We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is significantly lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.05 and observe that p'.
What is the meant by hypothesis test?Hypothesis test: A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.
Data are provided and noted.
X=6.8 display the sample mean
σ= 0.9 show the population's standard deviation.
n= 280 samples taken
μο=6.7 the value that we wish to test should be represented
α=0.1 signify the hypothesis test's level of significance.
The stat would be represented as z. (variable of interest)
p' indicate the test's p value (variable of interest)
Name the prevailing and competing hypothesis
The system of hypothesis must be tested to see if the true mean is below the criteria.
Null hypothesis: μ ≥ 6.7
Alternative hypothesis: μ < 6.7
Applying a z test to compare the actual mean to the reference value is preferable if the sample size is greater than 30 and we are aware of the population variation. The statistic is given by:
z=(X-μο)/σ[tex]\sqrt{n}[/tex] ......(1)
z-test: "enables the comparison of group means. One of the most widely used tests, it is used to determine whether the mean is (higher, lower, or not equal) to a given value ".
Calculate the statistic
We can replace in formula (1) the info given like this:
z=(6.8-6.7)/0.9[tex]\sqrt{280}[/tex]
P-value
Since is a one sided test the p value would be:
p'=p(z<0.0066)
We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is considerably lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.1 and observe that p'.
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Graph the solution to the following system of inequalities. Don’t forget to answer the point in the solution set.
Given the following System of Inequalities:
[tex]\begin{cases}7x+4y<16 \\ -5x+4y\ge12\end{cases}[/tex]You need to remember that the Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
The steps to graph the System of Inequalities are:
1. In this case, you know that the first line is:
[tex]7x+4y=16[/tex]So you need to solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 4y=-7x+16 \\ \\ y=\frac{-7}{4}x+\frac{16}{4} \\ \\ y=-\frac{7}{4}x+4 \end{gathered}[/tex]You can identify that the y-intercept is:
[tex]b_1=4[/tex]2. Since the value of "y" is zero when the line intersects the x-axis, you can substitute that value into the equation and solve for "x", in order to find the x-intercept:
[tex]\begin{gathered} 7x+4y=16 \\ 7x+4(0)=16 \\ 7x=16 \\ \\ x=\frac{16}{7}\approx2.286 \end{gathered}[/tex]3. Now you know that the first line passes through these points:
[tex](0,4);(2.286,0)[/tex]4. The second line is:
[tex]-5x+4y=12[/tex]So you can solve for "y" in order to write it in Slope-Intercept form:
[tex]\begin{gathered} 4y=5x+12 \\ \\ y=\frac{5}{4}x+\frac{12}{4} \\ \\ y=\frac{5}{4}x+3 \end{gathered}[/tex]Notice that the y-intercept is:
[tex]b_2=3[/tex]5. Knowing that "y" is zero when the line intersects the x-axis, you can substitute that value into the equation of the second line and solve for "x" to find the x-intercept:
[tex]\begin{gathered} -5x+4y=12 \\ -5x+4(0)=12 \\ -5x=12 \\ \\ x=\frac{12}{-5} \\ \\ x=-2.4 \end{gathered}[/tex]Which of the following is the correct factorization of the polynomial below?p3 - 21603O A. (0-360)(p? + 36pq + 692)O B. (p2 + 129) (03 + 36pq + 50%)O C. (2-6)(p2 + 6pq + 3602)O D. The polynomial is irreducible.
We have the polynomial:
[tex]p^3-216q^3[/tex]We have to factorize it.
We know that 216 is the cube of 6.
We then applied the property for the difference of cubes.
[tex]\begin{gathered} p^3-(6q)^3 \\ (p-6q)(p^2+p\cdot6q+(6q)^2) \\ (p-6q)(p^2+6pq+36q^2) \end{gathered}[/tex]The answer is Option C.
Difference of cubes property:
x^3-y^3 = (x-y)(x^2+xy+y^2)
1. Is 26 divisible by 2? (1 point)
ONO
O Yes, because 2 +6=8 and 8 is divisible by 2.
O Yes, because the last digit is 6, which is divisible by 2.
Answer:
Yes, because the last digit is 6, which is divisible by 2.
Step-by-step explanation:
The solution is, Yes, because the last digit is 6, which is divisible by 2.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
26 divisible by 2
i.e. 26/2 = 13
so, it is divisible.
now, we know that,
because the last digit is 6, which is divisible by 2.
Hence, The solution is, Yes, because the last digit is 6, which is divisible by 2.
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PLEASE ASAP HELP MEEEEThe longer leg of a right triangle is 3 inches longer than the shorter leg. The hypotenuse is 6 inches longer than the shorter leg. Find the side lengths of thetriangle.Length of the shorter leg:inchesLength of the longer leg:inchesinchesLength of the hypotenuse:
In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.
h: hypotenuse
c1: shorter leg
c2: longer leg
Longer leg c2 is 3 inches longer than c1:
c2 = c1 + 3
hypotenuse h is 6 inches longer than c1:
h = c1 + 6
The formula for the calculation of the hypotenuse is:
h² = c1² + c2²
you replace for h and c2 in terms of c1:
(c1 + 6)² = c1² + (c1 + 3)²
You solve the previous equation for c1:
c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9
c1² - 6c1 - 27 = 0
the roots of the previous equation are:
(c1 - 9 )(c1 + 3) = 0
c1 = 9
c1 = -3
You take the positive number because there is no length of sides with negative values.
Then, c2 and h are:
c2 = c1 + 3 = 9 + 3 = 12
h = c1 + 6 = 9 + 6 = 15
Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches
suppose an opaque jar contains 4 red marbles and 11 green marbles. this exercise refers to the experiment of picking two marbles from the jar without replacing the first one. what is the probability of getting a green marble first and a red marble second?
The probability of getting a green marble first and a red marble second exists 5/26.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Red marbles = 3
Green marbles = 10
So, the total marbles = 3 + 10 = 13
Probability = Favorable outcomes / Total outcomes
Since, here replacement is not allowed,
Therefore, the probability of getting a green marble and a red marble
= first red and second green + first green second red
= 3/13 × 10/12+ 10/13 × 3/12
= 2 × 3/13 × 10/12
= 30/78
= 5/13
The probability of getting a green marble first and a red marble second
= 10/13 × 3/12
= 30/156
= 5/26
Therefore, the probability of getting a green marble first and a red marble second exists 5/26.
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1) Find the volume of each cone.a. Estimate using 22 꼭 for n. Express theanswer as a fraction.
Volume of the cone = 50.29 mm³
Explanation:[tex]\text{Volume = 1/3}\pi r^2\text{ h}[/tex]radius = r = ?
height = 3mm
slant height = 5mm
To get the radius, we would apply pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse = 5mm
opposite = 3mm
adjacent = radius = ?
5² = 3² + radius²
25 = 9 + radius²
25 - 9 = radius²
16 = radius²
radius = √16
radius = 4
[tex]\text{Volume of the cone = }\frac{1}{3}\times\frac{22}{7}\times4^2\times3[/tex][tex]\text{Volume of the cone = }50.29mm^3[/tex]An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in aprofit of $50,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if theeconomy goes into recession, the investment will result in a loss of $50,000. You contact an economist who believes there is a 20%probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 20% probability theeconomy will slip into recession. What is the expected profit from this investment?The expected profit is $(Type an integer or a decimal.)
Answer:
6000
Explanation:
The expected profit from the investment can be calculated as the multiplication of each possible profit or loss by their respective probability.
Therefore, the expected profit is equal to:
E = 50,000(0.2) + 10,000(0.6) + (-50,000)(0.2)
E = 10,000 + 6,000 - 10,000
E = 6,000
Because there is a 20% of probability to win $50,000 (economy remain strong), there is a 60% of probability to win $10,000 (economy grows at a moderate pace), and there is a 20% of probability a loss of $50,000 (the economy goes into recession).
Therefore, the expected profit from this investment is:
6000
19. What is the mode of the following numbers?
12, 11, 14, 10, 8, 13, 11, 9
a. 11
b. 10
C. 14
d. 8
Answer:
a. 11
Step-by-step explanation:
What is the mode of the following numbers?
12, 11, 14, 10, 8, 13, 11, 9
a. 11
b. 10
C. 14
d. 8
the mode is 11 because it is the most frequent number in the list.
4.2(2) question 7 thankThe function f(x) = 3(x+15)² - 50
Domain are the inputs of the function. They are the x values of the function
The function gives a parabola. This means the values of x will be from negative infinty to positve infinity
[tex]\begin{gathered} In\text{ interval notation:} \\ \text{Domain: (}-\infty,\text{ }\infty)\text{ (option D)} \end{gathered}[/tex]Plotting the graph:
Range are the outputs of the function. They are the y values of the function
From the graph, we see tip of the parabola starts at y = -50 and extends upwards
The y value will be from -50 to positive infinity
[tex]\text{Range: \lbrack-50, }\infty)\text{ (option C)}[/tex]Alvin paddled for 2 hours with a 5-km/h current to reach a campsite. The returntrip against the same current took 7 hours. Find the speed of the boat in stillwater.
Given:
Alvin paddled for 2 hours with a 5-km/h current to reach a campsite.
Let n be the speed of boat.
Distance is calculated as,
[tex]\begin{gathered} d=rt \\ d=2\mleft(n+5\mright) \end{gathered}[/tex]The return trip against the same current took 7 hours.
[tex]\begin{gathered} d=rt \\ d=7(n-5) \end{gathered}[/tex]Equate both the equations,
[tex]\begin{gathered} 2(n+5)=7(n-5) \\ 2n+10=7n-35 \\ 7n-2n=10+35 \\ 5n=45 \\ n=\frac{45}{5} \\ n=9 \end{gathered}[/tex]Answer: the speed of the boat is 9 mph.
ben is walking with three dogs that weigh an average of 75 pounds each. ben begins to walk with a fourth dog, and the average weight of the dogs decreases to 70 pounds. what is the weight in pounds of the fourth dog?
The weight in pounds of the fourth dog, is 55 lbs.
What is weight?
The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.
As given, Ben is walking with three dogs that weigh an average of 75 pounds each. Ben begins to walk with a fourth dog, and the average weight of the dogs decreases to 70 pounds.
The total weight of the first three dogs is 225 pounds.
This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:
[tex]\frac{d+225}{4} = 70\\d + 225 = 280\\d = 280 - 225\\d = 55 lbs[/tex]
Therefore, the weight of the fourth dog is 55 lbs.
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Marilyn wants to use a non-price competitive marketing strategy to gain more customers. Which of the following might she use?
As Marilyn wants to use a non-price competitive marketing strategy to gain more customers, the strategy that she might use is offering a promotion.
What is a Non-price competition in marketing?In marketing, the non-price competition refers to a marketing strategy in which a firm tries to distinguish its product or service from competing products on the basis of attributes like design and workmanship.
This competition most often occurs in an imperfectly competitive markets because it exists between producers that sell goods and services at same prices but competes to increase their respective market shares through different non-price measures such as marketing schemes and greater quality.
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what is the doubling timefor this population of alligators ?
3 years
Explanations:The given function representing the population of alligators is:
[tex]P(t)\text{ = (}319)2^{\frac{t}{3}}[/tex]Find the intial population at t = 0
[tex]\begin{gathered} P(0)\text{ = 319 }\times2^0 \\ P(0)\text{ = 319 }\times\text{ 1} \\ P(0)\text{ }=\text{ 319} \end{gathered}[/tex]The population will double when:
P(t) = 319 x 2
P(t) = 638
The doubling time is the value of t at which P(t) = 638
[tex]\begin{gathered} P(t)\text{ = 319 }\times2^{\frac{t}{3}} \\ 638\text{ = 319 }\times2^{\frac{t}{3}} \\ \frac{638}{319}=2^{\frac{t}{3}} \\ 2\text{ }=2^{\frac{t}{3}} \\ 2^1=2^{\frac{t}{3}} \\ 1\text{ = }\frac{t}{3} \\ t\text{ = 3} \end{gathered}[/tex]The population will double after 3 years.
Therefore, the doubling-time for this population of alligators is 3 years
Can someone help me on this pleaser
Answer: it should be the third one down
Step-by-step explanation:
Tell whether the given situation is an example of Direct Variation or Inverse Variation. Write DV if it is a Direct Variation and IV for Inverse Variation. (NEED THE ANSWER ASAP)7. The height of a person and his weight
Given,
The statement is "The height of a person and his weight".
Required/
Identify the statement is inverse or direct variation.
As the height of the person increase then its their weight is also increased.
Similarly,
The height of the person decrease then its their weight is also decreased.
Hence, it is direct variation.
Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?A) B = G + 11 and B + G = 28B) G = B + 11 and B + G = 28C)B = G – 11 and B + G = 28D)B + 11 = G and B + G = 28
Mrs. Brown has 11 more boys than girls in her class
[tex]B=G+11[/tex]Total of 28 students.
[tex]B+G=28[/tex] The final answerOption AAnswer:
A) B = G + 11 and B + G = 28
Step-by-step explanation:
I need to find the value of x in this figure.
Please explain how to do so.
Answer: 2x^2
Step-by-step explanation:
(x+5)
x (2x - 9)
-----------------
X times 2x = 2x^2
4. the probability that an engine overheats is 0.12. the probability that an engine leaks oil is .08. (a) if overheating and leaking oil are independent, what is the probability that an engine overheats and leaks oil?
The probability that the engine over heats and leaks is 0.0096
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
Engine leaks oil AND overheats,
hence P(Engine overheats) = P(Engine overheats) X P(Engine leaks oil) = 0.12 X 0.08 = 0.0096
Hence the probability of leaking of engine due to over heating is 0.0096
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[tex]3 {}^{2} + ( - 4 {}^{2} ) + 5 {}^{2} [/tex]I'm confused on that can you help me please?
We have to replace the values in the equation
[tex]x^2+y^2+z^2=(3)^2+(-4)^2+(5)^2=9+16+25=50[/tex]Since the square of a negative number is a positive number, (-4)^2 = +16
f(x) = 3x2 + 2x and g(x) = -2x + 1, what is f g(x)?
Answer:
f g(x) = 12x^2 - 16x +5
Step-by-step explanation:
f(x) = 3x^2 + 2x
g(x) = -2x + 1
f g(x)
f g(x) = 3(-2x + 1)^2 + 2(-2x + 1)
f g(x) = 3(-2x + 1)^2 + -4x + 2
f g(x) = 12x^2 - 12x +3 + -4x + 2
f g(x) = 12x^2 - 16x +5
1 pts for spring break you and some friends plan a road trip to a sunny destination that is 1705 miles away. if you drive a car that gets 39 miles per gallon and gas costs $3.339/gal, about how much will it cost to get to your destination?
Answer:
woooooowwoowww your terrible
Step-by-step explanation:
gude
2. What is the slope-intercept form of 9x + 3y = 15?
y = 3x - 5
y = 3x + 5
y=-3x - 5
y=-3x+5
Answer:
y=3x+5
Step-by-step explanation:
can you help solve for y?
Answer:
Go ahead and color the nose red!
The solution is
[tex]y = \dfrac{n-9}{x}[/tex]
Step-by-step explanation:
[tex]\text{We have: }\\\\[/tex]
[tex]\rightarrow\; \dfrac{x}{y} + 9 = n\\\\\\\text{Subtract 9 from both sides:}\\\\\rightarrow\;\dfrac{x}{y} + 9 - 9 = n - 9\\\\[/tex]
[tex]\rightarrow\;\dfrac{x}{y} = n - 9\\\\[/tex]
Multiply both sides by y:
[tex]\rightarrow\; y \cdot \dfrac{x}{y} = y (n-9)\\\\\rightarrow\; x = y(n-9)\\\\\\[/tex]
[tex]\text{Divide both sides by (n-9)}:\\\\\\\rightarrow\; \dfrac{x}{n-9} = \dfrac{y (n-9)}{n-9}\\\\\\\rightarrow\; \dfrac{x}{n-9} = y\\\\\\[/tex]
By switching sides without changing the meaning, this can be re-written as :
[tex]y = \dfrac{x}{n-9} \\\\[/tex]
which of course means you can color the nose red
:)
What’s the answer plss
Answer:
B.15.9
Step-by-step explanation:
Trigonometry
7.7/SIN(29)=15.9
Answer:
3.7 cm
Step-by-step explanation:
See attached worksheet
Follow the guided instructions below to create the line of reflection that would map the pink figure onto the blue figure. Now write the slope of the line of reflection and any dotted line. 10 -9 -8 7 -6 5 4 3 2 y 10 2 8 2 73 6 -8 10 Slope of one of the dotted lines: Slope of the line of reflection:
Slope of one of the dotted lines: -1/3
Slope of the line of reflection: 3
From given figure, we can observe that the line of reflection passes through points (2, 8) and (0, 2)
We need to find the slope of the line of reflection and any dotted line.
