The value of c for a standard normal distribution, P(z < c) = 0. 9663 is 0.47.
What is standard normal distribution?
The standard normal distribution table gives the probability of a regularly distributed random variable Z, whose mean is equivalent to 0 and difference equal to 1, is not exactly or equal to z. The normal distribution is a persistent probability distribution.
What is z score?
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by
z = (x - μ)/σ
Where x is the raw score, μ is the mean and σ is the standard deviation.
Given that P(z < c) = 0. 9663; hence:
From the normal distribution table, c = 0.47
The value of c for a standard normal distribution, P(z < c) = 0. 9663 is 0.47.
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The graduation rate of a local high school is growing at a rate which can be estimated by thefollowing linear model, where y represents the graduation rate, as a percentage, x yearsafter2017.y = 74.18 +1.57%Use the model to predict the first year in which the school will exceed a 90% graduation rate.
Problem
The graduation rate of a local high school is growing at a rate which can be estimated by the
following linear model, where y represents the graduation rate, as a percentage, x years
after
2017.
y = 74.18 +1.57x%
Use the model to predict the first year in which the school will exceed a 90% graduation rate.
Solution
For this case we want to find where y>90
So then we can do the following:
74.18 + 1.57 x > 90
1.57 x> 90-74.18
1.57 x > 15.82
And dividing by 1.57 we got:
x > 10.076
So then approximately after 2027 they would have a graduation rate higher than 90%
Find the value of x which optimises the total surface area of the box, and showthat it minimises the total surface area.
Solution:
Given data:
Let the width of the box be
[tex]=x[/tex]The volume of the box is
[tex]V_{\text{box}}=400\operatorname{cm}[/tex]The height of the box is
[tex]=h[/tex]Let the length of the box be
[tex]=l[/tex]The length is four times the width of the base, this can be represented below as
[tex]\begin{gathered} l=4\times x \\ l=4x\ldots\ldots\ldots\text{.}(1) \end{gathered}[/tex]Part A:
Show that the height h of the box is given by
[tex]\frac{400}{x^2}[/tex]Concept:
To show that the height is given as above, we will use the volume of the box which is given below as
[tex]\begin{gathered} V_{\text{box}}=\text{length}\times width\times height \\ V_{\text{box}}=l\times x\times h \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V_{\text{box}}=l\times x\times h \\ \text{Substituite equation (1) in the formuka above,} \\ 400=4x\times x\times h \\ 400=4x^2h \\ \text{divide both sides by 4x}^2 \\ \frac{4x^2h}{4x^2}=\frac{400}{4x^2} \\ h=\frac{100}{x^2}(\text{PROVED)} \end{gathered}[/tex]Part B:
Show that the total surface area A of the box is given by
[tex]A=4x^2+\frac{1000}{x}[/tex]Concept:
To prove the above relation, we will use the formula of the area of the box below
[tex]\begin{gathered} A_{\text{box}}=2(lw+lh+wh) \\ \text{where,} \\ l=\text{length}=4x \\ w=\text{width}=x \\ h=\text{height}=\frac{100}{x^2} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{box}}=2(lw+lh+wh) \\ A_{\text{box}}=2(4x\times x+4x\times\frac{100}{x^2}+x\times\frac{100}{x^2}) \end{gathered}[/tex]By simplifying the relation above, we will have
[tex]\begin{gathered} A_{\text{box}}=2(4x\times x+4x\times\frac{100}{x^2}+x\times\frac{100}{x^2}) \\ A_{\text{box}}=2(4x^2+\frac{400}{x}+\frac{100}{x}) \\ A_{\text{box}}=2(4x^2+\frac{500}{x}) \\ A_{\text{box}}=8x^2+\frac{1000}{x} \end{gathered}[/tex]Hence,
The Total surface area of the box will be given below as
[tex]A_{\text{box}}=8x^2+\frac{1000}{x}[/tex]To determine the value of x which optimizes the total surface area of the box, and show
that it minimizes the total surface area, we will have to look for the first derivative of the function above
[tex]\begin{gathered} A_{\text{box}}=8x^2+\frac{1000}{x} \\ \frac{dA}{dx}=\frac{d}{dx}(8x^2+\frac{1000}{x}) \\ \frac{dA}{dx}=16x-\frac{1000}{x^2} \end{gathered}[/tex]To find the value of x, we will substitute the value of dA/dx to be = 0
[tex]\begin{gathered} \frac{dA}{dx}=0 \\ 16x-\frac{1000}{x^2}=0 \\ 16x=\frac{1000}{x^2} \\ \frac{16x^3}{16}=\frac{1000}{16} \\ x^3=62.5 \\ x=\sqrt[3]{62.5} \end{gathered}[/tex]To show the minimum value of x, we will have to look for the second derivative
[tex]\frac{d^2A^{}}{dx^2}[/tex][tex]undefined[/tex](Please help. Will be marked brainliest) Simplify the expression on the left and write your simplication in the first box below. After you submit your answer, the correct simplified expression will appear.
