Using the normal distribution, it is found that 495 readings fall within 5.15cm of the mean value.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
Mean of 5m, hence [tex]\mu = 5[/tex].Standard deviation of 2 cm, hence [tex]\sigma = 0.02[/tex]To find the proportion of readings that fall within 5.15cm of the mean value, first we need to find the following z-score:
[tex]z = \frac{0.0515}{0.02}[/tex]
[tex]z = 2.575[/tex]
The proportion is P(|z| < 2.575), which is the p-value of z = 2.575 subtracted by the p-value of z = -2.575.
Looking at the z-table, z = -2.575 has a p-value of 0.005, and z = 2.575 has a p-value of 0.995.
0.995 - 0.05 = 0.99
Out of 500 measurements:
(0.99)500 = 495
495 readings fall within 5.15cm of the mean value.
A similar problem is given at https://brainly.com/question/24663213
Find the indefinite integral|(12x+5)dx
[tex]\int {12x+5} \, dx[/tex]
For this problem, let's first apply the intergral sum rule.
[tex]\int {12x+5} \, dx = \int{12x} \, dx + \int{5}x \,dx[/tex]
Then, we'll use the reverse power rule on each of these integrals.
[tex]\int{12x} \,dx = 6x^2+C[/tex]
[tex]\int{5} \,dx = 5x+C[/tex]
So the indefinite integral of [tex]\int{12x+5} \,dx[/tex] is [tex]6x^2+5x+C[/tex].
Remember that we need our constant of integration, [tex]C[/tex], because of if we take the derivative of a constant, it'll be 0.
Hope this helps!
Hi there!
[tex]\int\limits {12x+5} \, dx[/tex]
Recall the following rules:
[tex]\int\limits {x^n} \, dx = \frac{x^{n+1}}{n+1}[/tex]
Use this rule to evaluate. Remember to include the constant:
[tex]\int\limits {12x+5} \, dx = \frac{12x^{1+1}}{1+1} + 5x +C[/tex]
[tex]\int\limits {12x+5} \, dx = 6x^2 + 5x + C[/tex]
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You buy clothing at a sale. You buy a sweater at
7
10
of its original price of $35. Answer each question and show all your work.
a. How much money did you spend?
b. How much money did you save?
c. What fraction of the total original price did you save?
The amount that will be spent is $24.50, the amount saved will be $10.50, and the percentage saved will be 30%.
The amount that will be spent will be:
= 7/10 × $35 = $24.50
The amount that will be saved will be:
= $35 - $24.50 = $10.50
The fraction of the original price that is saved will be:
= 10.50/35 × 100
= 30%
Read related link on:
https://brainly.com/question/25763817
work out the area of this quarter circle take p2b 3.14 to and read and other digits given by a calculator
Answer:
Step-by-step explanation:
area of a full circle is A = πr²
so a quarter of a circle area is A = πr²/4
A = 3.142(7²)/4
A = 38.4895 cm² picture answer
Using π = 3.14 results in
A = 3.14(7²)/4
A = 38.465 cm² written question answer
For comparison purposes,
Carrying the precision of π into many more significant digits results in
A = 38.484510006474...cm²
What does ± indicate when its used like 2±1?
Answer:
it is in quadratic equation meaning you use Plus or minus
Answer:
I is both the plus and minus sign so and 2+1 and subtract 2-1 both answers are the answer
Step-by-step explanation:
The plus–minus sign, ±, is a mathematical symbol with multiple meanings. In mathematics, it generally indicates a choice of exactly two possible values, one of which is obtained through addition and the other through subtraction.
The sign may also represent an inclusive range of values that a reading might have.
An object is dropped from a height of 288 feet. The equation, - 16t ^ 2 + 288t = h(t) represents the height, hof the object after tseconds. How long does it take the object to the ground?
0 seconds
16 seconds
18 seconds
88 seconds
18 seconds
Step-by-step explanation:
The object will reach the ground when its height h(t) = 0. Therefore, we can write
[tex]h(t) = 288t - 16t^2 = 0 \Rightarrow 16t^2 = 288t[/tex]
Solving for t, we get
[tex]16t = 288 \Rightarrow t = 18\:\text{s}[/tex]
H . E . L . P
this work is due tommorow, and i have absolutely no idea what the answer is. please help me if you can !
