I don't know what to do.
Answer:
True.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We can simply plug in the 3 variables to see if it forms a Pythagorean Triple:
6² + 13² = 14.32²
36 + 169 = 205.062
205 = 205 (rounded), so True.
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%
Answer:
D
Step-by-step explanation:
We calculate the z-score for each
Mathematically;
z-score = (x-mean)/SD
z1 = (1.9-2.1)/0.2 = -1
z2 = (2.3-2.1)/0.2 = 1
So the proportion we want to calculate is;
P(-1<x<1)
We use the standard score table for this ;
P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%
Answer:
68
Step-by-step explanation:
Use z scores to compare the given values. In a recent awards ceremony, the age of the winner for best actor was 34 and the age of the winner for best actress was 62. For all best actors, the mean age is 43.4 years and the standard deviation is 8.8 years. For all best actresses, the mean age is 38.2 years and the standard deviation is 12.6 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
Answer:
The actress had more extreme age when winning the award.
Step-by-step explanation:
We are given that for all the best actors, the mean age is 43.4 years and the standard deviation is 8.8 years. For all best actresses, the mean age is 38.2 years and the standard deviation is 12.6 years.
To find who had the more extreme age when winning the award, the actor or the actress, we will use the z-score method.
Finding the z-score for the actor;Let X = age of the winner for best actor
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean age = 43.4 years
[tex]\sigma[/tex] = standard deviation = 8.8 years
It is stated that the age of the winner for best actor was 34, so;
z-score for 34 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{34-43.4}{8.8}[/tex] = -1.068
Finding the z-score for the actress;Let Y = age of the winner for best actress
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{Y-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean age = 38.2 years
[tex]\sigma[/tex] = standard deviation = 12.6 years
It is stated that the age of the winner for best actress was 62, so;
z-score for 62 = [tex]\frac{Y-\mu}{\sigma}[/tex]
= [tex]\frac{62-38.2}{12.6}[/tex] = 1.889
Since the z-score for the actress is more which means that the actress had more extreme age when winning the award.
What is the solution of (4x-16)1/3=36
(4x-16)/3 = 36
4x-16 = 108
4x = 108+16
4x = 124
x = 124/4
x = 31
Answer:
x = 31
Step-by-step explanation:
=> [tex](4x-16)\frac{1}{3} = 36[/tex]
Multiplying 3 to both sides
=> [tex]4x-16 = 36*3[/tex]
=> 4x-16 - 108
Adding 16 to both sides
=> 4x = 108+16
=> 4x = 124
Dividing both sides by 4
=> x = 31
Question
An airplane is traveling at a constant speed of 585 miles per hour. How many feet does it travel in 6 seconds? Remember
that 1 mile is 5280 feet.
Convert the 6 seconds to hours:
5 seconds x x 1/60 ( minutes per seconds) x 1/60 (Hours per minute) = 6/3600 = 1/600 hours.
Distance = speed x time
Distance = 585 x 1/600 = 585/600 = 0.975 miles
Convert miles to feet:
0.975 x 5280 = 5,148 feet
The plane traveled 5,148 feet in 6 seconds.
Select two ratios that are equivalent to 7:6
Two ratios that are equal to 7:6 are 14:12 and 21:18, as they are the same, but 7 and 6 are multiplied by the same number (2 in the first, and 3 in the second.)
A postal service will accept a package if its length plus its girth is not more than 96 inches. Find the dimensions and volume of the largest package with a square end that can be mailed.
Answer:
Dimension - 16in by 16in by 32inVolume - 8,192in³Step-by-step explanation:
Let the length and width of the rectangular package be x and y respectively. Since end of the package is a square, the perimeter of the package will be expressed as P = 4x+y and the volume will be expressed as V = x²y
If a postal service will accept a package if its length plus its girth is not more than 96 inches, then the perimeter is equivalent to 96 inches.
96 = 4x+y
y = 96-4x
Substituting the value of x into the formula for calculating the volume, we will have;
V(x) = x²(96-4x)
V(x) = 96x²-4x³
To get the dimensions and volume of the largest package, we will find V'(x) and equate it to zero.
