Answer:
the computed value gets larger
Step-by-step explanation:
What is the image point of ( 1 , − 3 ) after the transformation y-axis R 90 ∘ ∘r y-axis ?
Answer: -3,1
Step-by-step explanation:
flip 1,-3 90 degrees clockwise
get 3,1
flip over y axis, which makes x negative
-3,1
Which equation is y = 2x2 – 8x 9 rewritten in vertex form? y = 2(x – 2)2 9 y = 2(x – 2)2 5 y = 2(x – 2)2 1 y = 2(x – 2)2 17
Answer:
Step-by-step explanation:
we have
\(y=2x2-8x+9\)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
\(y-9=2x2-8x\)
\(y-9=2(x2-4x)\)
\(y-9+8=2(x2-4x+4)\)
\(y-1=2(x2-4x+4)\)
\(y-1=2(x-2)2\)
\(y=2(x-2)2+1\)
the answer is the option C
\(y=2(x-2)2+1\)
The equation y = 2x² – 8(x + 9) can be rewritten in vertex form as y = 2(x – 2)² + 1 option (C) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
The equation is:
y = 2x² – 8(x + 9)
y = 2x² - 8x + 8 + 1
y = 2(x² - 4x + 4) + 1
y = 2(x – 2)² + 1
Thus, the equation y = 2x² – 8(x + 9) can be rewritten in vertex form as y = 2(x – 2)² + 1 option (C) is correct.
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Find the value of x, y, and z in the figure below:
ہ
2y
IN
2x
90°
t
Answer:
x=30°
y=15°
z=150°
Step-by-step explanation:
2x+90+x=180°
2x=180°-90°
x=90/3
x=30
2y=x
y= 30/2
y=15°
2y°+z°=180°
2(15°)+z°=180°
z=180°-30°
z=150°
Hope it helps! :)
7. Solve the equation r cubed = 216.
Answer:
6
Explaination:
r^3=216
r= cuberoot(216)
r= cuberoot(6x6x6)
r=6
Test at 20% significance level whether one of the drugs is more effective than the other.
(a) The absolute value of the critical value of this test is
(b) The absolute value of the calculated test statistic
(c) The p-value of this test is
Given,Test at 20% significance level whether one of the drugs is more effective than the other.
We need to calculate the absolute value of the critical value of this test, the absolute value of the calculated test statistic, and the p-value of this test.Solution:(a) The absolute value of the critical value of this test isThe level of significance is 20%.The degree of freedom is (r-1)(c-1) = (3-1)(2-1) = 2
From the chi-square table, the critical value for a chi-square distribution with 2 degrees of freedom and a level of significance of 0.20 is 3.219(i.e. critical value = 3.219)The absolute value of the critical value of this test is 3.219.(b) The absolute value of the calculated test statistic
The table is shown below: We have, Total = 69 Test at 20% significance level whether one of the drugs is more effective than the other.To check the difference in effectiveness, we will use a chi-square goodness of fit test.
The null hypothesis H0: The two drugs are equally effective.
The alternative hypothesis Ha: One of the drugs is more effective.
The expected values of the two drugs are: Expected Value of Drug A = (32+18) / 3 = 16 Expected Value of Drug B = (32+1) / 3 = 11 The calculations are summarized in the table below: The formula to calculate the chi-square value is, chi-square = ∑ (O - E)2 / E The calculated value of chi-square is 6.07.The absolute value of the calculated test statistic is 6.07.(c) The p-value of this test isThe degree of freedom is (r-1)(c-1) = (3-1)(2-1) = 2
The level of significance is 20%.From the chi-square table, the p-value for a chi-square distribution with 2 degrees of freedom and a chi-square value of 6.07 is 0.047 (i.e. p-value = 0.047)The p-value of this test is 0.047.
Answer:(a) The absolute value of the critical value of this test is 3.219.(b) The absolute value of the calculated test statistic is 6.07.(c) The p-value of this test is 0.047.
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We fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that one drug is more effective than the other at the 20% level of significance.
Below is the table of values for the drugs drug A and drug B
Group A 7 10 13 15 8 7 6 10 9 11 10 11
Group B 6 12 9 11 8 8 9 12 10 14
(a) The absolute value of the critical value of this test
The absolute value of the critical value of this test is given by the formula:
\(`z = |zα/2|`\)
where α = 0.2;
degree of freedom = `n1+n2-2` = `12+10-2` = `20`
From the standard normal table, the value of zα/2 at 0.2 is 1.645
Therefore, the absolute value of the critical value of this test is; `|1.645| = 1.645`.
(b) The absolute value of the calculated test statistic
The formula for the test statistic is given by;
\(`t=bar x1 -bar x2)/((s^2/n1)+(s^2/n2))`\)
where `bar x1` and `bar x2` are the sample means of the two groups,
`s^2` is the pooled variance, n1 and n2 are the sample sizes of the two groups
and \(`s^2 = ((n1 -1) s1^2 + (n2 -1) s2^2 )/(n1 + n2 - 2)`\)
Using the data given, we get:
Group A 7 10 13 15 8 7 6 10 9 11 10 11
`n1` = 12
\(`bar x1` = `(7+10+13+15+8+7+6+10+9+11+10+11)/12 = 9.583`\)
and `s1` = 2.818
Group B 6 12 9 11 8 8 9 12 10 14
`n2` = 10
\(`bar x2` = `(6+12+9+11+8+8+9+12+10+14)/10 = 9.9`\)
and `s2` = 2.205
\(`s^2` = `((12-1)2.818^2 + (10-1)2.205^2)/(12+10-2)` = `((11)(7.95)+(9)(4.86))/20` = `6.2155`\)
Therefore, \(`t= |9.583 - 9.9| / (6.2155[(1/12)+(1/10)])`= 0.3164\)
The absolute value of the calculated test statistic is 0.3164
(c) The p-value of this test is
The p-value of this test is 0.76 (rounded to two decimal places)
This indicates that the p-value is higher than the significance level, 0.2.
Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that one drug is more effective than the other at the 20% level of significance.
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For the figures given
below write the number
of lines of symmetry
and Rotational symmetry
Step-by-step explanation:
line of symmetry = 0. Rotational symmetry = 120°line of symmetry = 4. Rotational symmetry = 90°line of symmetry = 0. Rotational symmetry = 360°line of symmetry = 0. Rotational symmetry = 180°hope you are helped.
If x = 3.5, y = -2x + 4, what is y?
Answer:
x = 3.5
y = -2x + 4
y = ?
y = -2(3.5) + 4
y = -3
Step-by-step explanation:
whats the answer? look at photo plsssss
y = 1
A simple formula to solve inverse relations is y+x=k, where k is a constant
(8)+(-3) = 5
Now using 5 as the constant and x = 4, y can be solved by doing 4 + y = 5
y = 1
form a smimulatenous equation for : a cyclist completes a journey of 500 m in 22 seconds, part of the way at 10m/s and the remainder at 50m/s. How far does she travel at each speed?
The distance traveled in each section will be 150 meters and 350 meters.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
From a simultaneous equation for: A cyclist completes a journey of 500 m in 22 seconds, part of the way at 10m/s and the remainder at 50m/s.
Let x distance be covered with velocity 10 m/s in time t₁ and the remaining distance (500 - x) covered with velocity 50 m/s in time t₂. Then the equation will be
t₁ + t₂ = 22 ....1
Then the time t₁ will be
10 = x / t₁
t₁ = x / 10
Then the time t₂ will be
t₂ = (500 - x) / 50
Put the time in equation 1, then we have
x / 10 + (500 - x) / 50 = 22
5x + 500 - x = 1100
4x = 600
x = 150 meters
And the remaining distance will be
500 - x = 500 - 150
500 - x = 350 meters
The distance traveled in each section will be 150 meters and 350 meters.
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solve x-5/y = z for y
Answer:
y=5x−z
Step-by-step explanation:
Step 1: Multiply both sides by y.
xy−5=yz
Step 2: Add -yz to both sides.
xy−5+−yz=yz+−yz
xy−yz−5=0
Step 3: Add 5 to both sides.
xy−yz−5+5=0+5
xy−yz=5
Step 4: Factor out variable y.
y(x−z)=5
Step 5: Divide both sides by x-z.
y(x−z)x−z=5x−z
y=5x−z
Use the Central Limit Theorem to find the probability of the indicated event, assuming that the distribution of the population data is unknown. In a certain city, employees work an average of 18.9 hours of overtime every month, with a standard deviation of 7.8 hours. What is the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours? Provide a solution showing your calculations and submit your work for marking. Include a sketch as part of your complete solution. P(X > 20)=
The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.
To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.
Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).
For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.
To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.
In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.
Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.
Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.
Here's a sketch to visualize the calculation:
|
|
|
| **
| * *
| * *
| * *
| * *
| * *
| * *
-------------------|--------------------------
18.9 | 20
The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.
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At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town S at 1230 hours. On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours. Find the average speed of the lorry on the return journey.
The average speed of the lorry on the return journey is 58.5 km. If At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town S at 1230 hours. On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours.
Define speed.The speed of an object can be determined by calculating the distance it covers in a given length of time. For instance, if a car goes 70 miles in an hour, it is doing so at a pace of 70 miles per hour (miles per hour).
Given,
At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town S at 1230 hours.
On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours.
distance = speed × time
Average speed from town A to town B is 52 km/h at 3 3/4 hrs.
Distance = 52 km/h × 3 3/4 hrs ...eq1
Let speed in return journey = r
Then distance = r × 3 1/3 hrs ...eq2
From eq1 & eq2
52 ×3 3/4 = r × 3 1/3
52 ×15/4 = r × 10/3
r = (52×15×3)/(4×10) km
r = (13×3×3)/2 km
r = 117/2 km
r = 58.5 km
The average speed of the lorry on the return journey is 58.5 km.
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|-4|+|19|=?
Helpppppppppp
Answer:
23
Step-by-step explanation:
if y varies inversely as x and y=3 when x=8 what is x when y=4
Answer:
x = 6
Step-by-step explanation:
y varies inversely as x
y = k × 1/x. {where k is a constant}
when y = 3, x = 8
Therefore 3 = k/8 and k is 24
y = 24/x
When y = 4,
4 = 24/x
4x = 24
(dividing both sides by 4)
x = 6
How much greater is the sum of the first 50 counting numbers greater than the sum of the first 100 counting numbers?.
The difference between the sum of the first 50 counting numbers and the sum of the first 100 counting numbers is 3775.
Here we have to find the difference between the first 50 counting numbers and first 100 counting numbers.
Formula to find the sum of the number n is:
\(S_{n}\) = n/2( 2a + (n-1)d)
a = first number of the series
d = common difference
n = number of series
Sum of first 50 counting numbers:
\(S_{50}\) = 50/2( 2× 1 + (50-1) 1)
= 25 × 51
= 1275
Sum of first 100 counting numbers:
\(S_{100}\) = 100/2 ( 2×1 + (100- 1) 1)
= 50 × 101
= 5050
Now the difference between them:
\(S_{100}\) - \(S_{50}\) = 5050 - 1275
= 3775
Therefore the difference is 3775.
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What are the 3 ways in math?
Step-by-step explanation:
Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.
150 miles 3/4 tank of gas 3 hours how far can you drive on one tank of gas?
The car can travel for 4 hours on one full tank of gas.
150 miles 3/4 tank gas 3 hours how can you drive one tank of gas?Assuming that the rate of fuel consumption is constant, we can use the given information to estimate how far the car can travel on one full tank of gas.
First, we need to find the capacity of the gas tank. Since the car traveled 150 miles on 3/4 of the tank, it means that it could travel 200 miles on a full tank (since 150 miles is 3/4 of the tank, 1/4 of the tank would be used to travel the remaining 50 miles, so 1/4 of the tank = 50 miles, which means the full tank would be 4 times 50 miles = 200 miles).
Next, we need to find the car's average speed. Since the car traveled 150 miles in 3 hours, its average speed was 50 miles per hour (150 miles / 3 hours).
Finally, we can divide the estimated distance the car can travel on a full tank of gas (200 miles) by the car's average speed (50 miles per hour) to find how many hours the car can travel on one tank of gas.
200 miles / 50 miles per hour = 4 hours
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Read image for instructions The shape of the distribution is…
Ok, so
The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.
-4(x-1) I forgot how to simplify it
Answer:
Step-by-step explanation:
-4(x-1)
distribute the -4
-4x + 4
I don't understand this, what's the answer?
a) What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL;
Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.
a) The value of x is 155.56 mm (rounded to two decimal places).
b) The value of R is 4.44 mm (rounded to two decimal places).
c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:
UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)
The Lower Control Limit (LCL) for the diameter is calculated as:
LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)
d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:
UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)
The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.
e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:
UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)
LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)
Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.
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The complete question is:
What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5
YALL HELP‼️‼️‼️
It says to find the missing side of the triangle⁉️
Hi there!
you can use the Pythageron Therom for this one.
Basically you just need to apply this formula: a^2 + b^2 = c^2
And then find the root of the hypotenuse.
So, 15^2 + 8^2 = the hypotenuse^2
Which equals, 225 + 64 = 289
Square root of 289 = 17
17 is the answer you are looking for!
Please mark me brainliest if this helps!
Have a wonderful day!
Six more than twice a number is greater than negative fourteen. Solve the inequality for the unknown number
Answer:
Step-by-step explanation:
2x+6 > -14
Subtract 6 from both sides
2x > -20
Divide both sides by 2
x > -10
The solution of the inequality 2x + 6 > - 14 will be greater than the negative 10.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Six more than twice a number is greater than negative fourteen.
Let x be the number. Then the equation will be
2x + 6 > - 14
Simplify the inequality, then the value of x will be
2x > - 20
x > - 10
The solution of the inequality 2x + 6 > - 14 will be greater than the negative 10.
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A die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled. A) 60 B) 50 C) 7.1 D) 5.9
The number of 3s that will be rolled when dice is rolled 360 times will have a standard deviation of 7.1.
Define standard deviation.The standard deviation (or ) is a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
What does standard deviation tells you?The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean.
Let X = the total number of 3s produced by rolling the die 360 times. As a result, the number of 3s that will be rolled will have a standard deviation of 7.1.
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Which letter represents the first number in an ordered pair?
Step-by-step explanation:
Example: (5,2)
On a graph, the 5 goes on the x-axis and the 2 goes on the y-axis.
Also, in the world of variables, and the alphabet, x is before y.
So x represents the first number in an ordered pair.
hope it helps!
After Cynthia microwaves her bowl of morning porridge, it is either too cold, just right, or too hot. She estimates there is a 35% chance that it will be too cold and a 50% chance that it will be too hot. What is the probability that Cynthia's morning porridge will be just right
The probability Cynthia's porridge is just right is 15%.
A probability describes how likely is for an event to occur. Probabilities can be expressed using different but one of the most common ways to express probability is to use percentages or 0% to 100%.
Moreover, in some cases, the probability of an event occurring is directly related to the probability of another event. For example, if Cynthia porridge is hot, it means it is neither right nor cold.
Based on this, we can calculate the probability of one event by adding the probabilities of other events and subtracting the result to 100% (total events).
35% (probability the porridge is cold) + %50 (probability the prorridge is hot) = 85%100% - 85% = 15% (probability the porridge is neither hot nor cold or that the porridge is just right).
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Answer:
15%
Step-by-step explanation:
What divisor is represented by the synthetic division below?
N
12
-5
10 1 5
-10 0 -5
2 0 1 0
05
O 5
O x + 5
O x-5
B
Answer:
-5 is the answer
Step-by-step explanation:
we use the divisor which is dividing other
Which number is divisible by six and nine?
24 35 168 288 992
Answer:
288 !
Step-by-step explanation:
what is the pattern to 1,2,4,7,11
Answer:
1+1=2
2+2=4
4+3=7
7+4=11
so the patter is number + natural numbers (serially)
Step-by-step explanation:
Solve the system!
- 3x + 3y = 4
y=x+3
What is the solution?
Answer:
This system has no solution
Step-by-step explanation:
If this is the real question,it has no solution