The required percent of the coffee left is given as 66.67%.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
24 ounces of coffee Ms. Bobadilla,
And 8 ounces of coffee has been drinking,
Applying the percentage evaluation, in order to calculate the remaining coffee to Ms. Bobadilla.
Percentage of coffee remaining = 24 - 8 / 24 × 100%
Percentage of coffee remaining = 0.6667 × 100%
Percentage of coffee remaining = 66.67%
Thus, the percentage is given as 66.67%.
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Use the figure shown for Exercises 22 and 23.
What is m∠DEG if m∠DFE=70°
The value of ∠ DEG = 20° in the given triangle. The value of b in the given triangle is 22.6.
a) ∠ DEG = ? if ∠DFE = 70°
Here, ∠F = ∠D = 70°
∠G = 90°
Sum of triangle = 180°
∠D + ∠E + ∠G = 180°
70° + 90° + x = 180°
160° + x = 180°
x = 180° - 160°
x = 20°
b) if a = 8 , c =24 then b = ?
∠DGE is right angle. It follows Pythagoras theorem:
What is pythagoras theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.DG² + GE² = DF²
8² + X² = 24²
X² = 576 - 64
X² = 512
X = 22.6
Hence, the value of b in the given triangle is 22.6.
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Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below.
Negative 5 x minus 3.5 greater-than 6.5. Negative 5 x greater-than 10. x greater-than negative 50.
She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol
How to calculate errors did Parul make?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.
We are given
-5x - 3.5>6.5
Since, we have to solve for x
so, we will isolate x on anyone side
step-1:
Add both sides by 3.5
-5x - 3.5+3.5>6.5+3.5
-5x>10
step-2:
Divide both sides by -5
we know that whenever we divide both sides by negative sign , it's inequality gets revered
so, we get
-5x/5<-50/-5
we get
x<10
so,
She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol
The complete question is : Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below. What errors did Parul make? Check all that apply. She added 3.5 to both sides when she should have subtracted. She should have divided both sides by as her first step. She divided one side by -5 while multiplying the other side by -5. She did not change the > symbol to a < symbol. She used a closed circle instead of an open circle on the number line.
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y=3x-8- here is it’s the right answer
Given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the equation of line as -
y = 3x - 8
The given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
Therefore, given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
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don't deposited $7,000 in an account earning 10% interest compounded annually to the nearest cent how much interest will he earn in 4 years
Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.
Define simple interest.Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows $5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Given
Principal = $7000
Rate = 10%
Time = 4 years
Using simple interest formula,
PRT
7000 × 0.1× 4
2800
Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.
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Answer: 3,248.70
Step-by-step explanation: You can use this formula when working with compound interest:
B=p(1+r)t
In this formula, B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
The interest is the balance minus the principal.
solve
Write the rate as a decimal.
10%=0.10
Calculate the balance.
B
= p(1+r)t
= $7,000(1+0.10)4
= $7,000(1.10)4
= $7,000(1.4641)
= $10,248.70
Now use this to find the interest, which is the balance minus the principal.
$10,248.70–$7,000=$3,248.70
The interest will be $3,248.70.
Given the function h(x)= 2x+3/4x-5 find h⁻¹(x)
The inverse of the rational function h(x) = (2 · x + 3) / (4 · x - 5) is the rational function h⁻¹(x) = (5 · x + 3) / (4 · x - 2).
How to find the inverse of a rational function
In this problem we have the definition of a rational function:
h(x) = (2 · x + 3) / (4 · x - 5)
Of which we must determine the inverse of the rational function by using algebraic properties:
h⁻¹(x) = f(x)
First, use the following substitution on h(x):
x = h(x)
h⁻¹(x) = x
Second, substitute in the rational equation:
x = [2 · h⁻¹(x) + 3] / [4 · h⁻¹(x) - 5]
Third, clear h⁻¹(x) in the expression by algebraic properties:
x · [4 · h⁻¹(x) - 5] = 2 · h⁻¹(x) + 3
(4 · x - 2) · h⁻¹(x) = 5 · x + 3
h⁻¹(x) = (5 · x + 3) / (4 · x - 2)
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b. An investment worth i costs $10 to withdraw, then the remaining amount is shared
between four people. Suppose each person gets $40. How much was the
investment worth?
Equation:
Solve it:
Answer:
the equation 10 = x - y
Step-by-step explanation:
Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.
We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.
We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.
Therefore, the initial value of the investment was $50.
Thirty students in a chemistry class each completed a particular lab assignment. Gerald and Sharon each collected data from the students to estimate the mean time it took for the class to complete the assignment.
Gerald asked 4 of the students now long eacn one ortem took to complete the assionment and correcuy carculated d fie an time of 38 minutes. Sharon asked 10 different students in the class the same question, and correctly calculated a mean time of 32 minutes
Both Gerald and Sharon claim their calculated mean time for completing the assignment is the better estimate of the actual mean time for the whole class. Which of the following statements best explains who is correct?
Answer:
Step-by-step explanation:
It is likely that Sharon's calculated mean time is the better estimate of the actual mean time for the whole class. This is because she collected data from a larger sample of the class (10 students) than Gerald (4 students). A larger sample size generally results in a more accurate estimate of the population mean.
It is more likely for the mean time calculated by Sharon to be better estimate than that of Gerald.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Given,
Mean time to complete the assignment taken from 4 students by Gerald = 38 minutes.
Mean time to complete the assignment taken from 10 students by Sharon = 32 minutes
Population size = 30 students
When the sample size is more closer to the population size, the sample mean would be more closer to the actual mean.
So Sharon's estimate is a better option.
Hence the estimate value of mean calculated by Sharon is more likely to be closer to the actual mean.
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The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies. Note C D E F G A B Frequency(Hz) 261.6 293.7 329.6 349.2 392.0 440.0 493.9 Determine the ratio of the note B to middle C
Answer:
Step-by-step explanation:
To determine the ratio of the note B to middle C, we can divide the frequency of B by the frequency of C. Using the information provided, the frequency of B is 493.9 Hz and the frequency of C is 261.6 Hz. The ratio of B to C is therefore 493.9 / 261.6, which is approximately equal to 1.89. This means that the note B is approximately 1.89 times higher in pitch than the note C.
Conduct a test at the a=0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling.
Test whether p1>p2. The sample data are x1=119, n1=253, x2=134, and n2=311.
a) The hypothesis are given as follows:
Null: [tex]H_0: p_d = 0[/tex].Alternative: [tex]H_1: p_d > 0[/tex].b) The test statistic is of: z = 0.94.
c) The p-value is of: 0.1736.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that p1 is greater than p2, that is, if the subtraction is of zero, hence:
[tex]H_0: p_d = 0[/tex].
At the alternative hypothesis, it is tested if there is enough evidence that p1 is greater than p2, that is, if the subtraction is greather than zero, hence:
[tex]H_1: p_d > 0[/tex].
What are the mean and the standard error for the distribution of differences?For each sample, the mean and the standard error are given as follows:
[tex]p_1 = \frac{119}{253} = 0.4704, s_1 = \sqrt{\frac{0.4704(0.5296)}{253}} = 0.0314[/tex].[tex]p_2 = \frac{134}{311} = 0.4309, s_1 = \sqrt{\frac{0.4309(0.5691)}{311}} = 0.0281[/tex].Hence, for the distribution of differences, the mean and the standard error are given as follows:
[tex]p_d = p_1 - p_2 = 0.4704 - 0.4309 = 0.0395[/tex][tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0314^2 + 0.0281^2} = 0.0421[/tex]What are the test statistic and the p-value?The test statistic is given by the division of the estimate of the proportion of differences by the standard error, hence:
z = 0.0395/0.0421 = 0.94.
