The perimeter of a rectangle is 21.2 m, and its area is 23.68 m².
Find its length and width.
length: m
width: m
A triangle with an area of 40 in.² has a height that is four less than six times the base. Find the base and height of the triangle.
Answer: 9.32 inches.
Step-by-step explanation:
Question
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?
Select all correct answers.
Select all that apply:
{(2,−5),(−2,0),(−3,6),(2,−4)}
{(−1,5),(−4,8),(−4,14),(2,6)}
{(1,3),(−2,−1),(4,3),(8,1)}
{(−2,−5),(7,1),(7,−3),(4,−1)}
{(8,8),(4,1),(1,6),(−5,6)}
Answer:
(c) {(1,3),(−2,−1),(4,3),(8,1)}(e) {(8,8),(4,1),(1,6),(−5,6)}Step-by-step explanation:
You want the lists of ordered pairs that represent a functional relation.
FunctionA function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.
We only need to look at the first values of the ordered pairs.
(a) 2 is repeated
(b) -4 is repeated
(c) a function
(d) 7 is repeated
(e) a function
Answer:
(c) {(1,3),(−2,−1),(4,3),(8,1)}(e) {(8,8),(4,1),(1,6),(−5,6)}Step-by-step explanation:
You want the lists of ordered pairs that represent a functional relation.
FunctionA function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.
We only need to look at the first values of the ordered pairs.
(a) 2 is repeated
(b) -4 is repeated
(c) a function
(d) 7 is repeated
(e) a function
what is the value of the expression shown below
2 3/5 - 1 3/5
^ ^
TWO THREE-FIFTHS MINUS ONE THREE-FIFTHS
THE NUMBERS ARE MIXED FRACTIONS
Answer:
1
Step-by-step explanation:
1. One way to do this is converting both into improper fractions. To do this, multiply the whole number by the denominator and add that to the numerator.
2 3/5 --> 2*5 is 10 --> 10+3 is 13. --> 13/5
2. This leaves us with 13/5 - 8/5
3. Subtract the numerators
13/5 - 8/5 = 5/5
4. Simplify. If the numerator is the same number as the denominator, it's a whole number.
5/5 = 1
Construct a 95% confidence interval of the mean pulse rate for adult males ___bpm
The 95% confidence interval of the mean pulse rate for adult females is 68.2 bpm < μ < 76.4 bpm
For a 95% confidence interval, the Z-score is 1.96. Plugging in the values we have for the sample mean, sample standard deviation, and sample size, we get:
Confidence interval = 75.8 ± (1.96 × (3.7 / √50))
Simplifying the expression, we get:
Confidence interval = 71.5 bpm < μ < 80.2 bpm
This means that we can be 95% confident that the true population mean pulse rate for adult females falls within this range.
Now let's construct a confidence interval for adult males. We are given that the sample mean pulse rate for adult males is 72.3 bpm, and the sample standard deviation is 4.0 bpm. Using the same formula and Z-score as before, we can calculate the confidence interval as follows:
Confidence interval = 72.3 ± (1.96 × (4.0 / √50))
Simplifying the expression, we get:
Confidence interval = 68.2 bpm < μ < 76.4 bpm
This means that we can be 95% confident that the true population mean pulse rate for adult males falls within this range.
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3 A system of two linear equations is graphed on a coordinate plane. If the system of
equations has infinitely many solutions, which statement must be true?
a. On the graph, there are no points (x, y) that satisfy both equations.
b. On the graph, there is exactly one point (x, y) that satisfies both equations.
c. On the graph, any point (x, y) that satisfies one of the equations cannot satisfy the
other equation.
d.
On the graph, any point (x, y) that satisfies one of the equations must also satisfy
the other equation.
Answer:
d. On the graph, any point (x, y) that satisfies one of the equations must also satisfy the other equation.----------------------
If the system of linear equations has infinitely many solutions, it means the two lines overlap.
In other words, each point of one of the lines also belongs to the second line.
Choices a, b, c give us one or no solutions and therefore not the answer.
Choice d is reflecting the infinitely many solutions and hence is the correct one.
