The required 90% confidence interval for population mean age is (22.35,23.45)
Given,
Sample size, n = 20
Sample mean, μ = 22.9 years
Standard deviation, σ = 1.5 years
Significance level, α = 0.05
We have to find the 90% confidence interval;
Here,
x ± z(critical) σ/√n
Substituting the values;
z(critical) at α₀.₀₅ = ±1.64
22.9 ± 1.64 (1.5/√20)
= 22.9 ± 0.55
= (22.35, 23.45)
That is,
(22.35,23.45) is the required 90% confidence interval for population mean age.
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an active-high input s-r latch has a 1 on the s input and a 0 on the r input. what state is the latch in?
Q=1,Q'=0 as an active-high input s-r latch has a 1 on the s input and a 0 on the r input.
What is s-r latch?An SR latch (Set/Reset) is an asynchronous device that solely depends on the state of the S and R inputs and does not require any input from the control signals. The illustration demonstrates how two NOR gates with a cross-feedback loop may be used to build an SR latch. Set-reset, or S-R, latches are therefore the most basic type of bistable device. We can connect two NOR gates so that the output of one feeds back into the input of the other, and vice versa, to create an S-R latch, as shown below: The Q and not-Q outputs are supposed to be in opposing states.
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Pls help I don’t understand
Answer:
why u remove my answer
Step-by-step explanation:
Un árbol se vende en base a la circunferencia de su tronco. Si el tronco de un árbol tiene un radio de 4 pulgadas, ¿cuál es la circunferencia del tronco del árbol?
Answer:
25.12 pulgadas
Step-by-step explanation:
A research firm determined that the equation y=2x+80 can be used to model the total amount of spending by tourist in florida,y, in billions of dollars, for the years 2013-2017 where x is the number of years since 2013.
determine the key features for the context
domain? range? as x values increase,y values ? slope? x intercept? y intercept? thank ya
Slope of y = 2x +80 is 2, y-intercept is 80, x-intercept is -40.
What is Slope?Slope is defined as how much the y-coordinate changes with respect to the x-coordinate. Slope remains constant anywhere on the line.
Given equation is y = 2x + 80, where y is total amount of spending by tourist in Florida, in billions of dollars and x represents the number of years since 2013.
Equation of a line in slope-intercept form is,
y = mx + c, where m is the slope of the line and c is the y-intercept.
Comparing the given equation with slope-intercept form, we get,
m = 2 and c = 80
Domain of the equation includes number of years from 2013 - 2017 and the range of the equation is the corresponding y values.
Since slope is positive, as x value increases, y value also increases.
x- intercept is the point where the line touches the x-axis. y-coordinate will be zero at that point.
0 = 2x + 80 ⇒ x = -40
For the equation y = 2x +80, slope = 2, y-intercept = 80, x-intercept = -40.
Domain is the set of all number of years from 2013 - 2017 and range is the corresponding amount spend by tourist in the years from 2013-2017. As x value increases, y value also increases.
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Write a number in which the value of the digit in the thousands place has one-tenths the value of the digit in the ten-thousands place.
The answer is 10,000
Please help me fast! Which equation has the solution x = 5? Select each correct answer. Responses
32 − 4x = 12 , 11 + 6x = 22 , 18 − 2x = 9 , x/5 + 5 = 6 , 3x + 1 = 9 , 25/x + 4 = 9
Answer:
A ; D ; F
Step-by-step explanation:
32 - 4(5) = 12
32 - 20 = 12 (ok)
11 + 6(5) = 22
11 + 30 = 22
41 = 22 (false)
18-2(5) = 9
18 - 10 = 9
8 = 9 (false)
5/5 + 5 = 6
1 + 5 = 6
6 = 6 (ok)
3(5)+ 1 = 9
15 + 1 = 9
16 = 9 (false)
25/5 + 4 = 9
5 + 4 = 9
9 = 9 (ok)
the mid-state soccer conference has 6 teams. each team plays the other teams once. (a) how many games are scheduled?
