Answer:
48.45in
Step-by-step explanation:
To get the height of Dakota, we will use the SOH CAH TOA
Given the following
angle of elevation = 39degrees
distance from the top of Dakotas head to the tip of the shadow = 77in (Hyp)
Required
Height of Dakota (Opp)
Sin 39 = opposite/hyp
Sin39 = H/77
H = 77sin39
H = 77(0.6293)
H = 48.45in
Hence the Dakota is 48.45in
Convert the following to a simplified fraction. Show all your work.
Answer:
11/6
Step-by-step explanation:
Which histogram represents the following data set?
31, 67, 8, 37, 12, 87, 14, 34, 105, 57, 42, 8, 16, 54, 17, 20, 72, 23,
27, 63, 24, 52, 14, 44, 27, 5, 28, 22, 33, 15, 6, 36, 41, 21, 46
Answer:
Option A
Step-by-step explanation:
Histogram shows the range of data on the x-axis while the frequency of occurrence is on the y-axis.
We have the following ranges from the Histogram ;
0 to 11
11 to 22
22 to 33
33 to 44
44 to 55
55 to 66
66 to 77
77 to 88
88 to 99
99 to 110
From the given set of data, the frequency according to the range is as follows;
0 to 11; 4
11 to 22; 8
22 to 33; 7
33 to 44; 6
44 to 55; 4
55 to 66; 2
66 to 77; 2
77 to 88; 1
88 to 99; 0
99 to 110; 1
The only Histogram that corresponds to these frequency is option A
The running trail in the local park is 2.826 miles long. If the park board were planning to extend the trail by 1.46 miles, what would the new length of the running trail be?
Answer:
4.286
Step-by-step explanation:
you really need help with this ? you cannot just use your calculator ? that would have been faster than putting that question in here ...
remember, similar to the number positions in front of the decimal point, it is equally important to add the same positions after the decimal point.
we have 10th, 100th, 1000th, 10000th, 100000th, ... no end possible.
so we have
2.826 miles
and need to add 1.46 miles
2.826
1.46
----------
4.286
and the line of thinking goes from right to left
nothing plus 6 is 6
6 plus 2 is 8
4 plus 8 is 12, so we write 2 and carry over the 1
1 plus 2 plus 1 carry over is 4
if it helps, you can always add zeroes at the end of any digits after the decimal point, as you can also add zeroes in front to the digits before the decimal point to make both numbers have the same length and their decimal points are perfectly aligned.
our addition could have also looked like
2.826
1.460
with the same result
overall, if this is truly helping you, an example of using both leading and tailing zeroes could be
4278.9472081
0021.6380000
---------------------
4300.5852081
what is the measure of angle X in degrees
Answer:
If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal. Solve for X in interesting lines by finding the value of one adjacent angle and subtracting it from 180 degrees.
Step-by-step explanation:
in the number 36,802 if the 8 was replaced with a 2 would the value increase or decrease
Answer:
decrease
Step-by-step explanation:
I don’t understand these problems
Both E and F are sets.
E = {w | w ≤ 2}
means that E is the set of all numbers w satisfying the condition that w ≤ 2. In other words, E contains all real numbers less than and including 2.
Similarly,
F = {w | w > 9}
is the set of all real numbers strictly greater than 9.
The intersection of E and F, denoted E ∩ F, is the set that contains the overlap of the two sets, or all the numbers that are common to both sets. In this case, E ∩ F is the empty set; this is because all numbers small than 2 cannot be larger than 9, so E ∩ F = ∅.
The union of E and F, written as E ∪ F, is the set containing all elements from both sets. In interval notation, E = (-∞, 2] and F = (9, ∞), so E ∪ F = (-∞, 2] ∪ (9, ∞).
(3 points) Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson. Please upload your work for all of the parts at the end. (0.5 pts.) a) What is the probability that more than one accident occurs per year
Answer:
0.8743 = 87.43% probability that more than one accident occurs per year
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year.
This means that [tex]\mu = 3.1[/tex]
What is the probability that more than one accident occurs per year?
This is:
[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]
In which
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.6}*(3.6)^{0}}{(0)!} = 0.0273[/tex]
[tex]P(X = 1) = \frac{e^{-3.6}*(3.6)^{1}}{(1)!} = 0.0984[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0273 + 0.0984 = 0.1257[/tex]
[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1257 = 0.8743[/tex]
0.8743 = 87.43% probability that more than one accident occurs per year
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 144 millimeters, and a variance of 49 . If a random sample of 46 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2 millimeters? Round your answer to four decimal places.
Answer:
0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean diameter of 144 millimeters, and a variance of 49.
This means that [tex]\mu = 144, \sigma = \sqrt{49} = 7[/tex]
Sample of 46:
This means that [tex]n = 46, s = \frac{7}{\sqrt{46}}[/tex]
Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?
Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.
