State the given in the question.
It can be observed from the question that the following were given
[tex]\begin{gathered} \text{Probablility of success(p)=55\%=}\frac{55}{100}=0.55 \\ \text{Total number of trials=16} \\ \text{Therefore},\text{ the probability of failure (q)=1-p=1-0.55=0.45} \end{gathered}[/tex]State what we are supposed to find.
From the question, we are to find the probability of at least 10 workers.
In other to achieve this, the probability of at least 10 successes would be represented as below:
[tex]P(X\ge10)=P(10)+P(11)+P(12)+P(13)+P(14)+P(15)+P(16)[/tex]To find the individual probabilities for each success, X, we can either use a calculator's binomial probability distribution function (PDF), or we can use the binomial probability formula for each success, X. Then, find the sum of each of the individual probabilities.
For the question, we would solve for P(10) and P(11) using the binomial probability formula and use a calculator's binomial probability distribution function (PDF)
Let us find P(10) as shown below:
Please note that the binomial probability formula is given below:
[tex]\begin{gathered} P(X)=^nC_X(p^X)(q^{n-X}) \\ \text{Where} \\ n=\text{ number of trials} \\ X=\text{ number of successes} \\ p=\text{propability of success} \\ q=\text{probability of failure=1-p} \end{gathered}[/tex]Therefore P(10) would be as calculated below:
[tex]\begin{gathered} P(10)=^{16}C_{10}(0.55)^{10}(0.45)^6 \\ ^{16}C_{10}=\frac{16!}{10!(16-10)!}=\frac{16!}{10!6!}=8008 \\ 0.55^{10}=0.0025395162 \\ 0.45^6=0.00830376562 \\ P(10)=8008\times0.0025395162\times0.00830376562 \\ P(10)=0.16843255711 \end{gathered}[/tex]P(11) is as calculated below:
[tex]\begin{gathered} P(11)=^{16}C_{11}(0.55)^{11}(0.45)^5 \\ ^{16}C_{11}=\frac{16!}{11!(16-11)!}=\frac{16!}{11!5!}=4368 \\ 0.55^{11}=0.00139312339 \\ 0.45^5=0.0184528125 \\ P(11)=4368\times0.00139312339\times0.0184528125 \\ P(11)=0.11228837141 \end{gathered}[/tex]Using the binomial distribution calculator
[tex]\begin{gathered} P(12)=0.057183892845143 \\ P(13)=0.021505053719541 \\ P(14)=0.0056322759741655 \\ P(15)=0.00091785238097512 \\ P(16)=0.000070113723546711 \end{gathered}[/tex]We can now use the above calculations to find the probability that at least 10 workers are fully remote
[tex]\begin{gathered} P(X\ge10)=P(10)+P(11)+P(12)+P(13)+P(14)+P(15)+P(16) \\ P(X\ge10)=0.16843255711+0.11228837141+\cdots+P(16) \\ P(X\ge10)=0.36603011715589 \\ P(x\ge10)\approx0.366030117 \end{gathered}[/tex]Hence, the probability that at least 10 workers are fully remote is 0.366030117
what is the slope of the line
Solution
For this case we can find the slope with two points given (x1,y1) and (x2,y2) like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Find the perimeter of the rectangle. Be sure to write the correct unit in your answer. mm cm m -D 11 m Х ? 20 m Explanation Check 2022 McGraw HBLLC AL Rees
Given:
To Find:
Perimeter of a rectangle
Formula:
[tex]\text{Perimeter of a rectangle=2(l+w) units}[/tex]Explanation:
Let l and w be the length and width of the rectangle respectively.
[tex]\begin{gathered} \text{length(l)}=20\text{ m} \\ \text{width(w)}=11\text{ m} \end{gathered}[/tex][tex]\begin{gathered} \text{Perimeter of a rectangle=2(20+11)} \\ =2(31) \\ =62\text{ m} \end{gathered}[/tex]Final Answer:
Perimeter of a rectangle is 62 m.
Im unsure of how to set up this question so I can do the math to solve it, can you help me?