Using the formula of slope, the slope of the line of reflection would be,
m1 = (y2 - y1)/(x2 - x1)
m1 = (2 - 8)/(0 - 2)
m1 = -6 / (-2)
m1 = 3
The dotted lines are perpendicular to the line of reflection.
Let m2 be the slope of any dotted line.
We know that the product of slopes of any perpendicular lines is -1.
so, m1 * m2 = -1
3 * m2 = -1
m2 = -1/3
So, the slope of dotted any line = - 1/3
Therefore, Slope of one of the dotted lines: -1/3
Slope of the line of reflection: 3
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PLEASE HELP I AM GROUNDED AND NEED A BETTER GEOMETRY GRADE ASAP
Answer:
w = 9
Step-by-step explanation:
This is a 90-degree angle, so if you add both equations together, they will equal 90.
First, write the equation:
(4w - 7) + (7w - 2) = 90
Then you solve for w:
- add like factors
11w - 9 = 90
- add 9 to both sides
11w = 99
- divide both sides by 11
w = 9
So, the value of w is 9.
To check, plug your answer into the equation to check if it's true:
(4(9) - 7) + (7(9) - 2) = 90
(36-7) + (63-2) = 90
29 + 61 = 90
90 = 90
Even though I already got the question right,I need someone to show the work on how to get the answer for this question.
Given
Answer
[tex]\begin{gathered} \sin x=\frac{P}{H} \\ \sin x=\frac{5}{8.3} \\ x=\sin ^{-1}(\frac{5}{8.3}) \end{gathered}[/tex]Which is triangle 2
Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
The intervals on which the function is increasing, decreasing and constant are (-5,-3) and (2,5) on increasing (-3,0) on decreasing and (0,2) on constant.
What is intervals?
An interval in math is the measured in terms of the numbers. An interval to includes all the numbers that come between two of particular numbers. This is the range includes all of the realistic numbers between those two of numbers. Real numbers are the any kind of number you can definitely think of.
Sol-by showing in the figure the function is increasing on the (-3,0)
Decreasing on (-5,-3) and (2,5)
Constant on (0,2)
Thus, the correct option is A
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Multiply and write in standard form: 10x + 3)(2x - 1) Show all work
Explanation
[tex](10x+3)(2x+1)[/tex]Step 1
apply distributive property
[tex]\begin{gathered} (10x+3)(2x+1)=(10x\cdot2x)+(10x\cdot1)+(3\cdot2x)+(3\cdot1) \\ (10x+3)(2x+1)=20x^2+10x+6x+3 \end{gathered}[/tex]Step 2
add similar terms and order
[tex]\begin{gathered} (10x+3)(2x+1)=20x^2+10x+6x+3 \\ (10x+3)(2x+1)=20x^2+16x+3 \\ \text{the standard form is} \\ ax^2+bx+c,so \\ ax^2+bx+c\Rightarrow20x^2+16x+3 \end{gathered}[/tex]so, the answer is
[tex]20x^2+16x+3[/tex]I hope this helps you
Tayon wants to run a total of 16 miles this week. He has already run 5 miles. What percent of his goal has he finished?
Answer: the answer is 31.25%
Step-by-step explanation:
Divide 5 by 16, which is 0.3125. The you take that number and multiply it by 100: 0.3125 * 100= 31.25. So there for the answer is 31.25%
The percent of his goal he has finished is 31.25%.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
We need to calculate percentage here.
We have been given total distance and we have also been given the distance covered.
We have to find the percentage of his goal covered.
For this, we need his goal which is 16 miles and we know the goal covered by him which is 5 miles.
To find the percentage, we have to divide these both and multiply by 100.
Percentage of goal covered = Goal covered/total goal *100
= 5/16 * 100
= 31.25%
The percent of his goal is 31.25%.
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