the arena.
This means the estimated running costs for 12 months will be
13615.04(4) = £163,380.48
if you are flipping a coin what is the sample space
Answer:
Solution: {Heads, Tails}.
Step-by-step explanation:
Solution: {Heads, Tails}.
Sample space is a list of all the possible outcomes for the event. For flipping a coin the outcomes are {Heads, Tails}.
What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?
At a school carnival the diameter of the mat of a trampoline is 12 ft and the diameter of its metal frame is 14 ft what is the length in feet of the metal frame that surrounds the trampoline use 3.14 for pie and round your answer to the nearest tenth
The length in feet of the metal frame that surrounds the trampoline is 44 ft.
What is the circumference of a circle?The circumference of a circle is the distance round the circle.
The circumference of a circle = πD
3.14 x 14 = 44 ft
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