( don’t comment for points. )
Answer:
A) 25
B) 64
Step-by-step explanation:
Hope this helps :))
Step-by-step explanation:
x= 5
a) 5² = 5×5 =25
b) (5+3)² = 8²
= 8 × 8
= 64
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:
y=2x +5
Step-by-step explanation:
so 2 goes in the first blank and 5 goes in the second
Hope this helps!❆
The number of blocks has 9 in the ones place. The number in the hundreds place is one more than the number in tens place. Those two numbers equal 11. how many blocks are there?
Answer:
659
Step-by-step explanation:
11-1=10;10/2=5;5+1=6;6+5=11
the hundreds place has 6
the tens place has 5
the ones place has 9
659
Ratios:
The number of Anna's baseball cards is 3/4 the number of Patricia's cards. If Anna gives half of her cards to Patricia, what will be the ratio of Anna's cards to Patricia's cards?
Answer:
3/11
Step-by-step explanation:
thank you for the poits
intergrate, e^-x (e^-½) with limits from 0 to π
Answer:
Step-by-step explanation:
First off, your written problem doesn't match the one you typed. The written problem doesn't have a solution, so I'm going with the typed one (cuz I can solve that one!).
Begin by noting that [tex]e^{-\frac{1}{2}[/tex] is a constant and can be pulled out front of the integration symbol:
[tex]e^{-\frac{1}{2}}\int\limits^\pi _0 {e^{-x}} \, dx[/tex]
Choose u = -x, so du/dx = -1 and -du = dx. Put that - out front along with what's already there to get:
[tex]-e^{-\frac{1}{2}}\int\limits^\pi _0 {e^{-u}} \, du[/tex]
The antiderivative of e^-u is e^-u, so putting it all together and applying the First Fundamental Theorem of Calculus:
[tex]-e^{-\frac{1}{2}}(e^{-\pi }-e^0)[/tex] which simplifies to
[tex]-e^{-\frac{1}{2}}(e^{-\pi }-1)[/tex] which simplifies to
[tex]-e^{-\pi -\frac{1}{2}}+e^{-\frac{1}{2}}[/tex] which has a decimal equivalency of .5803200934
which is the first question in brainly
Answer:
this question
Step-by-step explanation:
Answer:
The first question was this: https://brainly.com/question/420 ur welcome :)
Step-by-step explanation:
answer fully please //////////
Answer:
yes,the distributive property can be rewrite as i have given below:
(8×8)-(8×4)
The figure below shows the graph of function f with domain [-1,1] and range [0,1].
The domain are the possible input while the range are the possible output
of a function.
(a) The domain = [-√2, √2], the range = [0, 2](b) The domain = [-1, 1], the range = [0, 1](c) The domain = [-1, 1], the range = [0, -1](d) The domain = [0, 2], the range = [0, 1](e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
Learn more here:
https://brainly.com/question/20391090
6 Cyclist A travels 55 km in 2 hours and 20 minutes.
Cyclist B travels 135 km in 5 hours and 36 minutes.
Which cyclist is travelling faster?
cyclist a speed is d = v × t
so you can find velocity of a and b.
then compare them both.
45 cows can graze a field in 13 days. How many cows will graze the same field in 9 days
Answer:
65 cows
Step-by-step explanation:
Inverse rule of three
[tex]45-------13\\x -------- 9[/tex]
[tex]x=\frac{(45)(13)}{9}=585/9=65[/tex]
Hope this helps
Rational numbers on the number line
Answers:
A = -5/4B = -0.5C = 2=====================================
Explanation:
The fraction -5/4 converts to -1.25 after using your calculator or long division. It represents the mixed number -1 & 1/4. So we go 1 full unit to the left to arrive at -1, then we move another 1/4 unit to the left to get to point A. That's why point A is located at -5/4 = -1.25 = -1 & 1/4.
Point B is directly midway between 0 and -1, so it must be at -0.5; you can use the midpoint formula.
juan visited a candy store
Answer:
ok lol
Step-by-step explanation:
In the figure below, BD and AC are diameters of circle P.
What is the arc measure of minor arc DC in degrees?
Answer: 19
Step-by-step explanation:
2 lines crossing create 2 pairs of equal angles. The opposite angles are the same. Same goes in a circle.
9514 1404 393
Answer:
arc DC = 19°
Step-by-step explanation:
The acute central angles are vertical angles, so have the same measure. Vertical angles with the same measure intercept arcs with the same measure. The measure of the arc is the measure of the central angle it subtends.
Arc AB = Arc DC = 19°
Use the quadratic formula to find the solution to the quadratic equation given
below.
x2-x* 1-0
D A
1+
14
2
1-IS
X =
D
B. x-
= -2
O c. x = 3
-
-1+
D.x =2 1-O
E.1 4x=
.
