The degrees of freedom for a sample size of 27 is 26, the alpha or significance level for a 98% confidence level is 0.02, and the t-critical value can be found using the t-table corresponding to a 98% confidence level and 26 degrees of freedom.
To find the degrees of freedom, alpha (significance level), and the t-critical value using the t-table, we need to consider the given information:
n = 27: This represents the sample size, which is 27 in this case.
CL = 98%: CL stands for the confidence level.
It indicates the level of confidence we want to have in our interval estimate.
In this case, the confidence level is 98%.
Degrees of Freedom (df): For a t-distribution, the degrees of freedom depend on the sample size.
Since we have a sample size of 27, the degrees of freedom would be n - 1.
Therefore, the degrees of freedom would be 27 - 1 = 26.
Alpha (α): Alpha, or the significance level, represents the probability of making a Type I error, which is rejecting a true null hypothesis.
The alpha level is determined by subtracting the confidence level from 1. In this case, the alpha level would be 1 - 0.98 = 0.02.
T-Critical Value: To find the t-critical value corresponding to a specific confidence level and degrees of freedom, we can consult the t-table. Since we have a confidence level of 98% and degrees of freedom of 26, we need to find the value that corresponds to the area of 0.01 (half of 1 - 0.98) in the t-distribution table.
The t-critical value would be the value from the table that matches these criteria.
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This number pattern -1:5 ;x; 35 ; ...
Is a quadratic number pattern.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.
This sequence 4;9; x; 37; .... is a quadratic sequence.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.
Answer:
[tex]\textsf{a)} \quad x = 17[/tex]
[tex]\textsf{b)} \quad T_n=3n^2-3n-1[/tex]
[tex]\textsf{a)} \quad x = 20[/tex]
[tex]\textsf{b)} \quad T_n=3n^2-4n+5[/tex]
Step-by-step explanation:
Given quadratic number pattern:
-1, 5, x, 35, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
[tex]\boxed{T_n=an^2 + bn + c}[/tex]
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=-1\\a+b+c&=-1\end{aligned}[/tex]
[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=5\\4a+2b+c&=5\end{aligned}[/tex]
[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=35\\16a+4b+c&=35\end{aligned}[/tex]
Rearrange the first equation to isolate c:
[tex]c=-a-b-1[/tex]
Substitute this into the second and third equations:
[tex]\begin{aligned}4a+2b+(-a-b-1)&=5\\3a+b&=6\end{ailgned}[/tex]
[tex]\begin{aligned}16a+4b+(-a-b-1)&=35\\15a+3b&=36\end{ailgned}[/tex]
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
[tex]b=-3a+6[/tex]
[tex]\begin{aligned}15a+3(-3a+6)&=36 \\15a-9a+18&=36\\6a&=18\\a&=3 \end{aligned}[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\begin{aligned}b&=-3a+6\\&=-3(3)+6\\&=-9+6\\&=-3\end{aligned}[/tex]
Finally, substitute the found values of a and b into the equation for c and solve for c:
[tex]\begin{aligned}c&=-a-b-1\\&=-3-(-3)-1\\&=-3+3-1\\&=-1\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\boxed{T_n=3n^2-3n-1}[/tex]
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
[tex]\begin{aligned}T_3&=3(3)^2-3(3)-1\\&=3(9)-3(3)-1\\&=27-9-1\\&=18-1\\&=17\end{aligned}[/tex]
Therefore, the value of x is 17.
