Using combinations, we concluded that the probability that fewer than 2 of the next 5 vehicles are from out of state is 0.907.
A checkpoint sees 75% of its traffic coming from within the state.
Therefore, there is a 0.75 percent chance that the car comes from the state.
1-0.75=0.25 represents the likelihood that the car is from outside the state.
Let x now act as the random variable. Consequently, n=9 and X=4
It is necessary to determine the likelihood that less than 2 of the following 5 automobiles are from another state.
We are to calculate the probability of x<2
p=0.25
q=0.75.
Using the formula,
P(x≤2) = ∑ ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
P(x≤2) = ∑ ⁵C₂ p² q³ + ⁵C₁ p¹ q⁴ + ⁵C₀ p⁰ q⁵
P(x≤2) = ∑ [tex]\frac{5!}{2! 3!}[/tex] (0.25)² (0.75)³ + [tex]\frac{5!}{1! 4!}[/tex] (0.25)¹ (0.75)⁴ + [tex]\frac{5!}{0! 5!}[/tex] (0.75)⁵
P(x≤2) = 10 × 0.065 × 0.421875 + 5 × 0.25 × 0.3164 + 0.2373
P(x≤2) = 0.2742 + 0.3955 + 0.2373
P(x≤2) = 0.907
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Select the correct answer.
What is the solution for x in the equation?
-x+3/7 = 2x - 25/7
A. X=3/4
B.x=4/3
C.x=-3/4
D. X-4/3
Answer:
B
The correct answer is B. x= 4/3
8% of the High School students have their license.If there are 1000 high school students in your neighborhood, how many have their license?
Percentages
To calculate the X% of a given number N, we proceed as follows:
X * N / 100
We know X=8% of the High School students have their license. There are N=1000 high school students, thus the number of students with their license is:
8 * 1000 / 100 = 80
80 students have their license
Find the indicated complement.
A certain group of women has a 0.04% rate of red/green color blindness. If a woman is randomly selected, what is the
probability that she does not have red/green color blindness?
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Mathematical expressions with the form, where x is the base and n is the exponent, are called powers. In powers, the base is the integer or variable that is continually multiplied, and the exponent designates how many times to multiply the base by itself.
Exponents should be subtracted when dividing powers by the same base, according to the quotient rule. For instance, dividing h(6) by h(2) yields h(6-2) = h(4). A quick and simple technique to make the problem simpler is to subtract the exponents.
Use the Quotient of Powers Rule to reduce the number of terms when splitting like terms with exponents. According to this rule, to determine the solution while dividing terms with the same base, simply remove their exponents. The trick is to only take out exponents with matching bases.
This means that every number raised to the power of zero is one because it is simply the result of no numbers at all, which is the multiplicative identity, or 1.
Hence we made the clear conclusions.
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Please help me!!! Thank you to anyone who does!!
Solve for x
Answer:
(4x - 5) + (3x + 11) = 104 (exterior angle)
7x + 6 = 104
7x = 98
x = 14
These are all apart of the same question so could you please label the answers 1 2 3
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Statement Reason
1. Line FI bisects angle GFH Given
2. Line FG is equivalent to line FH Given
3. Angle GFI is equivalent to angle HFI Definition of angle bisector
4. Line FI is equivalent to line FI Reflexive property of congruence
5. Triangle FHI is equivalent to Triangle FGI Side Angle Side ( SAS)
GUYSSSSS HELP ME PL,S PSP[JOWQHIFUEFIDoisd[jofbwkeqi
ITS SO HARDDD TO SOLVE
if you dig a 6 feet hole how deep is it?
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS HELPPPPPPPPPPPPPPPPPPP
Answer:
You're question is incomplete.Please try to make it more clear
I need help with this.
66 is 75% of what number?
Answer:
88
Explanation:
Let us call the number NUMBER, then we know that
[tex]\frac{75}{100}\times\text{NUMBER =66}[/tex]The above says that 75% of the number is 66.