OF.x
2
Answer:
x=-1/2
Step-by-step explanation:
using almighty formula
x= -b+or-√b²-4ac/2a
x=-1+ or -√-1+4(1)(1/4) divided by 2(1)
x=-1+ or -√-1+1 divided 2
x=-1+0 divided by 2
x=-1/2
A city dumps plastic shade balls into a reservoir to prevent water from evaporating during a drought. It costs $5760 for 16,000s shade balls. How much dose it cost for 12,000 shade balls?
Answer:
$4320
Step-by-step explanation:
it costs $5,760 for 16,000, so divide 5,760/16,000 to find the cost for each shade ball, .36 dollars. Then multiply .36 by 12,000 to find 4320. Then just don't forget your unit ! add a $ or 'dollars'
math
(5 points) will mark brainliest!! pls help :)
Answer: [tex]\frac{tv^3}{u^8}\\\\\\[/tex]
This is the fraction tv^3 all over u^8
=========================================================
Work Shown:
[tex]\frac{t^2uv^7}{tu^9v^4}\\\\\\\frac{t^2}{t}*\frac{u}{u^9}*\frac{v^7}{v^4}\\\\\\t^{2-1}*u^{1-9}*v^{7-4}\\\\\\t^{1}*u^{-8}*v^{3}\\\\\\\frac{t}{1}*\frac{1}{u^8}*\frac{v^3}{1}\\\\\\\frac{t*1*v^3}{1*u^8*1}\\\\\\\frac{tv^3}{u^8}\\\\\\[/tex]
In the third step, I used the rule (a^b)/(a^c) = a^(b-c)
To make the negative exponent turn positive, we apply the reciprocal to the base.
If a slingshot is used to shoot a marble straight up into the air from 2 meters above the
ground with an initial velocity of 30 meters per second, for what values of time t will the
marble be over 35 meters above the ground? (Refer to Exercise 25 in Section 2.3 for assistance
if needed.) Round your answers to two decimal places
Answer:
use this equation: GPE=mgh
Step-by-step explanation:
GPE = gravitational potential energy = J
m = mass = Kg
g = gravitational field = N/kg = world's gravitational field is 9.8N/kg
h = height = m
helppp please!!!!!!!!!!!!!!
Answer:
No
No
Yes
Yes
No
Step-by-step explanation:
In this case we are looking at substitution, so any where you find x put three(3) in replace of it.
And remember the answer should be 36,
I find it difficult to type the answer so I will take a picture instead.
please help.. no links
Use Pythagorean theorem,
[tex]29^2 = 21^2 + x^2 \\\\\implies x^2 = 29^2 -21^2 \\\\\implies x^2 = 400\\\\\implies x = \sqrt{400} = 20[/tex]
i need help! i will be giving brainliest if you actually show the work and dont troll :)
Answer:
you do 215 times $0.25 you get $53.75 you take that away from $3272.30 you get $3218.55 then you divide that by 215 you get $14.97 so the answer is she makes $14.97 on one pair of earrings.
Step-by-step explanation:
Plz mark brainliest
Plotting points in the four quadrants
Point S has the coordinates (6, -4)
Which point on the graph shows the reflection of point s across the y axis
Answer:
it's -4 is the answer by the way
It takes 14 pints of blueberries to make 4 jars of blueberry jam.
Answer:It takes 14 pints of blueberries to make 4 jars of blueberry jam.
Step-by-step explanation:
write an indirect proof that a triangle cannot have 2 right angles
Simplify the expression 4(x-5) / 2
a. 8x - 40
b. 2x -
C. 5x - 20
d. 2x - 10
HELP PLZZZZZZ
Answer:8x-40
Step-by-step explanation:
Because when we simply 4(x-5)/2
We multiply both sides by 2 because the inverse operations of division is multiplication. 2*4(x-5)*2/2 we cancel two by two then it leave us 4*2(x-5).
Next four times two is eight. So 8(x-5) we distribe eight that means eight times x and 5, 8x-40thos is the answer. Hope this help
A box of pens cost $6.50 and a box of pencils is $4.00. Jane gets 15% commission of each box of pencils sold. Calculate Jane's commission if sells 20 boxes
Answer:
$12
Step-by-step explanation:
Jane's commission is the product of sales and her rate.
commission = (20)($4.00)(0.15) = $12.00
Jane's commission is $12.00 if she sells 20 boxes of pencils.