Answer:
[tex]r=5[/tex]Explanation: We have to find the radius of the circle provided the central angle and the arc-length, the formula used to determine the radius is as follows:
[tex]\begin{gathered} S=r\theta\Rightarrow(1) \\ r=? \\ S=\frac{10\pi}{3} \\ \theta=\frac{2\pi}{3} \end{gathered}[/tex]Plugging in the known information in equation (1) and solving for the unknown variable r gives the following answer:
[tex]\begin{gathered} \begin{equation*} S=r\theta \end{equation*} \\ \frac{10\pi}{3}=r\frac{2\pi}{3}\rightarrow10=r2 \\ r=\frac{10}{2}=5 \\ r=5 \end{gathered}[/tex]Therefore the value of the radius is 5:
Can the A Similarity Postulate be used to prove the triangles below are similar?
The AA similarity postulate states that two triangles are similar if they have 2 congruent angles. Looking at the image we can see that we have 2 lengths and one angle, but the AA similarity postulate states that we need 2 angles, then no, we cannot use AA similarity postulate to prove that they are similar. because there is only one known angle measure.
So what can we use to prove that the triangle is similar? Here, we can use SAS (side, angle, side). Anyway, the final answer is: No, because there is only one known angle measure.
Jackson has a coin collection consisting of quarters and dimes. The total value of his collection is $16.70. His collection consists of eight less quarters than three times the number of dimes. Using the variables q and d to represent the number of quarters in his collection and the number of dimes in his collection respectively, determine a system of equations that describes the situation. Enter the equations below separated by a comma. How many dimes are in his collection? How many quarters are in his collection?
First, remember that:
• a dime values 10 cents;
,• a quarter values 25 cents.
So, using q for the number of quarters and d for the number of dimes, we have:
[tex]q=3d-8[/tex]The above equation tells us that the number of quarters is 8 less than three times the number of dimes.
Also, we have:
[tex]0.10d+0.25q=16.70[/tex]The above equation tells us that the total value of his collection is $16.70.
Thus, the equations are:
[tex]\begin{gathered} q=3d-8 \\ \\ 0.10d+0.25q=16.70 \end{gathered}[/tex]Now, solving that system, we obtain:
[tex]\begin{gathered} 0.10d+0.25(3d-8)=16.70 \\ \\ 0.10d+0.75d-2=16.70 \\ \\ 0.85d=18.70 \\ \\ d=\frac{18.70}{0.85} \\ \\ d=22 \end{gathered}[/tex]Now, we can use the previous result to find q:
[tex]\begin{gathered} q=3(22)-8 \\ \\ q=66-8 \\ \\ q=58 \end{gathered}[/tex]Therefore, there are 22 dimes and 58 quarters in his collection.
Wholesale price is 187.14 retail price is 247.02 what is the markup in dollars?
In order to calculate the markup in dollars, we can use the formula below:
[tex]markup=selling\text{ }price-cost[/tex]So, using a selling price of 247.02 and a cost of 187.14, we have:
[tex]markup=247.02-187.14=59.88[/tex]Therefore the markup is $59.88.
Referring to the figure, use the graph to estimate the roots of the equation: y= x^2 - 4
Given:
The graph of y= x^2 - 4
To determine the roots of the equation using the graph, we note
first that real roots of the function (or zeros of the function) represented by the graph are found where the graph crosses or contacts the x-axis.
As we can see on the given graph, it crosses at x= -2, x=2. Therefore, the roots of the equation y= x^2 - 4 are:
x=-2
x=2
Which point represents the center of the circle shown below?RMKA. Point TB. Point KC. Point RD. Point M
The center of the circle is a point from where all points lying on the circumference of circle are equidistant. It lies in the interior of circle and diameter always pass through the center of the circle.
From the circle, it can be observed that point R, point M and point T lies on the circumference of circle and only point K lies inside the circle. So point K is the center of given circle.
Answer: Point K
Option B is correct.
7x + 4 = 5 +3x + 1xSolve for x
x = 1/3
Explanations:The given equation is:
7x + 4 = 5 + 3x + 1x
Step 1: Collect the like terms
Note that 3x and 1x cross to the left hand side of the equality sign to become -3x and -1x respectively. 4 also crosses to the right hand side of the equality sign to become -4.