Then how do we find the value of NUMBER?
Multiplying both sides by 100/75 gives
[tex]undefined[/tex]I need help with this practice problem solving, having trouble.It is trigonometry.
The period of a function is the distance (x) between the repetion of this fuction.
As can be observed in the figure below:
Then, the period is: 7.5 - 1.5 = 6.
Answer: 6.
which system is represented by the graph?
Answer: (A)
Step-by-step explanation:
By elimination, none of the other answers choices fit the lines; B, C, and D all have at least one positive slope. Both lines shown in the graph have negative slopes, so both equations have to have a negative x value when simplified, so it's A.
David buys last year's best-selling novel, in hardcover, for $13.30. This is with a 30% discount from the original price. What was theoriginal price of the novel?
Since the price paid got 30% discount from the original price, so this price represents 70% of the original price.
Using the variable x to represent the original price, we can write the following equation and solve it for x:
[tex]\begin{gathered} 13.3=70\text{\% of x} \\ 13.3=\frac{70}{100}\cdot x \\ 13.3=0.7\cdot x \\ x=\frac{13.3}{0.7} \\ x=19 \end{gathered}[/tex]Therefore the original price is $19.
Hey, could anybody help me with this? thank you!
9) length of the tree is 22.165 meter
10 ) the length of the steel beams is 3.7464 meters
9 ) Given: The angle is 55.2 °
The length of the shadow is 15.5 meter.
To find : the length of the tree
The by using the formula tan θ = perpendicular / base
tan θ = length of the tree/ shadow
thus the length of the tree = length of shadow × tan θ
= 15.5 × tan 55.2
= 15. 5 × 1.43
= 22.165 meter
Thus the length of the tree is 22.165 meter
10) the angle of inclination = 42 °
The height of the slab is 5.6 meters
Thus the length of the steel beams is :
sin 42 ° = perpendicular / hypotenuse
hypotenuse = perpendicular × 0.669
hypotenuse = 5.6 × 0.669
= 3.7464 meters
Thus the length of the steel beams is 3.7464 meters.
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7. Isaiah has a summer internship at a technology company and is paid $3,000. After Federal and state taxes, Social Security, and Medicare are deducted, his take-home pay is $2,500. Which of the statements below is correct?
The correct statement regarding Isaiah is that A. His gross pay is $3,000 and net pay is $2,500
How to illustrate the information?Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay. Net pay, often known as take-home pay, is the amount that is left after all withholdings have been taken into account. Determining the number of pay periods you have throughout the year is the first step in calculating the gross compensation for a salaried employee.
The time range for which you pay your employee is known as a pay period. You must first determine your employee's gross compensation before you can determine their net pay. This is where you should start. The next thing you need to know is what payroll deductions your employee receives.
Since the take-home pay is $2,500, this is the net pay.
In conclusion, the correct option is A.
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Isaiah works at a technology company in the summer and earns
$3000. After federal, state, and Social Security/Medicare taxes are
deducted, his take-home pay is $2,500. Which of the statements
below is CORRECT? *
His gross pay is $3,000 and net pay is $2,500
His gross and net pay are $3,000
His gross and net pay are $2,500
His gross pay is $2,500 and net pay is $3,000
find the area of a circle with a radius of 6 centimeters use 3.14 for [tex]\pi[/tex]
Radius = 6 cm
The area of circle is given by:
[tex]\begin{gathered} A=\pi r^2\text{ } \\ \pi\text{ = 3.14} \\ A\text{ = 3.14 }\cdot6^2 \end{gathered}[/tex][tex]A=113.04cm^2[/tex]A = 113.04 cm^2
Find the value of x so that f ll g. 18x-44 8x-10
Answer:
x = 3.4
Step-by-step explanation:
18x - 44 = 8x - 10
+10
18x - 34 = 8x
-18x
-34 = -10x
/ 10
x = 3.4
Proof:
18 x 3.4 = 61.2 - ( 44 ) = 17.2
8 x 3.4 = 27.2 - ( 10 ) = 17.2
Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.