V'(x) = 192x-12x²
192x-12x² = 0
Factoring out x;
x(192-12x) = 0
x = 0 and 192-12x = 0
12x = 192
x = 192/12
x = 16
This shows that we have a maximum value at x = 16 and minimum at x = 0
To get y, we will substitute x = 16 into the expression y = 96-4x
y = 96-4(16)
y = 96-64
y = 32
- The dimensions of the largest package is therefore 16in by 16in by 32in
- Volume of largest package = x²y = 16²*18 = 8,192in³
What is the value of x in the figure above
the value of x is 115°.
hope its helpful to uh..
how much would $100 invested at 6% interest compounded monthly be worth after 20 years? Round your answer to the nearest cent a(t)=p(1+r/n)^nt
Answer:
Amount after 12 years is $205.42
Step-by-step explanation:
Fibal amount a is not given and to be found
Principal amount p = $100
Rate r = 6% ° 0.06
Years t = 20
Number if times computed n = 20*12
n = 240
a(t)=p(1+r/n)^nt
a = 100(1+0.06/240)^(240*12)
a = 100(1+0.00025)^(2880)
a= 100(1.00025)^2880
a= 100(2.054248)
a= 205.4248
To the nearest cent
a =$ 205.42
Amount after 12 years is $205.42
pls help help help hepl
Answer:
C
Step-by-step explanation:
undefined slope means tat the denominator=0 in the equation
m=y2-y1/x2-x1
A: m=-1-1/1+1=-2
B;2-2/2+2=0
C: 3+3/-3+3 = 6/0 undefined
D: 4+4/4+4=1
Solve the quadratic equation x2 + 14x = 51 by completing the square.
Question 3 options:
A)
x = –17, x = –3
B)
x = –17, x = 3
C)
x = 3, x = 17
D)
x = –3, x = 17
Answer:
B
Step-by-step explanation:
Given
x² + 14x = 51
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(7)x + 49 = 51 + 49 , that is
(x + 7)² = 100 ( take the square root of both sides )
x + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )
x = - 7 ± 10
Thus
x = - 7 - 10 = - 17
x = - 7 + 10 = 3
how many are 4 x 4 ?
4 times 4 is 16, think of it like 4 + 4 + 4 + 4.
4 times 4 is 16, think of it like 4 + 4 + 4 + 4.
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
y and z are whole numbers y<70 z 60 work out the largest possible value of y and z
Answer:
a) 12
b) 129
Step-by-step explanation:
a)
[tex]w, x \in \mathbb{Z}_{\ge 0}[/tex]
[tex]w>50\\x<40[/tex]
For the smallest value of [tex]w-x[/tex], we gotta figure out the smallest value for w and the highest value for x.
[tex]w>50 \Rightarrow \text{ smallest value is } 51[/tex]
For [tex]x[/tex], once [tex]-(-x)=x[/tex], we conclude that [tex]x[/tex] cannot be negative and therefore, [tex]x=39[/tex].
[tex]51-39=12[/tex]
b)
[tex]y, z \in \mathbb{Z}_{\ge 0}[/tex]
[tex]y<70\\z\leq 60[/tex]
For the largest value of [tex]y+z[/tex], we gotta figure out the highest value for y and z.
[tex]y<70 \Rightarrow \text{ highest value is } 69[/tex]
[tex]z\leq 60 \Rightarrow \text{ highest value is } 60[/tex]
[tex]y+z=69+60=129[/tex]
What is the difference between the estimated and real value of 55-21?
Answer: The difference between the estimated and real value of 55-21 is about 4 or 5
Step-by-step explanation:
Answer:
The difference between the estimate and the real value of 55-21 is that when you estimate you're giving an educated guess and the real value is when you're actually doing the work to prove your answer and not just guess.
Step-by-step explanation:
Real Value
55-21=34
55
- 21
34
Estimated
55-21=32
WHY CAN'T ANYONE HELP ME? In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998, number of vehicles).
Answer:
y = 640x +4760
Step-by-step explanation:
Given:
(x, y) = (years past 1998, number of vehicles) = (0, 4760), (3, 6680)
Find:
a slope-intercept form linear equation through these points
Solution:
The 2-point form of the equation of a line is a useful place to start:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (6680 -4760)/(3 -0)(x -0) +4760
y = 1920/3x +4760
y = 640x +4760 . . . . . the desired equation
student throws 3 coins in the air. Find the probability that exactly 2 landed on heads, given that at least 2 landed on heads.
Step-by-step explanation:
Head(H) Tails(T)
Sample space is S (HHH,HHT,HTH,THH)
Event(HHT,HTH,THH)
so the probability is 3/4
Answer:
3/4
Step-by-step explanation:
What is the surface area of this regular pyramid? A. 230 in2 B. 304 in2 C. 480 in2 D. 544 in2
Answer:
B: 304in^2
Step-by-step explanation:
One triangle face: (8)(15) ÷ 2 = 60
Four triangle faces: 60 x 4 = 240
Bottom Face: (8)(8) = 64
Total Surface Area: Four triangle faces + Bottom Face
Total Surface Area: 240 + 64
Total Surface Area: 304in^2
Maya is solving the quadratic equation by completing the square. 4x2 + 16x + 3 = 0 What should Maya do first?
Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The complete question is:
Maya is solving the quadratic equation by completing the What should Maya do first? square.
4x² + 16x + 3 = 0
Isolate the variable x².Subtract 16x from both sides of the equation.Isolate the constant.Factor 4 out the variable terms.We have a quadratic equation:
4x² + 16x + 3 = 0
To make the perfect square
Maya should do first:
Isolate the variable x²
To make the coefficient of x² is 1.
4(x² + 4x + 3/4) = 0
x² + 4x + 3/4 = 0
x² + 4x + 2² - 2² + 3/4 = 0
(x + 2)² - 4 + 3/4 = 0
(x + 2)² = 13/4
x + 2 = ±√(13/4)
First, take the positive and then the negative sign.
x = √(13/4) - 2
x = -√(13/4) - 2
Thus, Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.
Learn more about quadratic equations here:
brainly.com/question/2263981
#SPJ5
Write y = x + 7 in standard form using integers
Answer:
x - y = -7
Step-by-step explanation:
Standard Form: Ax + By = C
Step 1: Move the x over
-x + y = 7
Step 2: Factor out a -1
-1(x - y) = 7
Step 3: Divide both sides by -1
x - y = -7
Answer:
x-y = -7
Step-by-step explanation:
Ax + By = C is the standard form for a line where A is a positive number
y = x + 7
Subtract x from each side
-x+y = x+7-x
-x+y = 7
Multiply each side by -1
x-y = -7
determine the cross product b*a a=2i+2j-5k b=6i-j+2k
Recall the definition of the cross product:
i x i = j x j = k x k = 0
i x j = k
j x k = i
k x i = j
The cross product is antisymmetric, or anticommutative, meaning that for any vectors u and v, we have u x v = - (v x u).
It's also distributive, so for any vectors u, v, and w, we have (u + v) x w = (u x w) + (v x w).
Taking all of these properties together, we get
b x a = (6i - j + 2k) x (2i + 2j - 5k)
b x a = 12 (i x i) - 2 (j x i) + 4 (k x i)
............. + 12 (i x j) - 2 (j x j) + 4 (k x j)
............. - 30 (i x k) + 5 (j x k) - 10 (k x k)
b x a = 1 (j x k) + 34 (k x i) + 14 (i x j)
b x a = i + 34j + 14k
Answer:
Short answer, it is D) i+34j + 14k
Step-by-step explanation:
Edge 2021.
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Answer:
96.08% probability that their mean rebuild time is less than 8.9 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]
Find the probability that their mean rebuild time is less than 8.9 hours.
This is the pvalue of Z when X = 2.9.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.9 - 2.4}{0.2846}[/tex]
[tex]Z = 1.76[/tex]
[tex]Z = 1.76[/tex] has a pvalue of 0.9608
96.08% probability that their mean rebuild time is less than 8.9 hours.
Type 11/5 in the simplest form
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
11 ÷ 5 = 2 R 1 → [tex]2\frac{1}{5}[/tex]
Hope this helps! :)
divide 15 root 20 by 6 root 125
Answer:
15√20/6√125
=√20/√5
=2
Step-by-step explanation:
The function f(x) = 2x^3 + 3x^2 is:
(a) even
(b) odd
(c) neither
(d) even and odd
Answer:
neither
Step-by-step explanation:
First we must determine if both x and -x are in the domain of the function
since it is a polynomial function our first condition is satisfied
Then we should calculate the image of -x :
2x(-x)^3 + 3*(-x)² = -2x^3+3x²
it is not equal to f(x) nor -f(x)
Help me pls I need help
Answer:
C
Step-by-step explanation:
If two lines are parallel, their slopes are the same.
Since the slope of line l is 4/9, this means that the slope of line m must also be 4/9.
Answer:
C. 4/9
Step-by-step explanation:
Parallel lines have equal slopes.
Since line l and line m are parallel, then their slopes must be the same.
[tex]m_{l} =m_{m}[/tex]
We know that the slope of line l is 4/9
[tex]\frac{4}{9} = m_{m}[/tex]
Line l has a slope of 4/9, therefore line m must also have a slope of 4/9.
The correct answer is C. 4/9
How do you write 0.0026 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]2.6 \times {10}^{ - 3} [/tex]
Hope this helps you
Answer:
2.6 × 10⁻³
Step-by-step explanation:
To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.
In the decimal 0.0026, the first number that is 1 or higher is 2.
0.0026 ⇒ 2.6
When trying to figure out the exponent, here are some things to keep in mind:
- when you move the decimal to the right, the exponent is negative
- when you move the decimal to the left, the exponent is positive
You moved the decimal to the right three places. So the exponent will be -3.
The result is 2.6 × 10⁻³.
Hope this helps. :)
In her backyard, Mary is planting rows of tomatoes. To plant a row of tomatoes, mary needs 20/13 square feet. There are 40 square feet in Mary's backyard, so how many rows of tomatoes can mary plant??
Answer:
26 rows
Step-by-step explanation:
[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]
As part of a larger project to study the behavior of stressed-skin panels, a structural component being used extensively in North America, an article reported on various mechanical properties of Scotch pine lumber specimens. Data on the modulus of elasticity (MPa) obtained 1 minute after loading in a certain configuration and 4 weeks after loading for the same lumber specimens is presented here.
Observatio 1 min 4 Week Difference
1 16,620 9,110 1380
2 17,300 13,250 3370
3 15,480 14,720 2580
4 12,970 12,740 2740
5 17,260 10,120 2850
6 13,400 14,570 2690
7 13,900 11,220 2180
8 13,630 11,100 2800
9 13,260 11,420 2210
10 14,370 10,910 2350
11 11,700 12,110 2260
12 15,470 8,620 3080
13 17,840 12,590 2880
14 14,070 15,090 2750
15 14,760 10,550 3520
Required:
Calculate and interpret an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus; first check the plausibility of any necessary assumptions. (Use α = 0.05. Round your answer to the nearest whole number.)
Answer:
The upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.
Step-by-step explanation:
Compute the mean difference and standard deviation of the difference as follows:
[tex]\bar d=\frac{1}{n}\sum d_{i}=\frac{1}{15}\times [1380+3370+2580+...+3520]=2642.67\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}\\=\sqrt{\frac{1}{15-1}[(1380-2642.67)^{2}+(3370-2642.67)^{2}+...}=525.69[/tex]
The degrees of freedom is:
df = n - 1
= 15 - 1
= 14
Th critical value of t is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 14}=2.145[/tex]
*Use a t-table.
Compute the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus as follows:
[tex]\text{Upper Confidence Bound}=\bar d+t_{\alpha/2, (n-1)}\cdot \frac{S_{d}}{\sqrt{n}}[/tex]
[tex]=2642.67+2.145\cdot \frac{525.69}{\sqrt{15}}\\\\=2642.67+291.15\\\\=2933.82[/tex]
Thus, the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.
5c + 16.5 = 13.5 + 10c
Answer:
Hello!
________________________
5c + 16.5 = 13.5 + 10c
Exact Form: c = 3/5
Decimal Form: c = 0.6
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Answer:
3000+3d=noods
Step-by-step explanation: