The probabilities are:
a) P = 0.024
b) P = 0.5
How to get the probabilities?
a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.
There are 5 colas, and 16 drinks in total, so the probability is:
P = 5/16
The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:
Q = 4/15
Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:
Z = 4/14
The joint probability is:
prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024
b) If the two first persons grabed colas, then in the cooler we have:
3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.
Then the probability of grabbing a root beer is:
p = 7/14 = 1/2 = 0.5
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Difference between y and 23 is 12
Answer:
[tex]y=11[/tex]
Step-by-step explanation:
⇒ [tex]23 - y[/tex] (Difference means subtraction)
⇒ [tex]23 - y = 12[/tex] (Subtract 12 from 23)
⇒ [tex]y = 11[/tex] (The difference from 23 - 12)
Hii!
___________________________________________________________
Answer:
y=11
Step-by-step explanation:
Let's set up an equation.
"difference between y and 23" tells us to subtract y from 23, so we'll do just that.
23-y=12
Now subtract 23 from both sides
-y=-11
Divide both sides by -1
y=11 "We solved for the variable"
--
Hope that this helped! Best wishes.
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You started this year with $413 saved and you continue to save $21 per month.
Write an equation to model this situation (use m for months and s for savings)
Answer:
y = 21x + 413
Step-by-step explanation:
Use y = mx + b
m represents the slope which in this case is 21.
b represents the y - intercept which in this case is 413.
Now, just fill in the variables.
y = 21x + 413
Hope this helps!
-2y = x + 6 Graph A On a coordinate plane, a line goes through (negative 6, 0) and (1, negative 3). Graph B On a coordinate plane, a line goes through (0, 3) and (2, 4). Graph C On a coordinate plane, a line goes through (0, 3) and (2, 2). Graph D On a coordinate plane, a line goes through (0, negative 3) and (6, 0). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided
On a coordinate plane, a line goes through (negative 3, 0) and (0, negative 6).
The graph for the first equation of a system is shown in orange. The second equation is: 3y+30=6x
What is the solution to the system?
A. (2, –10)
B. (1, –8)
C. (–2, –14)
D. (2, –6)
Answer: 4.9/5
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Answer:
B. (1,-8)
Step-by-step explanation:
Slope of the first one:
(-6-0)/(0--3) = -6/3 = -2
y = -2x - 6
3y + 30 = 6x
y + 10 = 2x
-2x - 6 + 10 = 2x
4 = 4x
x = 1
y = -2(1) - 6
y = -8
3 more than half a number
Answer:
3 + a/2
Step-by-step explanation:
3 + a/2
Similar Polygons
Not quite sure how to get this question.
Answer:
No
Step-by-step explanation:
We know that the 3-4-5 and 9-12-15 right triangles are similar. If you add 6 units to the length of each side of both of these triangles, you obtain 9-10-11 and 15-18-21 triangles, which are not similar since 9/15 is not equal to 10/18.
[tex] \bold{(10x - 6x³ + 8x²) - (5x² + 12x³ - 4)}[/tex]
Answer:
[tex]\boxed{\sf -18x^3+3x^2+10x+4}[/tex]
Explanation:
[tex]\rightarrow \sf (10x - 6x^3 + 8x^2) - (5x^2 + 12x^3 - 4)[/tex]
distribute
[tex]\rightarrow \sf 10x - 6x^3 + 8x^2 - 5x^2 - 12x^3 + 4[/tex]
collect terms
[tex]\rightarrow \sf -6x^3-12x^3+3x^2+10x+4[/tex]
add similar terms
[tex]\rightarrow \sf -18x^3+3x^2+10x+4[/tex]
Answer:
[tex]-18x^3+3x^2+10x+4[/tex]
Step-by-step explanation:
Given:
[tex](10x-6x^3+8x^2)-(5x^2+12x^3-4)[/tex]
Apply the rule (a) = a:
[tex]\implies 10x-6x^3+8x^2-(5x^2+12x^3-4)[/tex]
[tex]\textsf{Use the distributive law} \quad -(a+b)=-a-b:[/tex]
[tex]\implies 10x-6x^3+8x^2-5x^2-12x^3-(-4)[/tex]
Apply the rule -(-a) = a:
[tex]\implies 10x-6x^3+8x^2-5x^2-12x^3+4[/tex]
Collect like terms:
[tex]\implies -6x^3-12x^3+8x^2-5x^2+10x+4[/tex]
Combine like terms:
[tex]\implies -18x^3+3x^2+10x+4[/tex]
How do I simplify the following expression by writing it as a term with only one trigonometric function?
