Testing the hypothesis using the z-distribution, it is found that since the p-value of the test is of 0.0262 < 0.05, it can be concluded that the new booklet is effective.
At the null hypothesis, we test if there has been no improvement, that is, the time is still of 3 hours. Hence:
[tex]H_0: \mu = 3[/tex]
At the alternative hypothesis, we test if there has been improvement, that is, the time is of less than 3 hours. Thus:
[tex]H_1: \mu < 3[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In this problem, the values of the parameters are: [tex]\mu = 3, \sigma = 0.2, \overline{x} = 2.9, n = 15[/tex].
Then, the value of the test statistic is:
[tex]z = \frac{2.9 - 3}{\frac{0.2}{\sqrt{15}}}[/tex]
[tex]z = -1.94[/tex]
The p-value of the test is the probability of finding a sample mean of 2.9 hours or less, which is the p-value of z = -1.94.
Looking at the z-table, z = -1.94 has a p-value of 0.0262.
Since the p-value of the test is of 0.0262 < 0.05, it can be concluded that the new booklet is effective.
A similar problem is given at https://brainly.com/question/25413422
Simplify fully
18(x−3)−6(x−3)2
Answer:
6(x - 3)
Step-by-step explanation:
18(x−3)−6(x−3)2 =>
18x - 54 - 12 (x - 3 ) =>
18x - 54 - 12x + 36 =>
18x - 12x - 54 + 36 =>
6x - 18 or 6(x - 3)
both answers are good, althoguth this second one 6 (x - 3) should be the one that you are looking for
I need help with this question. This is my first time using this app so I don’t know how to include multiple images in one message.
Answer:
<AC=11
Step-by-step explanation:
<AB=70 and <BC=99 what is <AC=?
180-70=110
110-99=11
11-11=0
Nathan usually drinks 33 ounces of water per day. He read that he should drink 59 ounces of water per day. If he starts drinking 59 ounces, what is the percent increase? Round to the nearest percent.
Step-by-step explanation:
33oz = 100%
1% = 100%/100 = 33/100 = 0.33oz
59 - 33 = 26oz increase
how many % are these 26oz compared to the original 33oz ?
we need to see how often 1% fits into 26oz.
26/0.33 = 78.78787878...%
rounded this means a 79% increase of drinking water.
The price increases 20% each week. The price of oranges this week is $4.50 . What was the price last week?
Answer:
3.60
Step-by-step explanation:
4.50 · 0.2 = 0.94.50 - 0.9= 3.60original · percent as decimal = original + or - answer to step one= answer
Answer:
last week the where 3.6
Step-by-step explanation:
100 point math question pls help, no fake answers
The sequence of the terms is -7,-1+5, and +11. A series is a collection of sequences.
What is the difference between a sequence and a series?A sequence is a collection of items that have been arranged in a logical order, with members appearing either before or after each other.
Given equation ;
[tex]\rm a_n = a_{n-1}+6[/tex]
If,
[tex]\rm a_1 = -13[/tex]
The next term in the sequence is;
[tex]\rm a_2 = a_{2-1}+6 \\\\ \rm a_2 = a_{1}+6 \\\\ a_2 = -13 +6 \\\\ a_2 =-7[/tex]
[tex]\rm a_3 = a_{3-1}+6 \\\\ \rm a_3 = a_{3}+6 \\\\ a_3 = -7 +6 \\\\ a_3 =-1[/tex]
[tex]\rm a_4 = a_{4-1}+6 \\\\ \rm a_4 = a_{3}+6 \\\\ a_4 = -1 +6 \\\\ a_4 =+5[/tex]
[tex]\rm a_5 = a_{5-1}+6 \\\\ \rm a_5 = a_{4}+6 \\\\ a_5 = 5 +6 \\\\ a_5 =11[/tex]
Hence, the sequence of the terms is -7,-1+5, and +11.
To learn more about the sequence, refer to https://brainly.com/question/9737262.
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A bag contains 12 red marbles. The ratio of red marbles to blue marbles is 3:4. Find the number of blue marbles in the bag. blue marbles
Answer: 4
Step-by-step explanation:
since they are comparing it red to blue marbles and in 3:4 ratio 4 is the second one and it is comparing red to BLUE the second 1 is blue
What’s these. Tell me I’m serious. What is these?
13
Step-by-step explanation:
2 short questions 1 pls help
9514 1404 393
Answer:
3. 1.8
4. 66
Step-by-step explanation:
3.The common difference is the difference between a term and the one before it.
5 -3.2 = 1.8
The common difference is 1.8.
__
4.The 8th term is found by putting 8 where n is and doing the arithmetic.
a₈ = 10·8 -14
a₈ = 80 -14 = 66
The eighth term is 66.
_____
Additional comments
The difference is only "common" if all pairs of adjacent terms have the same difference. When that is the case, any pair of adjacent terms can be used to find the common difference. The arithmetic is probably easier using ...
6.8 -5 = 1.8
__
In question 4, the sequence has a first term of -4 and a common difference of 10. The sequence is ...
-4, 6, 16, 26, 36, 46, 56, 66 . . . . the 8th term is 66.
c) How could you use estimation to determine if your answer is reasonable? Explain.
If you drew a line segment from the point when Kiley’s plane took off to the point when she got off the plane, at which point would the line segment end?
690
Step-by-step explanation:
Given the coordinates below, determine if ΔFGH and ΔJKL are congruent. If they are, give the reason, if they aren't choose "not congruent".
F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)
*enter your lengths to the NEAREST TENTH
Answers:
FG = 8.5 GH = 11.4 FH = 17.5 JK = 11.4 KL = 17.5 JL = 8.5The triangles are congruent by SSS=======================================================
Explanation:
Use the distance formula to compute the length of each segment. For instance, the distance from point F to point G is the length of segment FG.
I'll show the steps on finding the length of FG
[tex]F = (x_1,y_1) = (-5,10)\\\\G = (x_2,y_2) = (-2,2)[/tex]
[tex]d = \text{distance from F to G}\\\\d = \text{length of segment FG}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-5-(-2))^2+(10-2)^2}\\\\d = \sqrt{(-5+2)^2+(10-2)^2}\\\\d = \sqrt{(-3)^2+(8)^2}\\\\d = \sqrt{9+64}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\d \approx 8.5\\\\[/tex]
The length of segment FG is approximately 8.5 units. The other side lengths are handled in the same way. As an alternative, you can use the pythagorean theorem.
---------------------
Once you determine all six lengths, note we have the following three pairs of corresponding congruent sides:
FG = JL = 8.5GH = JK = 11.4FH = KL = 17.5Because we have three pairs of equal sides, this means we can use the SSS (side side side) congruence theorem to prove the triangles are congruent. In other words, we have two identical triangles. One triangle is a rotated and reflected copy of the other.
The diagram is below.
what number is 30 percent of 80
Answer:
24
Step-by-step explanation:
Answer:Thus 30% of 80 is (30/100) x 80 = 24.
please help with mark as brainliest please also show work
Answer:
D. -3x + 18
Step-by-step explanation:
3x - 9y = 18
y = 1/3 x - 2 ... x intercept 0 = 1/3x -2 x=6
perpendicular line slope: - 1/(1/3) = -3 and (6,0) 0n the line
equation: (y-0)/(x-6) = -3
y = -3x +18
Graph y + 14 = -7x help me pls
Answer:
see attached graph
Step-by-step explanation:
There are a couple of ways you can look at this.
Point-Slope Form
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Comparing this to the given equation, we see that ...
k = -14, m = -7, h = 0
That is, the equation describes a line with slope -7 through point (0, -14).
The slope is the ratio of rise to run. Usually, "run" is considered to be positive in the +x direction (to the right). Here, you run out of room on most graphs if you look for a point that is 7 units down and 1 unit right of the y-intercept at (0, -14). (That point is (1, -21).) So, it is more convenient to start at the y-intercept (0, -14) and go 1 unit left and 7 units up to find another point on the line. That point is (-1, -7). With two points plotted, you can draw the graph.
__
Slope-Intercept form
We discovered above that the y-intercept is -14. You can get there also by putting the equation in slope-intercept form:
y = mx +b . . . . . . line with slope m and y-intercept (0, b)
Adding -14 to both sides of the given equation gives you this form.
y = -7x -14
The method of plotting is substantially identical to that described above.
__
Standard form
The standard form of the equation is ...
ax +by = c
where a > 0, and a, b, c are mutually prime integers.
Adding 7x-14 to both sides of the equation puts it into standard form:
7x +y = -14
The x- and y-intercepts are found by setting the other variable to zero and solving for the one that is left. Here, that means the x-intercept is ...
c/a = -14/7 = -2
and the y-intercept is ...
c/b = -14/1 = -14
These x- and y-intercepts are easily plotted on the x- and y-axes. The graph will be the line drawn through them. The attached graph shows the line and the intercepts.
if buying a pound of something is 6$ how much is 2.6 pounds
Answer: 15.6
Step-by-step explanation: 2.6 x 6 = 15.6
Answer:
$15.60
Step-by-step explanation:
If buying a pound of something is $6 then 2 pounds is $12.
0.6 pounds would be $3.60
1 = $6
0.9 = $5.40
0.8 = $4.80
0.7 = $4.20
0.6 = $3.60
0.5 = $3.00
0.4 = $2.40
0.3 = $1.80
0.2 = $1.20
0.1 = $0.60
0 = $0.00
subtract by .60 or 60 cents
Determine if triangle PQR and triangle STU are or are not similar, and, if they are,
state how you know. (Note that figures are NOT necessarily drawn to scale.)
U
45
T
R
45
P
63
639
S
The triangles
similar
Answer:
They are similar using the angle-angle property.
Step-by-step explanation:
Since you know that 2 of the angles are congruent, you can use this to prove triangle similarity.
By AA similarity, triangle PQR similar to triangle STU.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
The two given triangles PQR and STU.
Here, ∠P=63° and ∠R=45°
In triangle STU, ∠S=63° and ∠U=45°
Now, ∠P=∠S=63° and ∠R=∠U=45°
Since angles of triangle are congruent
By AA similarity, ΔPQR similar to ΔSTU
Therefore, triangles are similar.
To learn more about the similar triangles visit:
https://brainly.com/question/25882965.
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Graph the lines y=3x+3
Answer:
Step-by-step explanation:
A table is on sale for $213, which is 29% less than the regular price.
What is the regular price?
The Math Club is sponsoring a bake sale. If their goal is to raise at least $200, how many pies must they sell at $4.00 each in order to meet that goal? Write, solve, and graph an inequality that represents this situation.
Answer:
Step-by-step explanation:
I TOO THE TEST ANSWER IS 12.67
someone plz help me asap
Answer:
1) 0.25
2) -2.342
Step-by-step explanation:
What is the total amount of fees if there were 6 withdrawals for cash in a month, 10 uses of an ATM,
and 16 debit card transactions? Enter a whole number, like 789
Answer:
34
Step-by-step explanation:
16+10+6=34
There are 25 students in a class. 20% of the the students are in a club. How many students are in a club?
Answer:
5
Step-by-step explanation:
When taking a percent of a number, multiply the number by the percent divided by a hundred:
[tex]25 * \frac{20}{100}[/tex]
You get an answer of
5
Answer:
5 students are in a club.
Step-by-step explanation:
To do 20% of 25, you must first move the % until all numbers are on the right side of the decimal.
Observe: 20% ---> 0.20 aka 0.2
Now, you must take 0.2 and multiply it by 25 to get 20% of 25.
0.2 x 25 = 5
There's your answer, 5 students in a club :)
Help please I really need it now
Answer:
To get the answer use the dinamic format of barnic, its super easy to use please look it up and use the steps provided
Step-by-step explanation:
It willl help you so much.
1 1/4% in simplest form
Answer:
It can be written as 0.25 in decimal form (rounded to 6 decimal places).
Step-by-step explanation:
Answer:
It is already in the simplest form, but you can convert It into many things.
Step-by-step explanation:
Make this into an improper fraction you: 1 x 4 + 1 then put the answer on the numerator and keep the denominator.
Mixed number = 5/4
Decimal = 1.25
because 1/4 = 0.25
and 1 is a whole number.
Given the formula a = s2 + 3b - c , find the value of a when s = 7, b = 13 and c = -24.
Answer:
a = 112
Step-by-step explanation:
[tex]a =s^{2} +3b-c[/tex]
Given that,
s = 7
b = 13
c = (-24)
Let's solve for a now.
[tex]a =s^{2} +3b-c[/tex]
[tex]a = 7^{2} +3*13-(-24)\\[/tex]
[tex]a=49+39+24\\[/tex]
[tex]a=88+24[/tex]
[tex]a=112[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
Diego can purchase
glass jars locally for
$4.50 each or order
them online for $4.05
each. What percentage
will he save ordering
them online?
Answer:
10%
Step-by-step explanation:
4.5-4.05=.45
.45/4.5=.1
0.1= 10%
Evaluate 7+q(r−8)2
7
+
q
(
r
−
8
)
2
when q = 3 and r = 10.
Answer:
the anwser is indeed 19 i just did the problem rn
Step-by-step explanation:
I JUST DID THE QUIZ
solve???????????????????????
Answer:
-3x\4
Step-by-step explanation:
multiply the number 3x(-1/4)= -3/4x
the combine -3/4x to -3x/4
3,720,950,600,000 which digit is the hundred million place
HELP ASAP DO NOT SPAM YOU WILL BE REPORTED 15 POINTS I WILL MARK BRAINIEST Graph the solution to this inequality on the number line. w – 0.7 > -1.1 First select the correct ray. Then select the location of the endpoint to plot the inequality on the number line.
