Answer:
The correct option is d
Step-by-step explanation:
From the question we are told that
The population size is [tex]N = 47000[/tex]
The sample size is [tex]n = 200[/tex]
The sample mean is [tex]\= x = 118.0 \ mmHg[/tex]
The standard deviation is [tex]\sigma = 11.0 \ mmHg[/tex]
Given that the confidence level is 95% then the level of significance can be calculated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from z-table , the value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error .
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } *\frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 *\frac{11.0 }{ \sqrt{200} }[/tex]
[tex]E = 1.5245[/tex]
The 95% confidence level interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]118.0 - 1.5245 < \mu < 118.0 + 1.5245[/tex]
[tex]116.5< \mu < 119.5[/tex]
[tex][116.5 , 119.5][/tex]
A factory manufactures chairs and tables, each requiring the use of three operations: cutting, assembly, and finishing. The first operation can use at most 40 hours; the second at most 42 hours; and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; a table needs 2 hours of cutting, 1 hour of assembly, and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 for a table, what is the maximum revenue? Round your answer to the nearest whole number. Do not include a dollar sign or comma in your answer.
Answer:
z(max) = 650 $
x₁ = 10 units
x₂ = 15 units
Step-by-step explanation:
That is a linear programming problem, we will use a simplex method to solve it
Formulation:
Let´s call x₁ number of chairs and x₂ number of tables then :
Item (in hours) cutting assembly finishing Profit ($)
Chairs (x₁) 1 2 1 20
Tables (x₂) 2 1 1 30
Availability 40 42 25
Objective Function
z = 20*x₁ + 30x₂ ( to maximize) subject to:
x₁ + 2x₂ ≤ 40
2x₁ + x₂ ≤ 42
x₁ + x₂ ≤ 25
x₁ , x₂ >= 0
Using excel or any other software we find:
z(max) = 650
x₁ = 10
x₂ = 15
The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674
Let x represent chairs, and y represent tables
So, the given parameters are:
Cutting:
Chairs: 1 hourTable: 2 hoursHour available: 40So, the constraint is:
[tex]\mathbf{x + 2y \le 40}[/tex]
Assembly:
Chairs: 2 hoursTable: 1 hourHour available: 42So, the constraint is:
[tex]\mathbf{2x + y \le 42}[/tex]
Finishing:
Chairs: 1 hourTable: 1 hourHour available: 25So, the constraint is:
[tex]\mathbf{x + y \le 25}[/tex]
The unit profit on the items are:
Chairs: $20Table: $30So, the objective function to maximize is:
[tex]\mathbf{Max\ z = 20x + 30y}[/tex]
And the constraints are:
[tex]\mathbf{x + 2y \le 40}[/tex]
[tex]\mathbf{2x + y \le 42}[/tex]
[tex]\mathbf{x + y \le 25}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
Using graphical method (see attachment for graph), we have the following feasible points:
[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]
Calculate the objective function using the feasible points.
[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]
[tex]\mathbf{z = 650}[/tex]
[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]
[tex]\mathbf{z = 580}[/tex]
[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]
[tex]\mathbf{z = 673.5}[/tex]
Approximate
[tex]\mathbf{z = 674}[/tex]
Hence, the maximum revenue is 674
Read more about linear programming at:
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An Article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family’s financial situation, 37% would like to talk about school, and 30%would like to talk about religion. These and other sampling were based on 522 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 90% confidence level. Express the answer in the form P hat+- E
Answer:
The estimate is [tex]P__{hat}} \pm E = 0.37 \pm 0.0348[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 522
The sample proportion of students would like to talk about school is [tex]\r p__{hat}} = 0.37[/tex]
Given that the confidence level is 90 % then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645[/tex]
Generally the margin of error can be mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }[/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }[/tex]
=> [tex]E = 0.0348[/tex]
Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is
[tex]P__{hat}} \pm E[/tex]
substituting values
[tex]0.37 \pm 0.0348[/tex]
Please Help!!!
Family Size. You selected a random sample of n = 31 families in your neighborhood and found the mean family size for the sample equal to 3.1, the standard deviation for the sample is 1.42? What is the 90% confidence interval for the estimate?
Step to step explanation:
Confidence interval for mean, when population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom
We assume the family size is normal distributed.