[tex]\hrulefill[/tex]
Given quadratic number pattern:
4, 9, x, 37, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
[tex]\boxed{T_n=an^2 + bn + c}[/tex]
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
[tex]\begin{aligned}T_1=a(1)^2+b(1)+c&=4\\a+b+c&=4\end{aligned}[/tex]
[tex]\begin{aligned}T_2=a(2)^2+b(2)+c&=9\\4a+2b+c&=9\end{aligned}[/tex]
[tex]\begin{aligned}T_4=a(4)^2+b(4)+c&=37\\16a+4b+c&=37\end{aligned}[/tex]
Rearrange the first equation to isolate c:
[tex]c=-a-b+4[/tex]
Substitute this into the second and third equations:
[tex]\begin{aligned}4a+2b+(-a-b+4)&=9\\3a+b&=5\end{ailgned}[/tex]
[tex]\begin{aligned}16a+4b+(-a-b+4)&=37\\15a+3b&=33\end{ailgned}[/tex]
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
[tex]b=-3a+5[/tex]
[tex]\begin{aligned}15a+3(-3a+5)&=33 \\15a-9a+15&=33\\6a&=18\\a&=3 \end{aligned}[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\begin{aligned}b&=-3a+5\\&=-3(3)+5\\&=-9+5\\&=-4\end{aligned}[/tex]
Finally, substitute the found values of a and b into the equation for c and solve for c:
[tex]\begin{aligned}c&=-a-b+4\\&=-3-(-4)+4\\&=-3+4+4\\&=5\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\boxed{T_n=3n^2-4n+5}[/tex]
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
[tex]\begin{aligned}T_3&=3(3)^2-4(3)+5\\&=3(9)-4(3)+5\\&=27-12+5\\&=15+5\\&=20\end{aligned}[/tex]
Therefore, the value of x is 20.
100 Points! Geometry question. Photo attached. Find x in the right triangle. Please show as much work as possible. Thank you!
Answer:
x = 12
Step-by-step explanation:
sin45 = x/17 (sin = opposite/hypotenuse)
x = (sin45)(17) = 12.02 ≈ 12
Which graph represents the solution set to the system of inequalities?
Y ≤ 2X+2
1/2X + Y <7
Y- 3 ≥ 0
ANSWER is Down Below
The solution set to the system of inequalities will be the overlapping region or the intersection of the shaded regions from all three inequalities.
The system of inequalities consists of three inequalities:
y ≤ 2x + 2
(1/2)x + y < 7
y - 3 ≥ 0
Let's analyze each inequality:
y ≤ 2x + 2 represents a shaded region below the line with a slope of 2 and a y-intercept of 2.
(1/2)x + y < 7 represents a shaded region below the line with a slope of -1/2 and a y-intercept of 7.
y - 3 ≥ 0 represents a shaded region above the line with a slope of 0 and a y-intercept of 3.
The solution set to the system of inequalities will be the overlapping region or the intersection of the shaded regions from all three inequalities.
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Please answer: h^-1(x) for this question
All the solutions are,
g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }
h⁻¹ (x) = 5x - 13
⇒ (h⁻¹ о h ) (- 3) = 3
We have to given that,
Functions g and f are defined as,
g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)
And, h (x) = (x + 13) / 5
Now, We can simplify for inverse function as,
For inverse function of g,
g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)
g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }
And, Inverse function of h is,
h (x) = (x + 13) / 5
y = (x + 13) / 5
Solve for x,
5y = x + 13
x = 5y - 13
h⁻¹ (x) = 5x - 13
So, We get;
⇒ (h⁻¹ о h ) (- 3)
⇒ (h⁻¹ (h (- 3))
⇒ (h⁻¹ (- 3 + 13)/5)
⇒ (h⁻¹ (2))
⇒ 5 (2) - 13
⇒ 10 - 13
⇒ - 3
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The top of a kitchen table measures 160cm by 90cm. A beetle walks diagonally across the table from one corner to the other. Calculate how far the beetle walks.
Answer: To calculate the distance the beetle walks diagonally across the table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right triangle formed by the table are 160 cm and 90 cm. Let's call the hypotenuse (the distance the beetle walks) "d."
So, applying the Pythagorean theorem, we have:
d^2 = 160^2 + 90^2
Simplifying:
d^2 = 25600 + 8100
d^2 = 33700
Taking the square root of both sides:
d ≈ √33700
d ≈ 183.54 cm
Therefore, the beetle walks approximately 183.54 cm diagonally across the kitchen table.
Why is °=(−°)? PLSS HELP NOW
A rectangles field is 135 meters long and 100 meters wide give the length and width of another rectangular field that has the same perimeter but a larger area
Answer: if the length of the second rectangular field is 200 meters, the width should be 35 meters to have the same perimeter but a larger area.
Step-by-step explanation:
STEP1:- Let's denote the length of the second rectangular field as L2 and the width as W2.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width).
For the first rectangular field with length L1 = 135 meters and width W1 = 100 meters, the perimeter is:
Perimeter1 = 2(135 + 100) = 470 meters.
STEP 2:- To find the length and width of the second rectangular field with the same perimeter but a larger area, we need to consider that the perimeters of both rectangles are equal.
Perimeter1 = Perimeter2
470 = 2(L2 + W2)
STEP 3 :- To determine the larger area, we need to find the corresponding length and width. However, there are multiple solutions for this problem. We can set an arbitrary value for one of the dimensions and calculate the other.
For example, let's assume the length of the second rectangular field as L2 = 200 meters:
470 = 2(200 + W2)
470 = 400 + 2W2
2W2 = 470 - 400
2W2 = 70
W2 = 35 meters
HENCE L2 = 200 meters and W2 = 35 meters
Two math students were asked to write an exponential growth equation that had a starting value of 300 and a growth rate of 2%. Pierre thinks the answer is y=300(1.02)^x and Scott thinks that the answer is y=300(1.2)^x. Are either of them right and why?
Incorrect, the correct exponential growth equation as it accurately represents a starting value of 300 and a growth rate of 2%. Scott's equation
Neither Pierre nor Scott has the correct exponential growth equation.
The exponential growth equation represents a relationship where a quantity increases or grows exponentially over time. It is typically represented as y = a(1 + r)^x, where "a" represents the initial or starting value, "r" represents the growth rate (expressed as a decimal), "x" represents the time or number of periods, and "y" represents the resulting value after the growth.
In this case, Pierre's equation is y =[tex]300(1.02)^x.[/tex]This equation suggests a growth rate of 2% (0.02 as a decimal), which means that the quantity would increase by 2% with each period. This aligns with the given growth rate of 2%. Thus, Pierre's equation is correct.
On the other hand, Scott's equation is y = [tex]300(1.2)^x[/tex]. This equation suggests a growth rate of 20% (0.2 as a decimal), which means that the quantity would increase by 20% with each period. However, the given growth rate is 2%, not 20%. Therefore, Scott's equation is incorrect.
To summarize, Pierre's equation, y = 300(1.02)^x, is the correct exponential growth equation as it accurately represents a starting value of 300 and a growth rate of 2%. Scott's equation, y = 300(1.2)^x, does not match the given growth rate and is therefore incorrect.
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In The figure below, what are m<1,m<2,m<3,m<4? Give reasons for each one
The measure of unknown angles,
∠1 = ∠4 = 110 degree
∠2 = ∠3 = 70 degree
Labeling the figure,
Then from figure we have,
⇒ x + 40 + x = 180
⇒ 2x + 40 = 180
Subtract 40 both sides,
⇒ 2x = 140
Divide both sides by 2
⇒ x = 70
From figure,
⇒ ∠1 + 70 = 180
⇒ ∠1 = 180 - 70
⇒ ∠1 = 110 degree
And from figure,
⇒ ∠1 + ∠2 = 180
⇒ 110 + ∠2 = 180
⇒ ∠2 = 70 degree
Since,
∠2 = ∠3 = 70 degree
And ∠1 = ∠4 = 110 degree
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(a) Dewi has £460 to buy Chinese yuan.
Calculate
.
the maximum number of CYN Dewi can buy, and
how much, to the nearest penny, this will cost him.
The maximum number of CYN Dewi can buy is 4268.8 CYN and cost in pounds is £453.20.
Maximum number of CYN Dewi can buy:
Since £1 buys 9.28 CYN, Dewi's £460 can be converted to Chinese yuan by multiplying it by the exchange rate:
Maximum CYN = £460 × 9.28 CYN/£1
To calculate this, we multiply the pound amount by the exchange rate:
Maximum CYN = £460 × 9.28 CYN/£1 ≈ 4268.8 CYN
Cost in pounds to the nearest penny:
To calculate the cost in pounds, we divide the desired amount of Chinese yuan by the exchange rate:
Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1
To calculate this, we divide the Chinese yuan amount by the exchange rate:
Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1
= £453.20
Therefore, the cost in pounds, to the nearest penny, will be £453.20.
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Complete question
Buying chinese yuan (CYN) £1 buys 9.28 CYN
Selling chinese yuan (CYN) 9.42 CYN buys £1
(a) Dewi has £460 to buy Chinese yuan.
Calculate the maximum number of CYN Dewi can buy, and
how much, to the nearest penny, this will cost him.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: its D! not 8!!!
Step-by-step explanation:
2. Consider this dilation.
Pre-image
9 cm
B
Image
3 cm B
(a) Find the scale factor. Show your work. (5 points)
(2- a.) Scale factor= Image length
Pre-image length
Use a table of values to graph the following exponential function. (see attachment)
y= 2^x
Please graph
By using the table of values, a graph of the exponential function is shown in the image below.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.Based on the information provided above, we can logically deduce the following exponential function;
[tex]y = 2^x[/tex]
Next, we would create a table of values based on the exponential function;
when x = 0, the y-value is given by;
y = 2⁰
y = 1
when x = 1, the y-value is given by;
y = 2¹
y = 2
x y____
-2 0.25
-1 0.5
0 1
1 2
2 4
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need help! dont know what to do!
Answer:
y < 2x +6
Step-by-step explanation:
You want an inequality for the given graph.
What to doHere are some steps you can follow, in no particular order.
identify the type of boundary line: solid or dashed (dashed)locate the shading: above the line or below it (below)locate the y-intercept (+6)identify the slope (rise/run = 4/2 = 2)When you have this information, you can write the inequality in slope-intercept form.
Using the informationWhen the boundary line is dashed, the inequality symbol you use will not include the "or equal to" case. It will be one of < or >.
When the shading is below the line, the values of y that satisfy the inequality will be less than (<) those on the boundary line. If shading is above, the y-values will be greater than (>) those on the line.
The slope and intercept go into the inequality like this:
y < mx + b . . . . . . where m is the slope, and b is the y-intercept
For a dashed line, shaded below, with m=2 and b=6, the inequality is ...
y < 2x +6
__
Additional comment
There are two points identified on the boundary line: (-2, 2) and (0, 6). The slope formula can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (6 -2)/(0 -(-2)) = 4/2 = 2
The point (0, 6) on the y-axis is the y-intercept. The y-value there is 6.
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The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How
does this compare with the national average?
The average utility price in Orlando for the 6 month period, and the way it compares to the national average is d. $ 308. 83 ; higher than the national average .
How to find the average ?The information for Orlando is April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.
The average is:
= ( 288 + 310 + 325 + 294 + 293 + 343 ) / 6
= 1, 853 / 6
= $ 308. 83
This average is higher than the national average of $ 308. 83.
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Full question is:
The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How does this compare with the national average?
A graph titled Orlando, Florida, has month on the x-axis and utility price on the y-axis. In April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.
a. $370.60; higher than the national average
b. $292.17; higher than the national average
c. $38.35; lower than the national average
d. $308.83; higher than the national average
1.3 A cake recipe calls for 0.8 kg of flower, 650g of sugar and 900 000mg of butter. (2) 1.3.1 Determine the total mass of the ingredients. Give you answer in kilograms. 1.3.2 If sugar comes in 150g bags at cost of R5.95 per 150g, determine the total cost of the (2) sugar needed for this recipe.
1. The total in mass of the ingredients used is 2.35kg
2. The cost of sugar needed is R25.78.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
These statements are interpreted into mathematical equation or expression.
1. The recipes are ;
0.8kg = 800g
sugar = 650g
butter = 900000 mg = 900000/1000 = 900g
Therefore the total mass of ingredients
= 800 + 650 +900
= 2350g
in kilograms, 1000g is 1kg
2350g = 2350/1000
= 2.35kg
2. If 150g = R5.95
1g = 5.95/150
650g = 5.95 × 650/150
= R25.78.
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Recta de pendiente 1⁄4 que pasa por (3,0).
The equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.
To find the equation of a line with a slope of 1/4 that passes through the point (3,0), we can use the point-slope form of the equation of a line.
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values into the formula, we have:
y - 0 = 1/4(x - 3)
Simplifying:
y = 1/4(x - 3)
Distributing 1/4 throughout the expression:
y = 1/4x - 3/4
Therefore, the equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.
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I have 7/4 green counters, and 24 yellow counter, so how much green counters will i have
Answer: the question doesn't give that much information but you would have 7/4 or 1.75 green counters.
Step-by-step explanation: 7/4 as a decimal is 1.75
The size of a rectangular television screen is usually given by its diagonal measurement. If a flat television screen is 20 inches high and 25 inches wide, what is its size rounded to the nearest inch?
Answer:
32 inches Aprox
Step-by-step explanation:
To find the size of a rectangular television screen given its height and width, we can use the Pythagorean theorem. The diagonal measurement (size) is the hypotenuse of a right triangle formed by the height and width.
Given:
Height of the television screen (h) = 20 inches
Width of the television screen (w) = 25 inches
Using the Pythagorean theorem:
diagonal² = height² + width²
diagonal² = 20² + 25²
diagonal² = 400 + 625
diagonal² = 1025
Taking the square root of both sides:
diagonal ≈ √1025
diagonal ≈ 32.02
Rounding to the nearest inch, the size of the television screen is approximately 32 inches.
Therefore, the size of the rectangular television screen, rounded to the nearest inch, is 32 inches.
What is the value of x in the systems:
5x + 2y = 3
2x + 3y = -1
Answer: The value of x = 1 and y = -1
Step-by Step Explanation:
We have 5x + 2y = 3 -----(i)
and 2x + 3y = -1 -----(ii)
By substitution method,
from (i), x = 3-2y/5
Putting the value of x in equation (ii),
we get, 2(3-2y/5) + 3y = -1
6 - 4y/5 + 3y =-1
6 - 4y + 15y = -5
6 - 11y = -5
-11y = -5 - 6
-11y = -11
y = -1
And, x = 3-2(-1)/5
x = 3+2/5
x = 1
Therefore, x=1 and y=−1
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there's 240 candy bars 1/4 of candy bars are snickers 1/3 of the candy bars are twix 1/8 of the candy bars are hershey. how many candy bars are Mars? explain not with a lot of words but in numbers please.
Answer:
you have to add all the fractions of the candy1/4+1/3+1/8
=17/24
subtract from 1Step-by-step explanation:
1-17/24
=7/24
multiply with the total number of candy7/24×240
=70
Please help me solve this
There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.
To construct a 90% confidence interval for the mean number of books people read, we can use the following formula:
Confidence Interval = x ± (Z * (s / √n))
Where:
x = sample mean (12.4 books)
s = sample standard deviation (16.6 books)
n = sample size (1017)
Z = Z-score
Since the sample size is large (n > 30), we can assume the sampling distribution is approximately normal.
We can use the standard normal distribution to find the Z-score for a 90% confidence level.
The Z-score for a 90% confidence level is approximately 1.645.
Now we can calculate the confidence interval:
Confidence Interval = 12.4 ± (1.645 (16.6 / √1017))
Confidence Interval ≈ 12.4 ± (1.645 (16.6 / √1017))
Confidence Interval ≈ 12.4 ± (1.645 (16.6 / 31.95))
Confidence Interval ≈ 12.4 ± (1.645 x 0.518)
Confidence Interval ≈ 12.4 ± 0.85
There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.
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!!!!!PLEASE HELP 100 POINTS AND WILL MARK BRAINLIEST!!!!!
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent (!!!!!SHOW YOUR WORK!!!!!)
A) Inside the Square
B) Outside the Triangle
A square and a traingle are present in a large rectangle with given dimensions in the figure.
Area of the rectangle is :[tex]\qquad\displaystyle \tt \dashrightarrow \: 12 \times 8[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 96 \: \: unit {}^{2} [/tex]
Area of square :[tex]\qquad\displaystyle \tt \dashrightarrow \: 4 \times 4[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 16 \: \: unit {}^{2} [/tex]
Area of triangle :[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \: \: unit {}^{2} [/tex]
Problem 1 : Inside the square[ area of square / total area ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{16}{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{1}{6} [/tex]
Problem 2 : Outside the triangle[ total area except area of triangle / total area ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{96 - 10}{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{86 }{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{43}{48} [/tex]
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x in triangle STU is given as follows:
b) 8.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.Applying the Pythagorean Theorem for this problem, the value of x is obtained as follows:
x² + 15² = 17²
x² = 17² - 15²
x² = 64.
x = 8.
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d) Suppose you begin making a monthly payment of $75.00. Fill in the table.
Month Current balance
1
2
3
4
5
6
7
8
9
10
11
12
WYPIE
$2750.00
Interest
$45.38
Payment
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
Amount applied to principal
$29.62
Answer:
Step-by-step explanation:
Answer:
For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.
For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.
Point of view:
Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!
:)
Find x to the nearest hundredth.
16
X
40°
O A x = 24.89
O
OB. x = 13.43
O C. x 10.28
D. x = 12.26
Option C is correct, the value of x in the triangle is 10.28 units.
The given triangle is right angled triangle.
We know that the sine function is a ratio of opposite side and hypotenuse.
To the angle 40 degrees the opposite side is x.
The hypotenuse is 16.
Sin 40 degrees=x/16
0.6428=x/16
Apply cross multiplication:
x=16×0.6428
x=10.28
Hence, the value of x in the triangle is 10.28 units.
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A jug contains 36 fluid ounces of apple juice. How many pints of apple juice does the jug contain?
Answer: There are 16 fluid ounces in 1 pint. To determine the number of pints in the jug, we need to divide the total number of fluid ounces by 16.
Given that the jug contains 36 fluid ounces of apple juice, we divide 36 by 16:
36 fluid ounces ÷ 16 fluid ounces/pint = 2.25 pints
Therefore, the jug contains 2.25 pints of apple juice.
Given the diagram below, determine the measure of angles A, B, and C.
Hello!
A = 115° => opposite
B = 115° => corresponding angles
C = 65° => 180° - 115°
Answer:
A = 115 degrees
B = 115 degrees
C = 65 degrees
Step-by-step explanation:
A is opposite of 115 so it is 115 degrees.
B is 115 because it is on a parellel line to the one of 115
C is 180 minus B, which is 180 - 115 = 65
50 Points! Multiple choice geometry question. Photo attached. Thank you!
This is a simple one.
All you need to do is find the scale factor of the shapes. (How much has it decreased by?)
Wecan find this by doing 15 ÷ 20 (not the other way round because we want to find the scale factor for the bigger rectangle to the smaller)
15 ÷ 20 = 0.75
So to find the area all you need to do is times the area with the scale factor which is 0.75
500 x 0.75 = 375cm²
So the answer is
(A) 375cm²
Question 10 (1 point)
A
33
7 in.
B
C
The value of AB is,
⇒ AB = 5.9
(rounded to nearest tenth)
We have to given that,
A right triangle ABC is shown.
Now, By trigonometry formula,
we get;
⇒ cos 33° = Base / Hypotenuse
Substitute all the values, we get;
⇒ cos 33° = AB / 7
⇒ 0.84 = AB / 7
⇒ AB = 0.84 × 7
⇒ AB = 5.88
⇒ AB = 5.9
(rounded to nearest tenth)
Thus, We get;
AB = 5.9
(rounded to nearest tenth)
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