A bag has 30 cards it in. There are 10 red cards, 10 blue cards, and 10 yellow cards. What is the probability that you reach in without looking and pick a red card?
Calculus derivatives. Find f(x).
The solution equates to f(x) = 6x + 8.
How to explain the functionReiterating the same statement without reiteration, it is observed that f'(x) equals ƒ""(x), ultimately resulting in a value of 6. Subsequently, we can derive a complete expression for f(x) where C represents an integration constant.
It should be noted that to find this constant, since f(-1) = 2, plugging in x as -1 and f(x) as 2 into the above equation results in:
2 = 6(-1) + C
C = 8
As such, we can confirm that the entire expression of f(x) is simply 6 times x added to 8. Validating this answer, when assessing f(0) or f(1) , either result should match the given values from our initial problem which they do. Hence, the solution equates to:
f(x) = 6x + 8.
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In a different plan for area codes, the first digit could be any number from 1 through 7, the second digit was either 3, 4, 5, 6, and the third digit could be any number except 6, 7, or 8. With this plan, how many different area codes are possible?
Answer:
196
Step-by-step explanation:
There are 7 choices for the first spot.
4 choices for the second spot. And 7 choices for the third spot, which cannot be 6,7,8--so it can be 0,1,2,3,4,5 or 9 (7choices)
7 × 4 × 7 is 196
There are 196 possibilities for the three digit area code with this plan.
The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. Which equation correctly models the ball’s height as a function of time?
The maximum height at the moment is 191.0625 ft.
What is the projectile's height?
Let's find out the projectile's maximum height now that we know what it is. The highest vertical location along the object's flight is considered to be its maximum height. The range of the bullet is defined as its horizontal displacement.
Here, we have
Given: The equation for a projectile's height versus time is h(t)=-16t²+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second.
The equation for a projectile's height versus time is
h(t) = -16t²+Vt+h
h = 2
V = 110
Substitute these values into the function
h(t) = -16t²+110t+2
Take the first derivative
h'(t) = -32t + 110
Equate the derivative with zero h'(t) = 0
0 = -32t + 110
110 = 32t
t = 110/32
t = 3.4375
Find the maximum height at the moment
t = 3.4375 (s)
h(3.4375) = -16(3.4375)² + 110(3.4375) + 2
h(3.4375) = -189.0625 + 378.125 + 2
h(3.4375) = 191.0625 ft
Hence, the maximum height at the moment is 191.0625 ft.
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Calculate the area of the composite figure shown
The total area of the given figure is 525 cm² respectively.
What is the area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses.
The quantity of unit squares that cover a closed figure's surface is its area.
So, first, we will divide the figure into 2 parts which will be the triangle and the rectangle, and then add their area to get the total area as follows:
Triangle:
1/2 * b * h
1/2 * 15 * 20
15 * 10
150 cm²
Rectangle:
l*b
15*25
375 cm²
The total area of the figure: 375 + 150 = 525 cm²
Therefore, the total area of the given figure is 525 cm² respectively.
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Tyrone factored the polynomial completely. What is the value of B?
12x4+30x3+4x2+10x
Ax(Bx2+1)(2x+5)
2
3
5
6
Answer:
the value of B is 3
Step-by-step explanation:
We can start by factoring out the greatest common factor of the polynomial, which is 2x:
2x(6x3 + 15x2 + 2x + 5)
Now, we can factor the expression inside the parentheses by grouping:
2x[(6x3 + 2x) + (15x2 + 5)]
2x[2x(3x + 1) + 5(3x + 1)]
2x(2x + 5)(3x + 1)
Comparing this expression to the given expression:
Ax(Bx2+1)(2x+5)
We see that A = 2, B = 3, and the factor (2x + 5) is the same in both expressions. Therefore, the value of B is 3.
Need help with this problem
The sales tax on 250 dollars purchase is: $3865
How to find the equation model?We are told that sales tax is directly proportional to retail price. Thus:
S ∝ p
Any item that sells for 158 dollars has a sales tax of 10.22 dollars. Thus:
158 = 10.22k
where k is constant of proportionality
Thus:
k = 158/10.22
k = 15.46
Thus, the equation is:
S = 15.46p
Sales tax on 250 dollars purchase is:
S = 15.46 * 250
S = $3865
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To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B.
The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.6 feet.
The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.3 feet.
At α = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles?
Assume the samples are random and independent, and the populations are normally distributed.
(a) Identify the claim and state H_0 and H_a
(The mean braking distance is different for the two makes of automobiles.)
What are H_0 and H_a?
(b) Find the critical value(s) and identify the rejection region(s).
(c) Find the standardized test statistic z for μ_1 - μ_2
z = _____
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
Upper Critical Value; 1.645
p-Value; 0.0814
Reject the null hypothesis
How to solvea).
claim: A. The mean breaking distance is different for the two makes of automobiles
H0 and Ha.: E
[tex]\ H_0: \mu_1 = \mu_2 \ \ \ H_a: \mu_1 \neq \mu_2[/tex]
b).
critical values are (-1.645, 1.645)
Rejection region: E. z < -1.645 , z >1.645
c)
test statistic z= -1.743
d).
C. Reject H0. The stat statistic falls in the rejection region.
e).
At the 10% significance level, there is sufficient evidence to support the claim that means breaking distance of make A is different from mean breaking distance of making B.
m 2
M1
7t
Z Test for Differences in Two Means
Data
Hypothesized Difference
0
Level of Significance
0.1
Population 1 Sample
Sample Size
35
Sample Mean
42
Population Standard Deviation
4.9
Population 2 Sample
Sample Size
35
Sample Mean
44
Population Standard Deviation
4.7
Intermediate Calculations
Difference in Sample Means
-2
Standard Error of the Difference in Means
1.1477
Z Test Statistic
-1.7427
Two-Tail Test
Lower Critical Value
-1.645
Upper Critical Value
1.645
p-Value
0.0814
Reject the null hypothesis
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If a case of 24 water bottles is $8 per case, how much are you paying for each bottle?
Exit
Savvas Realize
8-6: MathXL for School: Practice & Problem Solving
★ Start Page
0 Assignment is past due (
The circumference of the hub cap of a tire is 83.90 centimeters. Find the area of this hub cap. Use 3.14 for x. Use pencil and paper. If the circumference
were smaller, explain how this would change the area of the hub cap.
The area of this hub cap is about 560 square centimeters.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.)
It can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.
How to solveGiven the circumference (C) of the hub cap as 83.90 cm, we can find the radius (r) using the formula C = 2 * π * r,
where π = 3.14.
Thus, r ≈ 13.363 cm.
To find the area (A), use the formula A = π * r^2, yielding A ≈ 560.509 cm². Rounded, the area is about 561 cm².
Therefore, it can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.
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Betty has 30 mls of cough medicine with breakfast.
She drinks half of her 4 ounce orange juice, and 25% of her 8 oz cup of coffee. How many mls total
did she consume?
Betty consumed a total of 148.294 milliliters of liquid with her breakfast.
To solve this problemWe can change the volumes of the coffee and orange juice to milliliters so that all of the measurements are in the same unit:
4 ounces = 4 * 29.5735, = 118.294 ml.
8 ounces = 8 x 29.5735, = 236.588 ml.
Half of Betty's 4-ounce glass of orange juice, or:
1/2 * 118.294 mls = 59.147 mls
She consumed 25% of her 8-ounce coffee, which is :
0.25 * 236.588 mls = 59.147 mls.
So, in total, Betty consumed:
30 mls of cough medicine + 59.147 mls of orange juice + 59.147 mls of coffee = 148.294 mls
Therefore, Betty consumed a total of 148.294 milliliters of liquid with her breakfast.
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Several years ago, the average earnings for male workers between the ages of 25 and 34 with a high school diploma was $31,680. Comparing this value in
constant dollars to the average earnings 21 yr later showed that the average earnings have decreased to $27,900. Find the average rate of change in dollars
year for this time period.
[ Hint: Use the ordered pairs (0, 31,680) and (21, 27,900).]
Answer:
For 25- to 34-year-olds who worked full time, year round, higher educational attainment was associated with higher median earnings.
