Answer:
B. More members prefer a beach vacation and a ski vacation than a cruise vacation.
ehat is the value of y=3x2-18x+15
The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y.
Explanation:The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y. For example, if we substitute x = 1, we get y = 3(1)^2 - 18(1) + 15 = 0. So, when x = 1, y is 0.
To find more values, we can create a table of values by substituting different x values into the equation. The resulting values of y can be plotted on a graph to see the pattern and shape of the equation.
Table of Values:
x = 0, y = 15x = 1, y = 0x = 2, y = 9x = 3, y = 18This equation represents a quadratic function in the form of y = ax^2 + bx + c, where a = 3, b = -18, and c = 15.
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find the measure of the arc or angle indicated. or find the value of x
Find the area. The figure is not drawn to scale
Answer:
D) 704 in.²
Step-by-step explanation:
The area is height × width.
So, the area =32 × 22 = 704 in.²
Rewrite the exponential function y = 12 (0.56)^(t/4).
Round your answer to two decimal places.
The exponential function will be written as:
y = 12 (0.56) ^ (t/4)
y=12 (0.56^ (1/4)) ^t
but
0.56^ (1/4) = 0.8651
thus plugging the value in y we get:
y=12 (0.8651) ^t
in two decimal places we get:
y=12 (0.87) ^t
If the probability of winning a carnival game was 2/5 and Max played it five times, write an expression that would calculate the probability he won the first three games and lost the last two
The probability of Max winning the first three games while losing the rest two is 0.023.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the probability of winning the game is 2/5. Since the sum of all the probability of an event is 1, therefore, the probability of losing the game can be written as,
Sum of all probability = Probability of winning + Probability of losing
[tex]1 = \dfrac25+\text{(Probability of losing)}\\\\\text{(Probability of losing)}=\dfrac35[/tex]
Thus, the probability of losing the game is 3/5.
As we need to calculate the probability of Max winning the first three games while he losing the rest two. Therefore,
[tex]P = \dfrac25 \times \dfrac25 \times \dfrac25 \times \dfrac35 \times \dfrac35 = \dfrac{72}{3125} = 0.023[/tex]
Hence, the probability of Max winning the first three games while losing the rest two is 0.023.
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Three tables are placed side by side by side. One table is 3 feet 11 inches wide, another is 6 feet 10 inches wide, and the third is 3 feet 7 inches wide. How wide are they combined?
To find the combined width of the three tables, add up their individual widths.
Explanation:To find the combined width of the three tables, we need to add up their individual widths.
The first table is 3 feet 11 inches wide, which is equivalent to 3 feet 11 inches + 0 feet 11 inches = 3 feet 22 inches.
The second table is 6 feet 10 inches wide, which is equivalent to 6 feet 10 inches + 0 feet 10 inches = 6 feet 20 inches.
The third table is 3 feet 7 inches wide, which is equivalent to 3 feet 7 inches + 0 feet 7 inches = 3 feet 14 inches.
Adding up the widths: 3 feet 22 inches + 6 feet 20 inches + 3 feet 14 inches = 12 feet 56 inches.
Therefore, the combined width of the three tables is 12 feet 56 inches.
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what is the solution to the equation 1/3 x = 6
In the figure, m and n are rays. Which statements are true? Select each correct answer.
A: m∠3=m∠1
B: m∠2=60°
C: m∠1=60°
D: m∠3=120°
The statements that are true about the intersecting rays are
A) m∠3 = m∠1
B) m∠2 = 60°
D) m∠3 = 120°
What are the angles formed by 2 intersecting lines?Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.
Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.
When lines intersect, two angle relationships are formed:
Opposite angles are congruent
Adjacent angles are supplementary
Given data ,
Let the two intersecting lines be m and n
Now , the angles formed are shown in the diagram
where the measure of ∠1 = ∠3 ( Opposite angles are congruent )
Now , the measure of ∠2 = 180° - ( 65° + 55° ) ( angles in a triangle = 180° )
The measure of ∠2 = 60°
So , the measure of ∠3 = 180° - ∠2 ( Adjacent angles are supplementary = 180° )
And , the measure of ∠3 = 120°
Hence , the angles in the intersecting lines are solved
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−4x−7+10x=−7+6x how many solutions
Step-by-step explanation:
[tex]-4x-7+10x=-7+6x\\\\(-4x+10x)-7=-7+6x\\\\6x-7=-7+6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-7=-7\qquad\bold{TRUE}\\\\Answer:\ \text{Infinitely many solutions}[/tex]
Final answer:
By simplifying the given linear equation and combining like terms, we find that the single solution is x = 0. Verification confirms that this solution is valid as it satisfies the original equation.
Explanation:
The equation presented by the student is a linear equation with the variables on both sides. To solve this equation, we will combine like terms and isolate the variable x on one side of the equation.
First, let's simplify the equation by combining like terms:
-4x - 7 + 10x = -7 + 6x
Combine x terms on the left side and numerical terms on the right:
6x = 0
Finally, divide by the coefficient of x to solve for x:
x = 0
This value of x is the single solution to the equation. It's important to note that there are no other solutions in this case, as it's a simple linear equation and not a quadratic or higher-order polynomial equation.
Verification
To verify that x = 0 is indeed a solution, we can substitute it back into the original equation:
-4(0) - 7 + 10(0) = -7 + 6(0)
All terms involving x drop out, confirming that -7 = -7 is an identity, making x = 0 a valid solution.
Given that the measurement is in centimeters, find the area of the circle to the nearest tenth.(Use 3.14 for n) Radius is 3
A) 18.9 cm2
B) 28.3 cm2
C) 37.7 cm2
D) 88.7 cm2
Answer:
The area of the circle is equal 28.3 cm² to the nearest tenth.
Step-by-step explanation:
To find the area of the circle that has a radius of 3, we will simply use the formula;
Area of a cirle = π r²
where π is a constand and r is the radius.
From the question given π = 3.14 and r=3
We can now proceed to insert the value into the formula;
Area of a cirle = π r²
=3.14×3²
=3.14×9
=28.26
≈28.3 cm²
Therefore, the area of the circle is equal 28.3 cm² to the nearest tenth.
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Part A: Write an algebraic expression for 6 more than 7 times a number.
Part B: Write a verbal expression for 3(n + 8).
In The Figure Below, Find X.
Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles.
Step-by-step explanation: We are given three rectangular figures A, B and C.
We need to determine which polygons are similar and which are not.
Note: The sides of similar figures are in proportion.
Let us check first A and B figures.
150/108 = 50/36
100/72 = 50/ 36.
We can see 150/108 = 100/72 = 50/ 36.
Sides are in proportion of Polygons A and B.
So, the Polygons A and B are Similar.Let us check first A and C figures.
150/132 = 25/22
100/80 = 5/4.
We can see 150/132 ≠ 100/80.
Sides are not in proportion of Polygons A and C.
So, the Polygons A and C are Not Similar.Let us check first B and C figures.
108/132 = 9/11.
72/80 = 9/10.
We can see 108/132 ≠ 72/80.
Sides are not in proportion of Polygons B and C.
So, the Polygons B and C are Not Similar.what is £747 by 2:7 in a ratio
the perimeter of the rectangle is 42 units. what are the dimensions?
In a scale drawing a plane has a length of 35 centimeters. The actual length of the plane is 87.5 feet. What is the scale of the drawing?
The scale of the drawing is [tex]\( \boxed{1 : 0.4} \).[/tex]
To find the scale of the drawing, we need to determine the ratio between the length in the drawing and the actual length.
Let x be the scale of the drawing.
According to the given information, the length of the plane in the drawing is 35 centimeters, and the actual length of the plane is 87.5 feet.
So, we can set up the proportion:
[tex]\[\frac{\text{Length in drawing}}{\text{Actual length}} = \frac{35}{87.5} = x\][/tex]
To find x , we solve for it:
[tex]\[x = \frac{35}{87.5} = 0.4\][/tex]
The scale of the drawing is [tex]\( \boxed{1 : 0.4} \).[/tex]
Witch is bigger 8 yards or 20 feet
Car A gets 25 miles per gallon and costs $13,000. Car B is a hybrid that gets 45 miles per gallon, but costs $25,000. Assume you drive 15,000 miles per year and that gas will cost $4 per gallon for the foreseeable future. How many years will it take for Car B's better fuel economy to outweigh its higher initial cost?
Answer: The answer is B) 11.25
Step-by-step explanation: I got it right
A repairman leans the top of an 8 ft ladder against the top of a stone wall the base of the ladder is 5.5 ft from the wall about how tall is the wall round to the nearest tenth of a foot
The height of the wall if A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall, is 5.81 feet.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine, cosine, and tangents are their names and acronyms (tan).
Given:
A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall,
Calculate the height of the wall as shown below,
Assume the height of the wall is x then,
x² + base² = ladder height²
x² + 5.5² = 8²
x² = 64 - 30.25
x² = 33.75
x = √33.75
x = 5.81 ft
Thus, the height of the wall is 5.81 feet.
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A cereal box is a rectangular prism that is 8 inches long and 2 1/2 inches wide. The volume of the box is 200 in^3. What is the height of the box
Find the range 3, -97,-15,-42
The range of the numbers 3, -97, -15, -42 is 100.
Explanation:The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 3, -97, -15, -42, we first need to find the largest and smallest numbers. The largest number is 3 and the smallest number is -97. Subtracting the smallest number from the largest number gives us a range of 100.
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The table represents f(x), and the graph represents g(x). Which statements about the functions are true for the interval [4, 10]?
x f(x)
______
3 1.33
4 1
5 0.8
6 0.66
10 0.4
Select ALL that apply
1- The average rate of change of f(x) is greater than the average rate of change of g(x).
2- The average rate of change of f(x) is less than the average rate of change of g(x).
3- Both functions have the same average rate of change.
4- The average rate of change of f(x) is 0.1, and the average rate of change of g(x) is 0.25.
5- The average rate of change of f(x) is -0.1, and the average rate of change of g(x) is -0.25.
Answer:
1- The average rate of change of f(x) is greater than the average rate of change of g(x).
5- The average rate of change of f(x) is -0.1, and the average rate of change of g(x) is -0.25.
Step-by-step explanation:
average rate of change of a function h(x) in the interval [a, b] is computed as follows:
average rate of change = h(b) - h(a)/(b - a)
So, for f(x) (see table):
average rate of change = f(10) - f(4)/(10 - 4) = (0.4 - 1)/(10 - 4) = -0.1
And for g(x) (see figure):
average rate of change = g(10) - g(4)/(10 - 4) = (1 - 2.5)/(10 - 4) = -0.25
How would you find the area of this shape? ( rectangle and congruent triangle )
A meter stick casts a shadow 2.4 m long at the same time a flagpole casts a shadow 9.7 m long. How tall is the flagpole
A cube that has side lengths measuring 7 inches
A cube with side lengths measuring 7 inches means that each side of the cube is 7 inches long.
To find the volume of the cube, you multiply the length, width, and height of the cube since all sides are equal:
Volume = length × width × height
For a cube, all these measurements are the same, so you can simply cube the length of one side:
Volume = 7 inches × 7 inches × 7 inches
Volume = 7³ cubic inches
Volume = 343 cubic inches
So, the volume of the cube is 343 cubic inches.
A cube with side lengths measuring 7 inches implies that each side of the cube is 7 inches long.
To find the volume of the cube, we use the formula for the volume of a cube, which is side length cubed.
Since all sides of a cube are equal, we simply cube the length of one side: 7 inches × 7 inches × 7 inches. This equals 7³ = 343 cubic inches.
Therefore, the volume of the cube is 343 cubic inches. In a cube, all sides, angles, and faces are congruent, making it a regular polyhedron with 6 square faces.
Complete Question:
A cube that has side lengths measuring 7 inches.
Does a trapezoid have obtuse angles
A = bh/2 solve for b
The value of b in the equation is [tex]b=\frac{2A}{h}[/tex].
What is simplification of an equation?Simplification of an equation is the process of writing an equation in the most efficient and compact form without affecting the value of the original equation.
For the given situation,
The equation is [tex]A=\frac{bh}{2}[/tex]
The equation can be simplified as
⇒ [tex]A=\frac{bh}{2}[/tex]
⇒ [tex]2A=bh[/tex]
⇒ [tex]b=\frac{2A}{h}[/tex]
Hence we can conclude that the value of b in the equation is [tex]b=\frac{2A}{h}[/tex].
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Without graphing estimate the x-intercepts of the graph of f(x)=7x^2+9x+1 to the nearest tenth.
setsuko has a rectangular piece of farbric that is 5/6 yard wide. The area of the fabric is 5/16 square yard. How long is setsuko's fabric
Find the value of x and the value of y