The probability that the first card drawn without replacement is a diamond and the second card drawn is red is approximately 0.12
Probability of an event without replacementThe probability for an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.
In a standard deck of cards, there is a total of 52 cards with 13 diamonds and 26 reds (including diamonds)
probability that the first card drawn is diamond = 13/52
probability that the first card drawn is red = 25/51 {because diamond is also a red and was drawn first without replacement}
So;
probability that the first card is a diamond and the second card is red = (13/52) × (25/51)
probability that the first card is a diamond and the second card is red = 325/2652
probability that the first card is a diamond and the second card is red = 0.1225
Therefore, the proprobability that the first card drawn without replacement a diamond and the second card is red is approximately 0.12
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A) What does the point (1,8) represent in the context of the situation? B) Is the amount of money proportional to the number of hours worked? C) Write an equation that represents this situation? D) What will be Amber’s Wages after 6 hours worked?
Answer:
A) Amber's wages for 1 hour is $8.
B) Yes
C) y = 8x
D)
Explanation:
A) Looking at the graph, we can deduce that the point (1, 8) shows how much Amber makes in one hour. So in 1 hour, Amber makes $8.
B)To determine whether the amount of money is proportional to the number of hours worked, we have to look at the graph and see if it starts from the origin (0, 0), if it does then we can conclude that they are proportional.
Since the graph starts from the origin (0, 0), then the amount of money is proportional to the number of hours worked.
C) The slope-intercept equation of a line is given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
So let's go ahead and determine the slope of the line at points (1, 8) and (2, 16) using the below formula;
[tex]m=\frac{y_2-y_1_{}_{}_{}}{x_2-x_1_{}}=\frac{16-8}{2-1}=\frac{8}{1}=8[/tex]Since the line starts from the origin, therefore the y-intercept, b, is zero.
Since m = 8 and b = 0, the equation can then be written as;
[tex]\begin{gathered} y=8x+0 \\ y=8x \end{gathered}[/tex]D
4^2 * 4^3 simplified
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]4^2\ast4^3[/tex]STEP 2: Simplify the expression using the law of indices
[tex]\begin{gathered} \mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c} \\ 4^2\cdot \:4^3=4^{2+3} \\ =4^{\left\{2+3\right\}} \\ =4^5=1024 \end{gathered}[/tex]Hence, the evaluation gives:
[tex]1024[/tex]write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the graph of the given equations(0,0); y = -6x+3y =
To find the equation of the line we need a point and the slope. We have the point but we need to find the slope, to do this we need to remember that two lines are perpendicular if and only if their slopes fullfils:
[tex]m_1m_2=-1[/tex]Now, the slope of the line given is -6, this comes from the fact that the line is written in the form y=mx+b, hence comparing both equation we conclude that.
Pluggin this value into the condition above we have:
[tex]\begin{gathered} -6m_1=-1 \\ m_1=\frac{-1}{-6} \\ m_1=\frac{1}{6} \end{gathered}[/tex]Therefore the slope of the line we are looking for is 1/6. The equation of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values of the slope and the point we have:
[tex]\begin{gathered} y-0=\frac{1}{6}(x-0) \\ y=\frac{1}{6}x \end{gathered}[/tex]Therefore the equation we are looking for is:
[tex]y=\frac{1}{6}x[/tex]Choose the correct answer. 1. Shari made a net of a box to find how much wrapping paper she will need to . wrap the box 8 in. 5 in.
The total area needed to be covered is 158 square inch.
It is calculated by adding all the area
[tex]2\ast(8\ast5)+\text{ 2}\ast(5\ast3)+2\ast(8\ast3)=158in^2\text{ }[/tex]If y varies inversely as x and y=−97 when x=28, find y if x=36. (Round off your answer to the nearest hundredth.)
For this problem, we were informed that two variables "x" and "y" vary inversely to each other. We were also informed about one data point on the relation between the two (28, -97). From this information, we need to determine the value of "y" when "x" is equal to 36.
We can write the expression between two variables that vary inversely according to a constant, K, as shown below:
[tex]\begin{gathered} y\cdot x=k \\ y=\frac{k}{x} \end{gathered}[/tex]We can find the value of k by applying the known datapoint.
[tex]\begin{gathered} -97=\frac{k}{28} \\ k=-97\cdot28 \\ k=2716 \end{gathered}[/tex]The full expression is:
[tex]y=\frac{2716}{x}[/tex]Now we can apply the value of "x" to calculate the desired "y".