We have a right-tailed test, as we are testing if the mean is greater than a value, with z = 0.94. Hence, looking at the z-table, the p-value is of:
0.1736.
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A pilot flew a jet from City A to City B, a distance of 2400 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 5 h 30 min. What was the speed from City A to City B?
The speed from City A to City B is 873.33 mi/h.
What is the speed, distance and time?
That is speed = distance ÷ time. Or to put it another way, distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.
Let's call the speed from City A to City B x. The speed on the return trip was 1.2x. The total distance traveled was 2400 + 2400 = 4800 mi. The total time taken was 330 minutes, which is 330/60 = 5.5 hours. The average speed is the total distance traveled divided by the total time taken, so:
4800 mi / 5.5 h = 873.33 mi/h
The total speed for both legs of the trip is 873.33 + 873.33 = 1746.66 mi/h
The speed for just one leg of the trip is half of the total speed, so the speed from City A to City B is 1746.66/2 = 873.33 mi/h.
Hence, the speed from City A to City B is 873.33 mi/h.
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Help me pls in math to solve these thank u
Step-by-step explanation:
y = mx + b
m = 3
b = 2
y = 3x + 2
______________________
y = mx + b
m = 1/2
b = -1
y = 1/2x + (-1)
y = 1/2x -1
Discuss the coordinates of a point P(x, y) on a coordinate plane, and how these can be
described by its distance, r, from the origin and the angle made with the positive x-axis.
The distance between any coordinate (x,y) and the origin is given by the equation presented as follows:
D = square root of (x² + y²).
The angle between these coordinates and the positive x-axis is given as follows:
Angle = arctan(y/x).
How to obtain the distance and the angle?The distance between two points on a coordinate line is equivalent to the hypotenuse of a right triangle.
The sides of the triangle are represented by the differences of the x-coordinates and the y-coordinates of each point.
For the origin, the coordinates are (0,0), hence the distance of any point from the origin is given by the equation presented as follows:
D = square root of (x² + y²).
For the angle, we have that:
The opposite side to the angle is the difference between the y-coordinates.The adjacent side to the angle is the difference between the x-coordinates.Hence the tangent is applied, as follows:
tan(Angle) = y/x
Angle = arctan(y/x).
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Mike has $90,000 to invest and can invest in two different funds. He invests some of the money at 5% per year and the rest at 8% per year. How much should mike invest in each fund in order to earn $5220 from both funds per year?
Using a system of equations, Mike should invest $66,000 in investment A and $24,000 in investment B to earn $5,220 from both funds per year.
How are the amounts determined?We can solve a system of equations to determine the amounts that should be invested in each fund to earn the stated amount yearly.
A system of equations is also called simultaneous equations because they can be solved together.
The total investible funds = $90,000
The expected annual earnings = $5,220
The earnings from investment A = 5% or 0.05
The earnings from investment B = 8% or 0.08
Equations:A + B = 90,000 ... Equation 1
0.05A + 0.08B = 5,220 ... Equation 2
Multiply equation 1 by 0.05:
0.05A + 0.05B = 4,500 ... Equation 3
Subtract Equation 3 from Equation 2:
0.05A + 0.08B = 5,220
-0.05A + 0.05B = 4,500
=0.03B = 720
= 24,000 (720/0.03)
B = $24,000
From Equation 1, substitute B = 24,000 to get A:
A + B = 90,000
A + 24,000 = 90,000
= 66,000
A = $66,000
Thus, we can conclude that Mike with $90,000 should invest $66,000 in Investment A earning 5% per year, and $24,000 in Investment B earning 8% annually to earn a total of $5,220 from both funds.
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Write the equation of each parabola in vertex form Vertex=(1,3) Point =(2,5)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\begin{cases} h=1\\ k=3 \end{cases}\implies y=a(x-1)^2 + 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=5 \end{cases} \\\\\\ 5=a(2-1)^2 + 3\implies 2=a(1)^2\implies \cfrac{2}{(1)^2}\implies 2=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 +3 \end{array}} ~\hfill[/tex]
The maximum temperature is: ______________________
Answer:
56.7C
Step-by-step explanation:
The highest temperature on the was 56.7C and it is recorded in United States on 10 July 1913
Supposed that on January 1 you have a balance of $5600 on a credit cars whose APR is 17%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1.
Parts:
A. Calculate your monthly payments.
B. When the card is paid off, how much will you have paid since January 1?
C. What percentage of your total payment from part (b) is interest?
Answer:
A. $510.75
B. $6,129.00
C. 8.63%
Step-by-step explanation:
You want the monthly payments, total amount paid, and fraction going to interest for the payoff of a $5600 credit card balance at an annual rate of 17% interest.
A. PaymentsThe monthly payments can be found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12)) . . . . . P is the principal amount, r is the rate
This formula gives the monthly payment for payoff in 1 year.
A = 5600(0.17/12)/(1 -(1 +0.17/12)^-12) ≈ 510.75
The monthly payment is $510.75.
B. Total paidYou will have made 12 monthly payments of $510.75, for a total of ...
12 × $510.75 = $6,129.00
You will have paid $6,129.00.
C. Fraction to interestThe fraction of your total payoff that goes to interest is ...
(6129 -5600)/6129 = 1 -(5600/6129) ≈ 0.0863 = 8.63%
About 8.63% of your total payment is interest.
__
Additional comment
Spreadsheets and calculator apps can be used to find these values. You need to be careful to specify that payments are made at the end of the month.
The amount to interest is slightly more than half the interest that would be due if the interest rate were used to calculate simple interest. Our answer of 8.63% is slightly higher than 17%/2 = 8.5%, so passes the reasonableness check.
Andrea skip counted using this number line to find the product of 4 and 7
Which division problem in the same fact family could Andrea use to check her work?
A. 0÷4=7
B. 7÷4 = 28
OC. 14÷4 = 7
D. 21+7=4
E. 28+7=4
Andrea could use 28÷7 = 4 this division problem to check her work.
Check one-by-one:
A. 0÷4=7
The answer to 7 divided by 0 is 0. This is due to the fact that dividing a non-zero number by zero is mathematically impossible. See complete response below.
B. 7÷4 = 28
The acronym PEMDAS, which stands for parenthesis, exponents, multiplication and division from left to right, as well as addition and subtraction from left to right, can be used to recall the order of operations.7 * 4 = 28 is the correct value where this value is 1.7
C. 14÷4 = 7
The value of the above is not equated because 3.5 ≠ 7
D. 21÷7 = 4
Where 21÷7 is 3. Hence this is also not a correct answer.
E. 28÷7=4
7 * 4 = 28, which is correct equation.
Hence, Andrea could use 28÷7 = 4 this division problem to check her work.
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an anova procedure is used for data that were obtained from five sample groups each comprised of six observations. the degrees of freedom for the critical value of f are . a. 5 and 26 b. 4 and 29 c. 4 and 25 d. 4 and 30
The correct option 4 and 25; the degrees of freedom for the critical value of f.
Explain the term degrees of freedom?The number of separate bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. It is determined by subtracting the number of constraints from the sample size. The greatest number of logical manner independent variables is, values with the freedom to change—in the data sample is referred to as the degree of freedom.The essential value F's degrees of freedom are (k-1,n-k).
Four sample groups are provided to us, so,
k = 5.
Additionally, we know that each of the five groups has six observations, therefore
n = 5*6
n = 30
The crucial factor F can vary in freedom.
(k-1,n-k)
(5-1, 30 - 5)
(4,25).
Its degrees of freedom again for critical F value are as a result (4,25).
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The height of a model rocket, H(t), is a function of the time since it was
launched, t.
Height (feet)
450-
400-
350-
300-
250-
200-
150-
100
50-
0
0
H(t)
10
30
20
Time (seconds)
What is the domain of H(t)?
40
Step-by-step explanation:
the domain is the interval or set of all valid x- (or input-)values. in our case here t-values.
the graph shows us
0 <= t <= 35
For the given condition on the graph, the domain of the function is
0 ≤ t ≤ 36.
What is function?A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences. A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output.
Here,
The correct answer is option B. 0 ≤ t ≤ 36
To do this question, the main thing is to look at picture.
We know from the graph that this is a quadratic function, So t has to be less than some positive number.
{ if t → -∞, H(t) → -∞, not in the line with the actual situation}
and look at the graph, the point where H(t) equals zero, one is 0 and one is 36.
The domain for the function is 0 ≤ t ≤ 36 for given condition in the graph.
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Find the slope (-2,-9) and (-1,-3)
-3+9. -6
------= ---
-2+3. -1
the answer is 6
Drag each tile to the correct box.
Arrange the numbers as they appear from left to right on a horizontal number line.
The numbers as they appear from left to right on a horizontal number line is Horizontal number line.
This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.
What's the equation of a horizontal line?
Horizontal lines have a slope of 0. Thus, in the slope-intercept equation y = mx + b, m = 0. The equation becomes y = b, where b is the y-coordinate of the y-intercept.
-2.76
-2.57
-2.5
-1.85
-1.58
2.5
2.85
On a number line, we have this horizontal line, meaning it moves left and right, and zero is placed in the middle.
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|-10-2| • 3(2x+7) -25+2y
x=2
y=3
Answer:
377 is answer
Step-by-step explanation:
12.33-25 +6
396-25+6
377
Simplify and state the restrictions on the domain:
Answer:
its the first option explanation is up top
Below is a graph showing the speed in meters/second of a cheetah s seconds after it starts running.
What interpretation can be made from the y-intercept? ____________.
How can the point (3.0, 12) on the graph above be interpreted? ___________.
What is the output value of this graph when the input value is 5.0? _________.
Does the graph above have a constant rate of change? ____________.
The graph in the problem is interpreted as follows
What interpretation can be made from the y-intercept?
the y-intercept shows start the timing started when the cheetah is not running
How can the point (3.0, 12) on the graph above be interpreted? At 3.0 s the cheetah was running at 12 m/s
What is the output value of this graph when the input value is 5.0?
the output is 30
Does the graph above have a constant rate of change?
No, the rate of change varies
What is rate of change?The term "rate of change" describes the rate at which something changes over time.
Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate).
When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant.
The slope is another name for the constant rate of change. The rate of change for linear functions will be constant.
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A garden table and a bench cost $1007 combined. The garden table costs $57 more than the bench. What is the cost of the bench?
Answer:
Below
Step-by-step explanation:
bench + ( bench + 57) = 1007
2 bench = 950
bench = $ 475
Please i need help right now Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work.
Part A:
This data appears to be modeling a geometric sequence because the time to complete each station is increasing by a constant factor. For example, the time to complete station 2 is 4 minutes, which is double the time it took to complete station 1. Similarly, the time to complete station 3 is 8 minutes, which is double the time it took to complete station 2, and so on.
Part B:
To find the time Aurora will take to complete station 5 using a recursive formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 5:
a_5 = a_1 * r^(5-1)
= 2 * 2^4
= 2 * 16
= 32
Therefore, Aurora will take 32 minutes to complete station 5.
Part C:
To find the time Aurora will take to complete station 9 using an explicit formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 9:
a_9 = a_1 * r^(9-1)
= 2 * 2^8
= 2 * 256
= 512
Therefore, Aurora will take 512 minutes to complete station 9.
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A company produces shotgun shells in batches of 350. A sample of 5 is tested from each batch, and if more than one defect is found, the entire batch is tested. (Round your answers to five decimal places.) (a) If 1% of the shells are actually defective and we assume independence, what is the probability of 0 defective shells in the sample?
(b) If 1% of the shells are actually defective and we assume independence, what is the probability of 1 defective shell in the sample?
(c) If 1% of the shells are actually defective and we assume independence, what is the probability of more than 1 defective shell in the sample?
a. The probability of defective shells from the given samples are:
a. Probability of zero defective shells of samples is equal to 0.9510.
b. Probability of one defective shells of samples is equal to 0.04803
c. Probability of more than 1 defective shells of samples is equal to 0.00107.
As given in the question,
Total number of batches = 350
Sample size used to test for each batch 'n' = 5
Actual defective shells (success) 'p' = 1%
= 0.01
Actual non-defective shells ' 1 - p ' = 1 - 0.01
= 0.99
a. Probability of zero defective shells from the given samples is
= ⁵C₀ × ( 0.01 )⁰ × (0.99)⁵⁻⁰
= [ (5!)/(5-0)!0! ] × 1 × ( 0.99)⁵
= 0.9510
b. Probability of 1 defective shells from the given samples is
= ⁵C₁ × ( 0.01 )¹ × (0.99)⁵⁻¹
= [ (5!)/(5-1)!1! ] × 0.01 × ( 0.99)⁴
= 5 × 0.01 × 0.9606
=0.04803
c. Probability of more than 1 defective shells from the given samples is
= P(2) + P(3) + P(4) + P(5)
= ⁵C₂ × ( 0.01 )²× (0.99)⁵⁻² + ⁵C₃ × ( 0.01 )³ × (0.99)⁵⁻³ + ⁵C₄× ( 0.01 )⁴ × (0.99)⁵⁻⁴+ ⁵C₅× ( 0.01 )⁵× (0.99)⁵⁻⁵
= 0.00097 + 0.000098 +0.000000044 +0.0000000001
=0.00107
Therefore, the probability of following conditions are as follow:
a. Probability of zero defective shells of samples is equal to 0.9510.
b. Probability of one defective shells of samples is equal to 0.04803
c. Probability of more than 1 defective shells of samples is equal to 0.00107.
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QR is a midsegment of triangle BCD. Solve for the value of x.
The value of x is 3 units.
What is the mid-point segment of the triangle?
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
We have,
In ΔBCD
QR = x - 2 units
BD = x + 7 units
A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
Mid-point segment of the triangle:
QR = 1/2(BD) .............(1)
x - 2 = 1/2(x + 7)
2(x - 2) = x + 7
2x - 4 = x + 7
2x - x = 7 - 4
x = 3
Hence, the value of x is 3 units.
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the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday. The high temperature was 21.3 C. What is the difference between the low temperature and the high temperature on Tuesday?
The difference between the low temperature and the high temperature on Tuesday is -1.1°C.
What is the difference between the low temperature and the high temperature on Tuesday?From the information given, the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday.
Therefore, the temperature on Tuesday will be:
= 1 1/4(14)
= 17.5
The difference in the temperature will then be:
= 16.4°C - 17.5°C
= -1.1°C.
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[tex]\int\limits x^3 \sqrt{x^2 +1} dx[/tex]
The solution to the given integration problem is;
[tex]\frac{[(x^{2} + 1)x^{\frac{3}{2} } *(3x^2 - 2)]}{15} + C[/tex]
How to evaluate an Integral?We want to integrate the function x³[√(x² + 1)dx]
This is expressed as;
∫x³[√(x² + 1)dx]
Preparing for substitution we have;
∫2x[x²√(x² + 1)/2dx]
Make u = x²
du/dx = 2x
dx = (1/2x) du
Thus, we now have;
¹/₂∫u√(u + 1)du
¹/₂∫(u^(3/2) - √u) du
Applying power rule and solving this gives us;
[tex]\frac{(x^2 + 1)x^{\frac{5}{2} } }{5} - \frac{(x^2 + 1)x^{\frac{3}{2} } }{3}[/tex]
= [(x² + 1)^(3/2) (3x² - 2)]/15 + C
Thus, that is the solution of solving the integration problem.
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