The equation then becomes:
7x - 3x - 1x = 5 - 4
3x = 1
Step 2: Divide both sides by 3
3x / 3 = 1 /3
x = 1/3
Identify the type of correlation for each data set based on the graphs shown
SOLUTION
Step 1 :
In this question, we are expected to differentiate the three major types of Correlation:
There are three possible results of a correlational study and they are :
1. A positive correlation,
2. A negative correlation,
3. No correlation.
Step 2 :
Based on the question, we are going to classify the graphs based
on the explanation in Step 1 :
Graph 1 = A negative correlation
Graph 2 = No correlation
Graph 3 = A positive correlation
CONCLUSION:
Graph 1 = A negative correlation
Graph 2 = No correlation
Graph 3 = A positive correlation
Question 5Look at the graph of the equation y = x2– 2x - 7.how does this graph compare with the graph of the equation in question 1?
We can rewrite the equation into its vertex form, as shown below
[tex]\begin{gathered} y=x^2-2x-7 \\ y=a(x-h)^2+k \\ \Rightarrow y=ax^2-2ah+ah^2+k \\ \Rightarrow\begin{cases}a=1 \\ -2ah=-2\Rightarrow h=1 \\ ah^2+k=-7\Rightarrow1+k=-7\Rightarrow k=-8\end{cases} \end{gathered}[/tex]Therefore, the vertex form of y=x^2-2x-7 is
[tex]y=(x-1)^2-8[/tex]On the other hand, the graph of the equation of question 1 seems to be the same graph like the one of the function y=x^2-2x-7. The y-intercept is the same (0,-7) and the vertex seems to be located on the same point (1,-8).
The two graphs are the same, only the scale changes.
These two graphs are the same.
Answer:
The graph is the same. Even though the equations have different forms, they are still equivalent.
Step-by-step explanation:
i re wrote it
3. Graph y = 1x +31 - 2 4. ** Graph y = -x] - 3 18 8 8 17 구 7 6 5 بيه * 12 고 1 -9 - 5 -4 -3 -2 1 2 3 5 6 g -93-7 -6 -5 -4 -3 -2 -1 2. 5 NA -A -2
Generally, graphs of equations containing absolute functions are v-shaped graphs, that take a certain value starting from the y-axis
With respect to this question,
We identify the point -3 on the x-axis and also locate the point -2 on the y-axis
We mark this coordinate, then draw a v-shaped graph that has an two intercepts on the x-axis and one on the y-axis
The intercepts on the x-axis according to this question are - 1 and -5
The intercept on the y-intercept is 1
A representation of the graph is shown below;
Joseph's lunch at a restaurant costs $13.00. without tax. He leaves. the waiter a tip of 17% of the cost of the lunch, without tax what is the total cost of the lunch, including the tip, without tax? is a math word problem I'm in 7th grade so pls dont make it that hard to explain.
Joseph's lunch costs $13 without tax.
He leaves the waiter a tip of 17% OF THE COST OF THE LUNCH. This means Joseph leaves a tip of
13 + (13 x 17%) = Total cost
Remember, the question specificies that his lunch is paid without tax. Therefore;
[tex]\begin{gathered} \text{Cost}=13.00 \\ \text{Tip}=13\times0.17\text{ (equals 2.21)} \\ (\text{Note that 17\% is mathematically written as 0.17)} \\ \text{Total cost of lunch}=\text{Cost}+\text{Tip} \\ \text{Cost}+\text{Tip}=13+2.21 \\ \text{Cost}+\text{Tip}=15.21 \\ \text{Total cost of lunch=\$15.21} \end{gathered}[/tex]The total cost of the lunch is $15.21
Write the following as an algebraic expression in u, u > 0.
SOLUTION
Given
[tex]tan\mleft(cos^{-1}\mleft(\frac{u}{3}\mright)\mright)[/tex]Using the following identity
[tex]tan\mleft(cos^{-1}\mleft(x\mright)\mright)=\frac{\sqrt[]{1-x^2}}{x}[/tex]It follows:
[tex]tan(cos^{-1}(\frac{u}{3}))=\frac{\sqrt[]{1-(\frac{u}{3})^2}}{\frac{u}{3}}[/tex]Simplify the right hand side
[tex]\frac{\sqrt[]{1-(\frac{u}{3})^2}}{\frac{u}{3}}=\frac{\sqrt[]{1-\frac{u^2}{9}}}{\frac{u}{3}}[/tex]This can further be reduce
[tex]\begin{gathered} \frac{\sqrt[]{1-\frac{u^2}{9}}}{\frac{u}{3}} \\ =\frac{\sqrt[]{\frac{9-u^2}{9}}}{\frac{u}{3}} \\ =\frac{\frac{1}{3}\sqrt[]{9-u^2}}{\frac{u}{3}} \\ =\frac{\sqrt[]{9-u^2}}{3\times\frac{u}{3}} \\ =\frac{\sqrt[]{9-u^2}}{u} \end{gathered}[/tex]Therefore the solution is:
[tex]\frac{\sqrt[]{9-u^2}}{u}[/tex]Hi I need help with this question please and thank you
Expression given:
[tex]64t^3+125v^6[/tex]Factoring:
0. Applying the Law of exponents
[tex]64t^3+125v^6=\mleft(4t\mright)^3+\mleft(5v^2\mright)^3[/tex]2. D = Sum of Cubes:
[tex]=(4t)^3+(5v^2)^3=(4t+5v^2)((4t)^2-4t\cdot\: 5v^2+(5v^2)^2)[/tex]Simplifying:
[tex]=\mleft(4t+5v^2\mright)\mleft(16t^2-20tv^2+25v^4\mright)[/tex]Then, the only Factoring Pattern we need is D.
Answer: D.
Find CE and DE. Pls help me and don’t be slow when answering pls.
The lengths of the two tangents from a point to a circle are equal therefore
CB=CD
23=x
CE=x+x-5
CE=23+23-5
CE=41
DE= BA
DE=x-5
DE=18
Write the equation of the parabola in vertex form with the following conditions:Vertex: (0,4)Directrix: y = 2
We are given the vertex of the parabola (0,4) and the directrix y=2. This is a parabola with its axis of symmetry parallel to the y-axis.
The standard form of the parabola is
[tex]\mleft(x-h\mright)^2=4p(y-k)[/tex]Where (h,k) is the vertex of the parabola and the directrix is given as
y = k - p
We can find the value of p:
p= k - y = 4 - 2 = 2
Substituting, we have the equation of the parabola:
[tex]\begin{gathered} (x-0)^2=4\cdot2(y-4) \\ x^2=8(y-4) \end{gathered}[/tex]The first choice is correct
In the diagram shown , the length of a side of the square is x cm , where x∈ℝ. Find the length of the diagonal of the square in terms of x
SOLUTION
Consider the figure below
The diagonal of the square is shown
Using Pythagoras theorem, it follows:
[tex]d^2=x^2+x^2[/tex]Solve the equation for d
[tex]\begin{gathered} d^2=2x^2 \\ d=\sqrt[]{2x^2} \\ d=x\sqrt[]{2} \end{gathered}[/tex]Therefore the diagonal of the square is
[tex]d=x\sqrt[]{2}[/tex]what is the function equation for the input/output table
P1 = (8, 4)
P2 = (17, 13)
1.- Find the slope
m = (y2 - y1) / (x2 - x1)
m = (13 - 4) / (17 - 8)
m = 9 / 9
m = 1
2.- Find the equation of the line
y - y1 = m(x - x1)
y - 4 = 1(x - 8)
y - 4 = x - 8
y = x - 8 + 4
y = x - 4
At 1 p.m., the work crew starts at the intersection of New Street and Main Street and moves toward the intersection of Main Street and Wilson Street, painting lane lines at an average speed of 5mi/h. The work crew will take its afternoon break when it is 3 mi from the intersection of Main Street and Wilson Street. Determine what time the work crew will take its afternoon break.Hints: you will need to use these equations: D=RT, y=mx+b and m=y1-y2/x1-x2 One more hint, draw the above image on graph paper, and make the intersection of North St. and Wilson St. the origin. Then you can make a bunch of linear equations to represent the roads. Find points of intersection of the lines. And use the points of intersection, with D=RT find out when the crew took their afternoon break.
From the question given
D = RT
D= distance in miles
R = rate in miles/hr
T = time in hour
d = 3miles
R = 5mi/h
since D = RT
make T the subject of the formula by dividing both sides by R
D/R = RT/R
T = D/R
T = 3 / 5
T = 0.6 hours
convert the hours to mins
60 mins ===== 1h
xmins ======== 0.6h
cross multiplication
x * 1 = 0.6 x 60
x = 36 mins
since the crew started work by 1pm, therefore they will have their break exactly 1h 36mins, that is 36 mins after they started the work
Point A has coordinates (3,4). After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, what are the coordinates of the image? Write your coordinates with a comma and no spaces inside parenthesis, for example (1,2).
If a point, (x, y) is translated c units to the left, the new coordinate would be
(x - c, y)
Given that point A with coordinates, (3, 4) is translated 4 units left, the new coordinate would be
(3 - 4, 4)
= (- 1, 4)
If a point, (x, y) is reflected across the x-axis, the sign of the x coordinate remains unchanged while the sign of the y coordinate would change. This gives us (x, - y). Thus, if (- 1, 4) is reflected across the x-axis, the new point would be
(- 1, - 4)
If a point, (x, y) is translated c units down, the new point would be (x, y - c)
Thus, if (- 1, - 4) is translated 2 units down, the new point would be (- 1, - 4 - 2)
= (- 1, - 6)
The final coordinate is
(- 1, - 6)
Find sn of the arithmetic seriesa1=22 d=-8 n=12
Given: An arithmetic series with:
[tex]\begin{gathered} a_1=22 \\ d=-8 \\ n=12 \end{gathered}[/tex]Required: To find the sum of n terms of the given series.
Explanation: The formula for the sum of n terms of an AP is:
[tex]S_n=\frac{n}{2}[2a_1+(n-1)d][/tex]Substituting the values in the above formula gives:
[tex]S_n=\frac{12}{2}[2\times22+(12-1)\cdot(-8)][/tex]Solving the above equation-
[tex]\begin{gathered} S_n=6(44-88) \\ S_n=-264 \end{gathered}[/tex]Final Answer: The sum of the arithmetic series is -264.
3 1 point What was the scale when the Blac inches and 12.5 inches tall.
we know that
1 in represent 22 ft
so
Applying proportion
Find out how many feet , 6 inches represent
22/1=x/6
solve for x
x=22*6
x=132 feet
the answer is 132 feet-10+w=-8w+8 how do i solve for w?
w =2
Explanation:
-10 + w = -8w + 8
Collect like terms:
w + 8w = 8 + 10
Simplify:
9w = 18
Divide through by 9:
w = 18/9
w = 2
A small liberal arts college in the Northeast has 350 freshmen. Ninety of the freshmen are education majors. Suppose seventy freshmen are randomly selected (withoutreplacement).Step 2 of 2: Find the standard deviation of the number of education majors in the sample. Round your answer to two decimal places, if necessary.AnswerKeypadKeyboard ShortcutsTables
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
For each freshmen, there are only two possible outcomes. Either it is an education majors holder, or it is not. Seventy freshmen are randomly selected (without replacement). This means that the hypergeometric distribution is used to solve this question.
STEP 2: Give the formula for calculating the standard deviation
Standard deviation of the hypergeometric distribution:
We have that:
N is the population size.
n is the sample size.
s is the number of successes in the sample.
The standard deviation is given by:
[tex]\sigma=\sqrt{n(\frac{s}{N})(1-\frac{s}{N})(\frac{N-n}{N-1})}[/tex]STEP 3: Write the given data
[tex]\begin{gathered} N=350 \\ s=90 \\ n=70 \end{gathered}[/tex]By substitution,
[tex]\begin{gathered} \sigma=\sqrt{70(\frac{90}{350})(1-\frac{90}{350})(\frac{350-70}{350-1})} \\ \\ \sigma=\sqrt{10.7277937}=3.275331082 \\ \sigma=3.28 \end{gathered}[/tex]Hence, the standard deviation is given approximately as 3.28
solve the same using the Elimination method if there is no solution put no solution if there is infinite put infinite7.5p + k = 922.5p +3k =6
The system of equations is given as,
[tex]\begin{gathered} 7.5p+k=9 \\ 22.5p+3k=6 \end{gathered}[/tex]Let us eliminate the variable 'k' first.
The coefficient can be made equal by multiplying the first equation by 3,
[tex]\begin{gathered} (7.5p+k)\cdot3=9\cdot3 \\ 22.5p+3k=6 \end{gathered}[/tex]Simplify the system of equations,
[tex]\begin{gathered} 22.5p+3k=27 \\ 22.5p+3k=6 \end{gathered}[/tex]Subtract the second equation from the first,
[tex]\begin{gathered} (22.5p+3k)-(22.5p+3k)=27-6 \\ 22.5p+3k-22.5p-3k=21 \\ 0=21 \end{gathered}[/tex]Note that the result obtained does not hold true for any values of 'p' and 'k'.
So the given system of linear equations will have no solution.
State if each triangle is acute, obtuse, or right.3)4 mi3 mi√√8 miA) RightC) ObtuseB) Acute
STEP - BY - STEP EXPLANATION
What to do?
Determine if the triangle is acute, right or obtuse.
Given:
Let side a= √8
side b= 3
side c= 4
Let the angle opposite side c= angle C
Step 1
Solve for angle c using the cosine formula.
[tex]c^2=a^2+b^2-2ab\text{ }cosC[/tex][tex]4^2=(\sqrt{8})^2+3^2-2(\sqrt{8})(3)cosC[/tex][tex]6\sqrt{8}\text{ }cosC=8+9-16[/tex][tex]\begin{gathered} cosC=\frac{1}{6\sqrt{8}} \\ \\ cosC=0.05893 \end{gathered}[/tex][tex]C=cos^{-1}(0.05893)[/tex][tex]C=86.62[/tex]Step 2
Identify the measure of each given type of triangle.
Right - triangle is a triangle with angle 90 degree.
Acute triangle is a triangle with all angles less than 90 degree.
Obtuse triangle is a triangle with an angle more than 90 degree.
Step 3
Draw conclusion from the above definition.
Since the largest angle in the triangle is 86.62 degrees which is less than 90 degree, then it is an acute triangle.
ANSWER
B. Acute triangle.
Identify the slope in the equation 9x + 2y = -7
The slope of the equation is -9/2
Here, we want to identify the slope of the equation.
Firstly, what we need to do is to express the equation in the standard form
The standard form of the equation of a line is;
y = mx + c
where m represents the slope of the linear equation and c represents the y-intercept of the linear equation
So making y the subject of the equation, we have;
2y = -9x - 7
divide through by 2;
y = -9x/2 - 7/2
The slope of the equation is the coefficient of x which is -9/2
Write the standard form of the equation of each line. 3) y = -2x + 6 A) 2x + y = 6 C) 4x + y = -5 2 4) y = -x + 2 3 B) r-y=-5 D) 2x + y = -6 A) 3x - 5y = -6 B) 2x - 3y = -6 C) x - 5y = 6 D) x - 5y = -6Please help me
hello
to solve this question, we simply need to write the standard form of the equation y = -2x + 6
the standard form of the equation is
[tex]\begin{gathered} x+y=a \\ a=\text{intercept} \end{gathered}[/tex]in this question, we have y = -2x + 6
[tex]\begin{gathered} y=-2x+6 \\ 2x+y=6 \end{gathered}[/tex]the answer to this question is 2x + y = 6 and this corresponds to option A
which of the following is equivalent to the expression below? √96 - √54+ √24
Explanation:
The expression that we have is:
[tex]\sqrt{96}-\sqrt{54}+\sqrt{24}[/tex]And we need to find the equivalent expression.
Step 1. The first step is to simplify the square roots by looking for multiplications that result in the number inside that square root, and that one of those numbers has an exact square root.
Let's start with the square root of 96, we can write 16x6 instead of 96:
And then, since 16 has an exact square root (which is 4) we further simplify the expression to:
[tex]\sqrt{96}=4\sqrt{6}[/tex]Step 2. We do the same for the other two square roots:
Step 3. Using these results, our expression now is:
[tex]\sqrt[]{96}-\sqrt{54}+\sqrt{24}=4\sqrt{6}-3\sqrt{6}+2\sqrt{6}[/tex]To find the equivalent expression, since now we have that all of the square roots have the same number inside (6) we can just make the operations with the numbers 4, -3, and 2, and the result is:
[tex]4\sqrt{6}-3\sqrt{6}+2\sqrt{6}=\boxed{3\sqrt{6}}[/tex]which is option D.
Answer:
D
[tex]3\sqrt{6}[/tex]