Answer:
The answer is D.
Step-by-step explanation:
Distributive Property
4x3=12
4x7=28
28+12=40
Manuela and Stephen survey 250 people at a sporting event and ask if they prefer hamburgers or hot dogs, and if they prefer regular or diet soda.
Regular Soda Diet Soda Total
Hamburgers 90 40 130
Hot Dogs 70 50 120
Total 160 90 250
a. What is the probability that someone who prefers diet soda will also prefer hamburgers?
b. What is the probability that someone who prefers hot dogs will also prefer regular soda?
c. Are preferring diet soda and preferring hamburgers independent events? Explain.
d. Are preferring regular soda and preferring hot dogs independent events? Explain.
Answer:
a. 40/250
b. 70/250
c. Preferring diet soda and preferring hamburgers are not independent events
d. Preferring regular soda and preferring hot dogs are not independent events
Step-by-step explanation:
We are given:
Regular Soda Diet Soda Total
Hamburgers 90 40 130
Hot Dogs 70 50 120
Total 160 90 250
a. The probability that someone who prefers diet soda will also prefer hamburgers can be calculated as:
No. of people who prefer hamburgers and diet soda / Total no. of people
40/250
b. The probability that someone who prefers hot dogs will also prefer regular soda can be calculated as:
No. of people who prefer hot dogs and regular soda/Total no. of people
70/250
c. For two events to be independent, they must fulfill the condition:
P(A and B) = P(A) * P(B)
P(Diet Soda) = No. of people who prefer diet soda/total no. of people
= 90/250
P(Hamburgers) = No. of people who prefer hamburgers/total no. of people
= 130/250
P(Diet Soda and Hamburgers) = 40/250
Now, we need to check:
P(Diet Soda and Hamburgers) = P(Diet Soda) * P(Hamburgers)
40/250 = 90/250 * 130/250
40/250 ≠ 11700/62500
So, we can conclude that these two events are not independent events.
d. P(Regular Soda) = No. of people who prefer regular soda/total no. of people
= 160/250
P(Hot dogs) = No. of people who prefer hot dogs/total no. of people
= 120/250
P(Regular Soda and Hot Dogs) = 70/250
Now, we need to check if:
P(Regular Soda and Hot Dogs) = P(Regular Soda) * P(Hot dogs)
70/250 ≠ 160/250 * 120/250
So, these two events are not independent.
The solutions obtained are Part (a): The probability is 0.444, Part (b): The probability is 0.583, Part (c): Preferring diet soda and preferring hamburgers are not independent and Part (d): Preferring regular soda and preferring hot dogs are not independent.
Probability and Independence Analysis
Let's analyze the data provided from Manuela and Stephen's survey:
Regular Soda Diet Soda Total
Hamburgers 90 40 130
Hot Dogs 70 50 120
Total 160 90 250
→ Part A: Probability that Someone Who Prefers Diet Soda Also Prefers Hamburgers
The number of people who prefer diet soda is 90, and among them, 40 prefer hamburgers. Therefore, the probability is calculated as follows:
P(Hamburgers|Diet Soda) = 40 / 90
≈ 0.444
→ Part B: Probability that Someone Who Prefers Hot Dogs Also Prefers Regular Soda
The number of people who prefer hot dogs is 120, and among them, 70 prefer regular soda. Therefore, the probability is:
P(Regular Soda|Hot Dogs) = 70 / 120
≈ 0.583
→ Part C: Independence of Preferring Diet Soda and Preferring Hamburgers
To determine if these events are independent, we check if:
P(Diet Soda AND Hamburgers) = P(Diet Soda) * P(Hamburgers)
Calculations:
→ P(Diet Soda AND Hamburgers) = 40 / 250
→ P(Diet Soda) = 90 / 250
→ P(Hamburgers) = 130 / 250
→ P(Diet Soda AND Hamburgers) ≠ P(Diet Soda) * P(Hamburgers)
Since the equality does not hold, these events are not independent.
Part D: Independence of Preferring Regular Soda and Preferring Hot Dogs
We test the same independence condition for regular soda and hot dogs:
→ P(Regular Soda AND Hot Dogs) = P(Regular Soda) * P(Hot Dogs)
Calculations:
→ P(Regular Soda AND Hot Dogs) = 70 / 250
→ P(Regular Soda) = 160 / 250
→ P(Hot Dogs) = 120 / 250
→ P(Regular Soda AND Hot Dogs) ≠ P(Regular Soda) * P(Hot Dogs)
Therefore, these events are also not independent.
PLEASE HELP I WILL MARK YOU AS BRAINLIEST!
Answer:
12 units²
Step-by-step explanation:
Area = ½ × base × height
= ½ × 4 × 6
= 12 units²
A bag contains 5 red balls, 3 green balls, and 2 yellow balls. Find the sum of the probability of drawing a red ball, replacing it,
drawing a green ball, replacing it and drawing a yellow ball.
A)
0
B)
1
C)
10
D)
1/10
Answer:
d
Step-by-step explanation:
trust me
Answer:
B) 1.
Step-by-step explanation:
Prob(red) = 5/10
Prob(green) = 3/10
Prob(yellow) = 2/10
The sum = 5/10 + 3/10 + 2/10 = 10/10
= 1.
What is the solution to this equation?-x/-3=6
А. x= 18
в, x=-18
с, х= -2
D. х = 2
Answer:
A. x=18
Step-by-step explanation:
To solve this, we need to isolate the variable, x
-x/-3=6
Multiply both sides of the equation by -3
-3*-x/-3=6*-3
-x=-18
Divide both sides of the equation by -1
x=18
So, x=18, or choice A
I need help me with this ASAP
Answer:
Option B
Step-by-step explanation:
Diameter= 16cm
radius= 8cm
height = 3cm
[tex]volume = \pi {r}^{2} h[/tex]
[tex] =3.14 {(8)}^{2} \times 3[/tex]
[tex] = 3.14 \times 64 \times 3[/tex]
[tex] = 602.88 {cm}^{3} [/tex]
[tex] = 602.9 {cm}^{3} [/tex]
54 1/3 in simplified radical form
8-6 divided by j-k
j = 2 and k = 3
Step-by-step explanation:
[tex] \frac{8 - 6}{j - k} = \frac{2}{2 - 3} = \frac{2}{ - 1} = - 2 \\ [/tex]
Where will the different sections of the box plot be located? The box will go from 27. A line dividing the box will go at. The left whisker will go from 11 to. The right whisker will go from 33.
The five values for a data set are:
minimum = 11
lower quartile = 12
median = 23.5
upper quartile = 27
maximum = 33
A number line going from 0 to 40 in increments of 5.
Answer:
12 to 27
a long dividing the box will go at 23.5
11 to 12
the right whisker will go from 27 to 33
Step-by-step explanation: ^^^
The given sections of the box plot will be located, at the following places:
The box will go from 12 to 27 (IQR).
A line dividing the box will go at 23.5 (median).
The left whisker will go from 11 to 12.
The right whisker will go from 27 to 33 (see box plot in the image attached below).
What is a Boxplot?A boxplot shows the following values:
Minimum - which is located at the beginning of the left whiskerLower Quarter (Q1) - which is located at the beginning of the edge of the rectangular box.Median - the value at the point where a vertical line divides the boxUpper Quarter (Q3) - which is located at the end of the edge of the rectangular box.Maximum - which is located at the end of the right whisker.Therefore, the given sections of the box plot will be located, at the following places:
The box will go from 12 to 27 (IQR).
A line dividing the box will go at 23.5 (median).
The left whisker will go from 11 to 12.
The right whisker will go from 27 to 33 (see box plot in the image attached below).
Learn more about box plot on:
https://brainly.com/question/24335827
which statement is true
Answer:
a
Step-by-step explanation:
please help ASAP!!!
Answer:
x = 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 10[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 5[tex]\sqrt{3}[/tex]
The dot plots below show the number of hummingbirds spotted per day at two different feeders. The variability at each feeder is 3.168. The difference between the median number of hummingbirds spotted per day at each feeder is approximately how many times the variability?
Answer:
≈ 3
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
The median number is the middle value of the dot plots
In the feeder 1: 24 24 24 24 26 26 28 28 28 28 28 32 32 34 34 34 34 34 36=> the median number is: 28
In the feeder 2: 10 12 12 12 14 14 16 16 16 16 16 18 18 20 20 20 20 20 20 20 22 22 22 22 22=> the median number is: 18
=> The difference between the median number of hummingbirds spotted per day at each feeder is: 28 -18 =10 and it is = 10 / 3.168
≈ 3 times the variability
Micah paid $45 for 14.5 gallons of gas. What is the estimated cost of one gallon of gas?
Answer:
$3.00/ gallon
Step-by-step explanation:
Take the amount paid and divide by the number of gallons
We are estimating so round 14.5 gallons to 15
$45/15 gallons
$3.00/ gallon
the coat of a customers smartphone bill can be modeled by the equation C=10g+50 where g is the number of gigabits of data the customer per month.Factor this cost polynomial
Answer:
[tex]C=10(g+5)[/tex]
Step-by-step explanation:
Given the cost of a customers smartphone bill,
C=10g+50
We are required to factor the polynomial.
First, determine the G.C.D of both terms
The GCD of 10g and 50 is 10Next, we divide each of the term by 10 and balance it by multiplying the expression by 10.
[tex]C=10g+50\\=10(\frac{10g}{10}+\frac{50}{10})\\C=10(g+5)[/tex]
The cost polynomial factored is C=10(g+5).
Answer:
10g+60=10(g+6)
Step-by-step explanation:
thats the answer
Ella is making a cardboard box that is 10 inches by 6 inches by 3 inches. How much cardboard does she need to create the box?
Answer:
216
Step-by-step explanation:
What 3 ratios are equivalent to 5:15? pls help me ASAP! ʕ •ᴥ•ʔ
Answer: 13:65, 8:40, 18:90
Answer:
First of all that bear is adorable second 1:3, 10:30, and 15:45
Step-by-step explanation:
To do this you have to figure out if the ratios equal the fraction 1/3 which is the fraction for the ratio 5:15 all of those equal 1/3
I know I didn't explain that well but I still hope that this helps you :)
Find the area of figure above. Use 3.14 for pi.
Answer:
139.26990817 m² is the exact answer.
10*10=100
5²*pi + 100= 139.26990817
Hope this helped!! :)
help please :) i don't understand
Answer:
Blank 1: -6
Step-by-step explanation:
Because if you subtract 11-17 you get: -6
What is the value of the discriminant for the quadratic equation 0 = x + 2 + x^2?
Discriminant = b^2— Час
Answer:
The discriminant of the quadratic equation is -7.
Step-by-step explanation:
We are given the following quadratic equation in the question:
[tex]x^2+x+2 = 0[/tex]
Comparing to general quadratic equation:
[tex]ax^2+bx+c = 0\\a = 1\\b = 1\\c = 2[/tex]
We have to find the discriminant of the quadratic equation.
Formula:
[tex]d = b^2-4ac[/tex]
Putting values, we get,
[tex]d = (1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
Thus, the discriminant of the quadratic equation is -7.
Double bubble/ triple 100 points !!!!!!
Prove in full that the square 9.9cm diameter fits the circle.
Prove here again if you can help id appreciate it
1/2 the points are repeated on another question on my page.
Total including this is 40 points. + Brainliest.
Others unanswered 100 points in 3 questions.
Answer:
see below
Step-by-step explanation:
We need to find the diameter of the square
We can find this using the Pythagorean theorem
a^2+b^2 = c^2 where the legs are 7 and 7 and the diameter is c
7^2 +7^2 = c^2
49+49 = c^2
98 = c^2
Taking the square root of each side
sqrt(98) = sqrt(c^2)
9.899494937 = c
Since 9.9 is less than 11 which is the diameter of the circle it will never touch the circle.
Since the longest part of the square is less than the diameter of the circle, the square will fit inside the circle without touching
Answer:
Diagonal < Diameter
Step-by-step explanation:
The square will fit inside without touching if the diagonal length is less than the diameter
Diagonal = sqrt(7² + 7²)
7sqrt(2)
Diameter = 11
7sqrt(2) < 11
Because
(7sqrt(2))² < 11²
98 < 121
Help me Please! Find the volume and surface area for all.
Answer:
V =41.41³
A = 94.41²
----
V =225.16³
SA =283.25²
----
V = 64³
SA =113.32²
----
V =433.33³
SA = 378.57²
Step-by-step explanation:
Picture 2 = a = 1/2 base = 3.5 x 3.5 = 12.25 b= 5 x 5 = 25
c²= a² + b² = 3.5² + 5²
c ²= √12.25 + √25
c ²= √ 37.5 = 6.12372435696
c ² = 6.1237 missing side
Picture 1 + 2 formula SA = bh + (s1 + s2 + s3)H
V = V= 1/2 b x h h x SA
Picture 3 + 4 formula SA= a²+ 2a a² / 4 + h² V= a² h/3
Need help will mark brainiest
Answer:
a) 19
b) 3
Step-by-step explanation:
They are adding 3 sticks each time so n=3
I hope this helps
PLEASE ANSWER TO BE NAMED BRAINLIEST GET A THANK YOU AND A FRIEND REQUEST AND 10 P
If x = time, and y = the number of problems in the set, which equation models the relationship?
Question 3 options:
y = 12x
y = x + 12
y = 1.2x
y = x + 1.2
Answer:
C, y = 1.2x
Step-by-step explanation:
Notice that x, representing time, is multiplied by 1.2 each time to get y, representing the number of problems. You can find this out by dividing y by x. 36/30 = 1.2.
48/40 = 1.2.
And so on...
P.S.: If you ever come across a problem like this, subtract one y value by another y value, then subtract the corresponding x values from eachother, then make both numbers into one fraction with y as the numerator and x as the denominator. In this problem, that would look like this:
48 and 36 are both y values: 48 - 36 = 12
40 and 30 are the corresponding x values: 40 - 30 = 10
We get 12/10, which can be simplified to 1.2. The slope is 1.2.
This method will always work for a straight line and will be taught to you soon if you haven't learned it already.
Solve the equation -2c=-18
Answer:
c = 9
Step-by-step explanation:
-2c = -18
/-2 /-2 (Divide both sides by -2)
_______
c = 9
Answer:
c=-9
Step-by-step explanation:
-2c=18
divide the whole thing by -2
c=-9
HELP ASAP !!!!!!!!!! nnnnn
Answer:
45.8
Step-by-step explanation:
We can use the Pythagorean theorem with legs 3x and 4x+7
a^2+ b^2 = c^2
(3x^2) +(4x+7)^2 = c^2
Let x = 8
(3*8)^2 + (4*8+7)^2 = c^2
24^2+ 39^2 = c^2
576+1521 = c^2
2097 = c^2
Take the square root of each side
sqrt(2097) = sqrt(c^2)
45.79301257 =c
Rounding to the nearest tenth
45.8 =c
Answer:
45.8
Step-by-step explanation:
First solve for the other two sides by replacing x with 8
4(8)+7 = 39
3(8) = 24
Then use the pythagorean theorem ([tex]a^{2} + b^{2} = c^{2}[/tex]) to solve for the hypotenuse, c being the hypotenuse
[tex]39^{2} + 24^{2} = c^{2}[/tex]
1521 + 576 = [tex]c^{2}[/tex]
2097 = [tex]c^{2}[/tex]
[tex]\sqrt{2097} = \sqrt{c^{2} }[/tex]
45.8
Solve the equation. Then check your solution.
-16-10.2g = -14.7g + 16.85
a. 147.825
b. -7.3
c. 3.65
d. 7.3
Please select the best answer from the choices provided
Answer:
d. 7.3
Step-by-step explanation:
-16-10.2g = -14.7g + 16.85
4.5g = 32.85
g = 7.3
The solution for the equation -16 - 10.2g = -14.7g + 16.85 is g = 7.3. You can verify it by substituting the solution back into the original equation.
Explanation:To solve the given equation, -16 - 10.2g = -14.7g + 16.85, we must first isolate the variable, g, by moving all terms involving g to one side of the equation and constant terms to the other side. Add 10.2g to both sides of the equation, giving, -16 = -4.5g + 16.85. To further isolate g, subtract 16.85 from both sides resulting in -32.85 = -4.5g. Finally, divide by -4.5 to solve for g. Thus, g = -32.85 / -4.5 = 7.3. We verify our solution by substituting 7.3 back into the original equation and confirming that the equality holds true.
Learn more about Equation Solving here:https://brainly.com/question/18262581
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A dolphin was swimming 20 feet below the surface of the water. It descended 8 feet to catch a fish. What integer represents its current depth?
Really need help on this problem
Answer:
7
Step-by-step explanation:
Answer:
7kg
Step-by-step explanation:
Write the word sentence as an inequality. Then solve the inequality. Three less than a number x is more than 15. An inequality that represents this word sentence is..??? Please help me??
Answer:
x-3>15
x>18
Step-by-step explanation:
usually its better to read it from right to left, more than 15 tells you its gonna be >. then you see 3 less than x, which is x-3. Then solve as if the > was an equal sign
x-3>15
+3 +3
x>18
The inequality representing 'Three less than a number x is more than 15' is x - 3 > 15. Solving this, we get x > 18. Hence, x should be greater than 18.
The word sentence given is: 'Three less than a number x is more than 15'. To write this as an inequality, we start by identifying the mathematical phrase for 'Three less than a number x', which is 'x - 3'.
The phrase 'is more than' translates to the inequality symbol '>'.
Therefore, we set up the inequality as follows:
x - 3 > 15
Next, we solve the inequality step-by-step:
Start with the inequality: x - 3 > 15Add 3 to both sides to isolate x: x - 3 + 3 > 15 + 3This simplifies to: x > 18So, the solution to the inequality is x > 18.
In summary, when converting word sentences to inequalities, ensure you accurately translate the phrases and solve them step-by-step to find the solution.
what is log7 1 equal to
Answer:
1.85
Step-by-step explanation:hope this helps god bless
Rewrite without parentheses.
- 2x² (5x² – 9x-2)
Answer: without parentheses it'll be : -2x square 2 2x square 2 9x-2!
Step-by-step explanation: well to start with,Nothing will change when you solve it just rember the PEMDAS and you'll be fine! Good luck :3