Answer:
(x, y) = (-3, -5) or (1, 3)
Step-by-step explanation:
You can equate the expressions for y, then solve the resulting quadratic.
-x^2 +4 = 2x +1
4 = x^2 +2x +1 . . . . add x^2
4 = (x +1)^2 . . . . . . . write as a square
±2 = x +1 . . . . . . . . . take the square root
x = -1 ±2 = -3 or +1 . . . subtract 1
So, the solutions have x-values of -3 or +1. The corresponding y-values can be found from ...
y = 2x +1
y = 2(-3) +1 = -5 or y = 2(1) +1 = 3
Solutions are ...
(x, y) = (-3, -5) or (1, 3)
What percent of this grid is unshaded?
The grid has 10 columns and 10 rows making 100 equal sized squares 5 rows are
unshaded. The sixth row has 6 squares unshaded.
Answer:
56% shaded
Step-by-step explanation:
if there are 100 boxes, then every box it 1%
5 rows (50%) + 6 extra boxes (6%) = 56%
suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, remove it from the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble? The multiplication rule says to use P(red) P(blue).
Describe the probability of finding a red marble?
Describe the probability of finding a blue marble?
Describe the process of finding the probability of finding a red marble followed by a blue marble if the first marble was permanently removed?
What affect did removing the first marble from the box have on the problem?
Describe the probability of finding a red marble followed by the blue marble if the first marble is removed?
Answer:
1) 2/9
2)3/9
Step-by-step explanation:
sorry,thats what i know so far
The circumference of a circle can be found using the
fortula C=2
Which is an equivalent equation solved for r?
r=CH
r= C(2)
or = 21
Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+16y=0. Separate your answers by commas. isn't the answer just ±4?
Answer: k = 4, k = -4 and k = 0.
Step-by-step explanation:
If we have y = sin(kt)
then:
y' = k*cos(kt)
y'' = -k^2*son(x).
then, if we have the relation:
y'' - y = 0
we can replace it by the things we derivated previously and get:
-k^2*sin(kt) + 16*sin(kt) = 0
we can divide by sin in both sides (for t ≠0 and k ≠0 because we can not divide by zero)
-k^2 + 16 = 0
the solutions are k = 4 and k = -4.
Now, we have another solution, but it is a trivial one that actually does not give any information, but for the diff equation:
-k^2*sin(kt) + 16*sin(kt) = 0
if we take k = 0, we have:
-0 + 0 = 0.
So the solutions are k = 4, k = -4 and k = 0.
hey guys plz help meee
the answers have to be in numbers.
Answer:
[tex]\overrightarrow{AB}=\frac{-9}{-4}[/tex]
[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]
Step-by-step explanation:
A vector quantity is represented by [tex](\frac{y}{x})[/tex]
where y = y-coordinate and x = x-coordinate
Since vector AB represents a vector in 3rd quadrant,
It starts from point A and ends at B,
Therefore, coordinates of B are (-9, -4)
[tex]\overrightarrow{AB}[/tex] = [tex](\frac{-9}{-4})[/tex]
Similarly vector CD starts with C and ends at D in the 2nd quadrant,
Therefore coordinates of D will be (-5, 4)
[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]
pls help me on this question
Hey there! :)
Answer:
Choice C: x + 8 = 3x.
Step-by-step explanation:
Solve this question by simplifying each answer choice:
a) 4x = 20
Divide both sides by 4:
4x/4 = 20/4
x = 5. This is incorrect.
b) x/2 = 8
Multiply both sides by 2:
x = 16. This is incorrect.
c) x + 8 = 3x
Subtract x from both sides:
8 = 2x
Divide 2 from both sides:
x = 4. This is correct.
d) x = x+5 /2
Multiply both sides by 2:
2x = x + 5
Subtract x from both sides:
x = 5. This is incorrect.
Therefore, choice C is the correct answer.
Answer:
C . x+8=3x
Step-by-step explanation:
[tex]x +8 = 3x\\Collect-like-terms\\8=3x-x\\8=2x\\\frac{2x}{2} =\frac{8}{2} \\x =4[/tex]
Suppose a marketing company wants to determine the current proportion of customers who click on ads on their smartphones. It was estimated that the current proportion of customers who click on ads on their smartphones is 0.42 based on a random sample of 100 customers.
Required:
Compute a 92% confidence interval for the true proportion of customers who click on ads on their smartphones and fill in the blanks appropriately.
Answer:
The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 100, p = 0.42[/tex]
92% confidence level
So [tex]\alpha = 0.08[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.08}{2} = 0.96[/tex], so [tex]Z = 1.75[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.3336[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.5064[/tex]
The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).
Can Anyone plz help me out with a question I’m struggling question 1 in the picture
Answer:
16x^2 + 8x.
Step-by-step explanation:
To find the area of the walkway, you need to do the area of the whole thing minus the area of the pool.
The area of the whole thing is (8x - 3)(2x + 7) = 16x^2 - 6x + 56x - 21 = 16x^2 + 50x - 21.
The area of the pool is (8x - 3 - x - x)(2x + 7 - x - x) = (6x - 3)(7) = 42x - 21.
So, the area of the walkway is 16x^2 + 50x - 21 - (42x - 21) = 16x^2 + 50x - 21 - 42x + 21 = 16x^2 + 8x.
If you want, you can factor that and make it 8x(2x + 1).
Hope this helps!
PLZ HELP!. Insert a digit to make numbers that are divisible by 24 if it is possible: 120...4..
Answer:
120
Step-by-step explanation:
As we can see that if we divide 120 by the 24, the remainder would be zero and the quotient be 5
As if we multiply 24 with the 5 it gives 120
And, the 4 is not a digit as it smaller than 24 so we have to carry the amount
Therefore if we insert 120 and divisible by 24 than it gives quotient 5 and the remainder is zero as it is completely divisible
Select the correct answer.
The function RX) = 2x + 3x + 5, when evaluated, gives a value of 19. What is the function's input value?
A. 1
B. -1
C. 2
D. -2
E. -3
Answer:
Correct option: C.
Step-by-step explanation:
(Assuming the correct function is R(x) = 2x^2 + 3x + 5)
To find the input value that gives the value of R(x) = 19, we just need to use this output value (R(x) = 19) in the equation and then find the value of x:
[tex]R(x) = 2x^2 + 3x + 5[/tex]
[tex]19 = 2x^2 + 3x + 5[/tex]
[tex]2x^2 + 3x -14 = 0[/tex]
Solving this quadratic function using the Bhaskara's formula (a = 2, b = 3 and c = -14), we have:
[tex]\Delta = b^2 - 4ac = 9 + 112 = 121[/tex]
[tex]x_1 = (-b + \sqrt{\Delta})/2a = (-3 + 11)/4 = 2[/tex]
[tex]x_2 = (-b - \sqrt{\Delta})/2a = (-3 - 11)/4 = -3.5[/tex]
So looking at the options, the input to the function is x = 2
Correct option: C.
What is the solution to this? Thank you for helping me 8 divided by 1 4/5
Answer:
40 /9 or also can be written as 4 4/9
Step-by-step explanation:
hope this helps
Graph on a piece of paper y= -3x-2
Hey there! :)
Answer:
To graph y = -3x - 2, we can start by solving for some points. Plug in x values for x in the equation to solve for the y value:
X Y
-2 4
-1 1
0 -2
1 -5
2 -8
Use these points to graph the line (Graphed below)
Simplify the expression.
(7-6)(-1)
-7 +0
-7-
7-6
7+ c
Answer:
7+c or 6
Step-by-step explanation:
Answer:
-89+c
Step-by-step explanation:
I'm assuming
"(7-6)(-1)
-7 +0
-7-
7-6
7+ c"
Is the whole equation.
(7-6)(-1) -7+0 -7- 7-6 7+c=
(1)(-1)-7+0-7-7-67+c=
-1-7+0-7-7-67+c=
-8+0-7-7-67+c=
-8-7-7-67+c=
-15-7-67+c=
-22-67+c=
-89+c
Find m^4+(1/m^4) if m-(1/m)=3 Please help with this.
Answer:
m^4+(1/m^4)= 123.4641 or 118.6
Step-by-step explanation:
m-(1/m)=3
m² - 1= 3m
m² -3m -1= 0
m = (3-√13)/2 = -0.3
Or
m =( 3+√13)/2= 3.3
m^4+(1/m^4) for m = -0.3
= (-0.3)^4 + (1/(0.3)^4)
= 0.0081 + 123.456
= 123.4641
m^4+(1/m^4) for m = 3.3
= (3.3)^4 + (1/(3.3)^4)
= 118.5921 + 0.008432
= 118.6
For n ≥ 1, let S be a set containing 2n distinct real numbers. By an, we denote the number of comparisons that need to be made between pairs of elements in S in order to determine the maximum and minimum elements in S.
Requried:
a. Find a1 and a2
b. Find a recurrence relation for an.
c. Solve the recurrence in (b) to find a formula for an.
Answer:
A) [tex]a_{1}[/tex] = 1, [tex]a_{2}[/tex] = 4
B) [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] + 2
C) [tex]a_{n} = 2^{n-1} + 2^n -2\\a_{n} = 2^n + 2^{n-1} -2[/tex]
Step-by-step explanation:
For n ≥ 1 ,
S is a set containing 2^n distinct real numbers
an = no of comparisons to be made between pairs of elements of s
A)
[tex]a_{1}[/tex] = no of comparisons in set (s)
that contains 2 elements = 1
[tex]a_{2}[/tex] = no of comparisons in set (s) containing 4 = 4
B) an = 2a[tex]_{n-1}[/tex] + 2
C) using the recurrence relation
a[tex]_{n}[/tex] = 2a[tex]_{n-1}[/tex] + 2
substitute the following values 2,3,4 .......... for n
a[tex]_{2}[/tex] = 2a[tex]_{1}[/tex] + 2
a[tex]_{3}[/tex] = 2a[tex]_{2}[/tex] + 2 = [tex]2^{2} a_{1} + 2^{2} + 2[/tex]
a[tex]_{4}[/tex] = [tex]2a_{3} + 2 = 2(2^{2}a + 2^{2} + 2 ) + 2[/tex]
= [tex]2^{n-1} a_{1} + \frac{2(2^{n-1}-1) }{2-1}[/tex] ---------------- (x)
since 2^1 + 2^2 + 2^3 + ...... + 2^n-1 = [tex]\frac{2(2^{n-1 }-1) }{2-1}[/tex]
applying the sum formula for G.P
[tex]\frac{a(r^n -1)}{r-1}[/tex]
Note ; a = 2, r =2 , n = n-1
a1 = 1
so equation x becomes
[tex]a_{n} = 2^{n-1} + 2^n - 2\\a_{n} = 2^n + 2^{n-1} - 2[/tex]
The respiratory rate (in breaths per minute) in newborns varies according to a distribution that is approximately Normal, with a mean of 50 and a standard deviation of 5. Use Excel to answer this question: What is the probability that a randomly chosen newborn has a respiratory rate between 40 and 55 breaths per minute
Answer:
[tex]P(40<X<55)[/tex]
And since we need to use excel the code in order to find the answer would be:
=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)
And the answer would be:
[tex]P(40<X<55)=0.819[/tex]
Step-by-step explanation:
Let X the random variable that represent the respiratory rate of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(50,5)[/tex]
Where [tex]\mu=50[/tex] and [tex]\sigma=5[/tex]
We are interested on this probability
[tex]P(40<X<55)[/tex]
And since we need to use excel the code in order to find the answer would be:
=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)
And the answer would be:
[tex]P(40<X<55)=0.819[/tex]
a child rolls a 6-sided die 6 times. what is the probability of the child rolling no more than three twos g
Answer:
Pr(Three 2's) = 1/27
Step-by-step explanation:
Let's assume the die is a fair die, on the first roll of the die, the child has a 1/6 chance of getting any number, including 6.
Second roll, the child has a 1/36 chance of getting any two numbers, including two 6's.
And on the third roll, the child has a 1/36×1/6=1/216 chance of getting any three numbers, including three 6's. And this is due to the fact that the rolls are independent, so the total possible outcomes multiply each roll with each roll's probability. Since each roll's probability is 1/6.
The probability of the child rolling no more than three twos will be =2/6×2/6×2/6
=1/3×1/3×1/3
=1/27
Therefore, the chances of three twos will be 1/27
What is the value of x to the power of 2 to the power of 4 when x = 8 and y =2
Answer:
x is 64 and y is 16 but if you can't comprehend thats 64/16 = 4
Step-by-step explanation:the power is the number multiplied by it self so 8 to the power if 2 is 8 x 8 and 2 to the power of four is 2 x 2 x 2 x 2= 16
The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $30,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.10 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised?