Then, in the second box, evaluate the simplified expression if:
x = -1 and y = 6
Answer:
Step-by-step explanation: x to the 2nd power −xy−5x−4
Help me plssssssss it’s so hard
How do you turn 8 1/3% into a proper fraction?
Answer:
multiply 3 with 8 and then add 1
25/3
Step-by-step explanation:
Select each answer choices that are correct for the slope of -2
The general equation of a circle is given as
[tex]\begin{gathered} y=mx+c \\ \text{Where,} \\ m=\text{slope} \end{gathered}[/tex]The first equation is given as
[tex]2x+y=10[/tex]Making y the subject of the formula and then comparing coefficient
Subtract 2x from both sides
[tex]\begin{gathered} 2x+y=10 \\ 2x-2x+y=10-2x \\ y=-2x+10 \\ \text{slope}=-2 \end{gathered}[/tex]The second equation is given as
[tex]-2x+y=8[/tex]Add 2x to both sides and compare coefficients
[tex]\begin{gathered} -2x+y=8 \\ -2x+2x+y=8+2x \\ y=2x+8 \\ \text{slope}=2 \end{gathered}[/tex]The third equation is given as
[tex]\begin{gathered} x=-2 \\ \end{gathered}[/tex]The equation above is a vertical line and hence, the slope is undefined
The fourth equation is given as
[tex]y=-2[/tex]The equation above is a horizontal line and as such,the slope is zero
Considering the graph of the equation of the line attached below
Bringing out coordinates from the graph, we will have
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(0,0) \\ (x_2,y_2)\Rightarrow(-10,5) \end{gathered}[/tex]The slope of a line passing through points (x1,y1) and (x2,y2) is calculated using the formula below
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]By substituting the values, we will have
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-0}{-10-0} \\ m=\frac{5}{-10} \\ m=-\frac{1}{2} \end{gathered}[/tex]Here, the slope is = -1/2
Considering the graph of the equation of the line attached below
Bringing out coordinates from the graph, we will have
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(0,0) \\ (x_2,y_2)\Rightarrow(-2,4) \end{gathered}[/tex]The slope of a line passing through points (x1,y1) and (x2,y2) is calculated using the formula below
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]By substituting the values, we will have
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{4-0}{-2-0} \\ m=\frac{4}{-2} \\ m=-2 \end{gathered}[/tex]Here,the slope is = -2
Therefore,
The equation with a slope of -2 is 2x +y =10
while the graph with a slope of -2 is given below
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a dilation with a scale
1
factor of
ios
3
B'
units
D'
A'
What is the length of segment CD?
Step-by-step explanation:
that simply means that A'B'C'D' was created by multiplying the point coordinates and/or the side lengths of ABCD by 1/3.
C'D' = 2
therefore,
CD = 2 × 1 / 1/3 = 2 × 3 = 6
Every week you buy a lottery ticket in 50 lotteries, in each
of which your chance of winning a prize is 0.01.
(a) Use the Poisson approximation to calculate the probability that you will winat least one prize in a randomly chosen week.
(b) Find the probability that you win at least once in a 4-week period.
(c) Find the probability that it takes exactly 5 weeks to win for the first time.