Given, n= 31 , [tex]\overline{x}=3.1[/tex], s= 1.42 ,
[tex]\alpha=1-0.9=0.10[/tex]
Critical t value for [tex]\alpha/2=0.05[/tex] and degree of 30 freedom
[tex]t_{\alpha/2}[/tex] = 1.697 [By t-table]
The required confidence interval:
[tex]3.1\pm ( 1.697)\dfrac{1.42}{\sqrt{31}}\\\\=3.1\pm0.4328\\\\=(3.1-0.4328,\ 3.1+0.4328)=(2.6672,\ 3.5328)\approx(2.67,\ 3.53)[/tex]
Hence, the 90% confidence interval for the estimate = (2.67, 3.53)
Find the area of the shaded region if the dimensions of the unshaded region are 12ft x 20ft . Use 3.14 for π as necessary. - - - no lengthy explanation needed! all I need is the answer! first answer gets brainliest!
Answer:
810.66 ft²
Step-by-step explanation:
Short answer:
Shaded region:
(12+2*7)*20 - 12*20 + 3.14*((12+2*7)/2)² =14*20 + 530.66 = 810.66 ft²Answer: 810.66 ft²
I agree.
suppose that two integers from the set of 8 integers {1,2,… ,8} are choosen at random. Find the probability that
i.5 and 8 are picked.
ii.Both numbers match.
iii.Sum of the two numbers picked is less than 4.
Answer:
Ok so we have a set of 8 numbers {1,2,...,8}
a) 5 and 8 are picked.The probability here is:
In the first selection we can pick 5 or 8, so we have two possible outcomes out of 8 total outcomes, then the probability for the first selection is:
P = 2/8 = 1/4.
Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8)
Then the probability is:
P = 1/8
The joint probability is equal to the product of the individual probabilities, so here we have:
P = (1/4)*(1/8) = 1/32 = 0.003
b) The numbers match:
In the first selection we can have any outcome, so the probability is:
P = 8/8 = 1
Now, based on the previous outcome, in the second selection we can have only one outcome, so here the probability is:
P = 1/8 = 0.125
The joint probability is p = 1/8
c) The sum is smaller than 4:
The combinations are:
1 - 1
1 - 2
2 - 1
We have 3 combinations, and the total number of possible combinations is:
8 options for the first number and 8 options for the second selection:
8*8 = 64
The probabilty is equal to the number of outcomes that satisfy the sentence divided by the total numberof outcomes:
P = 3/64 = 0.047
Using the probability concept, it is found that there is a:
i. 0.03125 = 3.125% probability that 5 and 8 are picked.
ii. 0.125 = 12.5% probability that both numbers match.
iii. 0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, two integers are chosen from a set of 8, hence, there are [tex]8^2 = 64[/tex] total outcomes.
Item i:
Two outcomes result in 5 and 8 being picked, (5,8) and (8,5), hence:
[tex]p = \frac{2}{64} = 0.03125[/tex]
0.03125 = 3.125% probability that 5 and 8 are picked.
Item ii:
8 outcomes result in both numbers matching, (1,1), (2,2), ..., (8,8), hence:
[tex]p = \frac{8}{64} = 0.125[/tex]
0.125 = 12.5% probability that both numbers match.
Item ii:
Three outcomes result in a sum of less than 2, (1,1), (1,2), (2,1), hence:
[tex]p = \frac{3}{64} = 0.046875[/tex]
0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.
A similar problem is given at https://brainly.com/question/15536019
Half of a quarter of a number is 3/4 .Find the number.
Answer:
[tex]\huge\boxed{6}[/tex]
Step-by-step explanation:
[tex]half=\dfrac{1}{2}\\\\quarter=\dfrac{1}{4}\\\\half\ of\ a\ quarter=\dfrac{1}{2}\cdot\dfrac{1}{4}=\dfrac{1\cdot1}{2\cdot4}=\dfrac{1}{8}\\\\\text{Let}\ n-\text{number}\\\\\text{The equation:}\\\\\dfrac{1}{8}n=\dfrac{3}{4}\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup\cdot\dfrac{1}{8\!\!\!\!\diagup}n=8\cdot\dfrac{3}{4}\\\\n=\dfrac{24}{4}\\\\n=6[/tex]
please help Find: ∠x ∠a ∠b
Answer:
x = 22
<a = 88°
<b = 92°
Step-by-step explanation:
To solve for x, <a, and <b, we'd need to recall some of the properties of parallel lines, then apply them in solving this problem.
To find the value of x, recall that consecutive interior angles are supplementary. (5x - 18), and (3x + 22) are consecutive interior angles. Therefore:
[tex] (5x - 18) + (3x + 22) = 180 [/tex]
Solve for x
[tex] 5x - 18 + 3x + 22 = 180 [/tex]
[tex] 5x + 3x - 18 + 22 = 180 [/tex]
[tex] 8x + 4 = 180 [/tex]
Subtract 4 from both sides:
[tex] 8x + 4 - 4 = 180 - 4 [/tex]
[tex] 8x = 176 [/tex]
Divide both sides by 8
[tex] \frac{8x}{8} = \frac{176}{8} [/tex]
[tex] x = 22 [/tex]
=>Find <a:
According to the properties of parallel lines, alternate interior angles are equal. Therefore:
<a = 3x + 22
Plug in the value of x
<a = 3(22) + 22 = 66 + 22
<a = 88°
=>Find <b:
According to the properties of parallel lines, corresponding angles are said to be equal. Therefore,
<b = 5x - 18
Plug in the value of x to find <b
<b = 5(22) - 18
<b = 110 - 18 = 92°
the Average temperature for one week in Alaska are as follows 10, 6, 9, 6, 2, 0, 3. what is the mean of thes temperatures? show all work.
Answer:
5 1/7
Step-by-step explanation:
To find the mean, add up all the numbers and then divide by the number of numbers
(10+ 6+ 9+ 6+ 2+ 0+ 3)/7
The sum of all the numbers is 36 and there are 7 numbers
36/7 =
7 goes into 36 five times with 1 left over
5 1/7
Answer:
5.143
Step-by-step explanation:
Add them all up then divide by the amount of numbers there are.
For which positive integer values of $k$ does $kx^2+20x+k=0$ have rational solutions? Express your answers separated by commas and in increasing order.d
When you solve this equation using the quadratic formula, you will get [tex]x = \frac{-20\pm \sqrt{400-4k^2}}{2k}[/tex]. The only way for this number to be irrational is for [tex]\sqrt{400-4k^2}[/tex] to be irrational. The square root of any number that is not a perfect square is irrational*, so the solutions of the quadratic are rational if and only if [tex]400-4k^2[/tex] is a perfect square. We can factor out the 4 (which is already a perfect square), which means that [tex]100-k^2[/tex] must be a perfect square. This occurs exactly when k is equal to one of the following:[tex]\sqrt{100},\sqrt{99},\sqrt{96},\sqrt{91},\sqrt{84},\sqrt{75},\sqrt{64},\sqrt{51},\sqrt{36},\sqrt{19}, \sqrt{0}[/tex].
Of these, the only positive integer values of k are: [tex]\sqrt{100}, \sqrt{64}, \sqrt{36}[/tex], or simply 6, 8, and 10.
* This is quite simple to show: Take any rational number, a/b. Without loss of generality, we can assume that a/b is in reduced form, that is, a and b have no common factors. (a/b)^2 is a^2/b^2, and since a and b have no common factors, neither do a^2 and b^2. Therefore, a^2/b^2 cannot be an integer. In the event that a/b is an integer, b would equal 1, and this proof would not hold.
Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent y values? Select both in the
list
Answer:
14 and 9
Step-by-step explanation:
Y values are always the second number in the parenthesis. The X value is the first one. I like to think of Y being dependent on X, so X goes first, then Y.
6th-grade math, fill out the table! :)
Answer:
21 wins, table is attached.
Step-by-step explanation:
The ratio of 7 wins to 2 losses is 7:2. A ratio is just saying that every time one value is increased by 7, the other is increased by 2.
So we can fill out the table, in every iteration wins increases by 7 and losses increases by 2.
When we fill this out, we find that when losses is 6, wins is 21, so when you have 2 losses you have 21 wins.
Hope this helped!
Richard is buying a subscription for video game rentals. The plan he has chosen has an
initial fee of $20 plus $2 per video game rented. This plan can be represented by the
function f(x) = 2x + 20. How much money will Richard pay this month if he rents 5 video
games?
Answer:
Richard will pay $30.
Step-by-step explanation:
Because "x" is equivalent to the amount of video games he rents, you would replace "x" with 5. Do the math, and you would get 10+20=30! Hope this helps!
A 6-ounce container of Greek yogurt contains 150 calories. Find the unit rate of calories per ounce.
Answer:
25
Step-by-step explanation:
150/6
The Unit rate of calories per ounce will be 25 calories per ounce.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Weight of the Greek yogurt container = 6 ounce
Calories per container = 150 calories
The Unit rate of calories per ounce = 150 / 6 = 25
Therefore, the unit rate of calories per ounce will be 25 calories per ounce.
Learn more about the unitary method;
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I need the co-ordinates to answer this can anyone give them to me? If not it's fine! :)
Hi there!
Answer:
Find points for the equation y = 2x + 1 by plugging in x values:
For example, when x = 1, substitute in the value of 'x' into the equation:
y = 2(1) + 1
y = 2 + 1
Solve for the y-value:
y = 3
Repeat this process for multiple points:
X Y
-2 -3
-1 -1
0 1
1 3
2 5
To get the graph of y = 2x + 1, simply graph these points. :)
What is the square root of -16?
Answer:-8
Step-by-step explanation:
Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet
The volume of a square pyramid is found by multiplying the area of the base by the height divided by 3.
32 = 4^2 x h/3
32 = 16 x h/3
Multiply both sides by 3
96 = 16 x h
Divide both sides by 16
H = 96/16
H = 6
The height is 6 feet
Answer:
6 ft
Step-by-step explanation:
Volume of the pyramid:
V= lwh/3, where l- base length, w- base width, h- heightGiven
V= 32 ft³l=w= 4 fth=?Then, as per formula, we can solve it for h:
32= 4×4×h/3h= 32×3/16h= 6 ftHeight of the pyramid is 6 ft
What does 20 * 1 * 2 equal?
Answer:
40
Step-by-step explanation:
20 * 1
= 20
20 * 2
= 40
Answer:
40
Step-by-step explanation:
The first step is to multiply 20 by 1. Whenever you multiply something by 1, it will always stay the same no matter what.
20*1=20
The next step is to multiply by 2. When multiplying anything by two, it is the same as adding the same number to itself. so
20*2=40 or 20+20=40
Hope this helps. Feel free to ask any follow-up questions if you are still confused
Have a great day! :)
What linear function defines the following Arithmetic Sequence?
-8, -4, 0, 4, 8, ...
A : an = -8 + 4(n - 1)
B : an= 8 + 4(n - 1)
C : an = -8 - 4(n - 1)
D : an = 8 - 4(n - 1)
The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, the sequence is -8, -4, 0, 4, 8, ...
a = -8
d = +4
The expression for the nth term will be written as,
an = a + ( n - 1 ) d
= -8 + ( n - 1 ) 4
To know more about arithmetic progression follow
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20 POINTS AND BRAINLEST A sample of restaurants in a city showed that the average cost of a glass of iced tea is $1.25 with a standard deviation of 7¢. If a new restaurant charges a price for iced tea that has a z-value of -1.25, then what is the tea’s actual cost? a. $1.00 c. $1.16 b. 89¢ d. $2.00 A student took two national standardized tests while applying for college. On the first test, SEE IMAGE. If he scored 630 on the first test and 45 on the second test, on which test did he do better? a. first test b. second test
Answer:
1) [tex] x= \mu +z\sigma = 1.25 -1.25*0.07= 1.16[/tex]
The best answer woud be:
c. $1.16
2) If we find the z score for the first test we got:
[tex] z=\frac{630-475}{75}= 2.07[/tex]
And for the second test:
[tex] z=\frac{45-32}{6}= 2.17[/tex]
The z score for the second test is greater so then the answer would be:
b. second test
Step-by-step explanation:
For the first question:
For this case we have the following parameters are:
[tex]\mu = 1.25 , \sigma =0.07[/tex]
And we also know that the z score is [tex] z=-1.25[/tex] and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And solving for x we got:
[tex] x= \mu +z\sigma = 1.25 -1.25*0.07= 1.16[/tex]
The best answer woud be:
c. $1.16
For the second question:
First test [tex]\mu = 475, \sigma =75[/tex]
Second test [tex] \mu= 32, \sigma=6[/tex]
630 for the first test and 45 for the second
If we find the z score for the first test we got:
[tex] z=\frac{630-475}{75}= 2.07[/tex]
And for the second test:
[tex] z=\frac{45-32}{6}= 2.17[/tex]
The z score for the second test is greater so then the answer would be:
b. second test
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
Answer:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
Which equation represents the total number of stamps Malik collected?
✔ x + y = 212
Which equation represents the difference in the number of foreign and domestic stamps Malik collected?
✔ x – y = 34
Which system of linear equations represents the situation?
✔ x – y = 34 and x + y = 212
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
This system of equations models the given information for both stamp types.
x – y = 34
x + y = 212
Solve the system of equations.
How many foreign stamps does Malik have?
✔ 89 foreign stamps
How many domestic stamps does Malik have?
✔ 123 domestic stamps
Step-by-step explanation:
its right on 2021 edge! :) hope this helps
helppppppppp pleaseeeeeeeeeeeeeee
Answer:
Number is yellow box=3
Step-by-step explanation:
We know this because the way we get that number is subtracting the two numbers above it, which is 8 and 5, which give us 3.
if you appreciated this, please consider giving me brainliest, it will help me a lot
Thank you,
Have a good day! :)
Need answer now in 10 min!!!
