Answer:
53
Step-by-step explanation:
Plugging in 32 for z, you get:
(32)/2+37=x
16+37=x
x=53
Hope this helps!
The solution of the linear equation z/2 + 37 = x at x at z = 32 will be 53.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
z/2 + 37 = x
Then the solution of the linear equation z/2 + 37 = x at z = 32. Then the equation will be
x = 32/2 + 37
x = 16 + 37
x = 53
Thus, the solution of the linear equation z/2 + 37 = x at z = 32 will be 53.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Which graph represents this equation y-4= -3(x+5)
Answer:
Graph B
Step-by-step explanation:
Simplify.
y - 4 = -3x - 15 Distribute
y = -3x - 11 Add 4 on both sides
The y-intercept should be negative, and option B has a negative y-intercept.
The graph of the given function will be represented by graph B so the correct answer is option B.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the function is attached with the answer below.
Simplify.
y - 4 = -3x - 15 Distribute
y = -3x - 11 Add 4 on both sides
The y-intercept should be negative, and option B has a negative y-intercept.
Therefore the graph of the given function will be represented by graph B so the correct answer is option B.
To know more about graphs follow
https://brainly.com/question/4025726
SPJ5
The image point using the translation (x,) + (x+4,y-1)
for the point (3,3) is
Answer: (7, 2)
Step-by-step explanation:
(x, y) → (x + 4, y - 1)
(3, 3) → (3 + 4, 3 - 1)
= (7, 2)
Which ordered pair is the best estimate for the
solution of the system of equations?
y =
3x + 6
y = 1x – 2
Answer:
-4, -6
Step-by-step explanation:
3x+6= 1x-2
2x+6= -2
2x= -8
x= -4
Now that you have your x variable, you can go back and plug it in to your original equations:
y= 3(-4)+6,
y= (-12)+6 therefore y= -6
y=1(-4) -2,
y= (-4) -2 therefore y = -6
Q‒4. Suppose A is the set composed of all ordered pairs of positive integers. Let R be the relation defined on A where (a,b)R(c,d) means that a+d=b+c.
Prove that R is an equivalence relation.
Find [(2,4)].
Answer:
Step-by-step explanation:
REcall that given a set A, * is a equivalence relation over A if
- for a in A, then a*a.
- for a,b in A. If a*b, then b*a.
- for a,b,c in A. If a*b and b*c then a*c.
Consider A the set of all ordered pairs of positive integers.
- Let (a,b) in A. Then a+b = a+b. So, by definition (a,b)R(a,b).
- Let (a,b), (c,d) in A and suppose that (a,b)R(c,d) . Then, by definition a+d = b+c. Since the + is commutative over the integers, this implies that d+a = c+b. Then (c,d)R(a,b).
- Let (a,b),(c,d), (e,f) in A and suppose that (a,b)R(c,d) and (c,d)R(e,f). Then
a+d = b+c, c+f = d+e. We have that f = d+e-c. So a+f = a+d+e-c. From the first equation we find that a+d-c = b. Then a+f = b+e. So, by definition (a,b)R(e,f).
So R is an equivalence relation.
[(a,b)] is the equivalence class of (a,b). This is by definition, finding all the elements of A that are equivalente to (a,b).
Let us find all the possible elements of A that are equivalent to (2,4). Let (a,b)R(2,4) Then a+4 = b+2. This implies that a+2 = b. So all the elements of the form (a,a+2) are part of this class.
Benjamin deposits $3,000 into each of two savings
accounts. The first savings account pays 5% interest
compounded annually. The second savings account
pays 5% simple interest annually. If Benjamin makes
no other deposits or withdrawals, what will be the
difference between the interest earned by the two
savings accounts after 4 years?
Answer:
So I have never stepped foot into this. But I have experience from this. So for the first one we can use the compound intrest formula - A = P(1+r/n)^nt so if we do that we get.
A = 3000(1+0.05/1)^1*4
So then we get A is equal to 3646.52
The next one we need to calculate
A = P (1 + rt)
So now we do A = 3000(1+0.05*1)
A = 3000*1.05 = 3150. We add them together and we get 6796.52.
So we subtract 6000 from that. He earned
796.52 dollars
Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)
Answer:
dA/dt = 12 - 2A/(100 + t)
Step-by-step explanation:
The differential equation of this problem is;
dA/dt = R_in - R_out
Where;
R_in is the rate at which salt enters
R_out is the rate at which salt exits
R_in = (concentration of salt in inflow) × (input rate of brine)
We are given;
Concentration of salt in inflow = 4 lb/gal
Input rate of brine = 3 gal/min
Thus;
R_in = 4 × 3 = 12 lb/min
Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min
So, after t minutes, there will be (100 + t) gallons in the tank
Therefore;
R_out = (concentration of salt in outflow) × (output rate of brine)
R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min
R_out = 2A(t)/(100 + t) lb/min
So, we substitute the values of R_in and R_out into the Differential equation to get;
dA/dt = 12 - 2A(t)/(100 + t)
Since we are to use A foe A(t), thus the Differential equation is now;
dA/dt = 12 - 2A/(100 + t)
If 3 boxes of apples weigh 105 pounds, how much would 2 boxes of apples weigh?
Answer:
70 pounds
Step-by-step explanation:
3 boxes= 105 pounds
2boxes= x pounds
Cross Multiply
3*x=105 *2
3x=210
3x/3=210/3
x=70 pounds
Answer:
70
Step-by-step explanation:
105/3=35
35x2=70
So 70 is the answer
A textile manufacturer has historically found an average of 0.1 flaws per square meter of cloth. Let X be the number of flaws in a bolt of 2000 square meters of cloth. How is X distributed
Answer:
Poisson distribution
Step-by-step explanation:
Given that :
There is an average of 0.1 flaws per square meter of cloth
So X = the number of flaws in a bolt of 2000 square meters of cloth.
The objective is to deduce how is X distributed.
Well, we can say X undergoes Poisson distribution.
Because, the flaw can be randomly positioned on the cloth and also dictate how many times the event is likely to occur within a specified period of time.
Most time Poisson distribution is majorly used for independent events.
An independent is an event which contains two types of events occuring at a time say event [tex]E_1[/tex] and event [tex]E_2[/tex] and the event [tex]E_1[/tex] does not in any way affects the occurrence of the event [tex]E_2[/tex] .
Adam drew a line that was 6 4/10 inches long. If he drew a second line that was 2 2/3
inches longer, what is the length of the second line? Answer as a mixed number.
Answer:
The length of the second line is [tex]9\frac{1}{15}[/tex] inches
Step-by-step explanation:
Given
Length of first line = [tex]6\frac{4}{10}[/tex] inches
Length of second line = [tex]2\frac{2}{3}[/tex] inches longer
Required
Length of second line.
Let the length of the second line be represented by x.
From the question, x is [tex]2\frac{2}{3}[/tex] inches longer than the first line;
This implies that:
[tex]x = 2\frac{2}{3} + 6\frac{4}{10}[/tex]
Convert both fractions to improper fractions
[tex]x = \frac{8}{3} + \frac{64}{10}[/tex]
Take LCM
[tex]x = \frac{80 + 192}{30}[/tex]
[tex]x = \frac{272}{30}[/tex]
Convert to mixed fraction
[tex]x = 9\frac{2}{30}[/tex]
Reduce fraction to lowest term
[tex]x = 9\frac{1}{15}[/tex]
Hence, the length of the second line is [tex]9\frac{1}{15}[/tex] inches
1. Find the equation of the line passing through the point (2,−4) that is parallel to the line y=3x+2 y= 2. Find the equation of the line passing through the point (1,−5) and perpendicular to y=18x+2 y=
Answer:
Step-by-step explanation:
1) Parallel lines have same slope
y = 3x + 2
m = 3
(2, -4) ; m = 3
equation: y - y1 = m (x - x1)
y - [-4] = 3(x - 2)
y + 4 = 3x - 6
y = 3x - 6 - 4
y = 3x - 10
2) y = 18x + 2
m1 = 18
Slope the line perpendicular to y = 18x + 2, m2 = -1/m1 = -1/18
m2 = -1/18
(1 , -5)
[tex]y-[-5]=\frac{-1/18}(x-1)\\\\y+5=\frac{-1}{18}x + \frac{1}{18}\\\\y=\frac{-1}{18}x+\frac{1}{18}-5\\\\y=\frac{-1}{18}x+\frac{1}{18}-\frac{5*18}{1*18}\\\\y=\frac{-1}{18}x+\frac{1}{18}-\frac{90}{18}\\\\y=\frac{-1}{18}x-\frac{89}{18}\\\\[/tex]
Researchers want to know about the true proportion of adults with at least a high school education. 1000 adults are surveyed, and 710 of them have at least a high school education. Create a 95% confidence interval for the true population proportion of adults with at least a high school education. Interpret this interval in context of the problem.