(4-2sec^2(x))/(sec^2(x))
Answer:
2 cos (2x)
Step-by-step explanation:
[tex]\frac{4 -2 sec^2x}{sec^2x} \\=\frac{4-\frac{2}{cos^2x} }{\frac{1}{cos^2 x} } \\=\frac{\frac{4 cos^2x-2}{cos^2 x} }{\frac{1}{cos^2x} } \\=\frac{2(2 cos^2x-1)}{cos^2x} \times \frac{cos^2x}{1} \\=2(2cos^2x-1)\\=2cos(2x)[/tex]
What is the domain of the function represented by the list of ordered pairs?
(0, 2), (-3, 6), (4, 8), (2, 5), (-2, 4)
Answer:
D: (-3,4).
Step-by-step explanation:
There is really no need to solve it. Plot those points onto a graph and draw lines. I have done it on desmos. Looking at the x-axis to find the domain. From the left to right x-axis we can see that the domain should be D: (-3,4).
(x^4) (3x^3-2) (4x^2+5x)
Answer:
12x^7+15x^6
Step-by-step explanation:
Change 3x^3-2 to 3x
(x^4)(3x)(4x^2+5x)
Multiply your single terms
(3x^5)(4x^2+5x)
Then distribute
12x^7+15x^6
Jade bought a home for $129,500. She sold it fifteen years later for $9000 less than twice the amount she originally purchased for. Find the percent change in the purchase price of her home
Answer:
See below
Step-by-step explanation:
129 500 original price
selling price = 2 ( 129 500) - 9000 = 250 000
% change Questions worded like this are often up for debate as to exactly answer the question
250 000 / 129 500 = 193 % Selling price was 193% of original price
(250 000 - 129500)/ 129500 = 93 % INCREASE
Jaira is completing construction of a regular hexagon inscribed in a circle, as shown below: What should be the next step in her construction?
Jaira is completing the construction of a regular hexagon inscribed in a circle, as shown below: The next step in her construction should be:
construct another pont E by placing her compass at the locus DRepeat the process to get 6 more points on the given circle then join all of them together.A closed polygon with six equal sides and six equal angles is called a regular hexagon.
Thus, the steps highlighted above will help Jaira complete her construction.
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Which graph shows the solution to the system of linear inequalities?
y≥ 2x + 1
y≤2x-2
Answer:
g
Step-by-step explanation:
jjnnkvigific and it's a boy f a horse y
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. If this continues, what will Tacoma's population be in 2019?
The population of Tacoma in 2019 would be 1,028,332.
What will be the population in 2019?The population can be represented with an exponential equation that has the form:
FV = P (1 + r)^n
FV = Future populationP = Present population R = rate of growth N = number of years200,000 (1.09)^19 = 1,028,332.
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Select The correct answer.
Segment AB Is tangent to the circle at point B. Which equation describes the relationship between the tangent and secant line segments?
B
D
OA
(AD)² = (AC) (AB)
OB. (AB)2 = (AC)(CD)
OC. (AB)2 = (AC)(AD)
OD. AB=(AC + AD)
According to the tangent-secant theorem, the relationship of the tangent and secant in the given circle is: C. AB² = (AC)(AD).
What is the Tangent-Secant Theorem?The secant tangent theorem defines the relationship between the lengths of the secant and the tangent line segments when they meet outside a circle.
Based on the tangent-secant theorem, using the image given, the equation that describes the relationship of the tangent and secant in the given circle is:
C. AB² = (AC)(AD)
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Answer: C
Step-by-step explanation:
got it right on my test!!
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.54 and a standard deviation of 0.42. Using the empirical rule, what percentage of the students have grade point averages that are less than 2.96? Please do not round your answer.
Using the Empirical Rule, it is found that 84% of the students have grade point averages that are less than 2.96.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, 2.96 is one standard deviation above the mean. We have that:
The normal distribution is symmetric.Of the 50% of the measures below the mean, all are below 2.96.Of the 50% of the measures above the mean, 68% are below 2.96.Hence the percentage is given by:
P = 50% + 0.68 x 50% = 50% + 34% = 84%.
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Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
[tex]\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;[/tex]
it is clear, the required constant is 12 (12 per hour).
question is attachment
The degree of dispersion in your data collection is indicated by variance.
It is given by the formula:
[tex]\overline{d}= \sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}[/tex]
To determine the values of a certain set of scattered data, the standard deviation formula is utilized. The dispersion of the quantities or data from the mean is how the standard deviation is simply defined. The conclusion drawn from a lower standard deviation is that the results are fairly near to the average. Higher values, on the other hand, indicate a significant dispersion from the mean. The standard deviation number can never be negative, it should be positive.
It is given by the formula:
[tex]s_d = \sqrt{\sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}} =\sqrt{\overline{d}}[/tex]
We have that the mean of the values is:
at 8 AM [tex]\overline{x}=\frac{97.9+99.3+97.9+97.6+97.4}{5}=98.02[/tex]
at 12 AM [tex]\overline{x}=\frac{98.5+99.7+98+97.4+97.6}{5}=98.24[/tex]
Using the above definitions we have that
at 8 AM [tex]\overline{d}=\frac{(98.02-97.9)^2+(98.02-99.3)^2+(98.02-97.9)^2+(98.02-97.6)^2+(98.02-97.4)^2}{5}=0.4456[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.4456}=0.6675[/tex]
at 12 AM
[tex]\overline{d}=\frac{(98.24-98.5)^2+(98.24-99.7)^2+(98.24-98)^2+(98.24-97.4)^2+(98.24-97.6)^2}{5}=0.6744[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.6744}=0.8212[/tex]
In general, [tex]\mu_d[/tex] represents the mean of the differences from the population of matched data.
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how many ml of 40 percent acid should be added to pure acid to make 70ml of 65 percent acid?
The amount of the acid will be equal to 113.75 Ml.
What is concentration?Concentration in chemistry is calculated by dividing a constituent's abundance by the mixture's total volume.
In chemistry, to solve this kind of exercise, dilutions, and concentrations are common to use the following equation
C1 x V1 = C2 x V2
V1 refers to volume 1, in this case, is 70mL because is the quantity I have, the solution I can use to obtain another solution. C1 refers to the concentration of the solution I also have, in this case, 65%.
C2 and V2 refer to the volume and concentration of the solution I am looking for. So, if want to know V2, which is the volume I need to add, the only thing to do is find V2 in the equation:
V2 = ( C1 x V1 ) / C2
V2 = ( 65% x 70mL) / 40%
V2 = 113.75 Ml.
Therefore the amount of the acid will be equal to 113.75 Ml.
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Write the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x-y=7.
We can rewrite the equation of the given line to be in slope-intercept form as follows.
[tex]x-y=7\\x=y+7\\y=x-7[/tex]
Thus, the slope of the given line is 1.
Since parallel lines have equivalent slopes, the slope of the line we want to find is also 1.
Substituting into point-slope form,
[tex]y-0=1(x-1)\\\\\boxed{y=x-1}[/tex]
A manufacturer makes two type if products X and z at each if two different locations A and B. the materials used to make each if the products are steel, glass and plastic. suppose it takes three units of steel, one unit of glass and two units of plastic to make one unit of product X and four units of steel and one half units of glass and three units of plastic to make one unit of product Z. suppose further that steel, glass and plastic cost birr 10, 2, and 3 per unit respectively at location A. at location B steel, glass abd plastic cost 9,3 and 4 per unit respectively. using matrix algebra. find the material cost of making one of each product at each of the two locations.
Using matrix algebra, the material cost of making one of each product at each location is as follows:
Product X Product Z
Location A birr 38 birr 50
Location B birr 38 birr 49.5
What is matrix algebra?Matrix algebra involves the arrangement of numbers in a rectangular array.
Matrices are arranged in columns and rows to express some mathematical values.
Data and Calculations:Matrix O: Materials Requirement Per UnitSteel Glass Plastic
Product X 3 1 2
Product Z 4 0.5 3
Matrix P: Materials Cost Per UnitSteel Glass Plastic
Location A 10 2 3
Location B 9 3 4
Matrix R: (O x P) Material Cost of Product XSteel Glass Plastic Total
Location A 30 2 6 38
Location B 27 3 8 38
Matrix R: (O x P) Material Cost of Product ZSteel Glass Plastic Total
Location A 40 1 9 50
Location B 36 1.5 12 49.5
Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.
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Please help me answer this mathematics question
Answer:
[tex]x = 172.75[/tex]
Hope this help!!!
Have a good day♡
Need help with this geometry question
2) [tex]\overline{EK} \cong \overline{KG}, \overline{HK} \cong \overline{KF}[/tex]
3) Opposite sides of a parallelogram are congruent.
4) [tex]\triangle EF \text{ }K \cong \triangle GHK[/tex]
Solve x2 + 4x + 12 = 0 by completing the square.
x = –2 + 2i, x = –2 –2i
x = –2 + i, x = –2 – i
x = –2 + 2i, x = –2 – 2i
x = 0, –4
Answer:
See below
Step-by-step explanation:
x2 + 4x + 12 = 0 Complete the square ( take 1/2 of the 'x' coefficient, then square it and add it to both sides of the equation
x^2 + 4x + 2^2 + 12 = 2^2 Subtract 12 from both sides
x^2 + 4x + 4 = -8
(x+2)^2 = - 8 sqrt both sides
(x+2) =± sqrt (-8) simplify just a bit
x+2 = ±(2i sqrt2) subtract 2 from both sides
x = -2 ± 2i sqrt 2 <===== I do not see that answer listed
Use the drawing tool(s) to form the correct answer on the provided graph.
Consider the function given below.
Plot this piecewise function on the provided graph.
Drawing Tools
Select
Point
Open Point
Line Segment
Ray
●
O
y = -2;
-10
--5;
Click on a tool to begin drawing.
-8
7;
-6
-8 <
-2 < <5
≤ 9
5 < 1
10
8-
6-
4-
2
< -2
Delete
Undo
8
Reset
10
The attached graph represents the piecewise function.
How to plot the graph?The complete question is in the image
The function is given as:
[tex]f(x) = \left[\begin{array}{cc}3&x \le -3\\2x + 1&-3 < x < 4 \\-2&x \ge 4\end{array}\right[/tex]
Next, we plot the functions by their domain
See attachment for the piecewise function.
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The scatter plot shows a correlation between the cost of a helmet and the consumer rating.
The line of regression models that correlation.
Enter a number to complete each statement.
Answer:
1. 65
2. 52
3. 13
Step-by-step explanation:
For these answers, we can look at the graph:
Question 1:
For the helmet that costs 35 dollars, we look at the x-axis until we find the helmet that aligns with 35.
Then, we look at the y-axis and find the blue dot. The blue dot is the actual consumer rating that was recorded, NOT the red line. The red line is the predicted consumer rating in correlation to the price.
Hence, the consumer rating is 65.
Question 2:
For this, we can look back at the graph and apply the same concept as above. Notice how the 65 plot is 13 points away from the point predicted by the red line.
Therefore, 65 - 13 = 52
Question 3:
Just like the last two questions, we can look at the graph for this. The green line gives us this answer flat out, displaying the distance from the actual rating to the predicted rating.
Hence, the actual consumer rating was 13 above the predicted rating.
Which expression
is equivalent to 4(x+2)?
Answer:
[tex]\huge\boxed{\sf 4x + 8}[/tex]
Step-by-step explanation:
Given expression:= 4(x + 2)
Distribute
= 4x + 8
[tex]\rule[225]{225}{2}[/tex]
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?
Let x be multiple-choice questions
Let y be short-answer questions
x + y = 28
3x + 5y = 100
Which pair of expressions are equivalent using the Associative Property of Multiplication?
4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
4(2a ⋅ 5) = 8a ⋅ 20
4(2a ⋅ 5) = (2a ⋅ 5) ⋅ 4
4(2a ⋅ 5) = 4 ⋅ 2a ⋅ 5
Answer:
4 (2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
Step-by-step explanation:
6. Divide:
6x²+7x-2/3x-1
using Long Division.
Step-by-step explanation:
3x-1) 6x^2 + 7x -2 ( 2x+3
-6x^2 -2x
+
0 + 9x -2
- 9x -3
+
1
Simplify: √64(6z-7)² (square root over entire equation)
[tex]\sqrt{64(6z-7)^2}=\sqrt{64}\cdot\sqrt{(6z-7)^2}=8\cdot |6z-7|=8|6z-7|[/tex]