Probability the sample mean is below 142:
p-value of Z when X = 142, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}[/tex]
[tex]Z = -1.94[/tex]
[tex]Z = -1.94[/tex] has a p-value of 0.0262
2*0.0262 = 0.0524
0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.
add 7/8 + 2 3/24 + 6 1/6
Answer:
9 4/24 or 9 1/6
Find the LCM(lowest common multiple) of 8, 24 and 6.The LCM of 8, 24 and 6 is 24.We now want to turn all the denominators into 24 so we are going multiply 7/8 by 3 and 1/6 by 4. We won't need to turn the denominator of 3/24 into 24 because it's already 24Whatever you do to the denominator you have to do to the numerator, so you also have to multiply the numerator of 7/8 by 3 and the numerator of 1/6 by 4That now results in 21/8 + 2 3/24 + 6 4/24Now you have to add all the fractions together which is going to equal to 28/24Because 28/24 is more than the whole, subtract 28 from 24 which gives us 4. That 4 is now our new numeratorWe are now going to all the whole numbers 6+2+1=9. Incase you're wondering, the '1' came from the 28/24The answer you should get should be 9 4/24 or if it should be simplified it would be 9 1/6
Lauren flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will
show heads, the spinner will land on green, and the cube will show an even number.
Lauren will get 2/25 because the coin only lands on heads or tail
What is y=-2(x+3)^2+2
Answer:
y = -2(x + 3)² + 2
y = 2{ -(x + 3)²+ 1}
y = 2{ -(x² + 6x + 9) + 1}
y = 2{ -x² - 6x - 9 + 1}
y = 2{ -x² - 6x - 8 }
y = -2 { x² + 6x + 8}
OR
y = -2{(x + 4)(x + 2)}
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
Find the measure of angle C of a triangle ABC, if angle A=a and angle B= 2a.
*The answer is not 180-3a
The angle C of the triangle ABC is ( π - 3a ).
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
The angle will be calculated as follows:-
We know that the sum of the angles of the triangle is 180 degrees or π in radians.
∠A + ∠B + ∠C = π
a + 2a + ∠C = π
∠C = π - a - 2a
∠C = π - 3a
Therefore angle C of the triangle ABC is ( π - 3a ).
To know more about an angle follow
https://brainly.com/question/25770607
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What is the solution to this system of equations y=x+6 and y=-.5x+3
Answer:
x=-6, y=0
Step-by-step explanation:
it's impossible to fully solve an equation where 2 variables are unknown. So we have to make it equal to 1 set. to do this, we have to think logically.
if y=x+6, then that means wherever it says y, we can put x+6. because x+6=x+6, right? so we plug x+6 into the second equation and get.
x+6=0.5x+3
to solve for x we subtract 6 from one side and 0.5 from the other and get
0.5x=-3
then we multiply both sides by 2 to make be a whole number
x=-6
now we just plug this into either equation. because the first one is easier, we can just set it up as
y=(-6)+6
which means y=0
help pls i don't get the question
Answer:
pretty sure it could
Step-by-step explanation:
Answer:
What it's asking is for 2 angles at different angles of attack, are parallel
Step-by-step explanation:
for example, // these two slashes are parallel because they wont ever touch, it wants you to find if the angles are parallel or not.
Given the points (-7, -1) and (8, 5) find the slope.
Answer:
(-7, -1) =(x1,y1)
(8, 5)=(x2,y2)
now
[tex]slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]or = \frac{5 - ( - 1)}{8 - ( - 7)} [/tex]
[tex]or = \frac{5 + 1} {8 + 7} [/tex]
[tex]or = \frac{6}{15} [/tex]
[tex]or = \frac{2}{5} [/tex]
Step-by-step explanation:
Explanation is in the attachmenthope it is helpful to you ☺️
A tax form asks people to identify their age, annual income, number of dependents, and social security number. For each of these four variables, identify the scale of measurement that probably is used and identify whether the variable is continuous or discrete.
Variable Nominal Ordinal Interval Ratio
Social security number
Annual income
Number of dependents
Variable Discrete Continuous
Social security number
Annual income
Number of dependents
Answer:
Types of variables:
Continuous variable include: income
Discrete variable include: number of dependents
Scale of measurement:
Nominal data include: Social security number
There is no ordinal data included
There is no interval data included
Ratio data include: Annual income,
Number of dependents.
Explanation:
Continuous variables are variables that are obtained by just counting, example: counting the number of times someone eats in a day.
Discrete variables are simply variables that are measured and are usually more precise than continuous variables, example: time, weight, length etc.
Nominal data are data types that are in the form of labels or names and do not have any particular order, example :social security number basically identifies a person and is not ranked or ordered in any way.
Ordinal data are data types that also in the form of names but with ranking and order.
Interval data are data types that rank and order data but with continuous measurement that may take on negative values, example measure of temperature.
Ratio data is same as interval data but does not take negative values, example we can not say that someone is -6 years old.