(a) The probability of winning at least one prize in a randomly chosen week is 0.3935.
(c) The probability that it takes exactly 5 weeks to win for the first time is 0.041.
A lottery ticket is bought every week in 50 lotteries. The chance of winning a prize in each of the lotteries is 0.01.
The Poisson's distribution is given below :
P(X=x) = (e^-λ)(λ^x)/x!
λ = np
λ = 50*0.01 = 0.5
The probability of getting at least one prize is :
P(x≥1) = 1 - P(x<1)
P(x≥1) = 1 - P(x=0)
P(x≥1) = 1 - [(e^-0.5)(0.5^0)/0!]
P(x≥1) = 1 - 0.6065
P(x≥1) = 0.3935
The probability of winning exactly in the fifth week is :
The probability of losing in the first four weeks and winning in the fifth week is :
P = [(e^-0.5)^4]*P(x=1)
P = [(e^-0.5)^4]*(e^-0.5)(0.5)
P = [(e^-0.5)^5]*(0.5)
P = (e^-2.5)*(0.5)
P = 0.041
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Can i change the language to English
Answer:
Yeah you can change the language
Answer:
yes of course you can do it.
Skill plans A Math GA Stan Fifth grade > AA.6 Identify trapezoids FZD You hav Select all the trapezoids. Submit
The Trapezoids are the First and the Fourth shape
Identify the angles that each have a measure of 135° 1 2 3 3 4 un 16 135° 00 o 21 O 25 O 22 O 26 23 O 28 O 24
As the lines that cross the vertical line are parallel we can say that the following angles are also 135:
The angles would be: < 2, < 3 and < 6
there are 14 boy and 16 girls in Mr. Allen's class. What is the ratio of girls to the total numbers of students in the class? Write the ratio in 3 ways
Answer:
16/30, 8/15, 24/45
Answer:
8:15
8/15
8 to 15
Step-by-step explanation:
What is the area of this regular octagon that has been divided into eight congruent triangles?A)90 cm2B)360 cm2C)45 cm2D)180 cm2
Given:
One octagon is given
Required:
To calculate the area of regular octagon
Explanation:
Since we have been divided regular octagon into eight congruent triangles
so firstly we calculate area of triangle with base 5 cm and height 9 cm and then gonna multiply this 8 times to calculate the total area
In the first step we are calculating the area of triangle
Use the slope formula to find the slope of a line that passes through M(3, 7) and N(3,-1). m =
the formula of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) is a right point from (x1,y1)
on this case the points are the same distance, so we can use any order
[tex]\begin{gathered} m=\frac{-1-7}{3-3} \\ \\ m=\frac{-8}{0} \end{gathered}[/tex]the slope cannot be calculated because the division between 0 dosnt exist, and the line is a vertical line x=3
the line is
Change the expression to an equivalent expression in radical notation. Assume all variables are positive
Take into account that tany expression of the form f(x)^m/n, can be expressed as follow:
[tex]f(x)^{\frac{m}{n}}=\sqrt[n]{f(x)^m}[/tex]then, for the expression (4y)^2/5, you have:
[tex](4y)^{\frac{2}{5}}=\sqrt[5]{(4y})^{2}[/tex]
9. On your paper, solve the inequality & answer it below. For or 2 signs,
copy and paste into your answer. ENTER ANSWER WITH NO SPACES.
Format: x<5 If the answer is no solution, write NS. If the answer is infinitely
many solutions, write IMS.
4x + 2(x -
2(x - 12) and 6(x + 1) < 10(x + 7)
Jhry
Your answer
Hello,I need help with the following question. 9. Find the domain and range of the function shown.y 4 (-2,2)(2,2) x -5 5-4 If the graph is that of a function, what are the domain and range of the function? Select the correct choice below and fill in any answer boxes within your choice.A. The domain is . The range is . (Type your answers in interval notation.)B. The graph is not a function.A screenshot is posted below
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
A.
From the graph, we can conclude:
The domain is:
[tex](-\infty,\infty)[/tex]The range is:
[tex](-\infty,2\rbrack[/tex]B.
A function is a specific type of relation in which each input value has one and only one output value. Therefore, this graph represents a function
What is the slope of the line passing through the points (-1, 7) and (4, - 1)?
Answer:
− 8/5
Step-by-step explanation:
The base of a triangle exceeds the height by 3 yards. If the area is 65 square yards, find the length of the base and the height of the triangle.
The length of the base is 13 yards and the height of the triangle is 10 yards.
Let h = ht of the triangle
let (h + 3) = base of triangle
A = (1/2)bh is the formula for the area of a triangle
65 = (1/2) (h + 3)h
130 = [tex]h^2[/tex] + 3h
[tex]h^2[/tex] + 3h - 130 = 0
(h + 13)(h - 10) = 0
h = -13, h = 10
Height = 10 yards, base = 13 yards
What is geometry ?
Geometry is one of the oldest branches of mathematics, along with arithmetic. It concerns the properties of space, like the distance, shape, size and relative position of figures. A mathematician who works in geometry is called a geometer.
Three geometries
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3. Choose the type of variation that relates the variables in the table.хy512.14.23.57combined variationjoint variationdirect variationinverse variation
Answer:
Inverse variation
Step-by-step explanation:
An inverse variation is when y varies inversely as x if there is some nonzero constant k such that, xy=k or y=k/x.
For Inverse variation equations, you say that y varies inversely as x as we can see in the table above.
Bob deposits $5000 at the end of each year in an ordinary annuity paying 12% interest compounded annually. Find the amount he will have on deposit after 7
years. Round to the nearest cent.
The amount that Bob will have on deposit after seven years is
$ 313,742,585,000.
What is compound interest and how is it calculated?
Interest that is added to a loan or deposit sum is known as compound interest. The interest calculated on the principle and the interest accrued over the prior period is known as compound interest. It differs from simple interest in that simple interest does not take the principal into account when calculating the interest for the following month. In math, compound interest is typically represented by the letter C.I.
Mathematically, the amount A after the compound interest is imposed can be calculated as:
Amount, A = P [1 + (r/t)]ⁿ, where P = principal, r = rate of interest, t = number of times interest is compounded per year, n = time in years.
Given, the principal Bob shall deposit = P = $ 5000
Rate of interest paid to Bob in percentage = r =12
Number of times interest is compounded per year = t = 1
Time of deposit in years = n = 7
Let the amount that Bob will have on deposit after seven years be = A
Substituting all the given values in the formula established in the literature part, we get,
A = 5000 [1 + (12/1)]⁷ = 5000*13⁷ = 313,742,585,000
Therefore, the amount that Bob will have on deposit after seven years is $ 313,742,585,000.
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How to get 16 using numbers 6, 9, 2, 2
(can be -16 or 16)
The expression that gives a solution of 16 using the numbers is 6 + 9 + 2/2
How to get a solution of 16?From the question, we have the following parameters that can be used in our computation:
Solution = 16
Numbers to use = 6, 9, 2, 2
There are no straight ways to solve this question
So, we make use of the trial-by-error
This trial-by-error method would be done mostly off this worksheet
After several trials, we have the following expression
6 + 9 + 2/2
When the above equation is solved, we have
6 + 9 + 2/2 = 16
Hence, to get a solution of 16 we can use the equation 6 + 9 + 2/2
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The histogram below shows the number of children per student in one section of MAT110 during the spring semester of 2015. (*If you can't see the histogram below, click on the attached pdf to view.) MAT 110-002 students, Spring 2015 12. 10 Frequency 2 O 2 3 Number of children
mean = (12 + 4 + 3 + 2 + 0 + 1)/6 = 3.6666
Describe the complement of a given event77% of a persons credit card purchases are $50 a more
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sets
[tex]77\%\text{ of a person's credit card purchases are \$50 and more}[/tex]STEP 2: find the complement
The complement will be the percentage that cannot purchase $50 and more.
Since percentages equal 100, therefore the complement will be:
[tex]100\%-77\%=23\%[/tex]Hence, the answer in % is given as 23
A grain silo has a cylindrical shape. Its radius is 9.5 ft, and its height is 43 ft. What is the volume of the silo?
Use the value 3.14 for I, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Check
9.5 ft
43 ft
Answer:
13487 ft³
Step-by-step explanation:
Volume of a Cylinder: 2πr²*h
π = 3.14
r = 9 ft
h = 53 ft
Volume = 2(3.14)(9)²*53 = 13486.86 ft³
Rounded to nearest whole number
Volume of the Cylindrical Water tank is 13487 ft³
●
Set up and solve a proportion to answer this question:
If 2 ft. = 0.6096 m, then 675 m≈
feet. Round to the nearest foot.
675m=2224.619 feet by using the concept of proportion that states when two ratios are equal, they are said to be in proportion.
For If 2 ft. = 0.6096 m.What is proportion?When two ratios are equal, they are said to be in proportion. For instance, the time it takes a train to travel 50 kilometers per hour is equal to the time it needs to travel 250 kilometers in 5 hours. e.g., 250km/5 hours at 50 km/h.What is the ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.Now, if 2 ft. = 0.6096 m, then 675 m≈feet.
let it be x ft.2/0.6069=x/675(2/0.6069)*675≈2224.419 feetRounding off to nearest feet=2224.42 ft
Using the proportion concept that states, when two ratios are equal, they are said to be in proportion., 675 m can be converted to 2224.619 feet if 2 feet equal 0.6096 meters.
Therefore, 675m=2224.619 feet by using the concept of proportion that states when two ratios are equal, they are said to be in proportion.
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A student ran a distance of 3 1/2 miles each day for 5 days. Then the student ran a distance of 4 1/4 miles eah day for the next 5 days. What
was the total distance in miles the student ran during these 10 days?
Answer:
3 1/2 x 5 = 17.5
4 1/2 x 5 = 22.5
17.5 + 22.5 = 40
The student ran 40 miles in those 10 days.
Answer:
38.75 or 38 3/4
Step-by-step explanation:
3 1/2 * 5 = 17.5
4 1/4 * 5 = 21.25
17.5 + 21.25 = 38.75
Graph the inequality: 24x+20y<24
The given inequality is:
24x + 20y < 24
Let x = 0
24(0) + 20y < 24
20y < 24
y < 24/20
y < 1.2
Let y = 0
24x + 20(0) < 24
24x < 24
x < 24/24
x < 1
Considering the points:
For y = 0, x < 1
For x = 0, y < 1.2
The graph of the inequality is plotted below
James and lin got married and got new jobs. Lin earns $3100 more per year than James. Together they earn $82,000 How much does each of them earn per year?
James and lin got married and got new jobs. Lin earns $3100 more per year than James. Together they earn $82,000 How much does each of them earn per year?
Let
x ----> amount earned by James
y ----> amount earned by Lin
we have
x+y=82,000 -----> equation A
y=x+3,100 -----> equation B
solve the system
substitute equation B in equation A
x+(x+3,100)=82,000
2x+3,100=82,000
2x=82,000-3,100
2x=78,900
x=39,450
Find the value of y
y=39,450+3,100
y=42,550
therefore
amount earned by James is $39,450amount earned by Lin is $42,550Find the weighted mean. Round your answer to the nearest tenth. Deliveries Each Week 2 4 6 8 Frequency 3 7 5 2 Weighted mean =
Given:
Deliveries each week: 2 4 6 8
Frequency: 3 7 5 2
Let's use the deliveries each week as the weighting.
We have:
Deliveries x Frequency:
[tex]\begin{gathered} 2\ast3\text{ + 4}\ast7\text{ + 6}\ast5\text{ + 8}\ast2\text{ } \\ =\text{ 6 + 28 + 30 + 16 = 80} \end{gathered}[/tex]Now, add up the number of deliveries each week:
2 + 4 + 6 + 8 = 20
To find the weighted mean, we have:
[tex]\text{Weighted mean = }\frac{80}{20}=\text{ 4}[/tex]Therefore, the weighted mean is 4
ANSWER:
Weighted mean = 4
