Answer:
Z = \(\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }\) = 1.6
we reject the Null hypothesis
Step-by-step explanation:
The correct test statistic
Assume :
Null Hypothesis : H_0 : p = 0.08
Alternative hypothesis : H_a : p ≠ 0.08
p = proportion of residents that are unemployed
x = unemployed residents = 22
n = sample size = 200
To get the sample of the population that is unemployed we use this equation
\(p = \frac{X}{n}\) = 22 / 200 = 0.11
now we apply the test of of significance of single proportion
= Z = \(\frac{p - P}{\sqrt{pq/n} }\)
therefore Z = \(\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }\) = 1.6
Therefore we reject the Null hypothesis
Testing the hypothesis, it is found that the test statistic used is z = 1.6.
At the null hypothesis, it is tested if the proportion is of 8%, that is:
\(H_0: p = 0.08\)
At the alternative hypothesis, it is tested if the proportion is different of 8%, that is:
\(H_1: p \neq 0.08\)
The test statistic is given by:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
In which:
\(\overline{p}\) is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: \(p = 0.08, n = 200, \overline{p} = \frac{22}{200} = 0.11\)
Hence, the value of the test statistic is:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(z = \frac{0.11 - 0.08}{\sqrt{\frac{0.08(0.92)}{200}}}\)
\(z = 1.6\)
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Daniels fish tank holds 24 liters of water he uses a 4 liter bucket to fill the tank how many buckets of water are needed to fill the tank
Answer:
6
Step-by-step explanation:
4 x 6 = 24 L
Please answer this!!
(Can’t get option b)
1. The two vectors parallel to the plane: Vector AB = (8, -5, 4) and Vector AC = (0, 7, 6)
2. The vector perpendicular to the plane is (-58, -48, 56).
How do we calculate for vectors parallel and perpendicular to the plane?
To find the vectors parallel to the plane, we begin by finding the vectors AB and AC.
Vector AB = B - A = (11 - 3, -5 - 0, 2 - (-2)) = (8, -5, 4)
Vector AC = C - A = (3 - 3, 7 - 0, 4 - (-2)) = (0, 7, 6)
To find a vector perpendicular to the plane, we can take the cross product of the two vectors we found in part (a), AB and AC.
AB × AC = (AB_y * AC_z - AB_z * AC_y, AB_z * AC_x - AB_x * AC_z, AB_x * AC_y - AB_y * AC_x)
If we insert the figures, it will be
= ((-5) x 6 - 4 x 7, 4 x 0 - 8 x 6, 8 x 7 - (-5) x 0)
= (-30 - 28, -48, 56)
= (-58, -48, 56)
Consider the plane determined by the points A(3, 0, -2), B(11, -5, 2) and C(3, 7, 4).
a. Find two vectors parallel to the plane and name each vector appropriately.
b. Find a vector perpendicular to the plane.
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Solve for x. Round to the nearest tenth, if necessary.
Using Trigonometry, the value of x in the right triangle is 17.1
Since we have a right angle triangle ; The angle L can be obtained thus ;
L = 180 - (90+67)
L = 23
Using Trigonometry:
Sin23° = opposite/ hypotenuse
Opposite= 6.7
hypotenuse= x
Sin23° = 6.7/x
x = 6.7/sin(23°)
x = 17.14
Therefore, the value of x to the nearest tenth is 17.1
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Use mental math, estimation, and the division algorithm to evaluate the expressions.
What is the answer ?
118.4 divided by 6.4 ?
Answer:
18.5
Step-by-step explanation:
According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41% of college students nationwide engage in "binge drinking" behavior, having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 162 admitted to having engaged in binge drinking.
Required:
Using the most conservative estimate, what sample size would be required to reduce the margin of error to 2 percentage points?
Answer:
The sample size required is 2188.
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
\(CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\)
The margin of error for this interval is:
\(MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\)
The information provided is:
X = 162
n = 462
MOE = 0.02
Assume the confidence level as 95%.
Compute the sample proportion as follows:
\(\hat p=\frac{X}{n}=\frac{162}{462}=0.351\)
The z-critical value for 95% confidence interval is:
\(z_{0.025}=1.96\)
Compute the sample size required as follows:
\(MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\)
\(n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\)
\(=[\frac{1.96\times\sqrt{0.351(1-0.351)}}{0.02}]^{2}\\\\=2187.781596\\\\\approx 2188\)
Thus, the sample size required is 2188.
a house on the market was valued at 446000 after several years of value increased by 15% by the how much did the house value increase in dollars what is the value of the house
Answer:
the house will have gained $66,900$ worth of value putting the house worth at $512,900$
Step-by-step explanation:
446,000 ➗ 100 X 15 = 66,900
446,000 + 66,900 = 512,900
hope this help if you need any more help P.M. me.
Grace earned £22,000 last year.
She worked for 35 hours a week for 48 weeks.
Calculate her pay per hour.
Give your answer to 2 decimal places.
Answer:
13.09 pounds, 13,10 pounds if you have to round, which is not clear (result is 13.095).
what is 3 2/3+2.3 the 2.3 is a repeating decimal
Answer:
5.96 with the repeating sign over the 6
Step-by-step explanation:
Answer:
6.
Step-by-step explanation:
Convert the decimal to a fraction:
2.33333.... = 2 1/3, so it is:
3 2/3 + 2 1/3
= 3 + 2 + 2/3 + 1/3
= 3 + 2 + 1
= 6.
You are selling candy bars for the school to
pay for your senior trip which costs $300. If
each candy bar costs $1.25 and you already
have $50 in sales. How many more candy
bars do you need to sell?
Answer:
200 bars
Step-by-step explanation:
$300 - $50 = the amount of money you still need, $250
250 dollars/$1.25 per bar = 200 bars you need to sell to get 300 dollars
How could expanded land acreage and pricing be viewed as some to be a bad thing
for the recovering Great Plains?
Increased land prices and acreage on the Great Plains could be seen as negative owing to potential ecological impact, as a disruption for Traditional communities and unsustainable resource use.
Why expanded land acreage and pricing in Great plains is considered negative?Ecological impact: Increased land acreage and price may cause habitat loss, biodiversity loss, soil erosion, and water pollution, all of which might be detrimental to the area's natural ecosystem.Disruption of traditional farming and ranching communities: Increasing land prices and greater parcel sizes may make it harder for small-scale farmers and ranchers to compete, which might result in the consolidation of land ownership and the eradication of traditional farming and ranching communities.Unsustainable resource use: Increasing land area might result in more water being used for irrigation, thereby worsening the Great Plains' water shortage problems.Loss of grasslands: The Great Plains are renowned for their distinctive grassland ecosystems, which are essential for biodiversity and carbon sequestration. More land being used for construction or agriculture might lead to the extinction of grasslands, which would have detrimental ecological effects.Degradation of the soil: Intensive agricultural techniques, such as monoculture and extensive chemical usage, may result in the loss of fertility and accelerated erosion of the soil. Long-term, this can have a negative effect on the sustainability and production of agricultural areas.Increased use of chemical inputs: Increasing land area may result in higher usage of chemical pesticides and fertilisers, which might impact regional ecosystems and contribute to environmental degradation.Danger of overproduction: Increased land acreage and pricing may lead to overproduction of agricultural products, which might lead to unstable prices, unstable farmer livelihoods, and potential market saturation.Potential for land speculation: Increasing land prices may encourage speculative investment, which might result in land being bought and retained for financial gain rather than for productive use. This could push up land prices even more and restrict access to land for local farmers and ranchers.Risks to wildlife and biodiversity: Include habitat fragmentation, the loss of wildlife corridors, and the displacement of native species, all of which might have an effect on the biodiversity and animal populations of the area.Learn more about land acreage and pricing here:
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Which of the following sets of numbers could represent the three sides of a triangle? \{13,20,35\}{13,20,35} \{11,24,35\}{11,24,35} \{11,24,32\}{11,24,32} \{10,20,31\}{10,20,31}
The correct sets of numbers which represent the three sides of a triangle will be;
⇒ { 11, 24, 32 }
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sides of a triangle are shown.
Now,
We know that;
The sum of two sides of triangle is greater than the third side.
Hence, We get;
First option;
⇒ [ 13, 20, 35 ]
Cleary, 13 + 20 = 33 < 35
Thus, It is not possible.
Second option;
⇒ [ 11, 24, 35 ]
Cleary, 11 + 24 = 35 = 35
Thus, It is not possible.
Third option;
⇒ [ 11, 24, 32 ]
Cleary, 11 + 24 = 35 > 32
Thus, It is possible.
Therefore, The correct sets of numbers which represent the three sides of a triangle will be;
⇒ { 11, 24, 32 }
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Reuben made a shirt using 7/8yards of red fabric and 1/4yards of yellow fabric. How many more yards of red fabric did Reuben use?
Answer and Step-by-step explanation:
To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:
7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8
So, Reuben used 5/8 yards more red fabric than yellow fabric.
By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0
By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.
To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.
Let's start by graphing the constraints:
1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.
2. Plot the line -x + 3y = 6 using a similar process.
3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.
Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.
Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.
Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.
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Which side lengths form a right triangle?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
3, \sqrt9, \sqrt{18}3,
9
,
18
3, comma, square root of, 9, end square root, comma, square root of, 18, end square root
(Choice B)
B
3, 4, 53,4,53, comma, 4, comma, 5
(Choice C)
C
7, 7, \sqrt{98}7,7,
98
Answ
Step-by-step explanation:
Answer:
All of them A,B, and C
Step-by-step explanation:
Khan says so.
When Tyee runs the 400 meter dash, his finishing times are normally distributed with a mean of 61 seconds and a standard deviation of 1.5 seconds. If Tyee were to run 39 practice trials of the 400 meter dash, how many of those trials would be faster than 62 seconds, to the nearest whole number?
To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.
We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.
The z-score formula is:
z = (x - μ) / σ
Where:
x = value (62 seconds)
μ = mean (61 seconds)
σ = standard deviation (1.5 seconds)
Calculating the z-score:
z = (62 - 61) / 1.5
z ≈ 0.6667
Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.
Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.
To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:
Number of trials = Proportion * Total number of trials
Number of trials = 0.7461 * 39
Number of trials ≈ 29.08
Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.
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What is the equation of this line?
a.y = 2x
b.y=−12x
c.y=12x
d.y=−2x
Answer:
Im thinking its y=-2x but Im not 100% sorry if its wrong
Gabriel multiplied a number by 5 instead of 3. The answer that he got was
12 more than the correct answer. What was the original number?
Answer:6
Step-by-step explanation:
The original number that was multiply by 5 instead of 3 is 6.
What is the orignal number?The equation that can be used to represent the informatioin in the question is:
5x - 3x = 12
Where x is the original number
In order to determine the value of x, take the following steps
Combine similar terms: 2x = 12
Divide both sides by 2
x = 6
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Question 2
Graph the system of equation on graph paper or in your calculator,
y=−43x+4
y=−23x−2
Which statements are true about the solution to the system of equations?
Select EACH correct answer.
Question 2 options:
The ordered pair that is the solution to the system lies in Quadrant I.
The ordered pair that is the solution to the system lies in Quadrant IV.
The x-coordinate of the solution is 8.
The x-coordinate of the solution is 9.
The y-coordinate of the solution is -8.
The y-coordinate of the solution is 9.
The solution to the system of equation is (0.3, -8.9). This shows that the ordered pair that is the solution to the system lies in Quadrant IV.
Given the systems of equations
y=−43x+4
y=−23x−2
We need to get the solution to the system of equation and then graph
Since both expressions have the same output variable, we will equate it to have:
\(-43x + 4 = -23x - 2\)
Collect the like terms
\(-43x+23x=-2-4\\-20x=-6\\x=\frac{3}{10}\)
Substitute \(x=\frac{3}{10}\) into the value of y above to have:
\(y=-23(\frac{3}{10} )-2\\y=\frac{-69}{10}-2\\y=-6.9-2\\y=-8.9\)
Hence the solution to the system of equation is (0.3, -8.9). This shows that the ordered pair that is the solution to the system lies in Quadrant IV.
The graph of the equation is attached.
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HELP!! Image inculded
Answer:
B.\( \frac{ - 3}{ {x}^{2} - 5x + 6 }\)
hope it helps
Use the drawing tool(s) to form the correct answers on the provided graph. In the given equation, y is a function of x. Graph the function in the coordinate plane. Use the Mark Feature tool to indicate the x- and y-intercepts of the function.
Answer:
Here is the graph of y is a function of x.
if a binomial trial has a success of .3, how many successes would you expect out of 500 trails
Answer:
gfs
Step-by-step explanation:
Please look at the pic and help!!
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
Solve (t-3)^2=6
The arrow is at a height of 48 ft after approx. ___ s and after ___ s.
The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.
To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:
s = v0t - 16t^2
Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.
Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:
48 = 96t - 16t^2
Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.
Rearranging the equation:
16t^2 - 96t + 48 = 0
Dividing the equation by 16 to simplify:
t^2 - 6*t + 3 = 0
We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
t = (6 ± √((-6)^2 - 413)) / (2*1)
t = (6 ± √(36 - 12)) / 2
t = (6 ± √24) / 2
Simplifying the square root:
t = (6 ± 2√6) / 2
t = 3 ± √6
Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.
In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.
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Note the complete question is
The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?
Solve (t-3)^2=6
The arrow is at a height of 48 ft after approx. ___ s and after ___ s.
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
©s is inversely proportional to t.
When s 0.9, t = 5
Work out t when s = 90
0.9 * 100 = 90
5 * 100 = 500
t = 500
Answer:
Step-by-step explanation:
0,9÷90=0,01
t= 5×0,01=0,05
Tyrone jogged 5 miles along the fitness trail. How many feet did he jog? How many inches did he jog?
Answer: Tyrone is body built so you can assume he takes very big steps so i'll say about 69 inches
Step-by-step explanation: The math is common sense
Sebastian is 3 years older than twice Amy's age. Sebastian is 33 years old. How old is Amy?
Answer:
15 years old
Step-by-step explanation:
You would have to create a equation. 2x+3=33, 2x=30, x=15.
Translation how many units right followed by a dilation with a scale factor of?
Help please!
Answers:
Translation 1 unit to the right.
Followed by a dilation with scale factor 2
==========================================================
Explanation:
The ultimate goal is to somehow turn the smaller blue triangle (ABC) into the green triangle (XYZ).
This means that we want to do three things:
Move point A to XMove point B to YMove point C to ZThis works because any triangle is uniquely defined by the three corner points.
Let's focus on point C. Right now, it is located at (1,1). If we move it 3 units to the right, then it arrives at (4,1). We have the correct x coordinate, but the y coordinate is not correct. We're one unit below our target, which is where Z is located.
But what we could do is instead of moving 3 units to the right, we can move 1 unit to the right. Point C will go from (1,1) to (2,1). Now apply a dilation with scale factor 2. This will multiply the coordinates by 2. So (2,1) doubles to (4,2) which is exactly where point Z is located. This process is effectively trial and error, so we got a bit lucky and didn't have to do much work to move C to Z.
-----------------
We'll do the same steps for points A and B to see if we can get them to move to X and Y respectively.
Point A is located at (2,3). Shifting one unit to the right lands us on (3,3). Double the coordinates to get to (6,6). This is where point X is located.Point B is at (3,1). It moves to (4,1) after shifting one unit to the right. Then it moves to (8,2) when we double the coordinates, and this is where point Y is located.So the process of "shift one unit to the right, double the coordinates" works for points A and B also.
Keep in mind that the order of the transformations is important. We cannot double the coordinates first, and then shift one unit to the right. If we did that, then point C would move to (3,2) which is not where point Z is located.
Please someone solve this
Answer:
a)
(4a - 3b + 4) + (a + 3b - 1) =
4a - 3b + 4 + a + 3b - 1 =
5a + 3
b)
(2x^2 - 3x - 3) + (-x^2 - 6x + 8) =
2x^2 - 3x - 3 - x^2 - 6x + 8 =
x^2 - 9x + 5
c)
(3m^2 + 5m - 6) + (-m^2 - 4n + 5) =
3m^2 + 5m - 6 - m^2 - 4n + 5 =
m^2 + 5m - 4n -1
d)
(4x^3 - 3xy^2) + (x^3 - 5xy^2 - 5y^2) =
4x^3 - 3xy^2 + x^3 - 5xy^2 - 5y^2 =
7x^3 - 8xy^2 - 5y^2
e)
(5m + 2lm) + (l^2 - 3m^2 - 2lm) =
5m + 2lm + l^2 - 3m^2 - 2lm =
5m + l^2 - 3m^2
Translate the sentence into an equation
two less than the product of 5 and a number equals 9
Use the variable y for the unknown number
Answer:
5y-2=9
Step-by-step explanation:
Hopefully this helps :)