29.7 29.4 31.7 29.0 29.1 30.5 29.1 29.8
Required:
a. State the null hypothesis and the alternate hypothesis.
b. State the decision rule for 0.05 significance level.
c. Compute the value of the test statistic.
d. What is the conclusion regarding the null hypothesis?
Answer:
Step-by-step explanation:
Mean = (29.7 + 29.4 + 31.7 + 29.0 + 29.1 + 30.5 + 29.1 + 29.8)/8 = 29.7875
Mean = 29.7875 × 1000 = $29787.5
Standard deviation = √(summation(x - mean)²/n
n = 8
Summation(x - mean)² = (29.7 - 29.7875)^2 + (29.4 - 29.7875)^2 + (31.7 - 29.7875)^2 + (29.0 - 29.7875)^2 + (29.1 - 29.7875)^2 + (30.5 - 29.7875)^2 + (29.1 - 29.7875)^2 + (29.8 - 29.7875)^2 = 5.88875
Standard deviation = √(5.88875/8
s = 0.88
s = 0.88 × 1000 = $880
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0:µ ≤ 30000
For the alternative hypothesis,
H1:µ > 30000
This is a right tailed test.
b) The decision rule is to reject the null hypothesis if the significance level of 0.05 is greater than the probability value. If it is otherwise, we would fail to reject the null hypothesis.
c) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 29787.5
µ = population mean = 30000
s = samples standard deviation = 880
t = (29787.5 - 30000)/(880/√8) = - 0.68
We would determine the p value using the t test calculator. It becomes
p = 0.26
d) Since alpha, 0.1 < the p value, 0.26, then we would fail to reject the null hypothesis.
This Venn diagram represents the science subjects studied by students what is the probability chosen at random that that child does not study chemistry
Answer:
Step-by-step explanation:
Looking at the Venn diagram,
The total number of students surveyed is 7 + 5 + 8 + 6 + 2 + 4 + 3 + 6 = 41
The number of children that studies none of the subjects is 6
The number of children that study only biology is 7
The number of children that study only physics is 5
The number of children that study only physics and biology is 2
Therefore, the number of students that do not study chemistry is 6 + 7 + 2 + 5 = 20
Probability = number of favorable outcomes/total number of outcomes
Therefore, the probability that a child chosen at random does not study chemistry is 20/41 = 0.49
Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes. How long does it take for both Wilma and Rocky to mow the lawn if they are working together?
===================================================
Explanation:
Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.
Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.
Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.
--------------------------
Another approach
Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is
1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute
x = number of minutes
(combined rate)*(time) = number of jobs done
(1/24)*x = 1
x = 1*24
x = 24 is the time it takes if they worked together without getting in each other's way.
Effectively, we are solving the equation
1/A + 1/B = 1/C
with
A = time it takes Wilma to do the job on her own
B = time it takes Rocky to do the job on his own
C = time it takes the two working together to get the job done
The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.
So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.
Together they can mow the lawn in 24 minutes.
What are the relation between time, work, and efficiency?Time and efficiency are inversely proportional to each other.
Time and work are directly proportional to each other.
Given, Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes.
Assuming total work to be 120 as it is the LCM of 40 and 60.
So, The efficiency of Wilma is (120/60) = 2 and the efficiency of Rocky is
(120/40) = 3.
Now together their efficiency is (2 + 3) = 5.
∴ Together they can complete the work in (120/5) = 24 minutes.
learn more about time and work here :
https://brainly.com/question/3854047
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Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value t Subscript alpha divided by 2,(b) find the critical value z Subscript alpha divided by 2,or (c) state that neither the normal distribution nor the t distribution applies.Here are summary statistics for randomly selected weights of newborn girls: nequals235,x overbarequals33.7hg, sequals7.3hg. The confidence level is 95%.
Answer:
To construct a confidence interval, Normal distribution should be used since the sample size is quite large (n > 30)
From the z-table, at α = 0.025 the critical value is
[tex]z_{\alpha/2} = 1.96[/tex]
Step-by-step explanation:
We are given the following information:
The sample size is
[tex]n = 235[/tex]
The mean weight is
[tex]\bar{x}= 33.7 \: hg[/tex]
The standard deviation is
[tex]s = 7.3 \: hg[/tex]
Since the sample size is quite large (n > 30) then according to the central limit theorem the sampling distribution of the sample mean will be approximately normal, therefore, we can use the Normal distribution for this problem.
The correct option is (b)
The critical value corresponding to 95% confidence level is given by
Significance level = α = 1 - 0.95 = 0.05/2 = 0.025
From the z-table, at α = 0.025 the critical value is
[tex]z_{\alpha/2} = 1.96[/tex]
What is Normal Distribution?
A Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
AABC - ADEF
Find the value of x
Answer:
[tex]\boxed{x = 4}[/tex]
Step-by-step explanation:
If ΔABC ~ ΔDEF
Then their sides must be proportional such that:
=> [tex]\frac{x}{3} = \frac{8}{6}[/tex]
Cross Multiplying
=> x * 6 = 8*3
=> 6x = 24
Dividing both sides by 6
=> x = 4
Answer:
4
Step-by-step explanation:
ΔABC ~ ΔDEF
AB/DE = BC/EF
x/3 = 8/6
Cross multiply.
6 × x = 3 × 8
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, find the mean of the remaining three numbers. I cannot solve this. Please help on it.
Answer:
81
Step-by-step explanation:
Let's do this systematically:
Four numbers: a, b, c, d
Whose mean is 85: [tex]\frac{a + b + c + d}{4} = 85[/tex]
Whose largest number is 97: [tex]\frac{a + b + c + 97}{4} = 85[/tex]
Lets solve for the other numbers:
a+b+c+97 = 85*4 = 340
340 - 97 = 243
a+b+c = 243
at this point it doesn't matter what the numbers are, they just need to add up to 243.
We can do 243÷3=81, which is our answer
pls help i give brainliest
Answer:
Step-by-step explanation:
672532 to nearest thousand = 673000
hope this helps
plz mark as brainliest!!!!!!!!!
Find the number in the thousand place 2 and look one place to the right for the rounding digit 5.
Round up if this number is greater than or equal to 5 and round down if it is less than 5.
So, 673000 is your answer.
The test statistic of zequals2.31is obtained when testing the claim that pgreater than0.9.a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.b. Find the P-value.c. Using a significance level of alphaequals0.10,should we reject Upper H 0or should we fail to reject Upper H 0?
Answer:
Step-by-step explanation:
a) From the information given, we can state the hypothesis as follows:
For null hypothesis,
p = 0.9
Or
p ≤ 0.9
For alternative hypothesis,
p > 0.9
Because of the greater than inequality symbol in the alternative hypothesis, it means that it is a right tailed test.
b) Since z = 2.31, we would determine the p value by looking at the probability corresponding to the area above the z score from the normal distribution table. Thus
P value = 1 - 0.9896 = 0.0104
Using a significance level of alpha equals 0.10, since alpha, 0.10 is > p value, 0.0104, then we would reject the null hypothesis.
On a multiple choice test with 24 questions each question has four possible answers one of which is correct for students who guess at all answers find the variance for the number of correct answers
Answer:
The variance for the number of correct answers is 4.5.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the correct answer is guessed, or it is not. Questions are independent of each other, so we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
24 questions
This means that [tex]n = 24[/tex]
Each question has four possible answers one of which is correct
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
Find the variance for the number of correct answers
[tex]V(X) = np(1-p) = 24*0.25*0.75 = 4.5[/tex]
The variance for the number of correct answers is 4.5.
Assume that the random variable X is normally distributed, with mean 60 and standard deviation 16. Compute the probability P(X < 80). Group of answer choices
Answer:
P(X < 80) = 0.89435.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 60, \sigma = 16[/tex]
P(X < 80)
This is the pvalue of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 60}{16}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.89435.
So
P(X < 80) = 0.89435.
Sal wrote the statement below to represent the inequality 8n - 5 ≥ 25. Which words should Sal use to complete the verbal statement? The product of 8 and n decreased by 5 is _____25. less than greater than less than or equal to greater than or equal to
The symbol [tex]\ge[/tex] can be thought of a greater than sign over top an equal sign, like this [tex]\stackrel{>}{=}[/tex] though the second horizontal line is erased to keep things relatively more simple (in terms of having to write it out).
Simplify the expression where possible. (6 3) -3
Answer:
-189
Step-by-step explanation:
(63) -3
Calculate the product
-3(63)
Multiply both numbers
-3 × 63
= -189