The value of y of the inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.
How to Solve an Inequality?Inequalities can be solved the way a normal algebraic equation is being solved. It is solved by isolating the value of the variable.
The inequality given is, 4y + 1/5 ≤ 4/5. Solve as shown below:
Subtract both sides by 1/5:
4y + 1/5 - 1/5 ≤ 4/5 - 1/5 [subtraction property of equality]
4y ≤ 3/5
Divide both sides by 4:
4y/4 ≤ 3/5 / 4
y ≤ 3/5 × 1/4
y ≤ 3/5 × 1/4
y ≤ (3 × 1) / (5 × 4)
y ≤ 3/20
The value of y is: y ≤ 3/20.
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Suppose a baker claims that the average bread height is more than 15cm. Several of this customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes 10 loaves of bread. The mean height of the sample loaves is 17 cm with a sample standard deviation of 1.9 cm. The heights of all bread loaves are assumed to be normally distributed. The baker is now interested in obtaining a 95% confidence interval for the true mean height of his loaves. What is the lower bound to this confidence interval? 2 cm (round to 2 decimal places) What is the upper bound to this confidence interval? cm (round to 2 decimal places) For the following situations, use RStudio to find the appropriate t-critical values that would be needed to construct a confidence interval. Round all critical values to the second decimal place. 1. n = 15, confidence level is 95%, x= 35 and s = 2.7, t-critical value- 2, n = 37, confidence level is 99%, x= 82 and s = 5.9 t-critical value- 2 3, n 1009, confidence level is 90%, x 0.9 and s-0.04 t- critical value = 2 2
The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm
To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.
The formula for a confidence interval for the population mean (μ) is:
Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))
For the first situation:
n = 15
Confidence level is 95% (which corresponds to an alpha level of 0.05)
x = 35 (sample mean)
s = 2.7 (sample standard deviation)
Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.
The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.
Plugging the values into the formula:
Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))
Calculating the confidence interval:
Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)
Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)
Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.
For the second situation:
n = 37
Confidence level is 99% (which corresponds to an alpha level of 0.01)
x = 82 (sample mean)
s = 5.9 (sample standard deviation)
The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.
The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.
Plugging the values into the formula:
Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))
Calculating the confidence interval:
Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)
Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)
Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.
For the third situation:
n = 1009
Confidence level is 90% (which corresponds to an alpha level of 0.10)
x = 0.9 (sample mean)
s = 0.04 (sample standard deviation)
The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.
The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.
Plugging the values into the formula:
Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))
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hello am trying to see if am doing this right
Given an expression below
\(\begin{gathered} \frac{p}{81}\text{ = 11} \\ \text{cross multiply} \\ \frac{p}{81}=\text{ }\frac{11}{1} \\ p\text{ }\times1\text{= 11 }\times\text{ 81} \\ p\text{ = 891} \end{gathered}\)Then the expresion will be equal once the value of p = 891
Hence the value of p = 891
Graph the line with slope -2/3 passing through the point (3, 3).
Answer:
Step-by-step explanation:
y - 3 = -2/3(x - 3)
y - 3 = -2/3x + 2
y = -2/3x + 5
-3.7z = 11.6
What is z
Answer:
-116/37
Step-by-step explanation:
Answer:
z = -3.1
Step-by-step explanation:
just divide both sides by -3.7, you get z = -3.135
I’ll give brainliest Write an inequality that represents this situation below.
Your suitcase for vacation will fit at most 11 outfits you already have 5 packed
Answer: 6 ≤ x ≤ 11
Step-by-step explanation:
Let x be the number of additional outfits that can be packed in the suitcase.
The suitcase will fit at most 11 outfits, which means that x cannot be greater than 11 outfits.
On the other hand, 5 outfits have already been packed, so the number of additional outfits that can be packed is at least 6.
Therefore, the inequality that represents this situation is 6 ≤ x ≤ 11.
Graph 5x + 3y = 15 on a graph
Help me out with this
Answer:
vertical angles
Step-by-step explanation:
The 2 given angles are vertical angles and are congruent
Which of the following correctly defines a population parameter?
A. a characteristic of the population
B. the difference between the maximum and minimum value of a sample
C. the difference between the maximum and minimum value of the population
D. a characteristic of a sample
The correct answer is A. a characteristic of the population.
A population parameter refers to a specific characteristic
A population parameter refers to a specific characteristic or numerical value that describes the entire population being studied. It is a fixed value that is typically unknown and estimated using sample data. Examples of population parameters include the population mean, population standard deviation, population proportion, etc.
Solve the equation.
t-12=3
Answer:
t = 15
Step-by-step explanation:
t - 12 = 3
t = 3 + 12
t = 15
HELP FAST!! ILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
Both of the games are the same i think that both are fair
Game A is not fair but Game B is fair
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, in Game A: Player 1 gets a point if the product of the numbers on the dice is even, and player 2 gets a point if the product on the numbers is odd Whereas in Game B the rule changes from product to sum
now the sample space of rolling two dice is given by S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6), or S(n)=36
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Now the product of two numbers is even Possibility 1) when both nos. are even
possibility 2) one is even other is odd
product of two nos. is odd when both nos. are odd so here for having an even product we can use: the 1-probability of getting odd multiplication
so the probability of getting odd no. on the first dice is 3/6=1/2
and the probability of getting an odd no. on the second dice is 3/6=1/2
so probability of getting odd product=(1/2)*(1/2)=1/4
so probability of getting even product=1-(1/4)=3/4
Thus clearly Game A is not fair
Game B Sample space for player 1 is S(even) = 18 thus probability P(even)=18/36 =1/2
Therefore Probability P(odd)= 1-1/2
= 1/2
Hence, Game B is the fair game.
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For what value of A is the function, (x), continuous at x=0?
(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3
(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1
(iii) h(0) = 1/7
The value of λ must be 7, for h(x) to be continuous at x = 0.
The given function is,
h(x) = 1/7, when x = 0
= 1 - 2 cos 2x, when x < π/2
= 1 + 2 cos 2x, when x > π/2
= x cos x/sin λx, when x < 0
Now,
(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3
(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1
(iii) h(0) = 1/7
Since the function is continuous at x = 0, so
\(\lim_{x \to 0}\) h(x) = h(0)
\(\lim_{x \to 0}\) x cos x/sin λx = 1/7
\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7
1/λ = 1/7
λ = 7
Hence the value of λ must be 7.
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ABCD has a perimeter of 27 units and is dilated by a scale factor of 1/3. What is the perimeter of A¹B¹C¹D¹?
Answer:
9 units
Step-by-step explanation:
First of all, let us understand the meaning of dilation.
Dilation means to change the size of any image or line or a figure.
Dilation can be used to enlarge (dilation by a factor greater than 1) the original figure.
OR
Dilation can be used to make the image smaller (dilation by a factor lesser than 1) the original figure.
Here, we are given that an image with 4 points ABCD is dilated by a scale factor of \(\frac{1}{3}\).
Its sides will be AB, BC, CD and DA.
Perimeter is equal to the sum of all the sides of a closed figure.
So, perimeter of ABCD = AB + BC + CD + DA = 27 units ...... (1)
Now, it is dilated by a scale factor of \(\frac{1}{3}\).
So, all the sides will become smaller i.e.
A'B' = \(\frac{1}{3}\) AB
B'C' = \(\frac{1}{3}\) BC
C'D' = \(\frac{1}{3}\) CD
D'A' = \(\frac{1}{3}\) DA
Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A' = \(\frac{1}{3}\)AB + \(\frac{1}{3}\)BC + \(\frac{1}{3}\)CD + \(\frac{1}{3}\)DA
\(\frac{1}{3}\) (AB + BC + CD + DA ) = \(\frac{1}{3} \times 27\)(By equation (1))
Perimeter of A'B'C'D' = 9 units
Which sum or difference is modeled by the algebra tiles
Answer:
i believe the answer that you picked is right ....i think ^^
6. It takes about 20 minutes to walk a mile. About how
long would it take to walk a half mile
please help me so love this problem?
Answer:
12.7 ==> distance of RS
24.2 ==> distance of RT
Step-by-step explanation:
Distance is always positive. So if you get a negative value, take the absolute value of the negative number:
For example, between point R and S:
-17.2 - (-4.5) =
-17.2 + 4.5 = ==> subtracting a negative number is equivalent to adding a
positive number
-(17.2 - 4.5) = -12.7
-12.7 ==> |-12.7| = 12.7 ==> distance of RS
For RT:
-17.2 - 7 =
-(17.2 + 7) = -24.2
-24.2 ==> |-24.2| = 24.2 ==> distance of RT
complete the cumulative frequency table
Answer:
'HOFHX'HJF M'VIKJPRGFPG'9FGUJPF'G TOOTHLESSILHGUDGSGS;UIGERGIFGUSUUFDIIGH;D,FMGF'DFDIJIDFFIFIJIJHJHJFOHJFJHJHOFHFGJHGJPJHOFJFGUHOGJC;C;JHC;OFHJFGIJF'IJHGHJ'CFJH'J'HGJP
FGH
KGK
OPHOGPF'HK
Step-by-step explanation:
HDHDTHJTIHPOTJYITOIJOIJHIFJOGJOHGGJFJGOIJOFHGM;LVHHPKPGJYJKTUYJY
Please help!!!!!! If the measure of angle 8 is 35 what is the measure of angle 4?
Answer:
35
Step-by-step explanation:
Comman knowlege. Also there is a fancy name for them because thay are the same way... Corresponding Angles
Answer:
35 degrees
Step-by-step explanation:
It is congruent to 8 and lined up so it is also 35 degrees.
Sarah walked ½ mile yesterday morning and ¾ mile yesterday afternoon. What was the total distance walked by Sarah?
Answer:
1.25 miles or 5/4
Step-by-step explanation:
Take the two distances and add them together and simplify.
Answer: 1 & 1/4 mile
Explanation:
1/2 = 2/4
She walked 2/4 of a mile in the morning and 3/4 of a mile in the afternoon. The total she walked is 5/4 of a mile. We add the numerators and place the sum over the common denominator.
The improper fraction 5/4 converts to the mixed number 1 & 1/4, since,
5/4 = (4+1)/4 = 4/4 + 1/4 = 1 + 1/4 = 1 & 1/4
Assume that a procedure yields a binomial distribution with a trial repeated n30 times. Use the binomial probability formula to find the probability of x5 successes given the probability p of success on a single trial. Round to three decimal places.
Answer:
The probability is \(P(X = 5) = 142506*p^{5}*(1 - p)^{25}\), in which p is the probability of a success on a single trial.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
The trial is repeated 30 times:
This means that \(n = 30\)
Find the probability of 5 successes given the probability p of success on a single trial
This is \(P(X = 5)\). So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 5) = C_{30,5}.p^{5}.(1 - p)^{25}\)
\(P(X = 5) = 142506*p^{5}*(1 - p)^{25}\)
The probability is \(P(X = 5) = 142506*p^{5}*(1 - p)^{25}\), in which p is the probability of a success on a single trial.
In complete sentences, answer the following question.
What are the elements of a body paragraph?
The weights of bags of chips are normally distributed with a mean of 180 grams and a standard deviation of 4 grams.
What percent of the bags of chips weigh less than 176 grams?
2.5%
16%
32%
34%
The percent of the bags of chips weigh less than 176 grams is b 16%
What percent of the bags of chips weigh less than 176 grams?From the question, we have the following parameters that can be used in our computation:
Mean = 180
Standard deviation = 4
Bags of chips weigh less than 176 grams
This means that
x = 176
So, the z-score is
z = (176 - 180)/4
Evaluate
z = -1
The percent of the bags of chips weigh less than 176 grams is represented as
P = P(z < -1)
Using a graphing calculator, we have
Percentage = 0.15866
So, we have
Percentage = 16%
Hence , the percentage is 16%
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Solve this :9x + 3 < 21
Answer:
Step-by-step explanation:
9x<21-3
9x<18
x<18/9
x<2
Someone pls help me i beg I will mark brainliest
Answer:
k=1
Step-by-step explanation:
The rise over run is 1, so the slope/constant of proportionality is 1.
PLEASE HELP ASAP OR ELSE ILL FAIL
#1-2: Find the value of x and the measure of all three angles
Show your work I’ll give brainliest :)
Answer:
1. x=20 ; the angles are 90 degrees31 degrees 59 degrees
2. x=16; the angles are 16 degrees 92 degrees 72 degrees
Step-by-step explanation:
1. 180=90+31+(3x-1)
180-90-31=3x-1
59=3x-1
60=3x
x=20
plug in x for the third angle
2. 180= x+5x-8+3x+44
180=9x+36
180-36=9x
144=9x
x=16
plug in x to all the angles to find the real value
9.8 x 100 =
0.040 x 1,000 =
61 divide 10 =
8.909 x 100 =
Answer:
9.8 * 100 = 980
0.040 * 1000 = 40
61 / 10 = 6.1
8.909 * 100 = 890.9
Step-by-step explanation:
Wyatt translates both lines 6 units
up and 2 units to the left. Which
of the following must be true?
A. After the translation, line f will not
intersect line g.
B. After the translation, line f will be
the same line as g.
C. After the reflection, line f will not
intersect the y-axis.
D. After the reflection, line g will not
intersect the x-axis.
If your Science class eats 168 slices of
pizza in 4 hours, how many slices is
that per hour?
Answer:
42 slices per hour
Step-by-step explanation:
Answer: 42 slices per hour
Step-by-step explanation: 168 divided by 4= 42
Or 42x4= 168
16-18 help please !!!!!!
Answer:
not sure but -2
Step-by-step explanation: I did on calculator
Mr. Shand had $59.75 in his bank account, but then he bought some new ties and some pancakes. After the purchase, he was in debt $75.10. Which of the following rational numbers best shows the change in Mr. Shand’s account balance?
STEP BY STEP EXPLINATION PLEASE!
Answer:
Ok so first he bought the road and pancakes with means he speant 134.85 dollars which mean he out himself in the negatives after he bought the his items
What is the slope of the line that passes through the points shown in the table?
х
y
-1
-5
0
-3
1
-1
2
1
slope
Answer:
Where is the table???
Step-by-step explanation:
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