A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like football Do not like football Total Like baseball A D G Do not like baseball B E H Total C F I Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points)
Answers
Total of students who like football = 77 students
Students who like football and baseball = 48 students
Students who like football and not baseball = 77 - 48 = 29 students
Students who do not like football = 100 - 77 = 23 students
Students who like baseball = 65 students
Students who like baseball but not football = 65 - 48 = 17 students
Students who do not like baseball = 100 - 65 = 35 students
These data can be represented in a two ways table as shown below
PART B:
The number of students who do not like either football or baseball is 29+17+6=52
The probability is 52/100 = 52%
PART C:
The number of students who don't like football is 17+6=23 students
The number of students who don't like baseball is 35 students
The survey result reveals a greater dislike for baseball
Related Questions
The Grand Prix Formula 1 race this weekend is in Singapore. The race consists of 61 laps around a 5.067 km long track. At 225 miles per hour, how long will it take to go around once?
Answers
5.067 km ≈ 5.067÷1.6 ≈ 3.2 miles
time travelled = distance ÷ speed
time travelled = 3.2÷225
time travelled = 0.0142 hour = 51.2 seconds
At an aquarium, 6 out of 18 deliveries are plants. Out of 15 deliveries in one week,how many are plants?
Answers
5 deliveries.
Assume that a procedure yields a binomial distribution with a trial repeated n times. use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. round to three decimal places. n = 14, x = 6 , p = 0.5
Answers
ⁿCₓ (p)ˣ (q)ⁿ⁻ˣ
Where q = 1 - p
We have
n = 14
x = 6
p = 0.5
q = 1 - 0.5 = 0.5
Substitute these values into the formula, we have
¹⁴C₆ × 0.5⁶ × 0.5⁸ = 0.183 (rounded to three decimal places)
A circular fountain has a circular walkway surrounding it with a width of 7 ft. The total area taken up by the walkway is 693π ft^2. Find the diameter of the pool.
Answers
[tex]\bf A=2\pi pw\quad \begin{cases} w=7\\ A=693\pi \end{cases}\implies 693\pi =2\pi p7\implies \cfrac{693\pi }{14\pi }=p \\\\\\ 49.5=p\\\\ -------------------------------\\\\ r=p-\cfrac{w}{2}\implies r=49.5-3.5\implies r=46[/tex]
now, that's just the radius of the pool, the diameter would be twice as much, or 2r.
Car rental at Q.T. Rental is $22 per day plus an initial deposit of $36.Which expression shows how much it will cost to rent a car for d number of days?
Answers
Answer:
The expression is Price = 36 +22*d where d is each day that pass.
Step-by-step explanation:
The inicial 36 are the independant term since it's not related to how many days the car is rented. 22 is the slope since it depends on the days the car is rented.
Given the following triangle, if a = 12 and ∠B = 48°, find b to the nearest whole number.
Answers
So, you can use the tangent ratio which relates the angle, the opposite leg and the adjacent leg:
tangent (angle B) = b / a => b = a * tan(B)
=> b = 12 * tan(48°) = 13.33≈ 13
Answer: 13
Answer:
The value of b nearest whole number is, 13.
Step-by-step explanation:
We know an [tex]\angle B=48^{\circ}[/tex] and the side adjacent to it i.e, a=12.\
In a right triangle BCA ,
the tangent(tan) of an angle is the length of the opposite side divided by the length of the adjacent side.
i.e, [tex]\tan B=\frac{opposite}{Adjacent}=\frac{b}{a}[/tex]
Substitute the value of a=12 and [tex]\angle B=48^{\circ}[/tex] to solve for b in above expression:
[tex]\tan 48^{\circ}=\frac{b}{12}[/tex]
we have the value of [tex]\tan 48^{\circ}=1.110613[/tex]
then, [tex]1.20012724=\frac{b}{12}[/tex]
On simplify we get,
[tex]b=1.110613 \times 12=13.327356[/tex]
Therefore, the value of b nearest whole is, 13
Using the given zero, find all other zeros of f(x).
-2i is a zero of f(x) = x4 - 32x2 - 144
a) 2i, 12, -12
b) 2i, 6i, -6i
c) 2i, 6, -6
d) 2i, 12i, -12i
Answers
Answer: C; 2i,6,-6
Answer:
c) 2i, 6, -6Step-by-step explanation:
The given function is
[tex]f(x)=x^{4}-32x^{2} -144[/tex]
The given zero to this function is
[tex]x=-2i[/tex]
Remember that a function has so many roots as its grade dictates. So, in this case, the function grade is four, which means it has four solutions.
Now, the given function is an imaginary number, which happens in pairs, that means the second root must be [tex]x=2i[/tex], because a function can have complex roots as pairs, 2, 4, 6,... many solutions.
The other two solutions are 6 and -6, because if we replace them into the function, it will give zero.
[tex]f(6)=6^{4}-32(6)^{2} -144=0\\f(-6)=(-6)^{4}-32(-6)^{2} -144=0[/tex]
Therefore, the other three solutions missing are: c) 2, 6, -6.
(The image attached shows the real solutions).
The area of one triangle is 150 square centimeters when it's height is 20 centimeters and it's base length is 15 centimeters. What is the area of a triangle having a height of 30 centimeters and a base length of 18 centimeters.
Answers
Where b is the base and h is the height.
Substitute the variables for the values.
[tex]A = \frac{1}{2}(30)(18)[/tex]
[tex]A = \frac{1}{2}540[/tex]
A = 270
So, the area is 270 square centimeters.
In a survey of 3450 registered voters who reside in California, 1789 were found to be republican. Construct a confidence estimate for the true percentage of republicans among registered voters in California. Use a confidence level of 95%.
Answers
n = 3450, sample size
p = 1789/3450 = 0.519 = 51.9%, proportion
Confidence level = 95%
The confidence interval is given by
[tex]p \pm z*\sqrt{ \frac{p(1-p)}{n} }[/tex]
where z* = 1.96 at the 95% confidence level.
[tex]1.96 \sqrt{ \frac{0.519(1-0.519)}{3450} } = 0.0167[/tex]
Therefore the 95% confidence interval is
(0.519 - 0.0167, 0.519 + 0.0167)
= (0.5023, 0.5357)
= (50.2%, 53.6%)
Answer:
At the 95% confidence level, the interval for the proportion is about (50%, 54%).
Mateo is constructing an equilateral triangle inscribed in a circle with center P. He draws the diameter of the circle through center P using a straight edge. Next he opens his compass to a width equivalent to the radius of the circle. What is his next step?
Answers
The next steps should be:
*He should draw the upper and lower arcs using the compass opened to a width equivalent to the radius of the sircle.
*Make a vertical diameter using centroid P as basis.
*Draw two right triangles facing the opposite directions using the top most point by which the vertical diameter of the circle touches the top most circumference of the circle.
Doing these steps, Mateo will be able to draw an equilateral triangle inscribed in a circle.
Shelley spent 17 minutes washing dishes. She spent 38 minutes cleaning her room. Explain how you can use mental math to find how long Shelley spent on the two tasks.
Answers
20+40=60
60-5+55
Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?
Answers
So for conjugate, you just flip the sign of the imaginary part:
2+8i will be the answer
The conjugate of the given complex number is:
[tex]2+8i[/tex]
Step-by-step explanation:We know that any complex number is written in the form of:
[tex]z=a+ib[/tex]
where a and b are real numbers.
The conjugate of the complex number is given by:
[tex]\bar z=\bar {a+ib}\\\\i.e.\\\\\bar z=a-ib[/tex]
Here we are given that:
We have a complex number such that the real part of a complex number is 2 and it's imaginary part is -8.
i.e.
a=2 and b= -8
i.e. the complex number is:
[tex]z=2+(-8)i[/tex]
Hence, the conjugate of this number is:
[tex]\bar z=2-(-8)i\\\\i.e.\\\\\bar z=2+8i[/tex]
on a certain planet, objects weight about 7/12 of what they weigh on earth. an object weights 13 5/12 pounds on the planet. solve the equation 7/12 w= 13 5/12 for w to find the objects weight on earth in pounds.
Answers
Let's simplify 13 5/12 first into an improper fraction.You do this by multiplying the denominator with the whole number and adding to it the numerator. This will be your new numerator, The denominator would still be 12. So, this is equal to (12*13 + 5)/12 = 161/2. Then,
(7/12) w = 161/12
By cross multiplication,
7*12*w = 161*12
w = 161/7 = 23
Therefore, w = 23 pounds which is the weight of the object on Earth.
Kevin is solving this problem. 737 × 205 What are the partial products Kevin will need to solve the problem? A. 3,685 and 147,400 B. 3,685 and 14,740 C. 3,685 and 1,474 D. 3,685 and 7,370 and 147,400
Answers
the answer is A
700 x 5 = 3500
30 x 5 = 150
7 x 5 = 35
3500 + 150 +35 = 3685
700 x 200 = 140,000
30 x 200 = 6000
7 x 200 = 1400
140000 + 6000 + 1400 = 147400
Carlos is putting money into a savings account. He starts with $750 in the savings account, and each week he adds $40 . Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Carlos has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 11 weeks.
Equation:
Total amount of money after 11 weeks:
Answers
Final answer:
The equation relating the total amount of money S in Carlos's savings to the number of weeks W he adds money is S = 750 + 40W. By substituting W with 11, we find that after 11 weeks, Carlos will have $1,190 in his savings account.
Explanation:
The question involves creating a linear equation to represent the relationship between the total amount of money S in Carlos's savings account and the number of weeks W he has been adding money. The equation can be written as S = 750 + 40W, where 750 represents the initial amount and 40 is the amount added each week. To find the total amount of money after 11 weeks, substitute W with 11:
S = 750 + 40(11) = 750 + 440 = 1190
Therefore, after 11 weeks, the total amount of money in the savings account would be $1,190.
What is the value of a?
Answers
Cross multiply and solve for 'a'
3/4 = 4/a
3*a = 4*4
3*a = 16
3*a/3 = 16/3
a = 16/3
a = (15+1)/3
a = (15/3)+(1/3)
a = 5+(1/3)
The answer is choice B)
If the minimum value of the function y = cos θ + d is –5, the value of d is...
Answers
-1 + d = -5
d = -4
The value of d, when the function is at its minimum is -4.
What is a Function?A function is a law that relates two variables namely, a dependent and an independent variable.
A function always has a defined range and domain, domain is all the value a function can have as an input and range is all the value that a function can have.
The function is of various types, logarithmic, exponential, quadratic, radical etc.
The function is y = cos [tex]\rm \theta[/tex] + d
The minimum value of the function, y = cos [tex]\rm \theta[/tex] + d is -5.
The minimum value is the lowest value of the function.
The minimum value of cos [tex]\rm \theta[/tex] is at 180 degree equals to -1
Substituting the value in the equation.
-5 = - 1 + d
d = -5 +1
d = -4
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What is the domain of y = sec(x)?
Answers
The domain of y = sec(x) is all real numbers except for values where the cosine function is zero.
Explanation:The domain of y = sec(x) is all real numbers except for values where the cosine function is equal to zero. Since the secant function is the reciprocal of cosine, it is undefined when cosine is zero.
So, the domain of y = sec(x) is all real numbers except for values of x where cos(x) = 0.
For example, if we consider the unit circle, the cosine function is equal to zero at π/2 and 3π/2. Therefore, the domain of y = sec(x) would exclude these values.
The domain of [tex]\( y = \sec(x) \)[/tex] is all real numbers except [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex], [tex]\( n \)[/tex] integer.
Let's find the domain of [tex]\( y = \sec(x) \)[/tex].
The secant function, [tex]\( \sec(x) \)[/tex], is defined as the reciprocal of the cosine function, [tex]\( \cos(x) \)[/tex]. So, [tex]\( \sec(x) = \frac{1}{\cos(x)} \).[/tex]
The cosine function is defined for all real numbers, except where the denominator becomes zero, because division by zero is undefined.
So, to find the domain of [tex]\( \sec(x) \)[/tex], we need to find where [tex]\( \cos(x) \)[/tex] is not zero.
The cosine function has a range between -1 and 1. It equals zero at [tex]\( x = \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x = -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
So, the domain of [tex]\( \sec(x) \)[/tex] is all real numbers except where [tex]\( \cos(x) = 0 \)[/tex]. Therefore, the domain of [tex]\( \sec(x) \)[/tex] is [tex]\( x \neq \frac{\pi}{2} + \pi \cdot n \)[/tex] and [tex]\( x \neq -\frac{\pi}{2} + \pi \cdot n \)[/tex], where [tex]\( n \)[/tex] is an integer.
In interval notation, the domain of [tex]\( \sec(x) \)[/tex] is:
[tex]\[ (-\infty, -\frac{\pi}{2}) \cup (-\frac{\pi}{2}, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \infty) \][/tex]
Find the area under the standard normal distribution curve to the left of z=-2.15 and to the right of z=1.62
Answers
So, what's being asked, in essence, is what is P(Z ≤ -2.15) and P(Z ≥ 1.62).
P(Z ≤ -2.15) = 1 - P(Z ≤ 2.15) = 1 - 0.9842 = 0.0158.
P(Z ≥ 1.62) = 1 - P(Z ≤ 1.62) = 1 - 0.9474 = 0.0526
Using the normal distribution table, which shows the percentage of the areas to the left a normal distribution, the area to the left z = - 2.15 and area to the right of z = 1.62 are 0.0158 and 0.0526 respectively.
1.)
The area under the normal distribution curve to the left of z = 2.15 can be expressed thus :
P(Z ≤ -2.15)
Using a normal distribution table ; the area to the left is
P(Z ≤ -2.15) = 0.0158
2.)
The area under the normal distribution curve to the right of z = 1.62 can be expressed thus :
P(Z ≥ 1.62) = 1 - P(Z ≤ 1.62)
Using a normal distribution table ; the area to the left is P(Z ≤ 1.62) = 0.94738
P(Z ≥ 1.62) = 1 - 0.94738 = 0.0526
Therefore, the area to the left z = - 2.15 and area to the right of z = 1.62 are 0.0158 and 0.0526 respectively.
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How long will it take a bird traveling at an average speed of 12 miles per hour to travel 202 miles while flying south for winter?
Answers
Answer:
16 50 min
Step-by-step explanation:
The sum of two consecutive even integers equals 6426?
Answers
Second integer: x+2
x+x+2=6426
2x+2=6426
2x=6424
x=3212
So your two integers are: 3212 and 3214
61702 67102 same or different?
Answers
Let me know if you need any more help!
Choose the solution for the equation.
d3=284? need help asap
Answers
Answer:
the answer is A
Step-by-step explanation:
ttm
A triangle has a perimeter of 10x+2. Two sides have lengths of 5x and 2x+9. What is the length of the 3rd side?
Answers
Let the third side = a.
So we can write perimeter as = 5x + 2x + 9 + a
As given perimeter = 10x + 2
So we can write 10x + 2 = 7x + 9 + a
10x + 2 - 7x - 9 = a
3x - 7 = a
So third side = 3x - 7.
A car uses 25L of petrol to travel 280km. What is the rate of petrol usage in kilometres per litre?
Answers
The rate of petrol per liter is 11.2 liter
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
In 25l car travels = 280km
For finding rate of petrol per liter we have to divide as
Rate of petrol = 280/25
Rate of petrol = 11.2 liter
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The rate of petrol usage for the car is 11.2 kilometers per litre, calculated by dividing the distance travelled, 280km, by the amount of petrol used, 25L.
The question asks to find the rate of petrol usage in kilometers per litre for a car that uses 25L of petrol to travel 280km. To calculate the fuel efficiency, you divide the distance travelled by the amount of petrol used.
Step-by-step calculation:
Distance travelled = 280 km
Amount of petrol used = 25L
Fuel efficiency (km/L) = Distance travelled / Amount of petrol used
Fuel efficiency = 280 km / 25L = 11.2 km/L
Therefore, the car's fuel efficiency is 11.2 kilometers per litre.
when I make macaroni and cheese for my brother and me, I use 2 2/3 tablespoons of butter. how much butter will I n need to make my macaroni and cheese dish for Thanksgiving dinner if 15 people are attending?
Answers
well [tex]\bf 2\frac{2}{3}\implies \cfrac{2\cdot 3+2}{3}\implies \cfrac{8}{3}\\\\ -------------------------------\\\\ \begin{array}{ccllll} \textit{butter spoons}&servings\\ -----&-----\\ \frac{8}{3}&2\\ x&15 \end{array}\implies \cfrac{\frac{8}{3}}{x}=\cfrac{2}{15}\implies \cfrac{\frac{8}{3}}{\frac{x}{1}}=\cfrac{2}{15} \\\\\\ \cfrac{8}{3}\cdot \cfrac{1}{x}=\cfrac{2}{15}\implies \cfrac{8}{3x}=\cfrac{2}{15}\implies 8\cdot 15=3x\cdot 2\implies 120=6x \\\\\\ \cfrac{120}{6}=x\implies 20=x[/tex]
how to simplify expression by distribution 3(2y-7)
Answers
Multiply 3 by everything inside the parenthesis
The daily mean temperature in a particular place is 83. how many cooling-degree days were accumulated?
Answers
In our case the daily mean temperature is 83°F and X is the number of cooling-degree days.
X=83-65
X=18
Write five numbers that round to 360 When rounded to the nearest 10.
Answers
If we reject the null hypothesis, can we claim to have proved that the null hypothesis is false? why or why not?