In a survey of 99 resorts, it was found that 31 had a spa. 39 had a children's club. 8 had a spa and children's club. 6 had all three features. 57 had a fitness center. 15 had a spa and a fitness center. 21 had a fitness center and children's club. Complete parts a) through e). a) How many of the resorts surveyed had only a spa? (Type a whole number.)
Answers
Ok, so
With this situation, we could make a Venn's diagram as follows:
Where S is the spa, C is the children's club and F is the fitness center.
a) Now, we want to know how many of the resorts surveyed only had a spa. For this, we can substract:
[tex]31-(2+6+9)=31-17=14[/tex]b) the number of the resorts that had exactly one of these features is:
Exactly spa is: 31-(2+6+9) = 14.
Exactly fitness center is: 57-(15+6+9) = 57-30 = 27.
Exactly a children's show is: 39-(15+6+2) = 16.
If we sum all these values, we got:
14+27+16 = 57
Therefore, the number of the resorts that had exactly one of these features is 57.
c) We want to know the number of the resorts that had at least one of these features. We can find this, if we first sum the number of the resorts that had exactly one of these features :
14+27+16 = 57.
Now, we're going to sum all the middle values in the diagram:
2+6+9+15 = 32.
Then, 57 + 32 = 89.
Therefore, the number of the resorts that had at least one of these features is 89.
d) the number of the resorts had exactly 2 of these features would be:
2+9+15 = 26.
e) the number of the resorts that had none of these features can be found if we substract the number of total resorts and the number of the resorts that had at least one of these features. This is:
99 - 89 = 10.
Related Questions
Which steps should be used to graph the equation below?
y – 4 = y minus 4 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)
a 1. Plot the point (2, 4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
b 1. Plot the point (2, 4).
2. From that point, count left 1 unit and down 3 units and plot a second point.
3. Draw a line through the two points.
c 1. Plot the point (–2,4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
d 1. Plot the point (–2,4).
2. From that point, count left 1 unit and down 3 units and plot a second point.
3. Draw a line through the two points.
Answers
The steps to grapj the given equation y – 4 = y minus 4 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2) is C.
1. Plot the point (–2,4).2. From that point, count left 3 units and down 1 unit and plot a second point.3. Draw a line through the two points.Calculations and ParametersGiven
y - 4 = (1/3) (x+ 2)
The steps should be used to graph the equation is given below:
y - 4 = (1/3) (x+ 2)
y - 4 = 0 => y = 4
x + 2 = 0 => x = -2
Plot point ( - 2 , 4)
count left 3 units and down 1 unit and plot a second point.
as for every 3 units change in x, there is one unit change in y
x going left & y going down is the same direction
Draw a line through the two points.
Therefore, the correct answer is option C.
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Explain how you could build on knowing the decimal form of 1/5, to find the decimal form of 3/5. Then write the decimal.
Answers
The decimal form of 3/5 is 0.6.
What is decimal?A group of numbers between integers on a number line are known as decimals.
Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are represented to the right of the decimal point.
The next place, which is (1/10)th or tenth place value, is (1/10) times smaller if we move immediately from the first place.
For illustration, look at the decimal place value chart for 12.45 that is shown below.
Given:
fraction 1/5
Now, we can divide
1/5 = 0.2
Now, we can use the decimal form of 1/5 in calculating the decimal from of 3/5 as
3/5
=3 x 1/5
= 3 x 0.2
= 0.6
Hence, the decimal form of 3/5 is 0.6.
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what is 3423553 x 3286328 to the 8th power divided by the sum of 293876+ 23483?
Answers
Answer:
1.467619e+53
Step-by-step explanation:
you do 3423553 times 3286328 which is 4.6576228e+58 then u do 293876 plus 23483 which is 317359 then u do 4.6576228e+58 divided by 317359 which is 1.4676196e+53.
An online article about an opinion poll says that "41% of Americans own a gun." The poll is based on online survey interviews with 2,700 adults chosen randomly from a numbered list of 750,000 responses from around the United States, excluding New England states.
Part A: What is the population and sample in this poll? (3 points)
Part B: What type of sampling is used? (3 points)
Part C: Are there any sources of bias present? Explain. (4 points)
Answers
A. The population and the sample in the poll are Americans and the sample is 2700 adults.
B. The type of sampling used is a random sampling.
C. There are no bias in the sources used.
What is a sampling?Sampling is simply used in research to get to get the needed information about a particular group of people.
In this case, the online article about an opinion poll says that "41% of Americans own a gun." The poll is based on online survey interviews with 2,700 adults chosen randomly.
This is a random sampling. In this case, everyone has an equal chance of being selected. There's no bias as it was fair.
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Question 291 ptHow many real solutions does the quadratic equation below have?y = 2? + 5x + 100 1 real solutionNo real solutions2 real solutionsInfinite number of real solutionsNexDrevious
Answers
The quadratic equation is:
[tex]y=2x^2+5x+10[/tex]To find if the number of solutions, we use the discriminant of the equation. But first, we compare the given equation with the general quadratic equation:
[tex]y=ax^2+bx+c[/tex]By comparison, we find the values of a, b, and c:
[tex]\begin{gathered} a=2 \\ b=5 \\ c=10 \end{gathered}[/tex]Now, as we said previously, we have to use the discriminant to find the number of solutions. The discriminant is defined as follows:
[tex]D=b^2-4ac[/tex]• If the value of D results to be equal to 0, there will be 1 real solution.
• If the value of D results to be greater than 0, there will be 2 real solutions.
• And if the value of D results to be less than 0, there will be no real solutions.
We substitute a, b and c into the discriminant formula:
[tex]D=5^2-4(2)(10)[/tex]Solving the operations:
[tex]\begin{gathered} D=25-4(2)(10) \\ D=25-80 \\ D=-55 \end{gathered}[/tex]As we can see, the value of D is less than 0 (D<0) which indicates that there will be no real solutions for this quadratic equation.
Answer: No real solutions
Please help me solve for X
I'll give brainlyest
Answers
Answer:
1. x = 8
2. x = 12
3. x = 11
4. x = 6
Step-by-step explanation:
1.
102 + 102 = 204
360 - 204 = 156
156 / 2 = 78
78 = 10x - 2
78 + 2 = 10x
80 = 10x
80 / 10 = x
x = 8
2.
81 = 7x - 3
81 + 3 = 7x
84 = 7x
84 / 7 = x
x = 12
3.
77 = 6x + 11
77 - 11 = 6x
66 = 6x
66 / 6 = x
x = 11
4.
115 + 115 = 230
360 - 230 = 130
130 / 2 = 65
65 = 8x + 17
65 - 17 = 8x
48 = 8x
48 / 8 = x
x = 6
on a necklace two-thirds of the bees are blue of the blue beads 1/4 or oval shaped what fraction of the necklace is made up of blue ovals
Answers
on a necklace two-thirds of the bees are blue of the blue beads 1/4 or oval shaped what fraction of the necklace is made up of blue ovals
we have that
2/3 ------> blue
1/4(2/3)=2/12-1/6
answer is 1/6
Coach Sikyta is measuring the basketball court in the Arena, he finds that the length is (x + 7) and the width is (3x - 1). Determinethe area of the court.
Answers
Show that the fundamental theorem of algebra is true by finding the zeros of the quadratic equation: x^ 2 -12x+12 = - 20
Answers
Answer
The fundamental theorem of algebra is true with quadratic equation x^2-12x+12=-20 with zeros of 4 or 8.
Finding the zeros of a quadratic equation:A quadratic equation is an equation with the highest power of unknown to be 2. It is given in the form Ax^2+ Bx+ C= 0
finding the roots or zeros of the equation x^2-12x+12=-20 can be done by factorization method;
we equate the equation to zero by bringing -20 to the LHS .
x^2-12x+12+20=0
x^2-12x+ 32 = 0
find the factors of +32 that their sum will give -12
x^2-8x-4x+32=0
grouping the above equation
(x^2-8x)(-4x+32)= 0
x(x-8)-4( x-8)= 0
(x-4))(x-8) = 0
for the equation above to be true.
x-4=0 or x-8 = 0
: x=4 or x=8.
In conclusion, the algebra theorem is obeyed because the zeros of the equation are real numbers
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11. Express the number 000000005864 in scientific notation.
Answers
Answer:
5.864*10^-9
Step-by-step explanation:
1)Find the total of each figure shown. Measured in cm ( not to scale ). width = 2
Answers
Answer:
54
Explanation:
To find the total volume of the figure, we will divide the figure into two parts as follows:
Where the volume of each figure can be calculated as:
V = length x height x width.
So, the volume of the first figure is:
V₁ = 3 x 4 x 2 = 24
And the volume of the second figure is
V₂ = 5 x 3 x 2 = 30
Therefore, the total volume will be
V = V₁ + V₂
V = 24 + 30
V = 54
So, the total volume of the figure is 54.
A prescription drug company produces a capsule shaped like a cylinder with a hemisphere attached to each base. The cylinder and hemispheres all have a diameter of 8 millimeters, and the cylinder has a height of 15 millimeters. The outside of the capsule is coated with a film to improve the flavor and protect the medicine.What is the approximate area of the capsule that is coated with the film?
Answers
1. Rectangular Prism: a. The measures: 1 =5, w = 7, h = 8.. b. The measures: h=7, w = 7,1 = 7. c. w = 3.6,1 = 4.2, h = 8.3 2. Cylinder a. r = 4, h = 7 b. h = 14.3, r = 8.5 3. Triangular Prism: a. Triangle area = 24, h = 5 b. Tri = b = 10, h = 9, and the height is 12 4. Sphere: a. r= 2 b. r = 4. c. In a and b, the radius of b is twice the radius of a. Is this also true for the volume of a spheres? Why? 5. Cone: a. r = 3, h = 9 b. h = 12, r = 5
Answers
For a rectangular prism, the
Triangle Congruence, Flowchart Proof (Level1) _ 10th Grade - Int.1
Answers
A closed pentagon has five sides and five angles and is a two-dimensional polygon. Different varieties of pentagons can be identified based on their characteristics. As follows:
Regular Pentagon: A pentagon with equal angles and sides on all sides.
Uneven Pentagon: A pentagon's internal angles and all of its sides' lengths differ from one another.
Convex Pentagon: All vertices point outward and all internal angles are smaller than 180°. The shape of a regular pentagon is convex.
Concave Pentagon: A pentagon is referred to as a concave polygon if one of its inner angles is more than 180 degrees and one of its vertices faces inward.
In Pentagon ABCDE it is given that:
∠A = 75°
∠C = 115°
∠D = 95°
∠B = ∠E
Let ∠B= x
We know that the sum of the interior angles of a pentagon is 540°
Therefore, ∠A + ∠B + ∠C + ∠D + ∠E = 540°
75 + 110 + 95 + 2x = 540°
2x = 260°
x = 130°
Hence ∠B and ∠E = 130°
(2) When the pentagon is reflected over line y=x, the angles become
∠A = ∠A¹
∠B = ∠B¹
∠A = ∠A¹
∠C = ∠C¹
∠D = ∠D¹
∠E = ∠E¹
So, 2x + 5 = 130°
2x = 125
x = [tex]\frac{125}{2}[/tex]
x = 62.5°
Similarly,
∠D = (3y - 4)°
95 = 3y - 4
3y = 99
y = 33°
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Help fast pls thanks so much
Answers
The exterior angle of the given triangle is X. The value of the angle X is 55°.
Triangle -
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
types of triangle
On the basis of length of the sides.Scalene TriangleIsosceles TriangleEquilateral TriangleOn the basis of measurement of the anglesAcute Angle TriangleRight Angle TriangleObtuse Angle TriangleThe exterior angle of a triangle is equal to the sum of two interior opposite angles.
X = 21° + 34°
X = 55°
The exterior angle of the given triangle is X. The value of the angle X is 55°.
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Find the missing values in the ratio table. Then write the equivalent ratios.
Boys 6. 3. blank
girls 10 blank 50
Answers
Answer:
3:5 , 30:50
Step-by-step explanation:
Since
6 : 10 = 3 : X
Then we know
10/6 = X/3
Multiplying both sides by 3 cancels on the right
3 × (10/6) = (X/3) × 3
3 × (10/6) = X
Then solving for X
X = 3 × (10/6)
X = 5
Therefore
6 : 10 = 3 : 5
Hi I need help with this question, please and thank you
Answers
1) Let's rewrite it into the z=a +bi form.
2) So we can write out the following noticing that i² =-1 as well as √-1=i
[tex]\begin{gathered} \sqrt[]{-1176}=\sqrt[]{-1}\cdot\sqrt[]{1176} \\ Factoring \\ \sqrt[]{-1}\cdot14\sqrt[]{6} \\ i\cdot14\sqrt[]{6} \\ 14\sqrt[]{6}i \end{gathered}[/tex]Note that in this number the real part "a" is equal to 0.
Fill in the missing numbers in the pattern,The first number is 280. The rule is to subtract 20.280,
Answers
We have the following:
[tex]\begin{gathered} 280-20=260 \\ 260-20=240 \\ 240-20=220 \end{gathered}[/tex]therefore, the answer is 260, 240, 240
A pool has the dimensions of 12 feet and 10 feet.
There is a sidewalk all the way around the pool that measures 3 feet wide.
What is the area of the sidewalk?
Answers
The area of the sidewalk is 78 sq. feet
we are given the dimensions of the pool to be,
length = AB or DC = 12 feet
breadth = BC or AD = 10 feet
area of the pool ABCD ( refer to the diagram attached) = length x breadth
= 21 x 10
= 210 sq. feet
now, to find the area of the rectangle PQRS, which includes the area of the pool and the sidewalk,
we have,
length = PQ or SR
SR = D'C' + SD' +C'R
= 12 + 3 + 3
= 18 feet
breadth = QR or PS
QR = QB' +B'C' + C'R
= 3 + 10 + 3
= 16 feet
thus, we know the area of a rectangle = length x breadth
= 18 x 16
= 288 sq. feet
now, to find the area of the sidewalk / the shaded part (refer to the diagram)
area of PQRS - area of ABCD
= 288 - 210
= 78 sq feet
Hence the area of the sidewalk is 78 sq. feet
What is area?
The measurement that expresses the size of a region on a plane or curved surface is called area.
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Let f(x) = x2 - 18 and g(x) = 20-x Perform the composition or operation indicated(F/g)(7)
Answers
f(x) = x^2-18
g(x)=20-x
Divide both functions and evaluate for 7
(F/g) (7) = (x^2-18) / (20-x)
(F/g) (7) = (7^2-18) / (20-7)
(F/g) (7) = (49-18) / 13= 31/13 = 2.38
I need help with the last one I need to find the median and the mean
Answers
First organice the data from lower to higher
15 21 22 25 27 28 36 37 39 41 43 50
The mean is the average
[tex]\frac{15+21+22+25+27+28+36+37+39+41+43+50}{12}=32[/tex]The median is the number in the middel when is organized from lower to higher
In this case are 28 and 36, usually in these cases you get the average or on of them
[tex]\frac{36+28}{2}=32[/tex]What equation would it be
Hurry quick please I don’t have much time left
Answers
Answer:
[tex]x^2-6x-13[/tex]
Step-by-step explanation:
[tex]\frac{-b+-\sqrt{b^2-4ac} }{2a} \\a=1\\b=-6\\c=-13[/tex]
the _______ of 2 is 2A. signB. absolute value C. opposite
Answers
The sign | | is used to refer to the absolute value of an expression or integer.
Given an integer x
[tex]\begin{gathered} |x|=x \\ |-x|=x \end{gathered}[/tex]The absolute sign will always return a positive value.
Therefore, the absolute value of 2 is 2.
The correct option is B.
ASAP
Which equation has no solution?
Answers
The equation 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1 has no solution.
What is zero solution?In Mathematics, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal when simplified. This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out when simplified.
How to determine the number of solutions?Based on the rule given above, the third equation fails. In order to determine the number of solutions that this equation has, we would simplify the equation by collecting like terms and then compare both sides of the equation as follows:
32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
34.5y - 5.1 = 34.5y - 5.1
34.5y - 34.5y = - 5.1 + 5.1
0 = 0
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Solve by factoring:[tex]5 {x}^{2} + 12x + 4 = 0[/tex]
Answers
The given equation is
5x^2 + 12x + 4 = 0
This is a quadratic equation. We would solve by applying the method of factorisation. The first step is to multiply 5x^2 with 4. It becomes 20x^2. We would find two terms such that their sum or difference is 12x and their product is 20x^2. The terms are 10x and 2x. By replacing 12x with 10x + 2x, we have
5x^2 + 10x + 2x + 4 = 0
The next step is to factorise by grouping. The groups are (5x^2 + 12) and (2x + 4). It becomes
5x(x + 2) + 2(x + 2) = 0
Since x + 2 is common, it becomes
(x + 2)(5x + 2) = 0
x + 2 = 0 or 5x + 2 = 0
x = - 2 or 5x = - 2
x = - 2 or x = - 2/5
a farmer is conducting an experiment to determine which variety of apple tree, fuji or gala, will produce more fruit in his orchard. the orchard is divided into 20 equally sized square plots. he has 10 trees of each variety and randomly assigns each tree to a separate plot in the orchard. what are the experimental unit(s) in this study?
Answers
The farmer is undertaking an experiment to see which type of apple tree, fuji or gala, would yield more fruit in his orchard, and the plots are the experimental units in this investigation. So, the plots are the solution.
Based on the given conditions,
In order to find out which apple tree would bear more fruit in his orchard, fuji or gala, the farmer is first conducting an experiment.The orchard is separated into square sections of equal size.Each kind has ten trees, and he divides the orchard into various plots according to chance.The plots act as the experimental units because they are the variables being measured.The type of apple trees, which vary the experimental unit by enduring two different treatments, is the explanatory variable. The farmer is doing the experiment, and the result is the number of apples.The orchard as a whole has no bearing on the experiment because each plot is being studied independently.The plots are the experimental units as they are the objects subjected to the measurements. The variety of apple trees is the explanatory variable since they promote change in the experimental unit through two different treatments (Fuji or Gala variety). The farmer is the one conducting the experiment and the number of apples is the result to be analyzed. The orchard as a whole does not interfere in the experiment since each plot is being studied.
Therefore,
The plots are experimental units in this study, then the farmer is conducting an experiment to determine which variety of apple tree, fuji or gala, will produce more fruit in his orchard. So ,the answer is the plots.
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Find the value of x
Answers
Answer:
x = 35
Step-by-step explanation:
110 + 110 = 220
360 - 220 = 140
140 / 2 = 70
70 = 2x
70 / 2 = x
x = 35
Answer:
x=35
Step-by-step explanation:
You can set the equation up like this
2x+110=180
Set x by itself
2x=70
Divide both sides by 2
x=35
a. Use the quadratic equation to find the zeros of the function. b. Average the zeros to find the x-coordinate of the vertex of the parabola.
Answers
y= x^2 - 13x + 36
Quadratic equation:
[tex]\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]Where:
a= 1
b= -13
c = 36
Replacing:
[tex]\frac{-(-13)\pm\sqrt[]{(-13)^2-4\cdot1\cdot36}}{2\cdot1}[/tex][tex]undefined[/tex]In the equation 7x+6=y what is the value of y when x= 2
Answers
We have the equation:
[tex]7x+6=y.[/tex]To find the value of y when x = 2, we replace x = 2 in the equation above, we get:
[tex]y=7\cdot2+6=14+6=20.[/tex]Answer: 20
you have torn a tendon and is facing surgery to repair it. the surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails in 13%, and both infection and failure occur together in 2%. what percentage of these operations succeed and are free from infection? give your answer as a whole number.
Answers
The percentage of the operations succeed and are free from infection = 86%
The probability of infection, P(infection) = 3% = 0.03
The probability of repair fails, P(repair fail) = 13% = 0.13
Probability of both infection and repair fail, P(infection ∩ repair fail) = 2% = 0.02
We know that, if A and B are two events, then,
P(A ∪ B) = P(A) + P(B) - P(A∩B)
So Probability of infection or repair fail = P(infection ∪ repair fail)
= P(infection) + P(repair fail) - P(infection ∩ repair fail)
= 0.03 + 0.13 - 0.02
= 0.14
Now P(not A) = 1 - P(A)
So probability of no infection and repair success
= P(no infection and repair success
= P(not [infection ∪ repair fail])
= 1 - P(infection ∪ repair fail)
= 1 - 0.14
= 0.86
Hence The percentage of the operations succeed and are free from infection = 0.86 x 100% = 86%
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