Answer:
The 99% confidence interval is
7.558 - 9.042
Explanation:
The formula for the confidence interval is:
[tex]Confidence\text{ }interval=\bar{X}\pm\frac{\sigma}{\sqrt{n}}[/tex]Where:
X is the mean
σ is the standard deviation
z is the z-score for the confidence interval
n is the sample size.
Also, the interval has:
[tex]Upper\text{ }limit=\bar{X}+\frac{\sigma}{\sqrt{n}}[/tex][tex]Lower\text{ }limit=\bar{X}-\frac{\sigma}{\sqrt{n}}[/tex]Then, in this case,
The sample size is n = 64
The mean is X = 8.3
The z-score for a 99% confidence interval is z = 2.58
The standard deviation is σ = 2.3
Then:
[tex]Lower\text{ }limit=8.3-2.58\cdot\frac{2.3}{\sqrt{64}}=9.04175[/tex][tex]Upper\text{ }limit=8.3+2.58\cdot\frac{2.3}{\sqrt{64}}=7.55825[/tex]Thus, the confidence interval, rounded to 3 decimals is
7.558 - 9.042
Which points are on the graph of a linear function? Select all that apply
We will determine the points that belong to a linear function as follows:
*First set: We calculate the slope of the three points:
[tex]m_1=\frac{5-7}{0-(-1)}\Rightarrow m_1=-2[/tex][tex]m_2=\frac{3-7}{1-(-1)}\Rightarrow m_2=-2[/tex]So, the first set belongs to a linear function.
*second set:
[tex]m_1=\frac{0-1}{0-(-1)}\Rightarrow m_1=-1[/tex][tex]m_2=\frac{1-1}{1-(-1)}\Rightarrow m_2=0[/tex]So, the second set does not belong to a linear function.
*Third set:
[tex]m_1=\frac{5-5}{2-0}\Rightarrow m_1=0[/tex][tex]m_2=\frac{14-5}{3-0}\Rightarrow m_2=3[/tex]So, the third set does not belong to a linear function.
*Fourth set:
[tex]m_1=\frac{5-(-3)}{2-0}\Rightarrow m_1=4[/tex][tex]m_2=\frac{13-(-3)}{4-0}\Rightarrow m_2=4[/tex]So, the fourth set belongs to a linear function.
How does the multiplicity of a zero determine the behavior of the graph at that zero? the drop down options are: is tangent to, crosses straight through, and crosses though while hugging
Given: A seventh-degree polynomial function has zeros of -6, 0 (multiplicity of 2), 1, and 4 (multiplicity of 3).
Required: To determine the behavior of the graph at the zeros.
Explanation: The given seventh-degree polynomial can be represented as
[tex]\left(x+6\right)\left(x-0\right)^2\left(x-1\right)(x-4)^3[/tex]Now, the graph will cross straight through at x=-6 and x=1.
We have an odd multiplicity at x=4; hence the graph will cross through while hugging.
We have an even multiplicity at x=0; therefore, the graph will be tangent.
Here is the graph of the given function-
Final Answer: The graph will cross straight through at x=-6 and x=1,
the graph will cross through while hugging at x=4,
the graph will be tangent at x=0.
which of the following expressions could be used to determine?
We have the following:
They tell us that the capacity is 350, therefore that is the maximum value, it means that we must subtract the exchange rate from this value, that is, the number od tickets per hour that are sold, 23
thus
[tex]350-23h[/tex]The answer is the option B.
whats the rate of change in the equation 0.860(17) + 3.302.
Given:
Let y= 0.860(17) + 3.302
The rate of change is the same as the slope of the equation
Comparing the given equation with the standard for of the equation y =mx + b
can you please help me
The slope intercept form is y = m x + b
We need to put the equation -x + 4y = -8 in this form
At first, add both sides by x
[tex]\begin{gathered} -x+x+4y=-8+x \\ 4y=-8+x \end{gathered}[/tex]Then divide both sides by 4 to make the coefficient of y = 1
[tex]\frac{4y}{4}=\frac{-8}{4}+\frac{x}{4}[/tex]-8/4 = -2
x/4 = 1/4 x
[tex]y=-2+\frac{1}{4}x[/tex]Now switch -2 and 1/4 x
[tex]y=\frac{1}{4}x-2[/tex]Let us find which choice is?
It is the first one for the equation
Let us choose the graph
For the graph, the line intersects the y-axis at (0, -2)
The slope is positive, then its direction to the right
The x-intercept is (8, 0)
Then it is the last graph you post with equation y = 1/4 x - 2
Do you see it
the heart of an elephant, at rest, will beat an average of 1560 beats in 60 minutes. what's the rate in beats per minute?
I need help on a problem
1.
[tex]PQ\cong RQ\to Given[/tex]2.
[tex]\begin{gathered} \angle PQS\cong\angle RQS\to Given \\ \end{gathered}[/tex]3.
[tex]QS\cong QS\to Reflexive_{\text{ }}property[/tex]4.
[tex]\Delta PQS\cong\Delta RQS\to SAS_{\text{ }}congruence[/tex]5.
[tex]\begin{gathered} \angle P\cong\angle R\to CPCTC_{} \\ \end{gathered}[/tex]Watch help videoKevin has a bag that contains orange chews, strawberry chews, and peach chews. Heperforms an experiment. Kevin randomly removes a chew from the bag, records theresult, and returns the chew to the bag. Kevin performs the experiment 32 times. Theresults are shown below:An orange chew was selected 5 times.A strawberry chew was selected 17 times.A peach chew was selected 10 times.Based on these results, express the probability that the next chew Kevin removesfrom the bag will be peach chew as a percent to the nearest whole number.Answer:Submit Answer
Divide the amount of times that a peach chew was selected over the total number of times that the experiment was performed to find the probability that the next chew will also be a peach chew:
[tex]\frac{10}{32}=0.3125=31.25\text{ \%}[/tex]Then, as a percent to the nearest whole number, the probability that the next chew Kevin removes from the bag will be a peach chew, is:
[tex]31\text{ \%}[/tex]the table below gives the price for different numbers of books. is the price proportional to the number of books? number of books 1- price 3 3 books price-9 4 books price-12 7 books price 18
Two quantities are proportional if the ratio between those quantities is always the same.
Find the ratio of price/number of books for each row in the table:
[tex]\begin{gathered} \frac{3}{1}=3 \\ \frac{9}{3}=3 \\ \frac{12}{4}=3 \\ \frac{18}{7}=2.57\ldots \end{gathered}[/tex]We can see that the ratio price:books is 3 if the number of books is 1, 3 or 4 but it is a different ratio when the number of books is 7.
Therefore, the price is not proportional to the number of books.
Sidenote:
If the number of books on the last row was 6 instead of 7, then the ratio would still be 3 and the price would be in fact proportional. Make sure that it is not a printing error of the problem sheet.
What is the value of x in the equation 7x+2y=48, when y=3?
We have the following equation:
[tex]7x+2y=48[/tex]Which represents a line, and we need to determine the value of x when y = 3.
To achieve that, we can proceed as follows:
1. Substitute the value of y = 3 into the equation:
[tex][/tex]Dirk is a physical therapist who specializes in leg injuries. His patients differ in age and type of injury. Knee pain Ankle pain 3 3 0-12 years old 13-19 years old 2 3 What is the probability that a randomly selected patient is 13-19 years old or suffers from ankle pain? Simplify any fractions.
The probability of a patient being 13-19 years old is
[tex]P=\frac{5}{11}[/tex]The probability of a patient who suffers from ankle pain is
[tex]P=\frac{6}{11}[/tex]Then, we use the following formula
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]Where,
[tex]P(A\cap B)=\frac{5}{11}\cdot\frac{6}{11}=\frac{30}{121}[/tex]Then,
[tex]P(A\cup B)=\frac{5}{11}+\frac{6}{11}-\frac{30}{121}=\frac{91}{121}\approx0.75[/tex]Hence, the probability is 91/121, or 75%.48, -24, 12, -6,... 50th term
For the next series we will calculate its expression
[tex]a_n=(-1)^{n+1}3\cdot2^{^{5-n}}[/tex]For n = 1
an = 48
For n = 2
an = -24
For n = 50
an = 8.5265128e-14
Mark used 0.08 of the gas in the tank. What % of the gas in the tank did Mark use?
We know that he used 0.08 of the gas in the tank where 1 represents 100%.
Let's multiply 0.08 by 100 to express it in percentage.
[tex]0.08\cdot100=8[/tex]Hence, Mark used 8% of the gas in the tank.The dot plot shows how many customers purchased different numbers of shirts at a sale last weekend.
The interquartile range IQR of a dataset is the difference between the upper and lower quartiles, Q3 and Q1
The median of the whole dataset is Q2 and corresponds to the value x=3.5
The value of Q1 is the median of the lower 3 values: Q1=2
The value of Q3 is the median of the upper 3 values: Q3=5
The IQR is: 5 - 2 = 3
Hello hope all is well. Can you help me with this i don't understand what I need to write
mean
Explanation:The measures of centaral tendency: mean, median and the mode
The most used one is the mean.
The mean obtained here = 86%
median = 85%
mose = 81%
Since the measures are not in a scale, the mode cannnot be used.
Also there are no missing information in the data set and there are no extreeme outliers.
Most of the data are within the range of the mean gotten.
Hence, Mario should use the mean to convince his parents that he is a maths superstar.
4. Pietro buys 24 candy bars for $6. He plans to sellall 24 candy bars in 1 day. He needs to make aprofit of $12 per day to meet his fundraising goal.How much must he charge for each candy bar?(Hint: He spent $6 on the candy bars so his startingprofit is $-6. How much does he need to make inorder to have a profit of $12?)He needs to charge $per candy bar.
The cost of the 24 candy bars is $6.
If he is to make a profit of $12, that means that he must sell all the candy bars for:
[tex]\Rightarrow12+6=18\text{ dollars}[/tex]Since there are 24 candy bars, the cost of 1 candy bar can be calculated to be:
[tex]\Rightarrow\frac{18}{24}=0.75\text{ dollars}[/tex]He needs to charge $0.75 per candy bar.
Find the distance between the points (2,4) and (8,2) round to the nearest tenth if necessary
6.3 units
Explanations
The formula for calculating the distance between two points is given as:
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given the following coordinate points
A(2,4) and B(8,2)
Substitute the given parameters into the formula to have:
[tex]\begin{gathered} D=\sqrt[]{(8-2)^2+(2-4)^2} \\ D=\sqrt[]{6^2+(-2_{})^2} \\ D=\sqrt[]{36+4} \\ D=\sqrt[]{40} \\ D\approx6.3\text{units} \end{gathered}[/tex]Hence the distance between the points (2,4) and (8,2) round to the nearest tenth is 6.3 units
Explain why this is true.6x1/9=3x2/9
prove that
[tex]6\cdot(\frac{1}{9})=3\cdot(\frac{2}{9})[/tex]start on the left side
[tex]\frac{6}{1}\cdot\frac{1}{9}=\frac{6}{9}=\frac{2}{3}[/tex]continue with the right side
[tex]\frac{3}{1}\cdot\frac{2}{9}=\frac{6}{9}=\frac{2}{3}[/tex]we can conclude that both expressions are equal to 2/3.
Identifies which property it belongs to1) 15^8/5^32) (8^2)^1
Given the calculation
[tex]\frac{15^8}{5^3}[/tex]Second calculation
[tex](8^2)^1[/tex]Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage rate of increase er decrease.y = 2500(1.04)
The equation of a exponential function is of the form
[tex]y=a(b)^x[/tex]where
b is the base of the exponential function
If the value of b>1 -----> is a growth function
If the value of b<1 ----> is a decay function
In this problem
b=1.04
1.04 > 1
therefore
Is a growth functionPart b
Determine the percentage rate of increase
we have that
b=1+r
r=b-1
r=1.04-1
r=0.04
convert to percentage
r=0.04*100
r=4%Determine whether the equation x + y2 = 5 is linear. If so, graph the function. If not, explain why.
Work each problem according to the instructions given.a. Solve:2r +3=8=Previewb. Find r when y = 0:2x + 3y = - 8T =Previewc. Find y when I = 0;21 + 3y =- 8y =Previewd. Solve for y:2x + 3y8y =Preview
a)
The given equationis expressed as
2x + 3 = - 8
To solve for x, the first step is to subtract 3 from both sides of the equation. We have
2x + 3 - 3 = - 8 - 3
2x = - 11
Finally, we would divide both sides of the equation by 2. We have
2x/2 = - 11/2
x = - 11/2
Ray and Jon play a game of chance with two dice. If the sum of the dice is seven, Ray pays Jon $15. But if the sum is anything else, Jon pays Ray $10. What is the expected value of the game for Jon?Answer:
Step 1
[tex]\text{Probability of any event = }\frac{\text{number of required outcomes}}{n\text{umber of possible outcomes}}[/tex]Step 2:
Draw the table of the possible outcomes.
Step 3:
Draw the table for the expected value
Number of the sum of seven = 6
Number of anything else = 30
Total possible outcomes = 36
[tex]\begin{gathered} \text{Expected value formula = Value }\times\text{ Probability of event} \\ \text{Expected value formula = xp(x)} \end{gathered}[/tex]Final answer
The expected value of the game for Jon
[tex]\begin{gathered} =\text{ }\frac{15}{6}\text{ + }\frac{50}{6} \\ =\text{ }\frac{65}{6}\text{ } \\ =\text{ 10.83} \end{gathered}[/tex]What is the value of the expression when y = 2?2-y+4 + y3(y + 2)yO 3212
We have the following:
[tex]\frac{2-y}{4+y}+\frac{3(y+2)}{y}[/tex]replacing, y =2:
[tex]\begin{gathered} \frac{2-2}{4+2}+\frac{3(2+2)}{2} \\ \frac{0}{6}+\frac{3\cdot4}{2} \\ 0+\frac{12}{2}=6 \end{gathered}[/tex]the answer is 6, the second option
.27 = as a percentage
.27 = as a percentage
To find out the number as percentage , multiply by 100
so
0.27*100=27%
Mailk earns 10 dollars per hour at his job. He wants to change to a job that will play 12 dollars per hour. What will be the porcent increase in Mailk's hourty pay if he makes this jobs change.:))))))))))))))))))))))))))))))))))))))
Identify the volume of a rectangular pyramid with length 7 cm, width 15 cm, and height 16 m.
To answer this question, we will use the following formula for the volume of a rectangular pyramid:
[tex]V=\frac{lwh}{3},[/tex]where l is the length, w is the width, and h is the height.
Substituting w= 15 m, l = 7 m, and h = 16 m in the above formula, we get:
[tex]V=\frac{15m\cdot16m\cdot7m}{3}\text{.}[/tex]Simplifying the above result we get:
[tex]V=560m^3.[/tex]Answer:
[tex]560m^3.[/tex]What is the average mean high temperature and low temperature for the five day period? please explain
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
temperature table
average high temperature = ?
average low temperature = ?
Step 02:
We must calculate the average for the temperatures.
Average high temperature:
Average HT = (22 + 12 + 9 + 23 + 32) °F / 5
= 98 °F / 5
= 19.6 °F ===> rational number
Average low temperature:
Average LT = (0 + (-6) + (-10) + (-14) + 4) °F / 5
= (0 - 6 - 10 - 14 + 4) °F / 5
= - 26 °F / 5
= - 5.2 °F ===> rational number
The answer is:
The average high temperature is 19.6 °F
The average low temperature is - 5.2 °F
Both are rational numbers
A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the standard deviation of the data. Round your answer to the nearest hundredth, if necessary.
The Solution:
Given:
We are required to find the standard deviation of the given data.
Find the sample mean of the given data.
Find the standard deviation of the data.
Therefore, the correct answer is 68.07
the coordinates of the point shown in fig 23.16 are (3,5)
Answer:
False
Explanation:
In the coordinate notation (x, y), the left entry represents the x-coordinate and the right entry the y-coordinate. Therefore, if we want to represent the point x = 5, y = 3, we would write
[tex](5,3)[/tex]Hence, the representation (3, 5) does not represent the point x =5, y = 3, rather, it represents x = 3, y = 5, and therefore, the statement given is false.