[tex]y=\frac{2716}{36}=75.44[/tex]The value of "y" is 75.44, when "x" is 36
ActiveApplying the Triangle Inequality Theoremin triangle ABC, AB measures 25 cm and AC measures 35 cm.The inequalitycentimeters.
Using the Triangle inequality:
[tex]zso:[tex]undefined[/tex]There are 14 girls and 12 boys in a class. What is the ratio of gris to students in simplest form
Number of girls = 14
Number of boys = 12
Number of students = 14 + 12 =26
Ratio of girls to students = 14/26 = 7 : 13
[tex]2x ^{2} - 6x + 10 = 0[/tex]solve by completing the square
We know that we can use the quadratic equation
Using this we have
[tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot2\cdot10}}{2\cdot2}=\frac{6\pm\sqrt[]{36-80}}{4} \\ =\frac{6\pm\sqrt[]{-44}}{4}=\frac{6\pm\sqrt[]{4\cdot-11}}{4}=\frac{6\pm2\cdot\sqrt[]{-11}}{4} \\ =2\cdot(\frac{3\pm\sqrt[]{-11}}{4})=\frac{3\pm\sqrt[]{-11}}{2}=\frac{3\pm\sqrt[]{11}i}{2} \\ =\frac{3}{2}\pm\frac{\sqrt[]{11}}{2}i \end{gathered}[/tex]So the answer is B)
13. Solve the inequality and share a graph on a number line
Given the following inequality:
[tex]-3(t\text{ - 2) }\ge\text{ -15}[/tex]We get,
[tex]-3(t\text{ - 2) }\ge\text{ -15}[/tex][tex]\frac{-3(t\text{ - 2)}}{-3}\text{ }\ge\text{ }\frac{\text{-15}}{-3}[/tex][tex]t\text{ - 2 }\ge\text{ }5[/tex][tex]t\text{ }\ge\text{ }5\text{ + 2}[/tex][tex]t\text{ }\ge\text{ }7[/tex]Graphing this on a number line will be:
Please help me solve question 6 on this algebra assignment
At the zero of the function, f(x) = 0. Substituting f(x) = 0, we get:
[tex]0=\frac{3}{5}x-\frac{4}{3}[/tex]Adding 4/3 at both sides of the equation:
[tex]\begin{gathered} 0+\frac{4}{3}=\frac{3}{5}x-\frac{4}{3}+\frac{4}{3} \\ \frac{4}{3}=\frac{3}{5}x \end{gathered}[/tex]Multiplying by 5/3 at both sides of the equation:
[tex]\begin{gathered} \frac{5}{3}\cdot\frac{4}{3}=\frac{5}{3}\cdot\frac{3}{5}x \\ \frac{5\cdot4}{3\cdot3}=x \\ \frac{20}{9}=x \end{gathered}[/tex]Therefore the coordinates of the zero of the function are:
[tex](x,f(x))=(\frac{20}{9},0)[/tex]
Need help with homework
Domain interval are the interval for the x - values on the linear graph
Therefore the domain intervals from the attached graph is
[tex]-3\leq x\leq4[/tex]f(x)=4•2^2x,g(x)=2^4x+2, and h(x)=4^2x+1
Let's use the following property:
[tex]x^y\cdot x^z=x^{y+z}[/tex][tex]\begin{gathered} f(x)=4\cdot2^{2x} \\ g(x)=2^{4x+2}=2^{4x}\cdot2^2=4\cdot2^{4x} \\ h(x)=4^{2x+1}=4^{2x}\cdot2^{1^{}}=2\cdot4^{2x} \\ \text{Therefore:} \\ \text{None of them are equivalent} \end{gathered}[/tex]In your Grandpa Will's recipe for a marinade, each serving uses 3.5 tablespoons of ketchup and 7 tablespoons of vinegar. If 31.5 tablespoons of ketchup will be used for a larger batch of marinade, how much vinegar is needed? tablespoons of vinegar are needed. Submit answer
The rate of ketchup to vinegar should be preserved. Let V be the volume of vinegar that will be used for the larger batch of marinade. Since the recipe uses 7 tablespoons of vinegar for each 3.5 tablespoons of ketchup, then:
[tex]\frac{V}{31.5}=\frac{7}{3.5}[/tex]Then, the volume of vinegar for the larger batch of marinade can be calculated as:
[tex]\begin{gathered} V=\frac{7}{3.5}\times31.5 \\ =63 \end{gathered}[/tex]Therefore, 63 tablespoons of vinegar are needed.
On 14 would I solve the 32x + 72 or is that the answer. The app stopped in the middle of the other tutor
The given expression is 8(4x+9)
Multiplying 8 to each term of (2x+9), we get
[tex]8(4x+9)=8\times4x+8\times9[/tex][tex]=32x+72.[/tex]the five number summary for a set of data is given in the picture.what is the interquartile range of the set of data?
ANSWER
[tex]IQR=13[/tex]EXPLANATION
The interquartile range can be found by finding the difference between the first quartile, Q1, and the third quartile, Q3.
That is:
[tex]IQR=Q3-Q1[/tex]Therefore, the interquartile range is:
[tex]\begin{gathered} IQR=81-68 \\ IQR=13 \end{gathered}[/tex]For each problem below find the missing factor by computing the inverse operation
Given:
There are given that the fraction:
[tex]4\frac{1}{2}-\text{ \lbrack \rbrack}=2\frac{7}{8}[/tex]Explanation:
Suppose missing information is x
Then,
Ater that we need to find the value of x
So,
[tex]4\frac{1}{2}-x=2\frac{7}{8}[/tex]Then,
[tex]\begin{gathered} 4\frac{1}{2}-x=2\frac{7}{8} \\ \frac{9}{2}-x=\frac{23}{8} \\ \frac{9}{2}-x-\frac{9}{2}=\frac{23}{8}-\frac{9}{2} \\ -x=\frac{23}{8}-\frac{9}{2} \end{gathered}[/tex]Now,
[tex]\begin{gathered} -x=\frac{23}{8}-\frac{9}{2} \\ -x=\frac{23-36}{8} \\ -x=\frac{-13}{8} \\ x=\frac{13}{8} \\ x=1\frac{5}{8} \end{gathered}[/tex]Final answer:
Hence, the missing factor is shown below:
[tex]x=1\frac{5}{8}[/tex]33<=105/p what is the answer
The answer is p≤35/11.
From the question, we have
33≤105/p
⇒p≤105/33
⇒p≤35/11
Inequality:
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
When the symbols ">", "", "", or "" are used to connect two real numbers or algebraic expressions, that relationship is known as an inequality.
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PLS HELP FAST I WILL GIVE 25 POINTS simplify 10^6/10^-3. answers:A. 1/10^3. B. 1/10^18. C. 10^3. D. 10^9
D
Let's simplify that expression
1) Remember of the Exponents Rule, we have to subtract them
2) Note that for the exponents 6 -(-3) = 6+3 = 9 So it's D
A couple took a small airplane for a flight to the wine country for a romantic dinner and then returned home. The plane flew a total of 5 hours and each way the trip was 233 miles. If the plane was flying at 170 miles per hour, what was the speed of the wind that affected the plane?
Answer:
114.26 miles per hour
Explanation:
Let us call
v = wind speed
Then
speed with the wind = 170 + v
speed against the wind = 170 -v
Therefore,
The time taken on the outward journey ( with the wind):
[tex]\frac{233}{170+v}[/tex]
Time take on the return journey
[tex]\frac{233}{170-v}[/tex]These two times must add up to 5 hours, the total time of the journey.
[tex]\frac{233}{170+v}+\frac{233}{170-v}=5[/tex]Solving the above equation for v will give us the wind speed.
The first step is to find the common denominator of the two rational expressions. We do this by multiplying the left rational expression by (180-v)/(180-v) and the right expression by (180 + v)/(180 + v).
[tex]\frac{170-v}{170-v}*\frac{233}{170+v}+\frac{233}{170-v}*\frac{170+v}{170+v}=5[/tex][tex]\frac{233(170-v)+233(170+v)}{(170-v)(170+v)}=5[/tex]Dividing both sides by 233 gives
[tex]\frac{(170-v)+(170+v)}{(170-v)(170+v)}=\frac{5}{233}[/tex]The numerator on the left-hand side of the equation simplifies to give
[tex]\frac{2\times170}{(170-v)(170+v)}=\frac{5}{233}[/tex][tex]\Rightarrow\frac{340}{(170-v)(170+v)}=\frac{5}{233}[/tex]Expanding the denominator gives
[tex]\operatorname{\Rightarrow}\frac{340}{170^2-v^2}=\frac{5}{233}[/tex][tex]\frac{340}{28900-v^2}=\frac{5}{233}[/tex]Cross multipication gives
[tex]5(28900-v^2)=340\times233[/tex]Dividing both sides by -5 gives
[tex]v^2-28900=-\frac{340\times233}{5}[/tex][tex]v^2-28900=-15844[/tex]Adding 28900 to both sides gives
[tex]v^2=13056[/tex]Finally, taking the sqaure root of both sides gives
[tex]\boxed{v=114.26.}[/tex]Hence, the speed of the wind, rounded to two decimal places, was 114.26 miles per hour.
I need help with number 7 the first question on the top of the page please
SK= 13x-5
KY= 2x+9
SY=36-x
By looking at the line segment we can state:
SY = SK+KY
Replacing with the values, and solving for x:
36-x=13x-5+2x+9
Sum and subtract alike terms
36+5-9=13x+2x+x
32= 16x
Divide both sides by 16:
32/16=16x/16
2=x
Replace the value of x in each expression:
SK= 13x-5=13(2)-5=26-5=21
KY= 2x+9=2(2)+9=4+9=13
SY=36-x =36-(2)=34
So, the answers are:
x=2
SK=21
KY=13
SY=34
if frita goes to the mall, then alice will go to the mall
Given
The statements,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
To find: The conclusion using the law of Syllogism.
Explanation:
It is given that,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
That implies,
If Wally goes to the mall, then Frita will go to the mall.
If Frita goes to the mall, then Alice will go to the mall.
Here, consider the statement Wally goes to the mall as p, the statement Frita will go to the mall as q, and the statement Alice will go to the mall as r.
Therefore,
[tex]Conclusion:\text{ }If\text{ }Wally\text{ }goes\text{ }to\text{ }the\text{ }mall,\text{ }then\text{ }Alice\text{ }will\text{ }go\text{ }to\text{ }the\text{ }mall.[/tex]Hence, the answer is option C).
The constant of variation for a function is 2. Which of the following graphs best represents this situation
The required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
Given that,
To determine the graphs which show the constant of variation for a function is 2.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
in the graphs only graph, A and B show the given condition of the constant of variation for a function is 2. Because in both graphs shows that y = 2x and 2y = x.
Thus, the required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
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Which of the following graphs could be a representation of a geometric sequence?Check all that apply.A.B.C.D.
SOLUTION:
We want to find the graph corresponding to a geometric sequence.
The equation of a geometric sequence is;
[tex]a_n=a_1(r)^{n-1}[/tex]This is clearly an exponential function with a starting value a.
The correct graphs are OPTION B and OPTION D
i inserted a picture of the questionif it helps i can give you my answer to my previous question
In order to determine the time it takes for the music player to fall to the bottom of the ravine, we shall find the solutions of t as follows;
[tex]\begin{gathered} t=\sqrt[]{\frac{8t+24}{16}} \\ \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} t^2=\frac{8t+24}{16} \\ \text{Cross multiply and we'll have;} \\ 16t^2=8t+24 \\ \text{ Re-arrange the terms and we'll now have;} \\ 16t^2-8t-24=0 \end{gathered}[/tex]We can now solve this using the quadratic equation formula;
[tex]\begin{gathered} \text{The variables are;} \\ a=16,b=-8,c=-24 \\ t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(16)(-24)_{}}}{2(16)} \\ t=\frac{8\pm\sqrt[]{64+1536}}{32} \\ t=\frac{8\pm\sqrt[]{1600}}{32} \\ t=\frac{8\pm40}{32} \\ t=\frac{8+40}{32},t=\frac{8-40}{32} \\ t=\frac{48}{32},t=-\frac{32}{32} \\ t=1.5,t=-1 \end{gathered}[/tex]We shall now plug each root back into the original equation, as follows;
[tex]\begin{gathered} \text{Solution 1:} \\ \text{When t}=1.5 \\ t=\sqrt[]{\frac{8t+24}{16}} \\ t=\sqrt[]{\frac{8(1.5)+24}{16}} \\ t=\sqrt[]{\frac{12+24}{16}} \\ t=\sqrt[]{\frac{36}{16}} \\ t=\frac{6}{4} \\ t=1.5\sec \end{gathered}[/tex][tex]\begin{gathered} \text{Solution 2:} \\ \text{When t}=-1 \\ t=\sqrt[]{\frac{8(-1)+24}{16}} \\ t=\sqrt[]{\frac{-8+24}{16}} \\ t=\sqrt[]{\frac{16}{16}} \\ t=\frac{4}{4} \\ t=1 \end{gathered}[/tex]From the result shown the ballon will deploy after 1.5 seconds for the first solution.
However t = -1 cannot be a solution since you cannot have a negative time (-1 sec)
ANSWER:
t =1.5 is a solution
simple interest interest: $50principal:$350rate: 6.5time:x
Given:
Interest (SI) = 50
Principal (P) = 350
rate (R) = 6.5. (Here, rate is 6.5 %)
To find time,
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=P\times R\times T \\ 50=350\times\frac{6.5}{100}\times x \\ x=\frac{50}{22.75} \\ x=2.197 \\ x\approx2\text{ years ( approximated) } \end{gathered}[/tex]Answer: x = 2 years.
Please help on average rate of change!
The average rate of change on the interval [-1, 2] is 1/3.
How to get the average rate of change?For any function f(x), we define the average rate of change on an interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
In this case, the function is graphed, and the interval is [-1, 2]
On the graph we can see that:
f(-1) = -3
and
f(2) = -2
Replacing these we will get:
r = ( f(2) - f(-1))/(2 - (-1))
r = (-2 + 3)/(3) = 1/3
The average rate of change is 1/3.
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(x + y)² – 3zz when X = -2, y = -4, and z = 5.
-39
Explanation
[tex]\begin{gathered} \mleft(x+y\mright)^2-3zz \\ \end{gathered}[/tex]Step 1
let
x=-2
y=-4
z=5
Step 2
Now, replace those values in the expression
[tex]\begin{gathered} (x+y)^2-3zz \\ (-2+(-4))^2-3\cdot5\cdot5 \\ (-2-4)^2-75 \\ (-6)^2-75 \\ 36-75 \\ -39 \end{gathered}[/tex]I hope this helps you
(calc) which graph shows a function and its inverse ?
Answer: We have to pick a graph that represents a function and its inverse function, or:
[tex]\begin{gathered} f(x)\rightarrow\text{ and }\rightarrow f^{-1}(x) \\ \end{gathered}[/tex]The inverse function switches the x and y variables, therefore the axes with it, the final result is two functions that are symmetrical about y = x line.
Example:
[tex]\begin{gathered} f(x)=\sqrt{x}\rightarrow\text{ Function} \\ \\ f^{-1}(x)=x^2\rightarrow\text{ Inverse Function} \end{gathered}[/tex]Graph:
Therefore the graph out of the options which has these properties is:
[tex]\text{ Graph\lparen C\rparen}[/tex]The answer, therefore, is Graph(C).
if the endpoints of KB are K(-4, 5) and B(2, -5), what is the length of KB?
The length of the line can be found by distance formula as,
[tex]\begin{gathered} KB=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ KB=\sqrt[]{(2-(-4)_{})^2+(-5-5)^2} \\ KB=\sqrt[]{(2+4)^2+(-10)^2} \\ KB=\sqrt[]{6^2+100} \\ KB=\sqrt[]{36+100} \\ KB=\sqrt[]{136} \\ KB=11.66 \end{gathered}[/tex]Select the correct answer.What is the image of this figure after this sequence of dilations?1. dilation by a factor of -1 centered at the origin2. dilation by a factor of 2 centered at (-1,1)
The coordinates of the original figure are:
(-2,1)
(3,1)
(1,3)
(-2,3)
A dilation by a negative scale factor produces an image on the other side of the center of enlargement.
As the first dilation is by a factor of -1 centered at the origin, the length of the sides doesn't change, but the new coordinates will be:
[tex](x,y)\to(kx,ky)[/tex]Apply this to the given coordinates:
[tex]\begin{gathered} (-2,1)\to(-1\cdot-2,-1\cdot1)\to(2,-1) \\ (3,1)\to(-1\cdot3,-1\cdot1)\to(-3,-1) \\ (1,3)\to(-1\cdot1,-1\cdot3)\to(-1,-3) \\ (-2,3)\to(-1\cdot-2,-1\cdot3)\to(2,-3) \end{gathered}[/tex]The image after the first dilation looks like this:
Now, the second dilation is by a scale factor of 2, centered at (-1,1).
As it is not centered in the origin, we can use the following formula:
[tex](x,y)\to(k(x-a)+a,k(y-b)+b)[/tex]Where k is the scale factor and (a,b) are the coordinates of the center of dilation.
By applying this formula to the actual coordinates we obtain:
[tex]\begin{gathered} (2,-1)\to(2(2-(-1))+(-1),2(-1-1)+1)\to(5,-3) \\ (-3,-1)\to(2(-3-(-1))+(-1),2(-1-1)+1)\to(-5,-3) \\ (-1,-3)\to(2(-1-(-1))+(-1),2(-3-1)+1)\to(-1,-7) \\ (2,-3)\to(2(2-(-1))+(-1),2(-3-1)+1)\to(5,-7) \end{gathered}[/tex]If we place these coordinates in the coordinate plane we obtain:
The answer is option B.
Answer:
B .
Step-by-step explanation:
Got the answer right.