The total number of games would be 15 games.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
Consider each team playing with the other team once
Total number of games scheduled = Number of ways of selecting 2 from 6 teams
[tex]=^nC_r\\\\=^6C_2\\\\=\frac{6!}{2!*4!}\\\\=15[/tex]
Hence the total number of games would be 15 games.
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30% of a is 18
Pls help!! Looking for what A is!
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 18}}{\left( \cfrac{30}{100} \right)18}\implies 5.4[/tex]
lupita bought 5 pounds of pretzels at a wholesale store for $12.75 how much would it cost lupita to buy 7 pounds of pretzels.
Answer:
17.85
Step-by-step explanation:
You first divide 12.75 by 5, to see the price for one pound of pretzels. Then, you times that by 7, because you want to know how much it would cost for Lupita to but 7 pounds of pretzels. That would equal 47.85, which is your answer.
BRAINLIEST, PLEASE!How many times smaller is 1.9 × 103 than 4.085 × 105?
a. 0.46
b. 2.15
c. 46
d. 215
The 1.9 × 103 is 2.15 times smaller than 4.085 × 105. (Option B)
In order to determine a number is how many times smaller than the other number, the second number is divided by the first number. Division and multiplication, both used in the situation are basic arithmetic operations. In the give case, the in order to determine how many times smaller 1.9 x 103 is than 4.085 x 105, is given by
4.085 x 105/1.9 x 103
First simplifying by multiplying the terms in the numerator and denominator
4.085 x 105/1.9 x 103
428.925/195.7
Dividing the numerator by denominator,
428.925/195.7 = 2.15
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simple interest on a $198,562 mortgage at 3.99%?
The simple interest on the amount $198,562 mortgage at 3.99% will be $7922.62.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year, the principal amount in simple interest remains constant.
As per the given,
Principle amount P = $198,562
Rate = 3.99%
Interest amount = 3.99% of $198,562
⇒ (3.99/100)198562 = $7922.62
Hence "The simple interest on the amount of $198,562 mortgage at 3.99% will be $7922.62".
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the board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?
This fails to reject the null Hypothesis.
What is z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
a recent survey reported that small businesses spend 24 hours a week marketing their business.
these businesses are spending less than 24 hours a week on marketing. the chamber conducts a survey of 58 small businesses within their state and finds that the average amount of time spent on marketing is 22.7 hours a week.
assuming that the population standard deviation is 6.1 hours.
z = x'- u / α(/√n) = (5.05-4.50/1.83/√38) = 1.85
Hence, This fails to reject the null Hypothesis.
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which number is bigger and why? (7/9 and 5/8) [word problem in attachment]
The player who has the better record between Jamal and Brian as required in the task content is; Jamal.
Which player has the better record of Jamal and Brian?It follows from the task content that the player who has the better record between Jamal and Brian is to be determined.
Since it is given that Jamal and Brian 7/9 and 5/8 of their free throws respectively;
It follows that when expressed as a percentage; we have;
For Jamal;
7 / 9 × 100% = 77.78%
For Brian;
5 / 8 × 100% = 62.5%.
Ultimately, the player who has the better record for free throws is; Jamal since he has a greater percentage success rate for free throws.
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Volcanic eruptions of Mt. Vesuvius follow a Poisson distribution with an average of 2.5 eruptions every 100 years. Use that to answer the following:
a) Find the probability that there will be exactly 3 eruptions in the next 200 years. (6 points) (Round your answer to 4 decimal places)
b) Find the probability the next eruption occurs between 25 and 50 years. (6 points) (Round your answer to 4 decimal places)
(a) The probability that there will be exactly 3 eruptions in the next 200 years is 0.1404
(b) The probability the next eruption occurs between 25 and 50 years is 0.2488
Let X be the random variable denoting the volcanic eruptions as follows
Poisson distribution with parameters λ.
the average of the eruption is λ=2.5 per year.
Also for 200 eruptions the average of the eruptions is λ=2.5 per year.
Also, for 200 eruptions, the average of the eruptions is λ=5 per year.
The probability is:
P(X=3) = e⁻³(5)³/3!
= 0.0067×125/3×2×1
= 0.8422/6
= 0.1404
(b) Let X be the random variable denoting the volcanic eruptions as follows
Poisson distribution with parameters λ and also let 2.5 eruptions in 100 years is same as waiting time of:
100/2.5
= 40 years per eruption
therefore, X ~ Exp(β=40)
the probability density function of X is:
f(x) = { 1/40 e⁻¹/⁴⁰ , x>0
0 , otherwise}
And cumulative distribution function is:
P(X≤x) = 1 - e, x>0
the probability is:
P(25<X<50) = P(X<50)-P(X<25)
P(25<X<50) = e²⁵/⁴⁰ - e⁵⁰/⁴⁰
= e⁻°·°²⁵ - e⁻¹·²⁵
= 0.5353 - 0.2865
= 0.2488
Hence we get the required answer.
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Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 30 mpgwith a standard deviation of 7 mpg. Thirty-one non-hybrid sedans get a mean of 20 mpg with a standard deviation of three mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test at the 5% level to evaluate the manufacturers claim.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
State the null hypothesis
State the alternative hypothesis.
In words, state what your random variable Xhybrid − Xnon−hybrid represents.
State the distribution to use for the test.
What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)
What is the p-value?
what is the Alpha?
Explain how you determined which distribution to use.
99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the Manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.
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A coin sold for $271 in 1976 and was sold again in 1988 for $417. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V, = 271.
k=
(Round to the nearest thousandth.)
well, let's noticed, the original amount is $271 and 12 years later it turned to $417, so
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$417\\ P=\textit{initial amount}\dotfill &271\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0\\ t=years\dotfill &12\\ \end{cases}[/tex]
[tex]417=271(1 + \frac{r}{100})^{12}\implies \cfrac{417}{271}=\left( \cfrac{100+r}{100} \right)^{12} \implies \sqrt[12]{\cfrac{417}{271}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[12]{\cfrac{417}{271}}=100+r\implies 100\sqrt[12]{\cfrac{417}{271}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{3.657\approx r} \end{array}}[/tex]
The triangle depicted in the scale drawing has an actual area of 81 square units. What is the scale factor from the scale drawing to the actual triangle? (Note: Each square on the grid has a length of 1 unit.)
The scale factor from the scale drawing to the actual triangle is; 1/3
How to determine the Scale Factor?The area of a triangle is calculated using the formula;
A = ¹/₂bh
Where;
A is area.
b is base.
h is height.
The two sides of the rectangle are 6 units and 3 units. Use the measurements in the formula. "u" is for units.
Thus;
A = ¹/₂(6)(3)
A = 9 square units
The scale factor, represented by the variable "k", tells you how much a shape enlarged or reduced. If "k" is greater than 1, the shape enlarged. If "k" is greater than 0 and less than 1, the shape reduced
In this case, since the drawing is smaller than the actual triangle, the scale factor will be a fraction less than 1 and greater than 0.
The scale factor is used for side length. When it's used to find a side length, we use "k" multiplied by a side. Since the information we know is area, we find k² first, then isolate "k".
Divide the depicted triangle area by the actual area.
k² = 9 ÷ 81
k² = 1/9
√k² = √(1/9)
k = 1/3
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a voice teacher selects 8 students from the class to sing for the trustees. the class has 12 men and 13 women. in how many ways can 8 students be selected and arranged in a row with 4 men in the middle and 2 women on each end?
The number of ways that the teacher can arrange the row is 185328000
Given,
Number of male students = 12
Number of female students = 13
Number of students teacher needs to select = 8
The row arrangement is like; 4 men in the middle and 2 women on each end;
Here,
Order of the arrangement is considered.
So, permutation can be used.
Female students selected = ¹³P₂
Male students selected = ¹²P₄
Then,
Number of ways for the arrangement = ¹³P₂ × ¹²P₄
= 15600 × 11880
= 185328000
That is,
The teacher can arrange a row with 4 men in the middle and 2 women on each end in 185328000 ways.
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What's the first step when solving the equation: -2(x + 5) - 4 = 5x?
Subtract 5x from both sides
Combine like terms on the left side
Distribute 2
Distribute -2
Answer:
i suggest using -2 to multiply the figures in the bracket as a first step
Step-by-step explanation:
then you'll have something like this
-2x - 10 - 4 = 5x
-2x - 14 = 5x
-14 = 5x + 2x
-14 = 7x
x = -14/7
x = -2. hope this helps
Graph the inverse for the relation on the same graph as the function.
The function in the graph is y = x² - 1 and the inverse of the function is y = √(x + 1) and the graph is attached
How to find the inverse functionExamining the graph the vertex is v(h, k) = (0, -1)
Quadratic equation is of the form
y = a(x + h)² + k
using the vertex we write the equation as
y = a(x + 0)² - 1
using point (1, 0) a is calculated
0 = a(1 + 0)² - 1
a = 1
The equation of the graph is
y = a(x + 0)² - 1
y = x² - 1
The domain of the equation is all real numbers and the range is calculated from the inverse
x = √(y + 1)
y + 1 ≥ 0
y ≥ -1
Inverse function
y = x² - 1
x² = y + 1
x = ±√(y + 1)
exchanging the variables
y = ±√(x + 1)
taking the positive function
y = √(x + 1)
here the domain and range is exchanged
range: all real numbers
domain: x ≥ -1
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ou need to buy some chicken for dinner tonight. you found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.29 a pound. is it worth the extra drive? first, determine what information you need to answer this question, then click here to display that info (along with other info). how much chicken will you be buying? 3 pounds how much far are the two stores? my neighborhood store is 2.3 miles away, and takes about 7 minutes. the store across town is 8.4 miles away, and takes about 22 minutes. how kind of mileage does your car get? it averages about 23 miles per gallon in the city. how many gallons does your car hold? about 14 gallons how much is gas? about $3.87/gallon right now. going to the close store is cheaper going to the further store is cheaper the cheaper option saves you $ give your answer to the nearest cent.
1) $9.27 (far store), $9.87 (near store)
2) $0.169 per mile
3) 4.6 miles , 16.8 miles
4) $0.78, $2.84
5) $10.05 to the far store, $12.71 to the near store
What is Cost?
A mathematical formula known as the cost function is used to graph how production costs will change depending on the output level. To put it another way, it calculates the overall cost of production based on the quantity that is produced.
1) Let's compare chicken costs:
$3.09 * 3 = $9.27 (far store)
$3.29 * 3 = $9.87 (near store)
2) Now let's look at how much it costs to travel in your car:
[tex]\frac{3.87}{23} = 0.169\ per \ mile[/tex]
= $0.169 per mile.
3) Next, let's look how much it costs to travel to each store from the gas used. Multiply by 2 because you not only have to drive there, but also back home for the round trip:
2.3 miles * 2 = 4.6 miles
8.4 miles * 2 = 16.8 miles
4) Now to find the cost of gas for the respective trips:
$0.169 * 4.6 = $0.78
$0.169 * 16.8 = $2.84
5) We can just eyeball it from here that it's not worth it to travel, but for completion's sake, let's add the gas and chicken costs together:
$9.27 + $0.78 = $10.05 to the far store
$9.87 + $2.84 = $12.71 to the near store
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FAST
If Gabriel has 25.65 kg an he sold 3.87 how many kg he has?
Correct answer gets a Brainliest and 5 stars.
Answer:
12.78
Step-by-step explanation:
He has 25.65, sold 3.87. 25.65-3.87=21.78
Find the values of the variables assuming the figures are parallelograms
Adjacent angles of a parallelogram are supplementary.
[tex]3x+10+8x+5=180 \\ \\ 11x+15=180 \\ \\ 11x=165 \\ \\ \boxed{x=15} \\ \\ \\ \\ 5y+3(15)+10=180 \\ \\ 5y+55=180 \\ \\ 5y=125 \\ \\ \boxed{y=21}[/tex]
Helpp Please i will give brainliest to first correct answers
The point of the coordinate plane is ( 0.5 , 1 )
what is coordinate plane ?
The definition of a coordinate plane is as follows: A coordinate plane, often referred to as a rectangular coordinate plane grid, is a two-dimensional plane made up of the Y-axis, a vertical line, and the X-axis, a horizontal line.
solution:
A( -3, -5) and B( 2, 7 ), m:n = 1:1
using section formula
P = [ { (mx2+nx1)/ (m+n) , { (my2+ny1)/ (m+n) }]
= [ 1(2) + 1(-3) / 2 , 1( 7 ) + 1(-5) / 2 ]
= ( 0.5 , 1 )
Hence the coordinate plane point is ( 0.5 , 1 )
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3+2 x what = 17? This is due tomorrow but I’m stuck pls help
Answer:
7
Step-by-step:
2 * 7 =14 first due to PEMDAS
3 + 14 = 17
Answer:
7
Step-by-step explanation:
Let "x" be denoted as the variable for "what".
The question posted is: 3 + 2x = 17
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, subtract 3 from both sides of the equation:
2x + 3 = 17
2x + 3 (-3) = 17 (-3)
2x = 17 - 3
2x = 14
Next, divide 2 from both sides of the equation:
(2x)/2 = (14)/2
x = 14/2
x = 7
7 is your answer.
~
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Lines KS, ME, and YE are shown.
Complete the table using the word bank to prove
Answer:
there's no picture
100 PTS!!!!PLS HELP ASAP!!! THE CHOICES ARE THE SAME FOR REASON 7 AND 6!! ANSWE BOTH REASONS
Answer:
CPCTC
Step-by-step explanation:
BD is perpendicular to AC, forming two right triangles. The hypotenuses are congruent, as is our leg that we will call b. If we use Law of Sines to find our angles a and c (no matter the values), we would find that because b is the same leg in both triangles and the hypotenuses are congruent, angles a and c are congruent, so therefore your missing angle in both triangles is congruent, and using a trig function will find that AD and CD are congruent, making all of both triangles congruent.
Find X : X/2 = 1
X=1/2
X=-2
X=1
X=2
Answer:
x=2
Step-by-step explanation:
x/2 = 1 (multiply by 2 both sides)
x= 2
PLS ANSWER ASAP!!! 60 PTS
Answer: I think the answer is A.
A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.
Years of experience Salary
0 $52,000
1 $53,150
2 $54,260
3 $55,285
4 $56,921
5 $57,126
Use the equation for the line of best fit to predict the salary for an employee with 6 years of experience? (Round your answer to the nearest dollar.)
$61,150
$58,587
$59,672
$57,990
The equation for the line of best fit to predict the salary for an employee with 6 years of experience is $58,587.
What is meant by slope?The letter m is frequently used to represent slope; the reason for this is unclear, although it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888, who wrote it as "y = mx + c."
Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. When the ratio is stated as a quotient ("rise over run"), the result is the same for each
We have to take any two points in the given information and find the value of slope.
Let the two points are (0, 52000), (1, 53,150)
m=(53150-52000)/(1-0)
m=1150
Therefore, slope=1150
Now, the equation of the line is y=mx+b
52000=1150(0)+c
c=52000
Therefore, y=1150x+52000
For 6 years experience,
Take x=6 then,
y=1150(6)+52000
y=6900+5200
y=58,900
y=$58,900≈58,587
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Answer:
$58,587.
Step-by-step explanation: