If Jody chooses the ginger ale, the probability that she also chooses root beer from her selection is 1/3.
Explanation:Jody has four bottles of soft drink: one bottle of cola, one of root beer, one of ginger ale, and one of orange. She chooses three of these bottles to take to a party. The question is, if she chooses the ginger ale, what is the probability she also chooses root beer?
Since Jody has already chosen the ginger ale, she now has to choose 2 more bottles from the remaining three (cola, root beer, and orange).
There are 3 choose 2 ways (which is 3 ways) for Jody to pick her remaining bottles.
Only one of these combinations includes root beer (ginger ale, root beer, and one of the others).
Therefore, the probability that she also chooses root beer, given she has chosen ginger ale, is 1/3.
A package of balloons contains 5 green, 3 yellow, 4 red, and 8 pink balloons. Suppose you reach in the package and choose one balloon at random. What is the probability of choosing a PINK balloon?
Probability of choosing pink balloon is [tex]\frac{2}{5}[/tex].
Step-by-step explanation:
Given,
Number of green balloons = 5
Number of yellow balloons = 3
Number of red balloons = 4
Number of pink balloons = 8
Total number of balloons = 5+3+4+8 = 20
To find the probability of pink balloon.
Formula
Probability of an even = number of outcomes ÷ total number of outcomes
So,
Probability of choosing pink balloon = [tex]\frac{8}{20}[/tex] = [tex]\frac{2}{5}[/tex]
Please help solve this system of inequalities:
{2x-12>0
{3x<9
Thank you
Answer: 6,3
Step-by-step explanation: 3/3 and then 9/3=3 • 0+12=12, 12/2=6,
Please give brainliest
The system of inequalities consists of x > 6 and x < 3, which have no overlapping solution. No number can satisfy both conditions simultaneously; hence, there is no solution to the system.
To solve the given system of inequalities, let's solve each inequality separately:
For the first inequality 2x - 12 > 0, we add 12 to both sides to get:
2x > 12
Now, we divide both sides by 2:
x > 6
This inequality means that x must be greater than 6.
For the second inequality 3x < 9, we divide both sides by 3:
x < 3
This tells us that x must be less than 3.
If we look at both solutions, x > 6 and x < 3, there is no overlap between these two sets of numbers.
Therefore, there is no solution to the system, since no number can be both greater than 6 and less than 3 at the same time.
After leaving camp for a three-day journey into the frozen tundra, Daniela has just returned to camp. The
three days of her journey can be described by displacement (distance and direction) vectors d , d), and dz.
where each vector indicates Daniela's displacement from the start of her day to the end of her day.
di = 8i +3
d, is not given
az = i +47
(Distances are given in kilometers, km.)
What distance did Daniela travel on day two?
kilometers
(Round your final answer to the nearest tenth.)
In what direction did Daniela travel on day two? Assume 0° is the rightward direction.
(Round your final answer to the nearest degree. Your answer should be between 0 and 360°.)
Answer:
a) 8.7 km
b) 187.6°
Step-by-step explanation:
Given
Travel vectors (distance)∠(direction) ...
d₁ = 8∠3°d₂ = unknownd₃ = 1∠47°total travel was a round tripFind
(Rounded to the nearest tenth ...)
a) |d₂|
b) ∠d₂
Solution
In order for the sum of the three travel vectors to represent a round trip, their sum must be zero. That is, the value of d₂ must be the opposite of the sum of the other two vectors. A vector calculator can find the desired value easily. Here, we will show the calculation using the law of cosines and the law of sines.
__
a) A diagram can be helpful. Since we want to find the opposite of the sum of the given vectors, we can start by drawing their sum. In our diagram, d₁ is segment AB, and d₃ is segment BC. Their sum is the segment AC.
The internal angle ABC is the supplement of the difference of the angles for d₁ and d₃, so is 180° -(47° -3°) = 136°. Then the law of cosines gives length AC as ...
AC² = AB² +BC² -2AB·BC·cos(B)
AC² = 8² +1² -2·8·1·cos(136°) = 65 -16cos(136°) ≈ 76.5094
AC ≈ √76.5094 ≈ 8.747
The distance traveled on day 2 is about 8.7 km.
__
b) Given the side lengths of a triangle and one angle, the law of sines can be used to find the other angles. Here, it is convenient to find the internal angle at A. The law of sines tells us ...
sin(A)/BC = sin(B)/AC
sin(A) = BC/AC·sin(B)
A = arcsin(BC/AC·sin(B)) = arcsin(1/8.747·sin(136°)) ≈ 4.555°
The direction angle from C to A will be the sum of the 3° direction angle of AB and the internal triangle angle A we just found, added to 180°. That sum is ...
∠CA = 180° +3° +4.6° = 187.6°
∠d₂ = 187.6°
Answer:
Distance traveled 8.6 kilometers on day two
Daniela traveled in a direcrion of 234degrees on day two
Step-by-step explanation:
I had the same exact question and found the answers after having it incorrect
Which binomials are a difference of squares?
Choose exactly two correct answers.
y4 + 9
9x2 – 16
m6 – 25
p7 – 1
Final answer:
The binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex], as both can be factored into the form (a + b)(a - b).
Explanation:
The question asks which binomials are a difference of squares. A difference of squares is a binomial in the form [tex]a^2 - b^2[/tex], which can be factored into (a + b)(a - b). Analyzing the given options:
[tex]y^4 + 9[/tex]: This is not a difference, it's a sum.
[tex]9x^2 - 16[/tex]: This is a difference of squares because [tex]9x^2 = (3x)^2[/tex] and 16 = [tex]4^2[/tex].
[tex]m^6 - 25[/tex]: This is a difference of squares because [tex]m^6 = (m3)^2[/tex] and [tex]25 = 5^2[/tex].
[tex]p^7 - 1[/tex]: This is not a difference of perfect squares; [tex]p^7[/tex] is not a perfect square.
Therefore, the binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex].
First question: A groundskepper needs grass seed to cover a circular field, 380 feet in diameter. A store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field. What is the fewest number of bags the groundskeeper must buy to cover the circular field?
I WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST AND IS ACCURATE!
Answer: 165 bags
Step-by-step explanation:
Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by h(x)=-(x+1)(x-7), left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 7, right parenthesis How many seconds after being thrown will the ball reach its maximum height?
When we graph the function, it has a vertex of (3, 16).
The maximum of the graph is the highest "x" value on the graph which is 3.
Since the maximum is 3, it will take 3 seconds for the ball to reach its maximum height.
A graph will be shown below showing the function and vertex.
Best of Luck!
Answer:
3 seconds
Step-by-step explanation:
We need to find where the maximum i. The maximum or minimum is at the vertex. We know where the zero are because the equation is written in the zero form
We know the vertex is 1/2 way between the zeros
h(x)=-(x+1)(x-7)
Using the zero product property
x+1 = 0 x-7 =0
The zeros are at -1 and 7
Adding the two together and dividing by 2
(-1+7)/2 = 6/2 =3
The maximum is at 3. We know it is the maximum because the equation is pointing down because of the negative out front.
Which of the following polynomials is a difference of squares? *
10 points
x^2+16
x^2+6x+9
x^2+5x+4
x^2-9
Answer:
x² - 9
Step-by-step explanation:
A difference of squares has the form
a² - b²
Thus
x² - 9
= x² - 3² ← is a difference of squares
Points and their residual values are shown in the table. A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries 2, 3.5, 5, 6.1, 8. The third column is labeled residual value with entries negative 0.4, 0.7, negative 0.2, negative 0.6. Which residual value is the farthest from the line of best fit?
Answer:
The residual value is the farthest from the line of best fit is 0.7.
Step-by-step explanation:
A simple linear regression line is given by,
[tex]\hat y = \alpha + \beta X + \hat e[/tex]
Here,
α = constant,
β = slope
e = residual.
The difference amid the observed value of the dependent variable (Y) and the predicted value (y) is known as the residual (e).
The formula to compute the residual is,
[tex]\hat e=y-\hat y[/tex]
The information provided is:
x y e
1 2.0 -0.4
2 3.5 0.7
3 5.0 -0.2
4 6.1 -0.6
5 8.0 0.0
The residuals are the difference between the actual value and the predicted value.
They can also be defined as the distance between the line of best fit and the actual value of the dependent variable.
The data point that is the farthest from the line of best fit is, y = 3.5.
The residual value of y = 3.5 is 0.7.
In terms of units distance, this value of y is the farthest from the line of bet fit.
Thus, the residual value is the farthest from the line of best fit is 0.7.
Write in equation that represents the line
Answer:
y = 6/5x -5
Step-by-step explanation:
Using the slope formula,
you can find the slope
or just divide the amount of units up by
the amount of units right.
Then find the y intercept which is (0,5)
Answer:
y = [tex]\frac{6}{5}[/tex]x -5
Step-by-step explanation:
Whenever we have a line such as this one, (A linear or straight line) we can write an equation with the form y = mx + b
m is the slope
b is the y-intercept
To calculate slope or "m" we see how many times the point goes up, and how many times it goes to the right, and then put it in a fraction.
(Units it goes up) / (Units it goes to the right)
The y-intercept is what number the line intersects on the y-axis.
On this line it intersects at the -5 point.
So the equation when you put in the values is y = [tex]\frac{6}{5}[/tex]x -5
Please helppppp
Consider the function f whose graph is shown above
Answer:
It is C. Just look at the farthest points, and those are the numbers in your inequality.
To analyze a function's graph, identify the domain and range, find the intercepts, assess whether the function is increasing or decreasing, and locate the extrema points.
Explanation:Without the graph, I can't provide a specific analysis. However, I can guide you on how to analyze a function graph. A function graph can give specific details such as the function's domain and range, its intercepts, whether it's increasing or decreasing, and any extrema points (maxima or minima).
To find the domain, you need to identify which 'x' values are included on the graph. The range refers to the 'y' values covered by the graph. The intercepts are points where the graph crosses the 'x' axis (x-intercepts) and 'y' axis (y-intercepts).
By checking if the function is rising (increasing) or falling (decreasing), and spotting the highest and lowest points (maxima and minima), you can explore the behavior of the function.
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A DVD has a diameter of 34 centimeters. What is the area of the DVD? Round your answer to the nearest
hundredth. Use 3.14 for it.
The area of the DVD is about
cm
Answer:
907.46cm
Step-by-step explanation:
Area of Cirlce = πr^2
R= 17
R^2= 289
289 x 3.14 = 907.46
907.46cm
Answer:
Area of the circle = [tex]907.46\;cm^2[/tex]
Step-by-step explanation:
Diameter of the DVD = [tex]34\;cm[/tex]
[tex]Radius=\dfrac{34}{2}=17\;cm[/tex]
Area of the circle= [tex]\pi \times r^2[/tex]
As,
[tex]\pi =\dfrac{22}{7}=3.14[/tex]
Area is:
[tex]=3.14\times 17\times 17\\\\=3.14\times 289\\\\=907.46\;cm^2[/tex]
Area of the circle is: [tex]907.46\;cm^2[/tex]
How do you write twenty five increased by six in a numerical expression
Answer:
25 + 6 = 31
Step-by-step explanation:
3. What is the volume of the figure?
A. 15 cm
B. 33 cm
C. 45 cm
D. 54 cm
Answer:
a
Step-by-step explanation:
5. Gina bought 8 bags of 32 animal
crackers and 8 bags of 48 animal
crackers. She says she bought
8 X (32 + 48) animal crackers in all.
Do you agree? Explain.