Step-by-step explanation:
This pattern was consistent for each year from 2010 through 2020. For example, in 2020, the median earnings of those with a master’s or higher degree were $69,700, some 17 percent higher than the earnings of those with a bachelor’s degree ($59,600). In the same year, the median earnings of those with a bachelor’s degree were 63 percent higher than the earnings of those who completed high school ($36,600).
Hannah is working in England for 3 months on a project for her company. One weekend Hannah decides to go to France with her car on the ferry, then explore the French countryside. In England, speed limit signs are posted in miles per hour (mph) and Hannah's rental car only shows the speed in miles per hour. In France, speed limit signs are posted in kilometers per hour (kph). Hannah looks up the conversion and learns that 1 kph = 0.62 mph.
On the road that Hannah is currently on, the posted speed limit is 130 kilometers per hour. What is the maximum whole-number speed, in miles per hour, that Hannah can drive without exceeding the speed limit?
A. 82 mph
B. 79 mph
C. 209 mph
D. 80 mph
Answer:
To convert kilometers per hour to miles per hour, we need to multiply by 0.62. Therefore, to find the maximum speed that Hannah can drive without exceeding the speed limit of 130 kilometers per hour, we can multiply 130 by 0.62:
130 km/h * 0.62 = 80.6 mph
Since Hannah needs to stay within the speed limit, the maximum whole-number speed she can drive is 80 mph, which is option D.
Step-by-step explanation:
Elisa finished her math assignment in 1/2 hours. Then she completed her chemistry assignment in 1/5 hours. What was the tot amount of time Elsa spent doing these two assignments? Write your answer as a fraction in simplest form.
An air traffic controller is tracking two planes. To start, Plane A is at altitude of 2639 feet and Plane B is just taking off. Plane A is gaining altitude at 35.25 feet per second and Plane B is gaining altitude at 80.75 feet per second
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude?
Answer:
Step-by-step explanation:
To find the number of seconds it will take for the planes to be at the same altitude, we need to set the altitude equations for both planes equal to each other and solve for time:
2639 + 35.25t = h (altitude equation for Plane A)
0 + 80.75t = h (altitude equation for Plane B)
where h is the altitude of both planes when they are at the same altitude, and t is the number of seconds that have passed.
Setting the two equations equal to each other and solving for t, we get:
2639 + 35.25t = 80.75t
45.5t = 2639
t = 58
Therefore, it will take 58 seconds for the planes to be at the same altitude.
To find their altitude at that time, we can substitute t = 58 into either of the altitude equations and solve for h:
2639 + 35.25t = h
2639 + 35.25(58) = h
h = 4818.5
Therefore, when the planes are at the same altitude, their altitude will be approximately 4818.5 feet.
Find the x-intercept and y-intercept of this equation.
y = 4x + 7
Question 10 options:
x-intercept (4,0), y-intercept (0,7)
x-intercept (-7,0), y-intercept (0,-4)
x-intercept (7/4, 0), y-intercept (0,-4/7)
x-intercept (-7/4, 0), y-intercept (0,7)
The intercepts of the equation are: D. D. x-intercept (-7/4, 0), y-intercept (0,7).
What is the X-intercept and Y-intercept of a Linear Equation?The x-intercept of an equation is simply the value of x when the corresponding value of y equals zero. Also, this is where the line of the equation cuts across the x-axis on a graph.
The y-intercept of an equation, on the other hand, is the value of y when the corresponding value of x equals zero. It is the point where the line of the equation cuts across the y-axis on a graph.
Thus, given the equation y = 4x + 7, the y-intercept is:
y = 4(0) + 7
y = 7
The x-intercept is:
0 = 4x + 7
-4x = 7
x = 7/-4
x = -7/4
The correct option is: D. x-intercept (-7/4, 0), y-intercept (0,7).
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A scatter plot is shown on a coordinate plane. The x-axis is numbered 0 to 15 and the y-axis is numbered from 2 to 26 in increments of 2. Points shown are located at (7, 2), (9, 1), (11, 3), (7, 6), (5, 8), (8.5, 8), (3, 12), (6, 13), and (4, 16). A line of best fit goes through points (5, 12) and (9, 4) and is extended to show it approaching the points (0, 22) and (11, 0).
Which equation represents the line of best fit?
The equation represents the line of best fit is y = -2x + 22.
What is an equation?A mathematical statement that represents a relationship between two or more quantities is typically expressed using symbols, numbers, and mathematical operations. Equations are used to express mathematical relationships, make predictions, and solve problems. An equation typically consists of an expression on each side of an equal sign (=), indicating that the values on both sides are equivalent.
According to the given information:
To determine the equation of the line of best fit in the scatter plot, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given that the line of best fit goes through points (5, 12) and (9, 4), we can calculate the slope (m) using the formula:
m = [tex]\frac{(y_{2}-y_{1})}{(x_{2}-x_{1} ) }[/tex]
Plugging in the values from the given points, we get:
m = [tex]\frac{(4-12)}{(9-5)}[/tex]
m = -8 / 4
m = -2
So, the slope of the line of best fit is -2.
Next, we can substitute the slope and one of the given points (5, 12) into the slope-intercept form to solve for the y-intercept (b):
12 = -2(5) + b
12 = -10 + b
b = 12 + 10
b = 22
So, the y-intercept of the line of best fit is 22.
Thus, the equation of the line of best fit is:
y = -2x + 22.
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Juan catches 80% of the passes thrown to him in football. If the quarterback throws to him 15 times during a game, what is the probability he will catch atleast 10 of them?
the probability that Juan will catch at least 10 passes out of 15 is approximately 0.987.
The binomial distribution, which models the number of successful trials (catches) in a certain number of independent trials (passes thrown), can be used to solve this problem.
The likelihood of not catching a pass is 0.2, but the likelihood of catching one is 0.8. The likelihood of catching at least 10 passes out of 15 can be calculated as follows:
P(X >= 10) equals P(X = 10) plus P(X = 11). + ... + P(X = 15)
where X is how many of the 15 passes were intercepted.
The probability of catching precisely k passes out of n can be calculated using the binomial distribution formula:
P(X = k) = (n choose k) × p²k × (1 - p)²(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Plugging in the values for n = 15, p = 0.8, and k = 10, 11, 12, 13, 14, and 15, we get:
P(X >= 10) = P(X = 10) + P(X = 11) + ... + P(X = 15)
= (15 choose 10) × 0.8²10 × 0.2²5 + (15 choose 11) × 0.8²11 × 0.2²4 + ... + (15 choose 15) × 0.8²15 × 0.2²0
≈ 0.987
Therefore, the probability that Juan will catch at least 10 passes out of 15 is approximately 0.987.
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resoudre l inequation (5x-4)(4x+3)<5(4x²-1)
Answer:
This shows the step by step process of rhetorical reduction of the question given
Emilio took a random sample of n=12 giant Pacific octopi and tracked them to calculate their mean lifespan. Their lifespans were roughly symmetric, with a mean of x= 4 years and a standard deviation of sx=0.5 years. He wants to use this data to construct a t interval for the mean lifespan of this type of octopus with 90% confidence.
What critical value t* should Emilio use?
Emilio can find that the critical value t* for a 90% confidence level and 11 degrees of freedom is approximately 1.796.
Define standard deviation?To construct a t interval for the mean lifespan with 90% confidence, Emilio needs to use a t-distribution with n-1 degrees of freedom. The confidence interval for the population is given by:
confidence interval = x ± t × (s·x/√n)
Where x is the sample mean, s·x is the sample standard deviation, n is the sample size, and t is the critical value of the t-distribution.
Since the sample size is n=12, the degrees of freedom for the t-distribution will be (n-1) = 11. To find the critical value t* for a 90% confidence level and 11 degrees of freedom, Emilio can use a t-distribution table or a statistical software.
Using a t-distribution table or calculator, Emilio can find that the critical value t* for a 90% confidence level and 11 degrees of freedom is approximately 1.796.
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what is the difference between the square of the sum and the square of a difference?
Answer:
The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared.
Step-by-step explanation:
Thus, this resulting binomial is called a difference of squares.