The solution of this equation has an error. Which of the following steps has the error? 18 − (3x + 5) = 8
Step 1: 18 − 3x + 5 = 8
Step 2: -3x + 23 = 8
Step 3: -3x = -15
Step 4: x = 5
Step 1 Step 2 Step 3 Step 4. ?
Answer:
Step 1
Because the number in front of the bracket is 1 and it is also affected by the negative sign(-),5 is supposed to be negative not positive because (negative by positive is negative)
And since the first step has an error in it,the remaining steps would also be wrong.
What angles can you construct using just a pair of compasses and a ruler?
Answer:
By using a pair of compasses and a ruler you can draw all angles
Math algebra 2 show you’re work plz
9514 1404 393
Answer:
(t, u, w) = (1, -2, -2)
Step-by-step explanation:
A graphing calculator makes short work of this, giving the solution as ...
(t, u, w) = (1, -2, -2)
__
There are many ways to solve this "by hand." Here's one of them.
Add the first and third equations. Their sum is ...
-3t +4w = -11 . . . . . [eq4]
Add this to twice the second equation. That sum is ...
(-3t +4w) +2(-4t -2w) = (-11) +2(0)
-11t = -11
t = 1
Substituting this into the second equation gives ...
-4(1) -2w = 0
w +2 = 0 . . . . divide by -2
w = -2 . . . . add -2
Substituting for t in the third equation lets us find u.
2(1) -2u = 6
-1 +u = -3 . . . . . divide by -2
u = -2 . . . . add 1
The solution is (t, u, w) = (1, -2, -2).
Is the point (-3,2) part of the solution set to the system y < -4x - 3, x + 8y > 7
Answer:
Yes
Step-by-step explanation:
If you replace each x with -3 and each y with 2 you get:
1) 2<-4*(-3)
2<12
True
2) -3+8*2>7
13>7
True
Therefore the point is part of the solution set
SOMEONE HELP PLEASE! So for this problem the answer I got is $4000. Is that the correct or incorrect answer? Can someone please help me if it is the incorrect answer. Thank you for your time.
Answer:
You're correct
Step-by-step explanation:
xp-q+1×xq-r+1×xr-p+1
Answer:
Look into the picture
Step-by-step explanation:
Let me know if there's something wrong to my answer
find the degree of polynomial of the following
[tex]3x^{3} - x ^{5} [/tex]
Answer:
the degree is the value of the biggest exponent = 5 (fifth degree)
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Since the highest power of x is 5, the degree of the polynomial x
3
−9x+3x
5
is 5.
Write the range of the function using interval notation.
Answer:
[-3, -1]
Step-by-step explanation:
The minimum y value is -3.
The maximum y value is -1.
-3 and -1 are included, so we use square brackets.
Answer: [-3, -1]
A scientist claims that 4% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%
Answer:
The probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%=0.00427
Step-by-step explanation:
We are given that
[tex]\mu_{\hat{p}}=p=4%=0.04[/tex]
n=662
We have to find the probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%.
q=1-p=1-0.04=0.96
[tex]\sigma_{\hat{p}}=\sqrt{p(1-p)/n}[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\frac{0.04(1-0.04)}{662}}[/tex]
[tex]\sigma_{\hat{p}}=0.0076[/tex]
Now,
[tex]P(\hat{p}>0.06)=1-P(\hat{p}<0.06)[/tex]
[tex]=1-P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}<\frac{0.06-0.04}{0.0076})[/tex]
[tex]=1-P(Z<2.63)[/tex]
[tex]=1-0.99573[/tex]
[tex]P(\hat{p}>0.06)=0.00427[/tex]
Hence, the probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%=0.00427
What is the product of
(5^-4)(5^-3)
Answer:
option one is the correct answer
Answer:
1/625
Step-by-step explanation:
You are planning to buy a house for $800,000. City bank offers a 30 year loan at 4.9 % apr ( Annual percentage interest rate) if you put 20 % down. Calculate your expected monthly payment.
Answer:
3396.65
Step-by-step explanation:
Let's start by cacluating the amount the bank is loaning us
800000*.8=640000
Let's now calculate the effective rate: .049/12= .004083333333
let x= payment
[tex]640000=x\frac{1-(1+.004083333333)^{-30*12}}{.004083333333}\\x=3396.651012[/tex]
Pls help this is rlly important!! You’ll get branliest bc this is hard and I’m stuck.
the median of restaurant b's cleanliness ratings is 2.
the median of restaurant b's food quality ratings is 4.
the median of restaurant b's service ratings is 3.
:))
Please help me >_< will give out brainliest
====================================================
Explanation:
We have an octagon because there are n = 8 sides. The diagram below shows one way to number the sides so you can count them efficiently (without missing any or double counting any).
----------------
Plug n = 8 into the formula below
S = 180(n-2)
S = 180(8-2)
S = 180(6)
S = 1080
The 8 interior angles add up to 1080 degrees.