The surface area and volume of the given pyramid are 800ft³ and 1280ft³.
What is a pyramid?The following is the general formula to determine the pyramid's surface area and volume: The base area of a pyramid is added to half the product of the base perimeter and slant height to determine its total surface area. The Total Surface Area of the Pyramid is, therefore (1/2)Pl + B square units.So, the formula for the surface area of the Right rectangular pyramid:
[tex]A = lw+l\sqrt{(\frac{w}{2})^{2}+h^{2} } +w\sqrt{(\frac{l}{2} )^{2}+h^{2} }[/tex]Now, l = 16, w = 16 and height = 15 feet.Substitute the values in the formula:(Refer to the image attached below for calculation)
The surface area of the pyramid is 800ft³.
The formula for the volume of the Right rectangular pyramid:
[tex]V = \frac{lwh}{3}[/tex]Now, l = 16, w = 16 and height = 15 feet.Substitute the values in the formula:(Refer to the image attached below for calculation)
The volume of the pyramid is 1280ft³.
Therefore, the surface area and volume of the given pyramid are 800ft³ and 1280ft³.
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11. Callie reads the same number of pages each month. How many pages will she have read after 4 months? Is an estimate or exact answer needed? A. 4.000; estimate B. 4.000: exact C. 4.128: estimate D. 4.128: exact 2. Grade 4. Chapte
EXPLANATION:
First we must know what data the exercise gives us; for exmple:
-Tells us that it reads a number of pages (unknown data) each month or per month.
-The exercise asks us, how many pages will have been read after 4 months.
We can see that we first have to find the number of pages in a month and then find the number of pages in 4 months.
The exercise is as follows:
[tex]\begin{gathered} p\rightarrow pages\text{ read; ( }in\text{ a month)} \\ x\rightarrow4\text{ months} \\ x=\frac{4\times(30)}{1(30)}=4.000\colon\text{ estimate } \\ \text{ANSWER:The correct option is A ; 4.000 Estimate (}we\text{ say }this\text{ because} \\ we\text{ do not know }exactly\text{ }the\text{ actual numbers of pages; }that\text{ is }why\text{ we} \\ \text{take }the\text{ 30 days }of\text{ the month }as\text{ a }probability) \end{gathered}[/tex]solve the system {x-y+z=0, 3x-2y+6z=9, -x+y-2z=-2}
The system of equations has a solution of x = -17, y = -15 and z = 2
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
x - y + z = 0
3x - 2y + 6z =9
-x + y -2z = -2
Add the first and the third equations
So, we have
x - x - y + y + z - 2z = 0 - 2
Evaluate
-z = -2
This gives
z = 2
Make z = 2 in the other equations
So, we have
x - y + 2 = 0
3x - 2y + 12 =9
-x + y - 4 = -2
This gives
x - y = -2
3x - 2y = -21
-x + y = 2
Make y the subject in -x + y = 2
y = x + 2
Substitute y = x + 2 in 3x - 2y = -21
3x - 2(x + 2) = -21
Expand
3x - 2x - 4 = -21
So, we have
x = -17
Recall that y = x + 2
So, we have
y = -17 + 2
Evaluate
y = -15
Hence, the solution for the system of linear equations x - y + z = 0, 3x - 2y + 6z =9 and -x + y -2z = -2 are x = -17, y = -15 and z = 2
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What is the scale factor of the dilation?
The scale factor for the square LMNO to L'M'N'O' is k = 1/2.
What is the scale factor of the dilation?Remember that for any length L, a dilation of scale factor k gives a new length L' such that:
L' = k*L
Look at line LM, it has a length:
L = √(6^2 + 2^2) = √40
Now line L'M' has a length:
L' = √(1^2 + 3^2) = √10
Then we can see that:
L' = k*L
√10 = k*√40
√10/√40 = k
√(1/4) = k
1/2 = k
The scale factor is 1/2.
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25×10 to the power of -3 to standard form
The standard form of the expression 25×10 to the power of -3 is 2.5×10⁻⁴
What exactly is meant by "scientific notation"?Scientific notation can be employed to reduce exceptionally large figures to positive exponential values, as well as very small figures to negative exponential values.When writing a number in m10n scientific notation, you can use decimal numbers and positive exponents to transform a long number to a shorter one.The Index Power Rule:
According to this formula, when the power of a number is raised to another power, this same indices are multiplied.This is the fourth index law, and it's the Index Law for Powers.For the given expression;
25×10 to the power of -3
This can be written as follows;
= 25×10⁻³
To write the expression in standard form, shift the decimal to the left of the number and add one more power to base 10.
= 2.5×10⁻⁴
Thus, the expression in the standard form becomes 2.5×10⁻⁴.
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Please expand (3x+4)(5x-2)(4x-3) and simplify fully.
The complete expansion of the expression would give; 60x^3 - 11x^2 - 74x + 24
How can the expression be expanded?To expand an expression means that we should be able to obtain the original long expression that was factorized in order to get it. In this case, the expression that we have is (3x+4)(5x-2)(4x-3). We would now have to carry out the expansion in stages.
1) (3x+4)(5x-2)
15x^2 - 6x + 20x - 8
2) We can now carry out the next step in the expansion as we multiply the bracket with the last term in the expression;
15x^2 - 6x + 20x - 8(4x-3)
60x^3 - 45x^2 - 24x^2 + 18x + 80x^2 - 60x -32x + 24
We can now collect the like terms;
60x^3 - 45x^2 - 24x^2 + 80x^2 + 18x - 60x - 32x + 24
60x^3 - 11x^2 - 74x + 24
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AB=5x + 10
BC=x + 38
Given: B is the midpoint of line segment AC
Prove:
x = 7
Answer:
Given: B is the midpoint of line segment AC.
Segment Additon: AB+BC=AC
Given: AB=5x + 10 and BC=x + 38
Symmetric Property: AB=BC
congruent property: 5x+10=x+38
Subtraction property: 4x+10=38
Subtraction property: 4x=28
Disivion property: x=7
A 1nch candle burns in 4hours at what rate does the candle burn in inches per hour
Answer:
4 1x4=4 so 4 is ur answer
Step-by-step explanation:
X =x² + 6x + 5 = 0b= ] ± √b22-4aaC
We have the following quadratic equation:
[tex]x^2+6x+5=0[/tex]And we have to use the quadratic equation to solve that equation.
1. To find the solutions, we need to start by using the quadratic equation:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \text{ when }ax^2+bx+c=0 \end{gathered}[/tex]2. Identify a, b, and c from the given quadratic equation:
[tex]\begin{gathered} x^2+6x+5=0 \\ \\ a=1,b=6,c=5 \end{gathered}[/tex]3. Apply the quadratic equation:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-6\pm\sqrt{6^2-4(1)(5)}}{2(1)} \\ \\ \\ \end{gathered}[/tex]4. And now, we can develop it as follows:
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{36-20}}{2} \\ \\ x=\frac{-6\pm\sqrt{16}}{2} \\ \\ x=\frac{-6\pm4}{2} \\ \\ \text{ Therefore:} \\ \\ x=\frac{-6+4}{2}=-\frac{2}{2}=-1 \\ \\ x=-1 \\ \\ x=\frac{-6-4}{2}=\frac{-10}{2}=-5 \\ \\ x=-5 \end{gathered}[/tex]Therefore, we finally have two solutions, x = -1, and x = -5.
Then the first step is given by:
[tex]x=\frac{-6\pm\sqrt{6^2-4(1)(5)}}{2(1)}[/tex]
I need the answer and the work it asks for
• Part A
Let be:
x: The number of minutes Angela plays soccer every day
ygolf
Then, we can write the following system of linear equations
[tex]\begin{cases}x+y=125\Rightarrow\text{ Equation 1} \\ x=45+y\Rightarrow\text{ Equation 2}\end{cases}[/tex]• Part B
To solve this question, we will solve the system of linear equations that we wrote above.
To do this, we can first substitute the value of x from Equation 2 into Equation 1, and then we solve for y:
[tex]\begin{gathered} x+y=125\Rightarrow\text{ Equation 1} \\ (45+y)+y=125 \\ 45+y+y=125 \\ \text{ Add similar terms} \\ 45+2y=125 \\ \text{ Subtract 45 from both sides of the equation} \\ 45+2y-45=125-45 \\ 2y=80 \\ \text{ Divide by 2 from both sides of the equation} \\ \frac{2y}{2}=\frac{80}{2} \\ y=40 \end{gathered}[/tex]Therefore, Angela spends 40 minutes playing golf every day.
• Part C
To solve this question, we can replace the value of y into Equation 1 and then solve for x
[tex]\begin{gathered} x+y=125\Rightarrow\text{ Equation 1} \\ x+40=125 \\ \text{ Subtract 40 from both sides of the equation} \\ x+40-40=125-40 \\ x=85 \end{gathered}[/tex]Therefore, Angela cannot possibly spend 80 minutes playing soccer every day because she actually spends 85 minutes.
HELP ALGEBRA 2!
One side of a square is increased by 2 inches, while adjacent side is decreased by 2 inches. The area of the resulting rectangle is 32 square inches. What were the dimensions of the original square?
Answer:
(x+2)(x-2)=32(x+2)(x-2)=32x^2+2x-2x-4=32(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+6)(x-6)=0(x+2)(x-2)=32x^2+2x-2x-4=32x^2-4-32=0x^2-36=0(x+6)(x-6)=0x-6=0x=6 the length of the original side of the square.(6+2)(6-2)=32(6+2)(6-2)=328*4=32(6+2)(6-2)=328*4=3232=32How to Calculate the missing value: P = 1000 W, E = ____, I = 20 A.
The voltage E of the electrical appliance using a power of 1000 watts is 50 Volts.
How to calculate voltage using the power formula?Power is simply the quantity of energy transferred per unit time. It can be expressed as;
P = E × I
Where E is voltage and I is current.
Given the data in the question;
Power P = 1000WCurrent I =20AVoltage E = ?To determine the voltage of the appliance, plug in the given values into the formula above and solve for E.
P = E × I
1000W = E × 20A
E = 1000 / 20
E = 50V
Therefore, the missing value voltage E is 50 volts.
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A toy costs 35 000 lndonesian rupiah (Rp).
The conversion rate is Rp 1000 = 5$0.145 598.
Without using a calculator, estimate the price of
the toy in S$.
The price of the toy on dollars is 5.22.
Here, we are given that a toy costs 35,000 lndonesian rupiah (Rp).
Further, the conversion rate is-
Rp 1000 = $0.145
Now, if 1000 Rp = $0.145 then 1Rp will be = $0.145/1000
= $0.000145
Thus, we get 1Rp = $0.000145
Now, we need to find how much 36,000 Rp is in dollars.
Since, 1Rp = $0.000145, 36,000 Rp will be = $(0.000145 × 36,000)
= 0.145 × 36
= 145/1000 × 36
36 can be written as- (40 - 4)
= 145 (40-4)/ 1000
= {(145 × 40) - (145 × 4)} / 1000
= (5,800 - 580)/1000
= 5,220/1000
= 5.22
Thus, the price of the toy on dollars is 5.22.
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13. The sum of three consecutive
integers is 48. What is the smallest
number in the group?