Answer:
(a)[tex]0.15731[/tex]
(b)0.02275
Step-by-step explanation:
We are given that
Mean=0
Standard deviation=0.5 g
True weight of a sample=166 g
Let X denote the normal random variable with mean =166+0=166
(a)
P(166.5<X<167.5)
=[tex]P(\frac{166.5-166}{0.5}<\frac{X-\mu}{\sigma}<\frac{167.5-166}{0.5})[/tex]
=[tex]P(1<Z<3)[/tex]
=[tex]P(Z<3)-P(Z<1)[/tex]
[tex]=0.99865-0.84134[/tex]
[tex]=0.15731[/tex]
(b)
[tex]P(X>167)=P(Z>\frac{167-166}{0.5})[/tex]
[tex]=P(Z>2)[/tex]
[tex]=1-P(Z<2)[/tex]
[tex]=1-0.97725[/tex]
[tex]=0.02275[/tex]
XYZ ∆ where Angle Y =90° , XZ= 14 m , XY = 6 m . Find YZ ?
( Show all your workings )
[tex]4 \sqrt{10} [/tex]
Step-by-step explanation:
Use Pythagoras
A^2 + b^2 = c^2
(6)^2 + b^2 = (14)^2
36 + b^2 = 196
B^2 =160
[tex]b = \sqrt{160} [/tex]
[tex]b = 4 \sqrt{10} [/tex]
PLEASE HELP
Fill in the blanks. Then, choose the property of addition you used.
(a)3+_= 3
(Choose one)
(b)4 + 7) + _1 = 4 + (7 + 3)
(Choose one)
(c)9+8 = 8+_
(Choose one)
Fill in the blank and choose a property
Answer:
3+ 0 = 3
( 4+7) + 3.0 × 1 = 4 + (7+3)
9 + 8 = 8 + 9
If a silver alloy that costs $6.75 an ounce is
going to be mixed with 55 ounces of a silver
alloy that costs $10 an ounce to make a
mixture that costs $8 an ounce, how many
ounces of the $6.75 an ounce alloy must be
used?
9514 1404 393
Answer:
88 ounces
Step-by-step explanation:
Let x represent the number of ounces of the less expensive alloy in the mix. Then the cost of the mix will be ...
6.75x +10(55) = 8(55+x)
110 = 1.25x . . . . . . subtract 440+6.75x
88 = x . . . . . . . . divide by 1.25
88 ounces of $6.75/oz silver must be used.
find the angle between following linesroot 3x-y=2,x-root 3y=7
Answer:
where I find? where is the directions
Find a vector equation and parametric equations for the line The line through the point (2, 2.4, 3.5) and parallel to the vector 3i 1 2j 2 k
Answer:
The vector equation
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Step-by-step explanation:
Given
[tex]Point = (2,2.4,3.5)[/tex]
[tex]Vector = 3i + 2j - k[/tex]
Required
The vector equation
First, we calculate the position vector of the point.
This is represented as:
[tex]r_0 = 2i + 2.4j + 3.5k[/tex]
The vector equation is then calculated as:
[tex]r = r_o + t * Vector[/tex]
[tex]r = 2i + 2.4j + 3.5k + t * (3i + 2j - k)[/tex]
Open bracket
[tex]r = 2i + 2.4j + 3.5k + 3ti + 2tj - tk[/tex]
Collect like terms
[tex]r = 2i + 3ti+ 2.4j + 2tj+ 3.5k - tk[/tex]
Factorize
[tex]r = (2 + 3t)i+ (2.4 + 2t)j+ (3.5 - t)k[/tex]
The parametric equation is represented as:
[tex]x = x_0 + at\\y = y_0 + bt\\z = z_0 + ct[/tex]
Where
[tex]r = (x_0 + at)i +(y_0 + bt)j+(z_0 + ct)k[/tex]
By comparison:
[tex]x = 2 + 3t\\y = 2.4 + 2t\\z = 3.5-t[/tex]
Write an equation that expresses the following relationship.
d varies directly with w and inversely with p.
In your equation, use k as the constant of proportionality.