Answer:
The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).
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 = 1000, \pi = \frac{710}{1000} = 0.71[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.6819[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 + 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.7381[/tex]
The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).
Analyze the diagram below and answer the question that follows.
Ruby has a bird feeder which is visited by an average of 13 birds every 2 hours during daylight hours. What is the probability that the bird feeder will be visited by more than 3 birds in a 40 minute period during daylight hours? Round your answer to three decimal places.
Answer:
62.93%
Step-by-step explanation:
We have to solve it by a Poisson distribution, where:
p (x = n) = e ^ (- l) * l ^ (x) / x!
Where he would come being the number of birds that there would be in 40 minutes, we know that in 2 hours, that is 120 minutes there are 13, therefore in 40 there would be:
l = 13 * 40/120
l = 4,333
Now, we have p (x> 3) and that is equal to:
p (x> 3) = 1 - p (x <= 3)
So, we calculate the probability from 0 to 3:
p (x = 0) = 2.72 ^ (- 4.33) * 4.33 ^ (0) / 0! = 0.01313
p (x = 1) = 2.72 ^ (- 4.33) * 4.33 ^ (1) / 1! = 0.0568
p (x = 2) = 2.72 ^ (- 4.33) * 4.33 ^ (2) / 2! = 0.12310
p (x = 3) = 2.72 ^ (- 4.33) * 4.33 ^ (3) / 3! = 0.17767
If we add each one:
0.01313 + 0.0568 + 0.12310 + 0.17767 = 0.3707
replacing:
p (x> 3) = 1 - 0.3707
p (x> 3) = 0.6293
Which means that the probability is 62.93%
what is the greatest common factor of 36 and 90?
Answer:
18
Step-by-step explanation:
The greatest common factor is 18. All of the common factors are: 1, 2, 3, 6, 9, 18.
Answer:
There is only one greatest common factor of 36 and 90 which is 18. There are also a number of common factors including 1, 2, 3, 6, 9, 18.
Step-by-step explanation:
what is 2/3 of 460? Just a little easy one for points
Answer:
2/3 * 460 = 306 and 2/3
Multiply 460 by 2/3 by first multiplying 460 by 2, then divide that by 3:
460 x 2 = 920
920 /3 = 306 2/3
The answer is 306 2/3
Which graph has the parent function 1/x?
Answer:
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
Step-by-step explanation:
A rational function is described as the fraction of polynomials, where the denominator has degree of at least 1 .
Or it can be said that there must be a variable in the denominator.
The general form of a rational function is:
[tex]\text{Rational Function}= f(x)=\frac{p(x)}{q(x)}[/tex]
In this case the parent function provided is: [tex]f(x)=\frac{1}{x}[/tex].
The function is rational.
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
The graph is attached below.
Math Activity #1
The number of the day is 1,853,604,297.
Write this number in word form:
how much alcohol must be added to 480grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?
Answer:
what she/he said
Step-by-step explanation:
Dustin is buying carpet for the living room. How many square feet of carpet will he need to buy?
Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
Simplify.
(8^3)7 = 8n
Answer:
448I think
Step-by-step explanation:
Answer:21
Step-by-step explanation:
determine whether these two functions are inverses.
Answer:
Yes,these two functions are the inverse of each other.
Step-by-step explanation:
They way of finding if two functions ([tex]f(x)\,\,and\,\,g(x)[/tex] ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:
[tex]f(x) \,o \,g(x)=f(g(x))=x[/tex]
in our case:
[tex]f(g(x))=\frac{1}{g(x)+4} -9\\f(g(x))=\frac{1}{(\frac{1}{x+9} -4)+4}-9\\f(g(x))=\frac{1}{\frac{1}{x+9} }-9\\f(g(x))={x+9} -9\\f(g(x))=x[/tex]
The composition does render the identity, therefore, these two functions are indeed the inverse of each other
The perimeter of the rectangle is below 76 units. Find the length of side AD. AB on rectangle 3y + 3 CB 2y
Answer:
14 units
Step-by-step explanation:
The perimeter of a figure is the sum of the lengths of all the sides.
Here, we know that ABCD is a rectangle, so by definition, AB = CD and AD = BC. We also are given that AB = 3y + 3 and BC = 2y, which means that:
AB = CD = 3y + 3
AD = BC = 2y
Adding up all the side lengths and setting that equal to the perimeter, which is 76 units, we get the expression:
AB + CD + AD + BC = 76
(3y + 3) + (3y + 3) + 2y + 2y = 76
10y + 6 = 76
10y = 70
y = 7
We want to know the length of AD, which is written as 2y. Substitute 7 in for y:
AD = 2y = 2 * 7 = 14
The answer is thus 14 units.
~ an aesthetics lover
Answer:
14
Step-by-step explanation:
The perimeter of a rectangle is found by
P = 2 (l+w)
P = 2( 3y+3+2y)
Combine like terms
P = 2(5y+3)
We know the perimeter is 76
76 = 2(5y+3)
Divide each side by 2
76/2 = 2/2(5y+3)
38 = 5y+3
Subtract 3 from each side
38-3 = 5y+3-3
35 = 5y
Divide each side by 5
35/5 = 5y/5
7 =y
We want the length of AD = BC = 2y
AD = 2y=2*y = 14
A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling the number 1, 3, or 4. If there is more than one element in the set, separate them with commas. Sample space: {} Event of rolling the number 1 3, or 4 :
Answer:
Sample space: [tex]\Omega=\{1,2,3,4,5,6\}[/tex]
Event of rolling the number 1 3, or 4 : A={1,3,4}
Step-by-step explanation:
When you roll a number cube with faces labeled from 1 to 6 once.
The possible outcomes are: 1,2,3,4,5 or 6.
Therefore, the sample space of this event is:
Sample space: [tex]\Omega=\{1,2,3,4,5,6\}[/tex]Given the event of rolling the numbers 1, 3, or 4.
Now we are required to give the outcomes for the event of rolling number 1,3 or 4. Let's call the event A. The set of possible outcomes for A has all the numbers 1, 3 and 4 as follows
Event of rolling the number 1 3, or 4 :A= {1,3,4}The probability of randomly selecting a white flower from a garden that has green, pink, yellow, and white flowers is 6%.
Which of the following describes the likelihood of selecting a white flower?
A.
likely
B.
unlikely
C.
neither unlikely nor likely
Answer:
b. unlikely
Step-by-step explanation:
I don't really know a step by step explanation :( sry
When Ryan was born, he weighed 7 pounds.At 6 months, he weighed 11.2 pounds. Amanda weighed 6 pounds when she was born, and 12.9 pounds at 6 months. Which baby had a greater percent increase in weight? Explain
Answer:
✅Amanda had a greater percent increase in weight.
Step-by-step explanation:
The percent change in Ryan’s weight was 42/7 or 60%. The percent change in Amanda’s weight was 6.9/6, or 115%. Amanda had a greater percent increase in weight.
IamSugarBee
Answer:
The percent change in Ryan’s weight was 4.2/7, or 60%. The percent change in Amanda’s weight was 6.9/6 , or 115%. Amanda had a greater percent increase in weight.
Step-by-step explanation:
its the sample answer i just did it
Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the past century, life expectancy from age 65 has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expectancy should increase no further. In 1900, life expectancy at birth was 45 years, and life expectancy at age 65 was 75 yr. In 2010, these figures had risen to 78.7 and 84.5, respectively. In both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, find the maximum life expectancy for humans.
Answer:
The maximum life expectancy for humans is approximately 87 years.
Step-by-step explanation:
We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.
NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.
The linear function for Life expectancy from birth can be calculated as:
[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]
The linear function for Life expectancy from age 65 can be calculated as:
[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]
Then, the time t where both functions intersect is:
[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]
The time t=136.36 corresponds to the year 1900+136.36=2036.36.
Now, we can calculate with any of both functions the maximum life expectancy:
[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]
The maximum life expectancy for humans is approximately 87 years.
A study conducted at a certain high school shows that 72% of its graduates enroll at a college. Find the probability that among 4 randomly selected graduates, at least one of them enrolls in college.
Answer:
[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]
And we can use the probability mass function and we got:
[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]
And replacing we got:
[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of graduates who enroll in college", on this case we now that:
[tex]X \sim Binom(n=4, p=0.72)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X \geq 1)[/tex]
And we can use the complement rule and we got:
[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]
And we can use the probability mass function and we got:
[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]
And replacing we got:
[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]
A four-year study of various brands of bottled water found that 25% of bottled water is just tap water packaged in a bottle. Consider a sample of sevenseven bottled-water brands, and let x equal the number of these brands that use tap water. Complete parts a through d.
a. Is x (approximately) a binomial random variable?
b. Give the probability distribution for x as a formula.
c. Find p(x = 2).
d. Find P(x <= 1).
Answer:
Answers below
Step-by-step explanation:
a. Is x (approximately) a binomial random variable?
b. Give the probability distribution for x as a formula.
c. Find p(x = 2).
d. Find P(x <= 1).
Z=1.23 z=0.86 WHAT is the area of the shaded region between the two
Answer:
The area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.
Step-by-step explanation:
To solve this question, we need to find the corresponding probabilities for the standardized values (or z-scores) z = 1.23 and z = 0.86, and then subtract both to obtain the area of the shaded region between these two z-scores.
We need to having into account that a z-score is given by the following formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
Where
x is a raw score from the distribution that we want to standardize using [1].[tex] \\ \mu[/tex] is the mean of the normal distribution.[tex] \\ \sigma[/tex] is the standard deviation of the normal distribution.A z-score indicates the distance of x from the mean in standard deviations units, where a positive value "tell us" that x is above [tex] \\ \mu[/tex], and conversely, a negative that x is below [tex] \\ \mu[/tex].
The standard normal distribution is a normal distribution with [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex], and has probabilities for standardized values obtained using [1]. All these probabilities are tabulated in the standard normal table (available in any Statistical book or on the Internet).
Using the cumulative standard normal table, for [tex] \\ z = 1.23[/tex], the corresponding cumulative probability is:
[tex] \\ P(z<1.23) = 0.89065[/tex]
The steps are as follows:
Consult the cumulative standard table using z = 1.2 as an entry. Z-scores are in the first column of the mentioned table. In the first row of it we have +0.00, +0.01, +0.02 and, finally, +0.03. The probability is the point that result from the intersection of z = 1.2 and +0.03 in the table, which is [tex] \\ P(z<1.23) = 0.89065[/tex].Following the same procedure, the cumulative probability for [tex] \\ z = 0.86[/tex] is:
[tex] \\ P(z<0.86) = 0.80511[/tex]
Subtracting both probabilities (because we need to know the area between these two values) we finally obtain the corresponding area between them (two z-scores):
[tex] \\ P(0.86 < z < 1.23) = 0.89065 - 0.80511[/tex]
[tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex]
Therefore, the area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.
We can see this resulting area (red shaded area) in the graph below for a standard normal distribution, [tex] \\ N(0, 1)[/tex], and [tex] \\ z = 0.86[/tex] and [tex] \\ z = 1.23[/tex].
The graph shows the amount of protein contain in a certain brand of peanut butter. Which statement describes the meaning of the point (6, 30) on the graph?
A.) There are 6 g of protein per tablespoon of peanut butter.
B.) There are 30 g of protein per tablespoon of peanut butter.
C.) There is 6 g of protein in 30 tablespoons of peanut butter.
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Answer:
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Step-by-step explanation:
Interpretation of the graph:
x-axis: tablespoons
y-axis: grams of protein.
Which statement describes the meaning of the point (6, 30) on the graph?
(6,30) means that x = 6 and y = 30.
This means that in 6 tablespoons there are 30g of protein.
So the correct answer is:
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Answer:
The answer is D
