A fence of 15 m with the start of the fence at coordinates (8,5), the coordinates of the other end of the fence is equals to the (5.75, 2).
Grady's father wants to build a 15-meter fence with the start point of the fence at coordinates (8,5). Midpoint of fence at coordinates (3.5,-1). We have to determine the coordinates of the other end of the fence. The midpoint is defined as the centre point of a line segment. It is at equal distance from both endpoints,
Let the cordinate of other side point be (x,y). Using the mid point formula, [tex](x,y) = (\frac{x_1 + x_2 }{2}, \frac{y_1 + y_2 {2}[/tex]), where
(x,y) --> coordinates of mid point(x₁, y₁) --> coordinates of first point (x₂,y₂)-->coordinates of second pointFor x-coordinate, 2x = 3.5 + 8
=> 2x = 11.5
=> x = 5.75
for y-coordinate, 2y = 5 - 1 = 4
=> y= 2
Hence, required value is (5.75, 2).
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A designer is working on a line of athletic equipment. He is designing a cylindrical punching bag. The designer wants to use a maximum of 1.3M^2 of material to make the bag, and has determined that the diameter of the bag should be 36cm. Determine the maximum possible height of the bag, to the nearest centimetre.
Please help me
The maximum possible height of the bag is 11.51 cm to the nearest centimeter.
What is the surface area of a cylinder?The surface area of a cylinder is defined as the sum of the surface area of the curved surface and the area of the two rounded bases of the cylinder. Area of cylinder = convex area of circular bases. SA. (π) = 2πr (h +r) square unit. Where π (Pi) = 3.142 or = 22/7. r = radius of the cylinder.
The surface area of the cylinder is given by the following formula:
SA = 2πrh + 2πr²
where r is the base radius, h is the height, and π is a constant approximately equal to 3.14.
Since the diameter of the bag is 36 cm, the radius is half that, ie. 18 cm.
We know that the maximum amount of material is 1.3 M². This means that the surface area (SA) of the cylinder must be less than or equal to 1.3 M²:
2πrh + 2πr² ≤ 1.3M²
We can rearrange this equation to solve for h:
h ≤ (1.3M² - 2πr²) / (2πr)
Substitute the values of r and π:
h ≤ (1.3M² – 2π(18cm)²) / (2π(18cm))
h ≤ (1.3M² – 2π(324cm²)) / (36π)
h ≤ (1.3M² – 648π) / (36π)
h ≤ 11.51 cm
Therefore, the maximum possible height of the bag is 11.51 cm to the nearest centimeter.
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Do larger sample sizes increase the certainty of the statistical test? why or why not?
Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results.
larger sample sizes generally increase the certainty of the statistical test. This is because larger samples provide more information and reduce the likelihood of chance variations affecting the results. The estimated parameter becomes more stable and accurate with a larger sample size. Additionally, larger sample sizes allow for the detection of smaller effect sizes and greater statistical power. However, it is important to note that sample size alone does not guarantee the validity of the statistical test. Other factors such as sampling methods, data quality, and appropriate statistical analysis must also be considered.
Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results. Additionally, larger sample sizes decrease the margin of error and increase the statistical test's power, allowing for better detection of true differences or relationships in the population. Overall, larger sample sizes lead to more reliable and valid conclusions in statistical tests.
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A parabolic archway is 25 meters high at the vertex. At a height of 23 meters, the width of the archway is 12 meters, as shown in the figure.
The width of the archway at ground level, given the height can be found to be 42.42 meters.
How to find the width ?To find the width of the parabolic archway at ground level, the formula is:
y = a ( x - h ) ² + k
The height given is 23 meters and the width is 12 meters so the value of a can be found to be :
23 = a ( 6 - 0 ) ² + 25
23 = a ( 6 ) ² + 25
-2 = 36 a
a = -1 /18
We can then find the width of the archway at ground level:
0 = ( -1 /18 )( x ²) + 25
x ² = 450
x = ± √ 450
The width of the archway at ground level is:
= 2 x √ 450
= 2 x 21. 21
= 42.42 meters
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Write the ratio as a fraction in simplest form.
213 feet : 412 feet
Answer:213/412
Step-by-step explanation:
To get a ratio to fraction, make first number numerator and second number as denominator.
213/412 has no LCM, which means it cannot be simplified
a bike lock has a 4 digit combination. each character can be any digit between 1-9. the only restriction is that all 4 characters cannot be the same (e.g. 1111, 2222, 3333... etc.). how many combinations are possible?