Answer:
Step-by-step explanation:
Square of the sum
square means you are multiplying something twice and looks like:
ex. [tex]x*x=x^{2}[/tex]
sum is the addition of numbers
so square of the sum looks like:
(a+b)²
Square of the difference
difference means subtraction of numbers
so square of the difference looks like:
(b-a)²
Answer:
The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared.
Step-by-step explanation:
Thus, this resulting binomial is called a difference of squares.
Answer:
Step-by-step explanation:
Square of the sum
square means you are multiplying something twice and looks like:
ex. [tex]x*x=x^{2}[/tex]
sum is the addition of numbers
so square of the sum looks like:
(a+b)²
Square of the difference
difference means subtraction of numbers
so square of the difference looks like:
(b-a)²
Ms. Shaddai writes 3q = 51 and \{15, 16, 17\} on the board. Tell if each value in the set is a solution of the equation. Show your work.
Only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.
How to find out if each value in the set is a solution of the equation?To check if a value is a solution of the equation 3q = 51, we substitute the value for q and check if the equation is true.
Let's check each value in the set {15, 16, 17}:
For q = 15, 3q = 3(15) = 45, which is not equal to 51. Therefore, 15 is not a solution of the equation 3q = 51.
For q = 16, 3q = 3(16) = 48, which is not equal to 51. Therefore, 16 is not a solution of the equation 3q = 51.
For q = 17, 3q = 3(17) = 51, which is equal to 51. Therefore, 17 is a solution of the equation 3q = 51.
Therefore, only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.
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Suppose a company wanted to find out whether a new highlighter lasted less than their original highlighters lasted.
The value of t= -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
To test the hypothesis that the highlighters last less than 14 hours, we will use a one-sample t-test. The null hypothesis for this test is that the mean continuous writing time for the highlighters is equal to or greater than 14 hours. The alternative hypothesis is that the mean continuous writing time for the highlighters is less than 14 hours.
In this problem, we are given that x = 13.6 hours and s = 1.3 hours. The sample size is n = 40. Substituting these values into the formula for the test statistic, we get:
t = (13.6 - 14) / (1.3 / √(40)) = -1.946
The p-value for the test can be found using a t-distribution table or a statistical software program. The p-value is the probability of observing a t-value as extreme as the one we calculated, assuming the null hypothesis is true. In this problem, the p-value is 0.029.
To make a decision about the null hypothesis, we compare the p-value to the significance level, which is typically set at 0.05. If the p-value is less than the significance level, we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.
In this problem, the p-value is less than 0.05, so we reject the null hypothesis. This means there is strong evidence to suggest that the highlighters last less than 14 hours. We can conclude that the manufacturer's claim that their highlighters can write continuously for 14 hours is not supported by the sample data.
Hence the correct option is (c).
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Complete Question:
Solve the problem. Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. Following are the summary statistics:
x =13.6 hours,
s =1.3 hours
Report the test statistic, p-value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.
a) z = 1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
b) t = -1.946; p = 0.029; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours. o
c) t= -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
d) z = 1.946; p = 0.974; Fail to reject the null hypothesis; there is not “strong evidence to suggest that the highlighters last less than 14 hours.
the angle of elevation from the horizontal to the sun is 38°. How long of a shadow would a 32 foot tree make at this time?
The length of the shadow would be approximately 41.7 feet if the angle of elevation from the horizontal to the sun is 38° at this time.
If the angle of elevation from the horizontal to the sun is 38°, then the tangent of that angle is equal to the opposite side (the height of the tree) divided by the adjacent side (the length of the shadow).
Therefore, we can set up the equation using trigonometric function tangent as,
tan(38°) = height of tree / length of shadow
Solving for the length of the shadow, we get:
length of shadow = height of tree / tan(38°)
Plugging in the given height of the tree (32 feet) and using a calculator to find the tangent of 38°, we get:
length of shadow = 32 / tan(38°) = 41.7 feet (rounded to one decimal place)
Therefore, the length of the shadow would be approximately 41.7 feet at this time.
To learn more about, Trigonometric functions, visit:
https://brainly.com/question/25618616