Answer:
Yes I agree, because 32 times 8 plus 48 times 8 equals 8x(32+48)
Step-by-step explanation:
Explain the relationship between a strategy, such as number sense, and a written method such as partial products or area models, for multiplying decimal numbers.
Final answer:
Number sense enhances a student's understanding of multiplication and helps them choose the most efficient written method. For example, 0.5 can be easily multiplied mentally, and this knowledge can be applied to written methods for multiplying decimals.
Explanation:
In mathematics, number sense refers to a person's understanding of numbers and their relationships. It involves the ability to perform mental calculations and estimate the magnitude of numbers. On the other hand, written methods such as partial products or area models are specific algorithms or procedures used to solve mathematical problems, including multiplying decimal numbers.
The relationship between number sense and written methods for multiplying decimal numbers is that number sense enhances a student's understanding of the concept of multiplication and helps them make connections between different strategies or methods. By developing number sense, students can choose the most efficient written method based on their understanding of the numbers involved and their relationships.
For example, if a student has a strong number sense, they may recognize the relationship between a decimal that can be easily multiplied mentally, such as 0.5, and other decimal numbers. They can then use this knowledge to apply a written method like area models or partial products to solve problems that involve multiplying decimals.
In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 4)3 + 6. The turning point of the graph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.
Answer:Look below
Step-by-step explanation:
f(x) = x^3
g(x) = f(x-4) which shifts f(x) 4 units to the right
g(x) = (x-4)^3
h(x) = g(x) + 6 shift g(x) 6 units up
h(x) = (x-4)^3 + 6
The turning point of f(x) is at (0,0), then shift 4 units to the right and 6 units up, I got (4,6)
What is the solution set of {x | x > -5} u {x | x < 5}?
A) all numbers except -5 and 5
B) the numbers between -5 and 5
C) the empty set
D) all real numbers
Answer:
The answer is D
Step-by-step explanation:
The solution set of {x | x > -5} u {x | x < 5} is given by all real numbers. so option D is correct.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. A set of such values is called a solution set to the considered equation or inequality.
We need to find the solution set of the following inequalities:
A set of {x | x > -5} u {x | x < 5} has the solution of all values of x greater than -5.
The solution is all values of x greater than -5.
This is the union of both the inequalities, therefore all the real numbers will justify the inequalities.
Then, the solution set of {x | x > -5} u {x | x < 5} is given by all real numbers. so option D is correct.
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Can anyone answer this question for me?
Answer:
The answer is about 1.732, the exact form being [tex]\sqrt{3}[/tex].
Step-by-step explanation:
The square root of 12 is 3.4641. You then divide this by 2 and you get approximately 1.732. This in the exact form is [tex]\sqrt{3}[/tex].
What value of g makes the equation true?
(xt7)(x-4)=x2+gx-28
Answer:
g = 3
Step-by-step explanation:
If you distribute (x+7)(x-4) you get:
x²+3x-28
Compare it to the question:
x²+gx-28
and it becomes obvious that g = 3
The solution is, the value of g makes the equation true is, g = 3.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
from the given information we get,
If you distribute (x+7)(x-4) you get:
x²+3x-28
Compare it to the question:
x²+gx-28
and it becomes obvious that g = 3
Hence, The solution is, the value of g makes the equation true is, g = 3.
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April has a sheet of paper that is 2 feet long. She cuts the length of paper into halves and then cuts the length of each of these 1/2 pieces into thirds. How many pieces does she have? How many inches long is each piece?
April has a total of 6 pieces of paper, with each piece being 4 inches long after she cuts the 2-foot paper into halves and then into thirds.
To solve this problem, we need to perform two cuts. The initial length of the paper is 2 feet. When April cuts the length of paper into halves, she now has two pieces each of 1 foot in length. Then, she cuts each of these halves into thirds. To find out how many pieces she has in total, we multiply 2 halves by 3, resulting in 6 pieces of paper in total.
To determine the length of each piece in inches, we start with the original measurement in feet. Since 1 foot is equivalent to 12 inches, we convert the 1-foot pieces to inches by multiplying by 12. Then, we divide by 3 to represent the three cuts that April makes:
1 foot = 12 inches
Each cut piece = 12 inches / 3
Each piece is 4 inches long.
Find the value of each expression.
2h – 4 + 5 if h = 8
Answer:
2 times 8 is 16. 16 minus 4 is 12 plus 5 is 17. answer is 17.
Step-by-step explanation:
since h=8
The steps of the value of the expression:
2(8)-4+5
16-4+5
12+5
17
What does 15x represent in this equation?
Answer:
I believe the answer is A
Un empleado recibe una comisión
equivalente a 5% de su salario, X. ¿Cuál
expresión representa el total de dinero que
recibirá el empleado?
4 1.5x
B 1.05x
C 0.5x
D 0.05x
Answer:
B
Step-by-step explanation:
English translation:
An employee receives a commission equivalent to 5% of your salary, X. What
expression represents the total money that will receive the employee?
Solution:
We have to find the expression that gives us the total money of the employee. His total money is what he gets, the salary, PLUS the commissions.
His salary is "x"
and his commissions is 5% of his salary.
5% = 5/100 = 0.05
So,
Commissions = 0.05x
Total Money = Salary + Commission = x + 0.05x = 1.05x
Correct answer is B
Please help —> What is the value of X?
Write the equation of the line that goes through the point (-5,3) and has a slope of -2
Answer:y=-2x+3
Step-by-step explanation:
the 3 is the y coordinate
the slope is -2
I need help again lol....
A.) SSS Postulate
B.) ASA Postulate
C.) AAS Theorem
D.) SAS Postulate
Check out the diagram below. Note how for the left triangle, the side ZW is not between the marked angles V and W. So we do not use ASA and instead go with AAS. The order matters. If for instance, we knew that VW = WY, then we would go with ASA.
A student uses 3.14 for π to calculate the approximate circumference of a circle, 150.72 meters. Given this, find the approximate area of the circle. Use 3.14 for π.
Answer:
area of a circle = 1808.64meters²
Step-by-step explanation:
given that ,
π = 3.14
circumference = 150.72meters
calculate the area of the circle.
to calculate the circumference of a circle
recall,
circumference of a circle = 2πr
circumference of a circle = 2 x 3.14 x r
circumference of a circle = 6.28r
150.72meteras = 6.28r
divide both sides by 6.26
150.72meters/6.28 = 6.28r/6.28
24meters = radius
radius = 24 meters
now to calculate the area of the circle
recall the formulae for finding the area of a circle is given to be = πr²
area of a circle = πr²
area of a circle = 3.14 x ( 24)²
area of a circle = 3.14 x 576meters²
area of a circle = 1808.64meters²
what is the answer to this?
Answer:
s = -18
b is correct option
Step-by-step explanation:
[tex]\frac{4}{s} =\frac{-2}{9}[/tex]
By cross multiplication
4×9 = -2×s
0r
-2×s = 4×9
s = 36 ÷ -2
s = -18
a gain of 180 feet is what?
Answer:
+180
Step-by-step explanation:
Six quarts of milk weigh 13 pounds .write three different proportions you could use to fin the weight of 10 quarts of milk
Answer:
1. 130/6
2. 65/3
3. 260/12
Step-by-step explanation:
The first thing is to calculate the weight of 10 quarts of milk, like this:
(13 pounds / 6 quarts) * 10 quarts = 130/6 pounds
The three fractions could be:
1. 130/6 pounds weigh 10 quarts of milk.
2. 65/3 pounds weigh 10 quarts of milk.
3. 260/12 pounds weigh 10 quarts of milk.