A survey was done on the drink preferences of shoppers at the mall. The results are shown in the table. What is the probability that a shopper, chosen at random, will prefer neither Drink D nor Drink C?
Answers
SOLUTION:
Case: probability
Method:
From the table,
The probability that a shopper will prefer neither D nor C is:
[tex]\begin{gathered} Pr(NotDorC) \\ =\frac{n(AorBorE)}{Total} \\ =\frac{9+11+5}{46} \\ =\frac{25}{46} \end{gathered}[/tex]Final answer:
The probability that a shopper will prefer neither Drink D nor C:
25/46
Related Questions
Find the Least Common Denominator of 1/4 and 5/6
Answers
Answer:
The Least Common Denominator of 1/4 and 5/6 is 12
Explanation:
The Least Common Denominator (LCD) of two fractions is smallest number that can be common denominator for the set of fractions.
Given 1/4 and 5/6
The denominators are:
4 and 6
Let us break each numbers down into multiplications of prime numbers
4 = 1 * 2 * 2
6 = 1 * 2 * 3
So, the LCD is: 1 * 2 * 2 * 3 = 12
-5m=8m-2 what solution? one solution.. two solutions... no solutions.. infinite solutions.. which solution?
Answers
Starting with the equation:
[tex]-5m=8m-2[/tex]Substract 8m from both sides:
[tex]\begin{gathered} -5m-8m=8m-2-8m \\ \Rightarrow-13m=-2 \end{gathered}[/tex]Divide both sides by -13:
[tex]\begin{gathered} \frac{-13m}{-13}=\frac{-2}{-13} \\ \Rightarrow m=\frac{2}{13} \end{gathered}[/tex]Therefore, the equation has one solution, which is:
[tex]m=\frac{2}{13}[/tex]What is the slope of the line segment?15129601 2 3 4 50-30-303
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Ok, so:
To find the slope of the segment, we have to take two points:
Let's take: A(2,6) and B(1,3).
We calculate the slope as this:
m =( ( y2 - y1 ) / ( x2 - x1 )).
Where A( x1, y1) and B( x2, y2) are the points we took.
Then, m = (3 - 6) / (1-2), this is m = -3/-1, and that's equal to m=3
a sphere has a diameter of 3.5 inches what's the volume?
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Solution
[tex]\begin{gathered} D\text{ = 3.5} \\ r\text{ = }\frac{D}{2}\text{ = }\frac{3.5}{2}\text{ = 1.75} \\ \text{Volume of a sphere = }\frac{4}{3}\times\pi\times r^2 \\ \text{ =}\frac{4}{3}\times\frac{22}{7}\times(1.75)^2^{} \\ \text{ =}\frac{26.95}{21}\text{ =12.83} \end{gathered}[/tex]Final Answer = 12.83
divide the question(4.8x10^9)/(2.0x10^3)
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We operate as follows:
[tex]\frac{4.8\cdot10^9}{2.0\cdot10^3}=2400000[/tex][tex]=2.4\cdot10^6[/tex]sadie has ananction figure collection of 200 action figures. She keeps 90 percent of the action figures on her wall. how many action figures does she keep on her wall
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we have the following:
[tex]\begin{gathered} n=200\cdot\frac{90}{100} \\ n=180 \end{gathered}[/tex]therefore, 180 action figures keep on her wall
can you please help with the 2 column proofs. It is not a test/quiz
Answers
COnsider the figure,
Two triangles are said to be congruent if all their three sides and three angles are equal.
SInce angle K and N are both right angles, we have,
[tex]<\text{MKL}=<\text{MNL}[/tex]The side ML is the shared side, and hence equal for both the triangles.
SInce LM bisects angle KLN, we have,
[tex]<\text{KML}=<\text{NML}[/tex]Thus, from AAS theorem ( stands for Angle-angle-side), when two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
Hence the triangles are congruent.
The line y-5= 9/7(x + 4) is graphed in the coordinate plane. Complete the sentences below describing this process. By inspecting the equation, the graph of the line has a slope of.............
Answers
We have a line with equation:
[tex]y-5=\frac{9}{7}(x+4)[/tex]The expression of the line is the slope-point form, that is:
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point of the line and m is the slope.
As in this case, m = 9/7, then the slope is 9/7.
By inspecting the equation, the graph of the line has a slope of 9/7.
We also know that (x0,y0) = (-4, 5), that belong to the line.
By inspecting the equation the graph of the line passes through the point (-4, 5).