Answer:
40 deg
Step-by-step explanation:
The vertical sides of the rectangle are parallel, so the triangle is a right triangle.
The triangle is a right triangle, so the acute angles are complementary.
The bottom right angle of the triangle measures 90 - 50 = 40 deg.
The bottom line and the top side of the rectangle are parallel, so corresponding angles are congruent. x and the 40-deg angle are corresponding angles, so they are congruent.
x = 40 deg.
A certain variety of pine tree has a mean trunk diameter of y = 150 cm and a
standard deviation of o = 30 cm.
A certain section of a forest has 500 of these trees.
Approximately how many of these trees have a diameter smaller than 120 cm?
Answer:
80 trees have a diameter smaller than 120cm
Step-by-step explanation:
Step 1
To solve this question, we would make use of the Z score formula.
z = x - μ/σ
Where
z = z score
x = Raw score = 120cm
μ = Population mean = 150cm
σ = Population standard deviation = 30cm
Hence,
z =120 - 150/30
z = -1
The z score = -1
Step 2
We find the Probability of the calculated z score using the z score table.
P(z) = P(z = -1) = P(x<120) = 0.15866
Approximately to the nearest hundredth = 0.16
Converting to percentage = 0.16 × 100 = 16%
The percentage of trees with a diameter smaller than 120cm = 16%
Therefore, the number of trees with a diameter smaller than 120cm
= 16% × 500 trees = 80trees
The _________ measures the strength and direction of the linear relationship between the dependent and the independent variable.
Answer:
Correlation Coefficient
Step-by-step explanation:
Assume that a sample is used to estimate a population proportion μ . Find the margin of error M.E. that corresponds to a sample of size 722 with a mean of 54.2 and a standard deviation of 13.1 at a confidence level of 90%.
Answer:
[tex]MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\[/tex]
Step-by-step explanation:
Since the sample size is quite large, we can use the z-distribution.
The margin of error is given by
[tex]$ MoE = z_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]
Where n is the sample size, s is the sample standard deviation and [tex]z_{\alpha/2}[/tex] is the z-score corresponding to a 90% confidence level.
The z-score corresponding to a 90% confidence level is
Significance level = α = 1 - 0.90= 0.10/2 = 0.05
From the z-table at α = 0.05
z-score = 1.645
[tex]MoE = 1.645\cdot \frac{13.1}{\sqrt{772} } \\\\MoE = 1.645\cdot 0.47147\\\\MoE = 0.776\\\\[/tex]
Therefore, the margin of error is 0.776.
Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function? 0.02 0.98 1.02 1.98
Step-by-step explanation:
Hal is expected to use 0.98, the reason is that 2% of $10,000 will give $200
i.e (2/100)*10,000= $200.
therefore 10,000-200= $9800.
Since the money is decreasing by 2%, we have 100-2= 98% = 0.98
hence when 10,000 is multiplied by 0.98 we have $200 which is 2% of $10,000
Answer:
It's B.
Step-by-step explanation:
I just took the test.
Translate the following into an algebraic expression: A number is 30% of 20% of the number x.
Answer: 0.06x
Step-by-step explanation:
An algebraic expression is an expression consist of integer constants, variables, and algebraic operations.The given statement: A number is 30% of 20% of the number x.
The required algebraic expression would be:
30% of 20% of x
[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex] [we divide a percentage by 100 to convert it into decimal]
[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]
Hence, the required algebraic expression would be :
0.06x
The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0,7).
Which statement must be true?
The circle has a radius greater than 7.
The circle has a radius equal to 7.
The slope of the line is equal to 7.
The slope of the line is not equal to 7.
Save and Exit
Next
Submit
Answer:
the radius of the circle =7
Step-by-step explanation:
the function of a circle:(x – h)^2 + (y – k)^2 = r^2
center(0,0) because the center of a circle is at the origin (h,k)
a line intersect at (0,7)
(0-0)^+7-0)^2=r^2
r^2=49 , r=√49
radius r=7
which of the following is a mathematical representation of a function that provides detailed information but can become unwieldy?
Answer:
C. Equation
Step-by-step explanation:
An equation generally provides the most specific information about a function. However, it cannot always be used for certain purposes—such as finding a specific inverse function value.
In the case of equations that are infinite series, even evaluating the function can become difficult when the series converges slowly.
Which one doesn’t belong? Why? Explain.
Answer:
THE M ONE
Step-by-step explanation:
IT HAS A DIFFERENT VARIABLE
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE