Answers
9514 1404 393
Answer:
12. x = 5
13. -8, 0
14. 6
Step-by-step explanation:
12. The area of a square with side length s is ...
A = s²
The problem statement tells us the relationship between the areas is ...
(x cm)² = (1/9)(15 cm)²
Taking the square root, we have ...
x cm = (1/3)(15 cm)
x cm = 5 cm . . . . . . . simplify
x = 5
__
13. The rule is ...
a[n] = (a[n-1] +8)/2 = (1/2)a[n-1] +4
For a[1] = -24, a[2] = (1/2)(-24) +4 = -8
For a[2] = -8, a[3] = (1/2)(-8) +4 = 0
The next two terms are -8 and 0.
__
14. The rule is ...
a[n] = (a[n-1] -1)×5
Solving for the previous term, we find ...
a[n] = 5·a[n-1] -5 . . . . . eliminate parentheses
a[n] +5 = 5·a[n -1] . . . . add 5
a[n-1] = (a[n] +5)/5 . . . . divide by 5
For a[3] = 120, a[2] = (120 +5)/5 = 25
For a[2] = 25, a[1] = (25 +5)/5 = 6
The first term of the sequence is 6.
Related Questions
A group of 80 people who had been diagnosed as prediabetic because of high blood glucose levels volunteered to participate in a study designed to investigate the use of cinnamon to reduce blood glucose to a normal level. Of the 80 people, 40 were randomly assigned to take a cinnamon tablet each day and the other 40 were assigned to take a placebo each day. The people did not know which tablet they were taking. Their blood glucose levels were measured at the end of one month. The results showed that 14 people in the cinnamon group and 10 people in the placebo group had normal blood glucose levels. For people similar to those in the study, do the data provide convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon?
a. No conclusion can be made about the use of cinnamon because the people in the stuey were volunteers
b. There is convincing statistical evidence at the level of 0.01
c. There is convincing statistical evidence at the level of 0.05 but not at the ver.01
d. There is convincing statistical evidence at the level of 0.10 any reason
e. There is not convincing statistical evidence
Answers
Answer:
E
Step-by-step explanation:
AP Classroom says so.
The data doesn't provide convincing statistical evidence for considered proportion comparison. We deduce that: Option E: There is not convincing statistical evidence
How to form the hypotheses?There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
How to calculate the value of z-test statistic for two sample proportions?Suppose we have:
[tex]\hat{p}_1[/tex] = first sample's proportion[tex]n_1[/tex] = first sample's size[tex]\hat{p}_2[/tex] = second sample's proportion[tex]n_2[/tex] = first sample's size[tex]\hat{p}[/tex] = overall proportionThen, we get:
[tex]Z = \dfrac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p}_1 )(\dfrac{1}{n_1} + \dfrac{1}{n_2}) }}[/tex]
If the level of significance = [tex]\alpha[/tex]critical value of Z is: [tex]Z_{\alpha/2}[/tex], and if [tex]Z > Z_{\alpha/2}[/tex]null hypothesis, else if [tex]Z_{\alpha/2} > Z[/tex] then we cannot reject it.
For this case, we want to know if the data provides convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon.
Thus, we get our hypotheses as:
Null hypotheses: They don't provide convincing evidence (and thus, cinnamon had no improvement on the proportion), and thus:
[tex]H_0: \hat{p}_1 \leq \hat{p}_2[/tex]
Alternate hypothesis: Data provides convincing evidence (that the use of cinnamon made increment in considered proportion), and thus:
[tex]H_a: \hat{p}_1 > \hat{p}_2[/tex]
The test is single tailed.
For this case, we have:
[tex]x_1[/tex] = quantity of intended object found in first sample = 14 (of those who take cinnamon tablets each day)[tex]n_1[/tex] = first sample's size = 40[tex]\hat{p}_1 = x_1/n_1 = 14/40 =0.35[/tex] [tex]x_2[/tex] = quantity of intended object found in second sample = 10 (of those who take placebo each day)[tex]n_2[/tex] = second sample's size = 40[tex]\hat{p}_2 = x_2/n_2 = 10/40 =0.25[/tex][tex]\hat{p}[/tex] overall proportion = [tex](x_1 + x_2)/(n_1 + n_2) = (10 + 14)/80 = 0.3[/tex]Thus, we get:
[tex]Z = \dfrac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p}_1 )(\dfrac{1}{n_1} + \dfrac{1}{n_2}) }} =\dfrac{0.35 - 0.25}{\sqrt{0.3(0.7 )(\dfrac{1}{40} + \dfrac{1}{40}) }} \approx 0.976[/tex]
At 0.01 level of significance ([tex]\alpha = 0.01 = 1\%[/tex]), we get the critical value of Z from z-tables as:
[tex]Z_{\alpha/2} = 2.576[/tex]
Since [tex]Z_{\alpha/2} > Z[/tex] , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.01
At 0.05 level of significance ([tex]\alpha = 0.05 = 5\%[/tex]), we get the critical value of Z from z-tables as:
[tex]Z_{\alpha/2} = 1.96[/tex]
Since [tex]Z_{\alpha/2} > Z[/tex] , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.05
At 0.10 level of significance ([tex]\alpha = 0.10 = 10\%[/tex]), we get the critical value of Z from z-tables as:
[tex]Z_{\alpha/2} = 1.645[/tex]
Since [tex]Z_{\alpha/2} > Z[/tex] , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.10
Remember that the conclusions can be made even if they were volunteers since that doesn't make it wrong as volunteers are randomly coming out people from real population.
Thus, we deduce that: Option E: There is not convincing statistical evidence
Learn more about two proportions z-test here:
https://brainly.com/question/4757147
PLZ HELP ILL MARK BRAINLIST!!!
Answers
Answer:
So, your answer would be 226.08 cubic meters of dirt.
Step-by-step explanation:
:D
Use the remainder theorem and synthetic division to find f(k) for the given value of k.
Answers
Answer:
3
Step-by-step explanation:
Given that,
[tex]f(x) =-x^3-8x^2-15x+3[/tex]
We need to find the value of f(x) when k = -5
Put x = -5 in th given function.
So,
[tex]f(-5) =-(-5)^3-8(-5)^2-15(-5)+3\\\\=3[/tex]
Hence, the value of the given function is equal to 3.
Question 1(Multiple Choice Worth 2 points)
(10.03 MC)
Select the sentence that correctly uses a prepositional phrase.
Andy in her backpack has extra supplies.
Around the corner. Belle spotted a lost dog.
Through her binoculars, Kathryn spotted a hawk.
Mika wore under her hiking boots thick wool sock
Answers
Answer:
i think the answer is c but im soo sorry if im wrong
Step-by-step explanation:
Solve 5.408 − 1.07
pls answer
Answers
Answer: 4.338
Step-by-step explanation: Calculator
The radius of a circle is 3 cm. Find its area in terms of \piπ.
Answers
Answer:
The area would be 28.27
The volume of the polyhedron is ______ cm3.
Answers
1. Kathy is building a bed for her dollhouse. She used her real bed as a guide for how to
create the dollhouse bed. Her bed is 36 inches wide and 60 inches long. If she wants
to scale this down by 1/10, what would be the dimensions of the dollhouse bed?
Explain how you got your answer.
*Use the term SCALE FACTOR in your explanation.
PLS ANSWER QUICKLY !!!
Answers
determine if the sequence below is arithmetic or geometric and determine the common difference/ ratio in simplest form 5,15,45,...
Answers
Answer:
It's geometric and common difference is 3
Step-by-step explanation:
15/5=3
45/15=3
Answer:
its geometric and the common ratio is 3
Step-by-step explanation:
work out the value of x.
Answers
Answer:
4.8
Step-by-step explanation:
area of rectangle = lxb = 8x
area of trapezium = (a+b)h/2 = ( x+13)6 /2 = 3x + 39
Aea of whole figure = 91.8
8x + 3x+ 39 = 91.8
11x = 91.8-39
x= 52.8 /11 = 4.8
I hope im right! !t
Brianna earns $19,500 per year. Lisa earns $1000 per month. Write a numerical expression that represents how much more Brianna earns per year than Lisa
Answers
Answer:
$19,500 - $1000
Step-by-step explanation:
the amount Brianna earns in excess of the amount Lisa earns can be determined by subtracting the amount Brianna earns from that Lisa earns
$19,500 - $1000 = $18,500
a person invested $330 in an account growing at a rate allowing the money to double every 8 years. Write a function showing the amount of money in the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year, to the nearest hundredth of a percent.
Answers
Answer:
The percentage of growth is of 9.05%.
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
Step-by-step explanation:
Amount of money after t years:
The amount of money in an account after t years is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial deposit and r is the growth rate, as a decimal.
Money doubles every 8 years.
This means that [tex]P(8) = 2P(0)[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]2P(0) = P(0)(1+r)^8[/tex]
[tex](1+r)^8 = 2[/tex]
[tex]\sqrt[8]{(1+r)^8} = \sqrt[8]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{8}}[/tex]
[tex]1 + r = 1.0905[/tex]
[tex]r = 1.0905 - 1[/tex]
[tex]r = 0.0905[/tex]
The percentage of growth is of 0.0905 = 9.05%.
Person invested $330
This means that [tex]P(0) = 330[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 330(1+0.0905)^t[/tex]
[tex]P(t) = 330(1.0905)^t[/tex]
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
solve the system of equations -3x+2y=-3 and -x-y=-11 by combining the equations
Answers
Answer:
-4x, 1y, -14
Step-by-step explanation:
Hope this helps :)
SOMEONE HELP ME PLS ASAP I WILL GIVE BRAINLIEST PROVE ABCD IS A PARALLELOGRAM
Answers
Answer:
It's a parallelogram because it has two parallel side (a,d)+(b,c) or (a,b)+(d,c). The shape is connected by the line "a,d"
Step-by-step explanation:
How many centimeters does it grow Bamboo grows 91 centimeters per day. per hour? (GIVING BRAINLIEST)
Answers
Answer:
3.79 centimetres
Step-by-step explanation:
1 day = 24 hours
91 ÷ 24 = 3.79 centimetres
Answer:
if the question you're asking is how many cm does bamboo grow per hour, then around 3.81 cm per hour.
Which steps are needed to solve this equation? 100 points for the first correct answer.
Answers
Answer:
the first one sub 6 from both =15
Step-by-step explanation:
b+6=21
-6 -6
b=15
If f(x) = |x – 2| then find f(-3).
Answers
Answer:
5
Step-by-step explanation:
f(x) = |x – 2|
f(3) = |-3 - 2| = |-5| = 5
The Pacheco family has a monthly income of $ 7,300 . They have monthly fixed expenses of $ 3,280 . In July, they had monthly variable expenses of $ 2,620 . They have annual expenses totaling $ 14,000 . Assuming annual expenses are paid off at an equal rate monthly, what was the Pacheco’s cash flow for July?
Answers
Answer:
Positive 233
Step-by-step explanation:
7300-3280-2620-1167(14000/12)=233.
Which polynomial is a difference of two squares? (4 points)
x2 - 12
x2 + 12
x2 – 36
x2 + 36
Answers
Answer:
[tex] {x}^{2} - 36 [/tex]
Step-by-step explanation:
[tex] {x}^{2} - 36 \\ \\ = {x}^{2} - {6}^{2} [/tex]
Classify the following triangle as acute, obtuse, or right.
Answers
Answer:
None, this is an isosceles triangle.
HELP ME OUTT PLSS BXJXID
Answers
Answer:
d
Step-by-step explanation:
Answer: D
Step-by-step explanation:
The probability of picking a brown pencil greater than the probability as NOT picking a brown pencil because there more brown pencils than purple so there is a higher chance you will get a brown than NOT get a brown.
Label 1/4 on the number line. Label 1/2 on the number line .
Answers
Answer:
it goes 0 then 1/4 in the first notch 1/2 in the second notch 3/4 in the third notch then the number 1 on the fourth
Step-by-step explanation:
Hope that helps.
What is the slope for coordinates (-1,3) (0,0) (1,-3)
Answers
Answer:
-3
Step-by-step explanation:
The slope should be -3 since the rise is -3 and the run is 1 it would be -3/1.
no links please or you will be reported .
Answers
Answer:
Step-by-step explanation:
2 should be 50 degrees as well. 1 should be 130 (to get the needed 180) 3 should be 130 degrees. Hopefully this is correct
Find the diameter of the object. 2 in
Answers
Answer:
Step-by-step explanation:
Can you write your questions clearly, so we can answer it well
Answer:
is it 2 inches?
Step-by-step explanation:
Write the equation of the following circle in general form and standard form. Show your work.
Answers
Answer:
Step-by-step explanation:
Standard equation of a circle is given by,
(x - h)² + (y - k)² = r²
Here, (h, k) is the center of the circle.
From the graph given in the picture,
Center of the circle → (-1, 1)
Radius of the circle = 3 units
Therefore, standard equation of the circle will be,
(x + 1)² + (y - 1)² = 3²
(x + 1)² + (y - 1)² = 9
General equation of the circle is the expanded form of the standard equation.
x² + 2x + 1 + y² + 1 - 2y = 9
x² + y² + 2x - 2y + 2 = 9
x² + y² + 2x - 2y - 7 = 0
Therefore, general equation of the given circle is,
x² + y² + 2x - 2y - 7 = 0
Is the formula V=LWH or V=BH or A=BH
PLEASE HELP!
Answers
Answer:
It's A=BH
Step-by-step explanation:
In the story the key words are there: Area, base/length, height
Answer:
It's A=BH
Step-by-step explanation:
if P = 5, 4 find the image of P under the following rotation
Answers
Answer:
(-4,5)
Step-by-step explanation:
90 degree rotation = (-y,x)
Find the median of the data in the dot plot below.
Answers
Answer:
41
Step-by-step explanation:
41 cause its the middle
Find the probability of drawing a 10 from a standard deck
of 52 cards,
Answers
Answer:
4/52 or 1/13 (simplified)
Step-by-step explanation:
There are 4 "10's" in a pack.
This means you have the chance to pick 4 10's.
So out of 52 cards, you can get 4.
4/52 -> Which can be simplified to 1/13.
This is the probability of getting a 10 (once) in a standard deck of cards.
The probability of drawing a 10 from a standard deck of 52 cards is 1/13.
Number of 10's in a standard deck of 52 cards =4
Total cards =52
What is probability?Probability is the measurement of the possibilities of events.
P(event) =Favorable outcomes/ Total possible outcomes
Here, Favorable outcomes =4
Total possible outcomes =52
P(10) =4/52
P(10) =1/13
So, the probability of drawing a 10 from a standard deck of 52 cards =1/13
Thus, the probability of drawing a 10 from a standard deck of 52 cards is 1/13
To get more about probability visit:
https://brainly.com/question/24756209