To find the value of y(3) we replace x with the value 3:
[tex]\begin{gathered} y-5=\frac{9}{7}(3+4)=\frac{9}{7}\cdot7=9 \\ y-5=9 \\ y=9+5 \\ y=14 \end{gathered}[/tex]The value of y(3) is 14. The point is (3, 14).
hello I'm confused on this question and need help thank you
Answers
Given the data:
36, 14, 18, 18, 34
Let's find the standard deviation of the sample distances.
To find the standard deviation, apply the formula:
[tex]S=\sum_{i\mathop{=}1}^n\sqrt{\frac{(x_i-x_{avg})^2}{n-1}}[/tex]Where:
n = 5
Let's first find the average/,mean:
[tex]\begin{gathered} avg=\frac{36+14+18+18+34}{5} \\ \\ avg=\frac{120}{5} \\ \\ avg=24 \end{gathered}[/tex]The mean of the sample is 24.
Now, to find the standard deviation, we have:
[tex]\begin{gathered} S=\sqrt{\frac{(36-24)^2+(14-24)^2+(18-24)^2+(18-24)^2+(34-24)^2}{5-1}} \\ \\ S=\sqrt{\frac{(12)^2+(-10)^2+(-6)^2+(-6)^2+(10)^2}{4}} \\ \\ S=\sqrt{\frac{144+100+36+36+100}{4}} \\ \\ S=\sqrt{\frac{416}{4}} \\ \\ S=\sqrt{104} \\ \\ S=10.20 \end{gathered}[/tex]Therefore, the standard deviation of the given sample distances is 10.20
ANSWER:
10.20
Question is shown in image below. Answer format is also shown in image.
Answers
For |2x-7|>1:
This absolute value inequality results in two inequalities: 2x-7>1 or 2x-7<-1.
Solve these inequalities to find the answer:
[tex]\begin{gathered} 2x-7>1 \\ 2x>1+7 \\ x>\frac{8}{2} \\ x>4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7<-1 \\ 2x<-1+7 \\ x<\frac{6}{2} \\ x<3 \end{gathered}[/tex]It means that the answer is x>4; x<3.
For |2x-7|<1:
This results in one complex inequality: -1<2x-7<1.
Solve it to find the answer:
[tex]\begin{gathered} -1<2x-7<1 \\ -1+7<2x<1+7 \\ 6<2x<8 \\ \frac{6}{2}It means that the answer is 3For |2x-7|=1:From the equation we can conclude that 2x-7=1 or 2x-7=-1.Solve these equations to find the answer:[tex]\begin{gathered} 2x-7=1 \\ 2x=1+7 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7=-1 \\ 2x=-1+7 \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]The answer is x=3; x=4.A slide of 4.1 meters long makes an angle of 27 degress with the ground. How high is the top of the slide above the ground? Round to the nearest hundreth meter.
Answers
Answer:
1.86 metres
Explanation:
Given the following
Length of the slide = 4.1m (hypotenuse)
Angle of elevation = 27 degrees
Required
Height of the slide above the ground
Using the trigonometry identity
sin theta = opposite/hypotenuse
sin 27 = H/4.1
H = 4.1sin27
H = 4.1(0.4539)
H = 1.86 metres
Hence the height ofthe slide above the pole is 1.86metre to the hundredth meters
May I please get help with this. For I have tried many times to figure out the right answers
Answers
Explanation:
Two figures are congruent if they have the same size and shape. In this case, figure B is greater than figure A, so they are not congruent.
However, Figures C and D are congruent and we can map figure C to D by a rotation of 90 degrees counterclockwise about the origin. For example, the point (2, 3) of figure C becomes point (-3, 2), so the rule is
(x, y) ---> (-y, x) which is the rule for a 90 degrees rotation counterclockwise.
Answers:
Are figure A and B congruent? No
Which transformation maps A to B? None of these
Are figure C and D congruent? Yes
Which transformation maps C to D? Rotate figure C counterclockwise 90 about the origin.
kamFind the area of the shaded sector.Round to the nearest tenth.167°17.8 ydArea = [ ? ]yd?Enter
Answers
We know the area of a cirlce is
[tex]A=\pi\cdot r^2[/tex]This is because, in radians, the angle of a whole circle is
[tex]2\pi[/tex]In order to proceed, we'll use the formula
[tex]167\cdot\frac{\pi}{180}\approx2.9147[/tex]Using this new value, we can now compute the area of the shaded region using the formula
[tex]A=\alpha r^2[/tex][tex]\text{Where }\alpha\text{ is the angle that generates the shaded region in radians}[/tex]In this case we have:
[tex]A=2.9147\cdot(17.8)^2=\text{ }923.493548[/tex]Round to the nearest tenth:
[tex]A=923.5yd^2[/tex]Israel y su amigo fueron al cine y compraron dos entradas de cine a 12.50 cada una también compraron dos bolsas de palomitas de maíz y dos bebidas cada bolsa de pantalones de maíz cuestan 2.25 gastaron un total de 33 en el teatro escribir resolver una ecuación para encontrar el costo de una bebida.Israel and his friend went to the movies and bought two movie tickets at 12.50 each they also bought two bags of popcorn and two drinks each bag of corn pants cost 2.25 spent a total of 33 in the theater write solve an equation to find the cost of a drink.
Answers
Let,
x = number of drinks/número de bebidas
y = number of popcorn/número de palomitas de maíz
z = number of tickets/número de entradas
A = price of drinks/precio de las bebidas
B = price of popcorn/precio de las palomitas de maíz
C = price of tickets/precio de las entradas
T = total cost/coste total
We get,
[tex]\text{ T = Ax + By + Cz}[/tex]But,
x, y, z = 2
B = 2.25
C = 12.50
T = 33.00
Conectemos los valores a la fórmula para poder determinar el precio de las bebidas.
[tex]\text{ T = Ax + By + Cz }\rightarrow\text{ 33 = A(2) + (2.25)(2) + (12.50)(2)}[/tex][tex]\text{33 = A(2) + (2.25)(2) + (12.50)(2) }\rightarrow\text{ 33 = 2A + 4.50 + 25.00}[/tex][tex]\text{ 33 = 2A + 29.5 }\rightarrow\text{ 2A = 33 -29.5 }\rightarrow\text{ 2A = 3.50}[/tex][tex]\text{ A = }\frac{3.50}{2}\text{ = 1.75}[/tex]Por tanto, el coste de las bebidas es 1.75.
a offers three kinds of meat toppings and 17 * a vegetable topping and how many different ways could you select a meat topping or a vegetable topping
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Since this restaurant offers three types of meat toppings and seventeen types of vegetable toppings we can use the fundamental counting principle to determine the number of possible outcomes. This is done below:
[tex]3\cdot(17)=51[/tex]We could select 51 possible combinations of meat and vegetable toppings.
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > - 2 x - 7
Answers
In order to determine a point that is part of the solution of the two given inequality, let's graph the two inequalities.
For both inequalities, they are already in a slope-intercept form y > mx + b where m = slope and b = the y-intercept.
For equation 1, y > x + 2, the y-intercept is 2 and slope is 1. Since the inequality is >, we will be using a broken line and the shade will be above the line.
The graph of inequality 1 is:
Moving on inequality 2, y > -2x - 7, the slope is -2 and the y-intercept is -7. Since the inequality symbol is >, we will be using a broken line on its border and the shade will be above the line.
The graph of inequality 2 is:
Combining the two graphs in one coordinate plane, we have:
The solution set of the given system of inequalities will be the common shaded area of both inequalities. There are infinite solutions for this.
We can get some coordinates from this common shaded area and this could be:
These coordinates can be (-3, 2), (-4, 3), (-2, 4), or (-2, 2).
We can also infer from the graph that the value of x is infinite however, the value of y must be greater than -1.
Given that sine = 0.87, using sin²0 + cos²0 = 1,
find cose (in Quadrant I). Show all your work for
credit - answer given to three decimal
approximation.
Answers
Work Shown:
[tex]\sin^2(\theta)+\cos^2(\theta)=1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = \sqrt{1-\sin^2(\theta)} \ \ \ \text{.... cosine is positive in Q1}\\\\\cos(\theta) = \sqrt{1-(0.87)^2}\\\\\cos(\theta) \approx 0.4930517\\\\\cos(\theta) \approx 0.493\\\\[/tex]
Given the triangle ABC at points A = ( 1, - 4 ) B = ( 4, - 5 ) C = ( 6, - 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.
Answers
Given: The coordinates of triangle ABC as
[tex]\begin{gathered} A=(1,-4) \\ B=(4,-5) \\ C=(6,-3) \end{gathered}[/tex]To Determine: The coordinates of triangle ABC after first reflect over the y-axis and then over the x-axis
Solution
The reflection over the y-axis rule is given as
[tex](x,y)\rightarrow(-x,y)[/tex]Let us apply the rule to the given triangle ABC
[tex]\begin{gathered} A(1,-4)\rightarrow A^{\prime}(-1,-4) \\ B(4,-5)\rightarrow B^{\prime}(-4,-5) \\ C(6,-3)\rightarrow(-6,-3) \end{gathered}[/tex]The reflection rule over the x-axis is given as
[tex](x,y)\rightarrow(x,-y)[/tex]Let us apply the rule to the given
[tex]\begin{gathered} A^{\prime}(-1,-4)\rightarrow A^{\prime}^{\prime}(-1,4) \\ B^{\prime}(-4,-5)\rightarrow B^{\prime}^{\prime}(-4,5) \\ C^{\prime}(-6,-3)\rightarrow C^{\prime}^{\prime}(-6,3) \end{gathered}[/tex]Hence, the new point of A'' = (-1, 4)
you pick a card at random and put it back and then pick another card at random what is the probability of picking an even number and then picking a five
Answers
STEP - BY - STEP EXPLANATION
What to find?
The probability of picking an even number and then picking a five.
Given:
Step 1
State the probability formula.
[tex]Probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}[/tex]Step 2
Identify the even numbers and the all possible outcome.
Even numbers =4, 6
Step 3
Find each of the probability.
Let A be the event of picking an even number and B be the event of picking a 5.
[tex]\begin{gathered} P(A)=\frac{2}{4} \\ \\ P(B)=\frac{1}{4} \end{gathered}[/tex]Step 4
Determine the compound probability.
[tex]\begin{gathered} P(A\text{ and B\rparen=P\lparen A\rparen}\times P(B|A) \\ \\ =\frac{2}{4}\times\frac{1}{4} \\ \\ =\frac{2}{16} \\ \\ =\frac{1}{8} \end{gathered}[/tex]Step 5
Convert to percentage.
[tex]\begin{gathered} Probability=\frac{1}{8}\times\text{ 100\%} \\ \\ =12.5\text{ \%} \end{gathered}[/tex]ANSWER
12.5 %
The average gas price in 2013 was $3.34. The probability that a gas price was less than $2.90 was 20%. What would be the standard deviation?
Answers
We know that the probability in a normal distribution can be obtained by the z score, the z score is given as:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where mu is the mean and sigma is the standard deviation. In this case we have:
[tex]\begin{gathered} P(X<2.9)=0.2 \\ P(Z<\frac{2.9-3.34}{\sigma})=0.2 \\ P(Z<\frac{-0.44}{\sigma})=0.2 \end{gathered}[/tex]Now, to have 20% (that is 0.2) we need that the z score to be -0.842, then we have:
[tex]\begin{gathered} -\frac{0.44}{\sigma}=-0.842 \\ \sigma=\frac{-0.44}{-0.842} \\ \sigma=0.52256532 \end{gathered}[/tex]Therefore the standard deviation is $0.52
how do you find a vertex in intercept form
Answers
Quadratic functions can be written in vertex form, or
[tex]y=a\mleft(x-h\mright)^2+k[/tex]This is especially useful because the vertex of the function is found at the point (h, k).
We can find this form by completing squares, for instance, let y be:
[tex]y=x^2+bx+c[/tex]we can see that this equation is equal to
[tex]y=x^2+2(\frac{b}{2})x+(\frac{b}{2})^2-(\frac{b}{2})^2+c[/tex]because
[tex]2(\frac{b}{2})=b[/tex]and
[tex](\frac{b}{2})^2-(\frac{b}{2})^2=0[/tex]However, in this form, we can see that the first 3 terms are a perfect square, that is
[tex]x^2+2(\frac{b}{2})x+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex]hence,
[tex]\begin{gathered} y=x^2+bx+c \\ y=(x+\frac{b}{2})^2-(\frac{b}{2})^2+c \end{gathered}[/tex]If we define
[tex]\begin{gathered} -(\frac{b}{2})^2+c=k \\ \text{and} \\ h=\frac{b}{2} \end{gathered}[/tex]we have that
[tex]y=(x+h)^2+k[/tex]the constant a arise when you have a leading term different from 1 in x^2.
The sum of the measures of angle M and angle R is 90°. The measure of angle M is (5x + 10)". The measure of angle R is 55° What is the value of x? Record your answer. Be sure to use the correct place value. B I UE E х, х? KY
Answers
Given data:
The given angle M is ∠M=(5x+10)°.
The given angle R is ∠R=55°.
The expression for the sum of both the angles is,
[tex]\angle M+\angle R=90^{\circ}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} (5x+10)^{\circ}+55^{\circ}=90^{\circ} \\ 5x=25^{\circ} \\ x=5^{\circ} \end{gathered}[/tex]Thus, the value of x is 5 degrees.
write each measure in radians and express the answer in terms of π4. 315 degrees 5. -450 degrees
Answers
The equivalent measure of (315) degrees in radians will be (7π/4) rads.
As per the question statement, we are provided with an angular measure of 315 in the units of degrees,
And we are required to convert the above mentioned angular measure into it's equivalent unit of radians.
To solve this question, first we need to know about the relation between the two units of angular measure, degrees and radians, which goes as,
[180° = (π) rads]
Now using the unitary method and the above conversion reference point, we get,
[180° = (π) rads]
Or, [1° = (π/180) rads],
And, [315° = {(π/180) * 315} rads]
Or, [315° = {π * (315/180)} rads]
Or, 315° = [π * {(5 * 7 * 3 * 3)/(3 * 3 * 4 * 5)} rads]
Or, [315° = {π * (7/4)} rads]
Or, [315° = (7π/4) rads]
To learn more about Degrees and Radians, click on the link below.
https://brainly.com/question/1369951
#SPJ9
Karen runs each lap in 7 minutes. She will run less than 63 minutes today. What are the possible numbers of laps she will run today? Use n for the number of laps she will run today. Write your answer as an inequality solved for n.
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
time for each lap = 7 min
today's time run less than 63 min
n = # laps
Step 02:
1 lap ------- 7 min
n laps ------ 63 min
n laps * 7 min = 1 lap * 63 min
n laps < 63 min * lap / 7 min
n laps < 9 laps
The answer is:
She will run less than 9 laps .
What Is the difference between 4×3 and 4^3 ? Prove your answer with the equations AND explain your thinking.
Answers
The given expressions are
4×3 and 4^3
4 x 3 means 4 multiplied by 3 and the result is 12
4^3 means 4 raised to the power of 3 and this means
4 muliplied by 4 multiplied by 4. Thus, we have
4 x 4 x 4 = 64
Alyssa spins a spinner with 10 sections of equal size. Each section is colored either blue, green, orange, or red. Alyssa spins the spinner 80 times
The results of the spins are shown.
Color
Number of Spins 16 8
Blue Green Orange Red
16
40
Move numbers to the table to show how many sections of each color are most likely on the spinner.
Color
Number of Sections
Blue Green Orange Red
2
3
4
5
6
Answers
Answer:
Answered below with assumption of numbers
Step-by-step explanation:
Using blue = 16 green = 8 orange = 16 red = 40
40/80 or 1/2 is red 1/2 * 10 = 5 sections
16 / 80 or 1/5 is blue or orange = 1/5 * 10 = 2 each
then the rest are green 8 out of 80 or 1/10 = 1
Sally has 71 peppermints. Bernard has p fewer peppermints than Sally. Write an expression that shows how many peppermints Bernard has.
Answers
an expression is:
y = 71 - p
Find the volume of the cone to the nearest 10th power you use 3.14 for pi. In the second box, take the exponent for the label.
Answers
The volume of a cone of radius r and height h is given by:
[tex]V=\frac{\pi r^2h}{3}[/tex]The cone in the figure has a radius of r = 2.1 cm and a height of h = 6.2 cm.
Substituting:
[tex]V=\frac{\pi\times\lparen2.1cm)^2\times6.2\text{ cm}}{3}[/tex]Using the value 3.14 for pi and calculating:
V = 28.62 cm 3
You should write 28.62 in the first box and 3 in the second box (for cubic cm)
Which strategy could you apply to find the distance between any two numbers on the number line? ©MPS
Answers
To find the distance between any two numbers on the number line you have to subtract the smallest to the greatest
which of the following is equivalent to the expression below? 3(5-2i)A. 15-2iB. 15-6iC. 8-2iD. 8-5i
Answers
ANSWER:
B. 15 - 6i
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3\left(5-2i\right)[/tex]We apply the distributive property and we are left with the following:
[tex]\begin{gathered} 3\left(5-2i\right)=3\cdot \:5-3\cdot \:2i \\ \\ 3\left(5-2i\right)=15-6i \end{gathered}[/tex]Therefore, the correct answer is B. 15 - 6i