The possible combination is 6552.
For each of the 4 numbers in the combination, there are 9 digits to pick from, making the following total number of possibilities entirely possible:
9 x 9 x 9 x 9 = 6561
The number of possibilities with identical values for all four digits must be subtracted, nevertheless.
There is only one combination for each of the nine possible ways to select the digit that will occur four times (1, 2, 3, 4, 5, 6, 7, 8, or 9).
Therefore, the total number of possible combinations with the given restriction is:
6561 - 9 = 6552.
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The arithmetic mean of the monthly salaries of two people is $4360. One person earns $3479 per month. What is the monthly salary of the other person?
If arithmetic mean of the monthly salaries of two people is $4360. One person earns $3479 per month then the monthly salary of the other person is $5241
The arithmetic mean of the monthly salaries of two people is $4360
One person earns $3479 per month
We have to find the monthly salary of the other person
Arithmetic mean = a+b/2
4360 = 3479+b/2
4360×2 = 3479+b
8720 = 3479+b
Subtract 3479 from both sides
8720-3479 =b
$5241 =b
Hence, $5241 is the monthly salary of the other person.
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Write the number 2414six in base five
The base five representation of 2414₆ is 43234₅.
Base five representation is a way of representing numbers using only the digits 0, 1, 2, 3, and 4. This system is also known as quinary or pentimal.
To convert the number 2414₆ to base five, we need to first convert it to base 10 and then convert the result to base five.
To convert 2414₆ to base 10, we can use the formula
2 × 6³ + 4 × 6² + 1 × 6¹ + 4 × 6⁰ = 432 + 144 + 6 + 4 = 586₁₀
Now we can convert 586₁₀ to base five using the following steps
586 ÷ 5 = 117 remainder 1
117 ÷ 5 = 23 remainder 2
23 ÷ 5 = 4 remainder 3
4 ÷ 5 = 0 remainder 4
2414₆ = 43234₅.
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Two milk containers contains 398 l and 436 l of milk. The milk is to be
transferred to another container with the help of a drum. While
transferring to another container 7l and 11l of milk is left in both the
containers respectively. What will be the maximum capacity of the drum
Answer:
Two milk containers = 398 +436= 834L
Left in both containers= 18L
Step-by-step explanation:
so maximum capacity of drum= 834-18=816L
which exspreshion is equivelent to -3(2x-8)+4x
a -2x-8
b -2x+24
c -10x-8
d -10x+24
-2x+24 is equivalent to expression -3(2x-8)+4x.
Option B is the correct answer.
We have,
First, simplify the expression inside the parentheses:
-3(2x-8) = -6x + 24
Then substitute this into the original expression:
-3(2x-8)+4x = -6x + 24 + 4x = -2x + 24
Therefore,
The equivalent expression is -2x+24.
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A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points A(−4,3), B(2,3), and C(2,−1). Point D is the fourth vertex of the rectangle.
What is the distance from point C to point D?
Enter your answer in the box.
An observer stands 120 feet away from a church and measures the angles of elevation of the top and bottom of the steeple to be 24. 4 degrees and 18. 2 degrees respectively. What is the height of the steeple to the nearest foot
The height of the steeple is approximately 62 feet (rounded to the nearest foot).
How to solve for the heightLet x be the height of the steeple, and y be the height from the ground to the bottom of the steeple. The distance from the observer to the church is 120 feet.
Using the tangent function for angle A:
tan(A) = y / 120
tan(18.2) = y / 120
Solve for y:
y = 120 * tan(18.2) ≈ 40.76 feet
Using the tangent function for angle B:
tan(B) = (y + x) / 120
tan(24.4) = (40.76 + x) / 120
Solve for x:
x = 120 * tan(24.4) - 40.76 ≈ 61.92 feet
The height of the steeple is approximately 62 feet (rounded to the nearest foot).
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Bank of America's Consumer Spending Survey collected data on annualcredit card charges in seven different categories of expenditures:transportation, groceries, dining out, household expenses, homefurnishings, apparel, and entertainment (U.S. AirwaysAttache, December 2003). Using data from a sample of 42 creditcard accounts, assume that each account was used to identify theannual credit card charges for groceries (population 1) and theannual credit card charges for dining out (population 2). Using thedifference data, the sample mean difference was = $850, and the sample standard deviationwas sd = $1,123.
a. Formulate the null abd alternative hypothesis to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
b. Use a .05 level of significance. Can you can conclude that the population mean differ? what is the p-value?
At the 0.05 level of significance, we can conclude that there is a significant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. The exact p-value is not provided, but since the t-statistic falls in the rejection region, we can infer that the p-value is less than 0.05.
a. The null hypothesis (H0) is that there is no significant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. The alternative hypothesis (Ha) is that there is a significant difference between the two population means.
b. To test the null and alternative hypotheses, we need to use a two-tailed t-test since we do not have any prior knowledge about the direction of the difference. We will use a level of significance of .05.
Using the formula for the t-test, we get:
t = (x1 - x2) / [s / sqrt(n)]
where:
x1 = sample mean for groceries
x2 = sample mean for dining out
s = sample standard deviation
n = sample size
Plugging in the values, we get:
t = (0 - 850) / [1,123 / sqrt(42)] = -4.72
The degrees of freedom (df) for this test is (n1 + n2 - 2) = 40.
Using a t-distribution table with df = 40 and a level of significance of .05, we find the critical values to be ±2.021. Since our calculated t-value (-4.72) is outside the critical values, we reject the null hypothesis.
The p-value for this test is the probability of getting a t-value as extreme or more extreme than our calculated t-value (-4.72) under the null hypothesis. Using a t-distribution table with df = 40, we find the p-value to be less than .0001. Therefore, we can conclude that there is a significant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
a. The null and alternative hypotheses can be formulated as follows:
Null hypothesis (H 0): μ1 - μ2 = 0 (There is no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)
Alternative hypothesis (H 1): μ1 - μ2 ≠ 0 (There is a difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)
b. Given the information provided, we have:
Sample mean difference (d) = $850
Sample standard deviation (sd) = $1,123
Sample size (n) = 42
Level of significance (α) = 0.05
To test the hypothesis, we need to calculate the t-statistic:
t = (d - 0) / (sd / √n) = (850 - 0) / (1123 / √42) ≈ 5.46
Using a two-tailed t-test with a level of significance of 0.05 and 41 degrees of freedom (n-1), the critical values are approximately -2.02 and +2.02.
Since the calculated t-statistic (5.46) is greater than the critical value (+2.02), we reject the null hypothesis.
Conclusion: At the 0.05 level of significance, we can conclude that there is a significant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. The exact p-value is not provided, but since the t-statistic falls in the rejection region, we can infer that the p-value is less than 0.05.
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Jacob works three days per week for Mr Nkosi at his playschool for pre-school
children. Jacob is paid R200 per day. Mr Nkosi paid R624 to the UIF for one year
in advance, regarding his employee Jacob.
a) What is Jacob's gross salary per year?
b) What percentage is R624 of Jacob's gross salary per year?
c) Does Jacob have to contribute to the UIF? Give a reason for your answer.
The R200 Jacob is paid per day, working three days per week, and the amount Mr Nkosi paid to the UIF, evaluated using percentages indicates;
a) R31,200
b) 2%
c) Jacob does not have to contribute to the UIF
What is a percentage?A percentage is a representation of a ratio of numbers or proportion of a quantity expressed as a fraction of 100.
The number of days Jacob works per week for Mr Nkosi at his playschool for pre-school = Three days per week
The amount
The amount Jacob is paid per day = R200
Amount Mr Nkosi paid to the UIF for one year in advance regarding Jacob = R624
a) Jacob's gross salary in a year = 52 × 3 × R200 = R31,200
b) The percentage R624 is of Jacob's gross salary = (R624/R31,200) × 100 = 2%
c) The amount Mr Nkosi has to contribute to the UIF regarding Jacob in a year is two percent (2%) of Jacob's gross salary, therefore;
Jacob does not have to contribute to the UIF
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A rectangle has a perimeter of 45 ft. The length and width are scaled by a factor of 1.5. What is the perimeter of the resulting rectangle?
Answer:
67.5
Step-by-step explanation:
The perimeter of the resulting rectangle is 67.5 ft
What is the perimeter of the resulting rectangle?
Given that
Perimeter = 45 ft
Scale factor = 1.5
So, we have
Resulting perimeter = 45 * 1.5
Evaluate
Resulting perimeter = 67.5
What is the area of this figure?
The area is the sum of the individual areas
The figure can be divided into two trapezoids
Using the above and the area formulas as a guide, we have the following:
Area = 1/2 * (3 + 5) * 2 + 1/2 * (3 + 7) * 4
Evaluate
Area = 28
Hence, the area is 28 sq units
Solve for z.
A = x+y+z
Answer:
A- x - y = z
Step-by-step explanation:
A = x + y + z
- x
A - x = y + z
- y
A- x - y = z
On a certain hot summer's day, 574 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1180.00. How many children and how many adults swam at the public pool that day?
Answer:
Let c be the number of children and a be the number of adults.
1.75c + 2.25a = 1,180->1.75c + 2.25a = 1,180
c + a = 574->1.75c + 1.75a = 1,004.5
-------------------------------
.5a = 175.5
a = 351, so c = 223
So there were 351 adults and 223 children that day.
un college de 620 eleves compte 372eleves demi pensionnaires Quel est le pourcentage d'eleves demi pensionnaires de ce college?
merciiii d'avance
Answer: Percentage of half board students in college is 60%
Step-by-step explanation:
We know that percentage of desired quantity is:
n% = ( number of desired quantity / total number of quantity ) * 100
n% = ( n / N ) * 100 .......... (i)
where n% = percentage of desired quantity.
N = total number of quantity.
n = number of desired quantity.
Now, as per the question:
Half board students in college = 372
Total students in college = 620
percentage of Half board students in college = (372/620) * 100
n% = (372/620)*100
n% = 60%
Therefore, at 372 half board students in college , percentage of half board students in college is 60%.
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a data analyst wants to create a visualization that demonstrates how often data values fall into certain ranges. what type of data visualization should they use?1 pointhistogramline graphcorrelation chartscatterplot
A data analyst who wants to create a visualization that demonstrates how often data values fall into certain ranges should use option A: histogram.
The distribution of a continuous variable is depicted by a histogram, a form of bar graph, by splitting the data into intervals, or bins, and charting the number of observations that fall within each bin. The range of values being measured are shown on the x-axis as intervals or bins, and the frequency or count of observations inside each bin is shown on the y-axis.
When presenting a distribution's shape, such as whether it is symmetrical or skewed, and when locating outliers or data gaps, histograms are especially helpful. They are frequently used to analyze and show data in disciplines including statistics, data science, and quality control.
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Correct question:
a data analyst wants to create a visualization that demonstrates how often data values fall into certain ranges. what type of data visualization should they use?
histogram
line graph
correlation charts
catter plot
The diameter of a circular cookie cake is 14 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14.
615.44 square inches
307.72 square inches
153.86 square inches
76.93 square inches
Answer:
Step-by-step explanation:
The area of a circle is given by the formula:
area = π x (radius)²
where the radius is half of the diameter. In this case, the radius of the cookie cake is:
radius = 14 / 2 = 7 inches
Using π = 3.14, the area of the entire cookie cake is:
area = 3.14 x 7² = 3.14 x 49 ≈ 153.86 square inches
To find half of the cookie cake, we need to divide this area by 2:
half area = 153.86 / 2 = 76.93 square inches
Rounding the answer to the nearest whole number, we get:
half area ≈ 77 square inches
Therefore, the answer is approximately 77 square inches. The closest option is D) 76.93 square inches.
answer this question.
Using the sine function with the given angle C and hypotenuse, we find that the length of the side x is approximately 16.23 units.
We can use the trigonometric ratios of the right triangle to find the length of the side x. Since we know the angle C and the hypotenuse, we can use the sine function, which relates the opposite side to the hypotenuse
sin(C) = opposite / hypotenuse
sin(37°) = x / 27
Multiplying both sides by 27, we get
x = 27 sin(37°)
Using a calculator, we find that
x ≈ 16.23
Therefore, the length of the side x is approximately 16.23 units.
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An item on sale costs 65% of the original price. The original price was $75 .
Use the ALEKS calculator to find the sale price.
Answer: 27 out of 65%
Spring break homework due tonight!! Please help!!
The names of the angles, vertices and sides are listed below
Naming the vertex and the sides of the anglesThe vertex is the point where two sides meet; and at this vertex, an angle is formed
Using the above definition as a guide, we have
Vertex: D; Sides: CD and DEVertex: R; Sides: QR and RSVertex: P; Sides: OP and PQVertex: J; Sides: MJ and JKNaming the angles in four waysThe names of the angles in four ways are
∠EFG, ∠GFE, ∠F and ∠S∠RST, ∠TSR, ∠S and ∠J∠GHJ , ∠JHG, ∠H and ∠S∠MNO, ∠ONM, ∠N and ∠SNaming the angles with the vertex VUsing the definition of vertex above, the names of the angles are
∠KVL and ∠JVK∠CVD, ∠DVE, and ∠EVF∠QVR and ∠RVS∠OVP, ∠PVQ and ∠QVRRead more about angles at
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use to potagreom thyreom to finmd 13 squared, 6, 7
Answer:
Step-by-step explanation:
Calculator allowed This is a new version of the question. Make sure you start new workings. Bookwork code: B10 4 Calculate the area of the shaded section of this shape 4 cm 6 cm 10% 11 cm 3 cm 1 8 cm Not drawn accurately
Step-by-step explanation:
Area of the large trapezoid :
height * average of bases
area = 8 * (6+11)/2 = 68 cm^2
MINUS the area of the parallelogram 4x3 =12 cm^2
68 - 12 = 56 cm^2 = shaded region
Susan rolled a die 744 times. Which of the following would be a good estimate of the number of times she rolled the number 3 on the die?
Surface area of the composite solid
The area of the composite solid is 602.88m²
What are composite solids?A composite solid is a solid that is composed, or made up of, two or more solids.
The solid consist of two cones. one big and one small cone
Area of a cone can be expressed as;
A = πr² + πrl
A = πr(r+l)
For the Big cone
A = πr(r+l)
A = 3.14 × 8 ( 8+10)
A = 25.12 × 18
A = 452.16m²
Area of the small cone
A = 3.14 × 4( 4 + 8)
A = 12.56 × 12
A = 150.72m²
Therefore the area of the composite solid
= 452.16 + 150.72
= 602.88 m²
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nformation on a packet of seeds claims that 93% of them will germinate. of the 200 seeds that were planted, only 180 germinated. a. find a 95% confidence interval for the true proportion of seeds that germinate based on this sample. b. does this seem to provide evidence that the claim is wrong?
a) The 95% confidence interval for the true proportion of seeds that germinate based on the sample is (0.856, 0.944).
b) The sample does not provide evidence that the claim of 93% germination is wrong, but it does suggest that the true proportion of seeds that germinate may be lower than the claimed proportion.
To find a confidence interval for the true proportion of seeds that germinate, we can use the following formula
CI = p ± z√(p(1-p)/n)
where p is the sample proportion, z is the z-score corresponding to the desired confidence level (95% in this case), and n is the sample size.
a. Using the given values, we have:
p = 180/200 = 0.9
z = 1.96 (from a standard normal distribution table for a 95% confidence level)
n = 200
Plugging these values into the formula, we get
CI = 0.9 ± 1.96√(0.9(1-0.9)/200) = (0.856, 0.944)
Therefore, we can be 95% confident that the true proportion of seeds that germinate is between 0.856 and 0.944.
b. To determine if this provides evidence that the claim is wrong, we can check if the confidence interval includes the claimed proportion of 0.93. Since 0.93 is within the confidence interval of (0.856, 0.944), we cannot conclude that the claim is wrong based on this sample. However, we can say that the sample provides evidence that the true proportion of seeds that germinate may be lower than the claimed proportion.
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Triangle A’B’C’ is a dilation of triangle ABC. What is the scale factor of the dilation?
The scale factor used in the dilation is 1/2
Determining the scale factor used.From the question, we have the following parameters that can be used in our computation:
ABC with vertices at A(-2, 6)A'B'C' with vertices at A'(-1, 3)The scale factor is calculated as
Scale factor = A'/A
Substitute the known values in the above equation, so, we have the following representation
Scale factor = (-1, 3)'/(-2, 6)
Evaluate
Scale factor = 1/2
Hence, the scale factor is 1/2
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ANSWER PLS Sketch the graph of 2x^(2)-3x-9=y using your graphing calculator.
What are the x-intercepts of this graph?
a.-3, -3/2
b.-3, 3/2
c. 3, 3/23
d. 3, -3/2
The x-intercepts of the given quadratic function are: d: 3, -3/2
How to draw the graph of a quadratic function?The general form of expression of a quadratic function is:
y = ax² + bx + c
The formula to find the roots of quadratic functions is:
x = [-b ± √(b² - 4ac)]/2a
We are given the quadratic equation as:
y = 2x² - 3x - 9
Thus:
x = [-(-3) ± √((-3)² - 4(2 * -9))]/2(2)
x = (3 ± 9)/4
x = 3, -3/2
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20POINTS!!!!Let f(x)=3/4x2−1. The function g(x) is a vertical stretch of f(x) by a factor of 8. What is the equation of g(x)?