9514 1404 393
Answer:
d = kw/p
Step-by-step explanation:
When d varies directly with w, the equation is ...
d = kw
When d varies inversely with p, the equation is ...
d = k/p
When d does both, the equation is ...
d = kw/p
All I need is number two
Given the following numbers: a = 12500000 b = 0.00125 c = 1120000
Calculate (ab)÷ (c) and write the answer in standard form. (2.5 marks)
d) Express the interval (-1.5, 4] as an inequality and then graph the interval.
Answer:
Answer to the following question is as follows.
Step-by-step explanation:
Given:
a = 12500000
b = 0.00125
c = 1120000
Calculate (ab) ÷ (c)
Given:
d) Express the interval [-1.5, 4] as an inequality and then graph
Computation:
(ab) ÷ (c) = (a)(b) / c
(ab) ÷ (c) = (12500000)(0.00125) / (1120000)
(ab) ÷ (c) = 25 / 1,792
Express the interval [-1.5, 4]
{x : -1.5 < x ≤ 4}
Graph.
._________._________.
-1.5 0 4
Find the value of z, the measure of the subtended arc.
86°
47°
188°
94°
Answer:
188 degrees
Step-by-step explanation:
The measure of the arc is the center angle, that is double of the circumference one
94 * 2 = 188 degrees
What is the slope of the line that passes through (17, −13) and (17, 8)?
(also can you try to explain ive been having trouble with these types of question)
Answer:
Slope is undefined. Line parallel to y-axis.
Step-by-step explanation:
By Analytic Geometry, we can determine the slope of a line by knowing two distinct lines and using the definition of secant line:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (1)
Where:
[tex](x_{1}, y_{1})[/tex] - Coordinates of the initial point.
[tex](x_{2}, y_{2})[/tex] - Coordinates of the final point.
[tex]m[/tex] - Slope.
If we know that [tex](x_{1}, y_{1}) = (17, -13)[/tex] and [tex](x_{2}, y_{2}) = (17, 8)[/tex], then the slope of the line is:
[tex]m = \frac{8-(-13)}{17-17}[/tex]
[tex]m = \frac{21}{0}[/tex]
The slope is undefined, which means that line is parallel to y-axis.
A die is rolled 5 times and a 5 or 6 is considered a success. Find the peobability of no success
Answer:
0.1317 = 13.17% probability of no successes.
Step-by-step explanation:
For each toss, there are only two possible outcomes. Either there is a success, or there is not. The probability of a success on a toss is independent of any other toss, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A die is rolled 5 times.
This means that [tex]n = 5[/tex]
5 or 6 is considered a success.
2 out of 6 sides are successes, so:
[tex]p = \frac{2}{6} = 0.3333[/tex]
Find the probability of no success:
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.3333)^{0}.(0.6667)^{5} = 0.1317[/tex]
0.1317 = 13.17% probability of no successes.
Which of the following intergers is least -5+(-2)
Answer:
I guess the question is incomplete
Lisa bought a house The value of the house increased by 1.5% each year for 2 years. At the end of 2 years, the value of the house was £123,627. Work out the value of the house when Lisa bought it.
Answer:
$370,881
Step-by-step explanation:
firstly we we multiply 1,5% by 2yrs. the answer we get is 3,0%. we then multiply 3 % by $123,627 and get $370,881
If Lisa bought a house The value of the house increased by 1.5% each year for 2 years. The value of the house was £123,627. The initial amount of the house is 95120.7.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
Lisa bought a house The value of the house increased by 1.5% each year for 2 years
By the end of 2 years, the value of the house was £123,627.
A=P(1+rt)
A is the final amount,
r is rate of interest
t is the time
P is principle amount.
123,627=P(1+1.5/100 (2))
123657=P(1+0.15(2))
123657=P(1+0.3)
123657=1.3P
Divide both sides by 1.3
P=95120.7
The initial amount of the house when Lisa bought is 95120.7
To learn more on Percentage click:
https://brainly.com/question/28269290
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The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1)is the number of hours spent studying, and the second independent variable (x2) is the student's GPA
Effects on ACT Scores
Study Hours GPA ACT Score
5 4 27
5 2 18
5 3 18
1 3 20
2 4 21
Step 1 of 2: Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
Step 2 of 2: Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.01 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.
Answer:
Pvalue = 0.1505
y = 0.550x1 + 3.600x2 + 7.300
Step-by-step explanation:
Given the data :
Study Hours GPA ACT Score
5 4 27
5 2 18
5 3 18
1 3 20
2 4 21
Using technology, the Pvalue obtained using the Fratio :
F = MSregression / MSresidual = 30.228571/ 8.190476 = 3.69
The Pvalue for the regression equation is:
Using the Pvalue from Fratio calculator :
F(1, 3), 3.69 = 0.1505
Using the Pvalue approach :
At α = 0.01
Pvalue > α ; Hence, we fail to reject H0 and conclude that ; There is not enough evidence to show that the relationship is statistically significant.
The regression equation :
y = A1x1 + A2x2 +... AnXn
y = 0.550x1 + 3.600x2 + 7.300
x1 and x2 are the predictor variables ;
y = predicted variable
She uses a scale of 1 centimeter to 6 inches
the scale drawing of the front face is
Answer:
change inches into centimeter and then divide it
hope this help
A pizza dough recipe calls for 6 1/2 cups of flour. The recipe makes 37 1/2 ounces of dough. How many ounces of dough does 1 cup of flour make?
Answer:
[tex]n = 5\frac{10}{13}[/tex]
Step-by-step explanation:
Given
[tex]Call = 6\frac{1}{2}[/tex] cups
[tex]Recipe = 37\frac{1}{2}[/tex] ounce
Required
Number of ounces per cup (n)
To do this, we simply divide the Recipe by the call
So, we have:
[tex]n = \frac{Recipe}{Call}[/tex]
[tex]n = 37\frac{1}{2} \div 6\frac{1}{2}[/tex]
Express as improper fraction
[tex]n = \frac{75}{2} \div \frac{13}{2}[/tex]
Rewrite as:
[tex]n = \frac{75}{2} * \frac{2}{13}[/tex]
[tex]n = \frac{75}{13}[/tex]
[tex]n = 5\frac{10}{13}[/tex]
Use sigma notation to represent the sum of the first seven terms of the following sequence: −4, −6, −8, …
Answer:
[tex]\sum_{n = 1}^{7} -2 -2n[/tex]
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference of consecutive terms is always the same, called common difference.
The nth term of a sequence is given by:
[tex]a_{n} = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
Sigma notation to represent the sum of the first seven terms
Sum going from the index starting at 1 and finishing at 7, that is:
[tex]\sum_{n = 1}^{7} f(n)[/tex]
Now we have to fund the function, which is given by an arithmetic sequence.
−4, −6, −8,
First term -4, common difference - 6 - (-4) = -6 + 4 = -2, so [tex]a_1 = -4, d = -2[/tex]
Then
[tex]f(n) = a_{n} = a_1 + (n-1)d[/tex]
[tex]f(n) = -4 + (n-1)(-2)[/tex]
[tex]f(n) = -4 - 2n + 2 = -2 - 2n[/tex]
Sigma notation:
Replacing f(n)
[tex]\sum_{n = 1}^{7} -2 -2n[/tex]
Mathematics I need help
You want to buy a $203,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. or a) How much is the loan amount going to be? $ b) What will your monthly payments be if the interest rate is 6%? $ c) What will your monthly payments be if the interest rate is 7%?
Answer:
The amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.
Step-by-step explanation:
Given that you want to buy a $ 203,000 home, and you plan to pay 10% as a down payment, and take out a 30 year loan for the rest, for A) determine how much is the loan amount going to be, B) determine what will your monthly payments be if the interest rate is 6%, and C) determine what will your monthly payments be if the interest rate is 7%, the following calculations must be made:
A) 100 - 10 = 90
203,000 x 0.90 = X
182,700 = X
B) (182,700 x 1.06) / (30 x 12) = X
193,662 / 360 = X
537.95 = X
C) (182,700 x 1.07) / (30 x 12) = X
195,489 / 360 = X
543.025 = X
Therefore, the amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.
I need help asap and a step by step!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
1. subtract 3.5-3.5 and 12.5-3.5
2.You should 4t=9
3. Divide 4 ÷ 4 and 9 ÷ 4
4. You should have t = 2.25
Answer:
t = 2.25
Step-by-step explanation:
4t + 3.5 = 12.5Step 1 :- Divide both side by 3.5.
4t + 3.5 - 3.5 = 12.5 - 3.54t = 9Step 2 :- Divide each side by 4.
4t / 4 = 9 / 4t = 2.25The function c(r)=2r+12.5 represents the cost c, in dollars, of riding r rides
at a carnival. How much does it cost to get into the carnival? *
1 point
A.$2
B. $12.50
C. $14.50
D.r
The first five terms of an arithmetic sequence are shown below:
20, 17, 14, 11, 8, . . .
Let n represent the term number and f(n) the term in the sequence.
Choose a function that represents the sequence.
The answer to this question is f(n) = -3 + 23
Now my question is, how do you find the solution? I was taught the explicit formula is f(n) = m(n) + b, but no matter how many times I've tried to plug in the numbers I cannot seem to get the right answer. Please help me and do show the entire process and the steps.
Answer:
The function represents the sequence is - 3 n + 23.
Step-by-step explanation:
20. 17, 14, 11, 8,......
Here, the first term is
a = 20
Common difference, d = -3
Let the nth term is Tn.
Tn = a + (n -1) d
Tn = 20 + (n -1) x (-3)
Tn = 20 - 3 n + 3
Tn = 23 - 3 n = - 3 n + 23
So, the function represents the sequence is - 3 n + 23.
Answer:
Y'all know what it is already, but I want points, so: f(n) = -3n + 23
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
find the HCF by prime factorization method 60 and 75
HCF=15
Hope it helps you...
Omgg please help right now
Answer:
64in^3
Step-by-step explanation:
6×3 = 18
18×2 = 36
4×7 = 28
36+28 = 64
Hope this helps! :)
If 2x^2 + 3x + 3 = Kx - K has real roots, find the possible values of k.
Answer:
Step-by-step explanation:
Dd
A confided aquifer has a piezometric height of 30 feet before being pumped. The well is then pumped at 250 gallons/day for a very long time and results in a drawdown of 10 feet at the well. If the transmissivity in the aquifer is 10.0 ft2/day and the radius of the well is 0.5 feet, estimate the drawdown in feet for a well 50 feet away
Answer:
[tex]d_2=-8.32ft[/tex]
Step-by-step explanation:
From the question we are told that:
Height of first draw down [tex]h=30[/tex]
Pump Discharge [tex]Q=250gallons/day[/tex]
Well 1 depth [tex]d_1=10ft[/tex]
Transmissivity[tex]\=T 10.0 ft2/day[/tex]
Radius[tex]r=0.5[/tex]
Well 2 depth [tex]d_2=50ft[/tex]
Generally the Thiem's equation for Discharge is mathematically given by
[tex]Q=\frac{2\piT(h_2-h_1)}{ln(\frac{r_2}{r_1})}[/tex]
[tex]250=\frac{2*\pi 10 (10-d_2)}{ln(\frac{50}{0.5})}[/tex]
[tex]1151.293=2*\pi 10 (10-d_2)[/tex]
[tex]d_2=-8.32ft[/tex]
The function f is defined by f(x)=2x+5/x+4 find f (3x)
Answer:
[tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{2x + 5}{x + 4}[/tex]
Step 2: Find
Substitute in x [Function f(x)]: [tex]\displaystyle f(3x) = \frac{2(3x) + 5}{3x + 4}[/tex]Simplify: [tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]How much do I need to subtract from 67/10 to make 6
Answer:
0.7
Step-by-step explanation:
67/10 is the same as 6.7 when you subtract the 0.7 you will remain with 6
Factorize 5b2-11b+6=0
Answer:
5b^2-(5+6)b+6=0
5b^2-5b-6b+6=0
5b(b-1)-6(b-1)=0
(5b-6)(b-1)=0
either
(5b-1)=0
5b=1
b=1/5
or
b-1=0
b=1
Step-by-step explanation:
firstly find out the mid term factor i e in above qn 11 should be break down so that its multiple should be coefficient of b and constant and additiqn should be equals to 11 .so we find out 5 and 6