Answer:
a) The intercepts of the graph are (-75, 0), (75, 0), (0, -75) and (0, 75).
b) The radius is 75 miles.
c) The area of the region is 17,671 square miles (to the nearest square mile).
Step-by-step explanation:
Part aThe x-intercepts are the points at which the graph crosses the x-axis, so when y = 0. Therefore, to find the x-intercepts, substitute y = 0 into the given equation.
[tex]\implies x^2+y^2=5625[/tex]
[tex]\implies x^2+(0)^2&=5625[/tex]
[tex]\implies x^2&=5625[/tex]
[tex]\implies x&=\sqrt{5625}[/tex]
[tex]\implies x&=\pm75[/tex]
The y-intercepts are the points at which the graph crosses the y-axis, so when x = 0. Therefore, to find the y-intercepts, substitute x = 0 into the given equation.
[tex]\implies x^2+y^2=5625[/tex]
[tex]\implies (0)^2+y^2&=5625[/tex]
[tex]\implies y^2&=5625[/tex]
[tex]\implies y&=\sqrt{5625}[/tex]
[tex]\implies y&=\pm75[/tex]
Therefore, the intercepts of the graph are:
(-75, 0), (75, 0), (0, -75) and (0, 75)[tex]\hrulefill[/tex]
Part bThe general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h, k) is the center and r is the radius of the circle.
By comparing the given equation with the general equation:
(h, k) = (0, 0)r² = 5625Take the positive square root of r² to find the radius of the circle (since length cannot be negative):
[tex]\implies r=\sqrt{5625}[/tex]
[tex]\implies r=75[/tex]
Therefore, the radius of the circle is 75 miles.
[tex]\hrulefill[/tex]
Part cThe formula for the area of a circle is:
[tex]A=\pi r^2[/tex]
where r is the radius.
To find the area of the region in which the broadcast from the station can be picked up, find the area of the circle with the radius from part b, r = 75:
[tex]\implies A= \pi \cdot 75^2[/tex]
[tex]\implies A=5625 \pi[/tex]
[tex]\implies A=17671.4586...[/tex]
Therefore, the area of the region is 17,671 square miles (to the nearest square mile).
Answer:
(75,0) ; (-75,0) ; (0,75) ; (0,-75)75 miles 17678.51 miles²Step-by-step explanation:
To find:-
The intercepts of the graph .Radius in miles.Area of the region.Answer:-
The given equation of the circle is ,
[tex]:\sf\implies x^2 + y^2 = 5625 \\[/tex]
[tex]\rule{200}2[/tex]
G R A P H : -
[tex]\setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\vector(1,0){6}}\put(0,0){\vector(-1,0){6}}\put(0,0){\vector(0,1){6}}\put(0,0){\vector(0,-1){6}}\put(.2,2.5){$\sf (0,75)$}\put(.2, - 2.7){$\sf (0,-75)$}\put(2.5,0.2){$\sf (75,0)$}\put( - 4.2,.2){$\sf ( - 75,0)$}\put(4,4){$\bigstar \: \: \sf Centre = (0,0) $}\put(4,3){$\bigstar \: \: \sf Radius = 75\ miles $}\put(4,-4){$\boxed{\bf \textcopyright \: \: Tony Stark }$}\end{picture}[/tex]
[tex]\rule{200}2[/tex]
Answer a :-
The intercepts are the points at which the circle cuts the x-axis and y-axis . At x intercept , the value of y coordinate becomes 0 and at y intercept the x coordinate becomes 0 .
So for finding x intercept , plug in y = 0 , in the given equation of circle, as ;
[tex]:\sf\implies x^2 + (0)^2 = 5625 \\[/tex]
[tex]:\sf\implies x^2 = 5625 \\[/tex]
[tex]:\sf\implies x =\sqrt{5625} \\[/tex]
[tex]:\sf\implies x =\pm 75 \\[/tex]
[tex]:\sf\implies \red{ x = +75 , -75} \\[/tex]
Hence the circle cuts the x-axis at (75,0) and (-75,0).
To find out y intercept plug in x = 0 in the given equation of the circle as ,
[tex]:\sf\implies (0)^2 + y^2 = 5625 \\[/tex]
[tex]:\sf\implies y^2 = 5625 \\[/tex]
[tex]:\sf\implies y=\sqrt{5626}\\[/tex]
[tex]:\sf\implies y = \pm 75 \\[/tex]
[tex]:\sf\implies \red{ y = +75,-75} \\[/tex]
Hence the circle cuts the y-axis at (0,75) and (0,-75).
[tex]\rule{200}2[/tex]
Answer b :-
Next we are interested in finding out the radius of the circle, for that we need to compare the given equation of circle to the standard equation of circle .
Standard equation of circle :-
[tex]:\sf\implies \red{ (x-h)^2 + (y-k)^2 = r^2}[/tex]
where ,
(h,k) is the centre of the circle.r is the radius.We can rewrite the given equation of circle as ,
[tex]:\sf\implies (x-0)^2 + (y-0)^2 = 5625 \\[/tex]
[tex]:\sf\implies (x-0)^2+(y-0)^2 = 75^2\\[/tex]
On comparing to the standard form, we have;
[tex]:\sf\implies \red{ radius = 75\ miles } \\[/tex]
Hence the radius of the circle is 75miles .
[tex]\rule{200}2[/tex]
Answer c :-
To find out the area we can use the formula of area of circle , which is ;
[tex]:\sf\implies \red{Area=\pi(radius)^2} \\[/tex]
We already got the radius to be 75 miles in the previous part of the question. Plugging in that value would give us the area , as ;
[tex]:\sf\implies Area =\pi (75\ miles )^2 \\[/tex]
[tex]:\sf\implies Area = \dfrac{22}{7}\times 5625\ miles^2\\[/tex]
[tex]:\sf\implies \red{ Area = 17678.57 \ miles^2 } \\[/tex]
Hence the area of the circle is 17678.57 miles² .
Part N
Now convert 1/5 to a decimal number by completing the long division. Remember to add 0s to the dividend as you work. Divide through the ten-thousandths place, and write your result.
Dividend is divided by divisor.
Part O
What will happen if you keep repeating the division process in part N?
Part P
You’ve just completed three long division calculations. What can you conclude about the quotient, or result, from the long division process? Does it end or does it continue indefinitely?
To convert 1/5 to a decimal number by long division, we divide 1 by 5 and keep adding 0s to the dividend until we have enough decimal places and 1/5 as a decimal number is 0.2.
The calculation looks like this:0.2 | 1.0000
|-------
| 0
|----
1
So, 1/5 as a decimal number is 0.2.
Part O:
If we keep repeating the division process in part N, we will get the same result of 0.2 because 1/5 has a finite decimal representation.
Part P:
From the three long-division calculations we have completed, we can conclude that the quotient, or result, from the long-division process can either end or continue indefinitely.
In part N, we found that 1/5 has a finite decimal representation, so the long division process ended.
However, for other fractions, such as 1/3, the long division process will continue indefinitely because the quotient has a repeating pattern of digits.
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you'll need to write an equation that relates x and y for points along the incline. what is this equation?
The equation whigh relates x and y points along the incline is: y = 2x - 3
We know that the general form of a slope - intercept form of equation of line is :
y = mx + c
m = slope
and c = y-intercept
We know that slope is nothing but angle of incline.
From figure we can observe that the line passes through points (3, 3) and (6, 9)
Using the formula of slope,
m = (9 - 3) / (6 - 3)
m = 6/3
m = 2
So the equation of line would be
y = 2x + c
As line passes though point (3, 3),
3 = 2(3) + c
3 = 6 + c
c = - 3
So, the equation that relates x and y for points along the incline is:
y = 2x - 3
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The complete question is:
All three points displayed are on the line. you'll need to write an equation that relates x and y for points along the incline. what is this equation?
Students rented buses and vans to go attend the southwood staff/ student hockey game. There were 8 vans and 12 buses for 360 students
a) write an equation to describe this relationship
b) if there were 12 students per van, how many students fit in each bus?
Therefore, each bus can hold 22 students if there were 12 students per van.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are symbols that can represent different values. Solving an equation means finding the value or values of the variable(s) that make the equation true.
Here,
a) Let V be the number of vans and B be the number of buses. We know that there were 8 vans and 12 buses, so we can write:
V + B = 20 (the total number of vehicles)
We also know that there were 360 students in total. If we assume that each van can hold 12 students, and each bus can hold some number of students, we can write:
12V + bB = 360 (the total number of students)
where b is the number of students that each bus can hold.
b) We can use the equation we derived in part a) and substitute V = 8 to solve for B:
V + B = 20
8 + B = 20
B = 12
So there were 12 buses in total. We can then use the equation 12V + bB = 360 and substitute V = 8 and B = 12 to solve for b:
12V + bB = 360
12(8) + b(12) = 360
96 + 12b = 360
12b = 264
b = 22
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Assume N || M Select all true statements.
Answer:
Step-by-step explanation:
when i got it it was d
(5) A light pole of height 8 metres gives a shade on the ground of length 5 metres, then the measure of the elevation angle of the sun at that moment to the nearest degree equals .....
The measure of the angle of elevation is 58°( nearest degree)
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The height of the pole will represent the opposite to the angle of elevation and the length of the shade will be the adjascent to the angle of elevation.
Represent the angle of elevation by x
Tan x = opp/adj
Tan x = 8/5
Tan x = 1.6
x = tan^-1(1.6)
x = 58° ( nearest degree)
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Sam has $150. She used 40% to buy a dog. How much did the dog cost?
Answer:
Step-by-step explanation:
60$. (((150 * 40 and divide by 100)))
Step-by-step explanation:
She used 40% of $150 :
40% * $150 = .40 * 150 = $ 60 for the pup-a-roo.
An aerial photographer who photographs real estate properties has determined that the best photo is taken at a height of approximately 420 ft and a distance of 896 ft from the building. What is the angle of depression from the plane to the building?
Thus, the angle of depression from the plane to the building is found as:
Ф = 27.90°.
Explain about the angle of depression?The angle of depression is indeed the angle formed by a line drawn from the observer's line of sight down to an object below it.
It is frequently used in navigating, surveying, and trigonometry to describe its position of an object in relation to an observer's point of view. Degrees are used to express the depression's angle.
Give data:
Let the height h = 420 ft.
Let the distance x = 896 ft.
angle of depression is found using the trigonometric formula:
tan Ф = height/distance
tan Ф = h/x
tan Ф = 420/896
tan Ф = 0.46875
Ф = tan⁻¹(0.46875)
Ф = 27.90°.
Thus, the angle of depression from the plane to the building is found as:
Ф = 27.90°.
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Help please i need this answered fast
Dale
rapide
veloce
The scale factor of the two rectangles show a common ratio of 4/5
What is scale factor?A scale factor in geometry is a ratio that indicates how much a figure has been extended or shrunk.
When two figures are comparable, the scale factor is the ratio of any matching lengths in the two figures.
A scale factor of higher than 1 indicates expansion, whereas a scale factor of less than 1 indicates decrease. The figure is the same size as the original when the scale factor is 1.
The dimensions of comparable figures can be calculated using scale factors. For instance, we can use the scale factor to determine the length of the corresponding side of the smaller rectangle if we know the scale factor between two identical rectangles and the length of one of its sides of the larger rectangle.
In the given figure;
12/15 = 36/45
Let's find the ratio here;
4/5 =4/5
The scale factor is 4/5
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Please help. Susie ran a race. She ran 5 miles an hour and the race took her T hours to complete how long was the race and write your answer as an expression.
Answer:
The expression you use to find the amount of miles would be 5xT=X miles.
or 5t
A line has a slope of -5 and passes through the point (1,-9) write its form in slope intercept form
Answer:
[tex]y = - 5x - 4[/tex]
Step-by-step explanation:
[tex] - 9 = - 5(1) + b[/tex]
[tex] - 9 = - 5 + b[/tex]
[tex]b = - 4[/tex]
[tex]y = - 5x - 4[/tex]
North America has an area of 9,365,000 square miles, which is about 136% the area of South America. How many times greater is an area of North America than South America? Write your answer as a decimal in as a mixed number.
I remember doing this but I don’t seem to remember
which of the following distributions have a sufficient estimator? (a). bernoulli. (b). poisson. (c). exponential. (d). none of the above or more than one answer.
A sufficient estimator is the distributions of exponential.The correct answer to this question is (c) exponential.
What is an estimator?An estimator is a rule or procedure that is used to determine an estimate of a parameter based on observed data. A statistic is used to estimate a parameter, and it is computed from the observed data. An estimator is a random variable that computes a statistic from the data.
The following distributions have a sufficient estimator:
Poisson Distribution with parameters λ and x is a Poisson distribution.
The rate of the occurrence is λ.
Exponential Distribution with parameters λ and x is an exponential distribution.
The mean waiting time is 1/λ.
Bernoulli The Bernoulli distribution is not sufficient for an estimator, but the binomial distribution, which generalizes the Bernoulli distribution, is. In the context of the binomial distribution, p is a parameter Exponential
The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, such as the amount of time until the next vehicle arrives at a traffic intersection or the amount of time a particular component lasts in a manufacturing process.
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what is the probability that either elsa or scott is president and the other is vice president? write your answer as a reduced fraction
The probability of Jose being the president and Ellen being the vice president in a committee of eight people choosing leaders at random is 1/56.
The probability of Jose being chosen as the president and Ellen being chosen as the vice president is:
P(Jose as president and Ellen as vice president) = P(Jose as president) * P(Ellen as vice president | Jose as president)
Since the assignments are made at random and there are no restrictions on who can be chosen for each position, the probability of Jose being chosen as president is 1/8, and the probability of Ellen being chosen as vice president, given that Jose is president, is 1/7 (since there are 7 remaining people who can be chosen for the position of secretary).
Therefore,
P(Jose as president and Ellen as vice president) = (1/8) * (1/7) = 1/56
So the probability that Jose is president and Ellen is vice president is 1/56.
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_____The given question is incomplete, the complete question is given below:
A committee of eight people must choose a president, a vice president, and a secretary.
Two of the committee members are Ellen and Jose. Assume the assignments are made at random. What is the probability that Jose is president and Ellen is vice president?
Create a proportion from each set of numbers ONLY use 4 numbers from each set:
1) 66, 99, 8, 11, 6, 88
2) 45, 14, 25, 35, 19, 10
3) 5, 48, 12, 18, 1, 4
4) 9, 45, 13, 75, 25, 5
5) 72, 9, 84, 12, 6, 54
Ok I really do not know what this is
The total area of the rectangle and square joined together is 27 cm².
What is the area of the geometry?First, let's find the area of the rectangle. The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width.
In this case, the length of the rectangle is 6 cm and the width is equal to the length of the square, which is also 3 cm. So, the area of the rectangle is:
A = 6 cm x 3 cm
A = 18 cm^2
Now let's find the area of the square. The formula for the area of a square is A = s^2, where A is the area and s is the length of a side.
In this case, the length of the side of the square is also 3 cm. So, the area of the square is:
A = 3 cm x 3 cm
A = 9 cm^2
To find the total area of the rectangle and square joined together, we simply add the two areas together:
Total area = area of rectangle + area of square
Total area = 18 cm^2 + 9 cm^2
Total area = 27 cm^2
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What are the approximate solutions of 2x^2 - x + 10 = 0?
-2, 2.5
-1.97, 2.47
-2.5, 2
No solution
The quadratic equation 2x^2 - x + 10 = 0 can be solved using the quadratic formula, which is:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Here, a = 2, b = -1, and c = 10. Substituting these values, we get:
x = [-(-1) ± sqrt((-1)^2 - 4(2)(10))] / 2(2)
x = [1 ± sqrt(1 - 80)] / 4
x = [1 ± sqrt(-79)] / 4
Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is "No solution".
What is the critical value t* for constructing a 99% confidence interval
for a mean with 11 degrees of freedom?
The critical value t for constructing a 99% confidence interval for a with 11 degrees of freedom is approximately 3.106.
What is t-distribution table?A t-distribution table is a table of values that shows the critical values for the t-distribution, which is a probability distribution used in statistics.
The table is typically organized by degrees of freedom and the level of significance (α) for a two-tailed test.
To find the critical value t* for a 99% confidence interval for a mean with 11 degrees of freedom, we can use a t-distribution table or a calculator.
Using a t-distribution table, we can find the critical value that corresponds to a 99% confidence level and 11 degrees of freedom.
The table shows that the critical value is approximately 3.106.
Alternatively, we can use a calculator that has a t-distribution function.
For example, using the function (0.005, 11) in Microsoft Excel will give us the same result of approximately 3.106.
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Calculator
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Enter your answer in the box.
The answer of the given question based on Quadrilateral ABCD is inscribed in the circle on finding the measure of the angle ∠B is 70°.
What is Quadrilateral?A quadrilateral is a geometric shape that consists of four straight sides, connected end-to-end to form a closed figure. Examples of the quadrilaterals are rectangles, squares, parallelograms, trapezoids, and rhombuses. In a quadrilateral, the interior angles add up to 360° degrees. Quadrilaterals can have opposite sides parallel (as in parallelograms) or opposite sides equal in length (as in kites). They are widely used in geometry and mathematics in general.
In a circle, the opposite angles of a quadrilateral inscribed in the circle are supplementary. Therefore, we have:
m∠B + m∠D = 180°
We are given that B = (4x - 20)°, so we can substitute this into the equation above and solve for x:
m∠B + m∠D = 180°
(4x - 20)° + 115° = 180° (Note that m∠D is given as 115° in the diagram)
4x - 20 + 115 = 180
4x + 95 = 180
4x = 85
x = 21.25
Now that we know x, we can find the measure of angle ∠B:
m∠B = 4x - 20°
m∠B = 4(21.25) - 20°
m∠B = 70°
Therefore, the measure of angle ∠B is 70°.
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the sum that shows how many concert tickets were sold if 100 was sold last week and 2/5 of the remaining tickets were sold thus week
The sum that shows how many concert tickets were sold using the given parameters is: ²/₅x + 60
How to solve Algebraic expressions?Algebraic expressions are defined as the simple idea of expressing numbers with the aid of letters or alphabets without even specifying their actual values.
Let the total number of tickets available for sale be denoted as x.
We are told that 100 tickets were sold last week. Thus:
Amount of tickets left unsold = (x - 100)
We are now told that 2/5 of the remaining tickets were sold this week. Thus:
Number of tickets sold this week = ²/₅(x - 100)
Thus:
Total Number of Tickets sold = 100 + ²/₅(x - 100)
= 100 + ²/₅x - 40
= ²/₅x + 60
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Lisa has 3 ribbons she won at the track meet over the weekend. A 1st place ribbon, a 2nd ribbon, and a 3rd place ribbon. The 2nd place ribbon is 4/5 of the length of the 1st place ribbon. The 2nd place ribbon is 1/2 the length of the 3rd place ribbon. The length of the 3rd place ribbon is 90 centimeters longer than the 1st place ribbon. How long is the 2nd place ribbon?
Answer:
20cm
Step-by-step explanation:
90cm ÷ 1/2 the length 90 = 20cm
Two more wrestlers join the team during the season. The addition of these wrestlers has no effect on the mean weight of the wrestlers, but the median weight of the wrestlers increases 3 pounds. Determine the weights of the two new wrestlers. Enter the weight of the new wrestlers (in pounds) in the boxes below (put the lower number for wrestler 1): Wrestler 1: Wrestler 2:
I need answer
The new weight of wrestler 1 is w_{(n+2)/2} = w_{(n+3)/2} - 1
The new weight of wrestler 2 is w_{(n+4)/2} = w_{(n+3)/2} + 2.
What are the weights of the wrestlers?Let's suppose the weights of the wrestlers before the two new wrestlers joined the team are arranged in increasing order as follows:
w_1 ≤ w_2 ≤ w_3 ≤ ... ≤ w_n
where;
n is the number of wrestlers before the two new wrestlers joined, and w_i represents the weight of wrestler i.Since the mean weight remains unchanged, we have:
(w_1 + w_2 + w_3 + ... + w_n) / n = (w_1 + w_2 + w_3 + ... + w_n + x + y) / (n+2)
where x and y are the weights of the two new wrestlers.
Simplifying the above equation, we get:
2(w_1 + w_2 + w_3 + ... + w_n) = nw_1 + nw_2 + nw_3 + ... + nw_n + 2x + 2y
which can be further simplified as:
2(w_1 + w_2 + w_3 + ... + w_n) - 2nw_n = (n-2)w_1 + (n-2)w_2 + (n-2)w_3 + ... + (n-2)w_{n-1} + 2x + 2y
Since the median weight increases by 3 pounds, the new median weight is the weight of the (n+3)/2-th wrestler.
where;
n+2 is the total number of wrestlers after the two new wrestlers joined.We can express this in terms of the weights of the original wrestlers and the weights of the new wrestlers as follows:
If n+2 is even, then the new median weight is the average of the (n+2)/2-th and (n+4)/2-th weights.
If n+2 is odd, then the new median weight is the (n+3)/2-th weight.
In either case, we have:
w_{(n+2)/2} + w_{(n+4)/2} = 2(w_{(n+3)/2} - 3)
Substituting the weights of the original wrestlers and the new wrestlers using the equation we derived earlier, we get:
[(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2} + 2x + 2y] + [(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2}] = 2[(n+2)w_{(n+3)/2} - 6]
Simplifying and rearranging the terms, we get:
4w_{(n+3)/2} - 2w_{(n+2)/2} - 2w_{(n+4)/2} = x + y - 3
Substituting x + y = 2w_{(n+3)/2} - 3, we get:
w_{(n+4)/2} - w_{(n+2)/2} = 3 - w_{(n+3)/2}
Since the weights are arranged in increasing order, we have:
w_{(n+2)/2} ≤ w_{(n+3)/2} ≤ w_{(n+4)/2}
Therefore, the only possible solution is:
w_{(n+2)/2} = w_{(n+3)/2} - 1
w_{(n+4)/2} = w_{(n+3)/2} + 2
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Please just answer this asap Dont need tot show work just give right answer and get brainly
A machine fills canisters with 40 ounces of popcorn. The weight of the canister and the popcorn should have a combined weight of 42 ounces. If the total weight is more than 0.9 ounces different from the desired weight, the filled canister is unacceptable and removed from the product line.
Which equation can be used to find the lightest and heaviest acceptable weights, x, for the filled canister?
|x−0.9|=42
vertical line x minus 0.9 vertical line equals 42
|x−42|=0.9
vertical line x minus 42 vertical line equals 0.9
x−0.9=42
x minus 0.9 equals 42
x−42=0.9
An equation that can be used to find the lightest and heaviest acceptable weights, x, for the filled canister include the following: B. |x − 42| = 0.9.
What is an absolute value function?In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).
Mathematically, an absolute value function can be represented by the following mathematical equation:
|x| = x, x ≥ 0.
|x| = x, x < 0.
Based on the information provided about the desired weight of the canister and the popcorn, an equation that models the situation is given by;
|x − 42| = 0.9.
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Determine the surface area of the trapezoidal prism to nearest whole number (no unit is required)
We can conclude after answering the provided question that As a result, rectangle the surface area of the trapezoidal prism is 180 to the nearest whole number.
What is rectangle?In Euclidean geometry, a rectangle is a triangular prism with four slight angles. It can also be described as a basic rule hexagon or one in which all of the angles are equal. A whole other option for the parallelogram is a straight angle. Four of something like the vertices in a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "vector graphics rectangle" at times. A rectangle is sometimes referred to as a parallelogram due to the equal and parallel sizes of its two sides.
Two trapezoidal faces and four rectangular faces comprise the trapezoidal prism.
To begin, we can use the formula to calculate the area of one of the trapezoidal faces:
Trapezoid area = (1/2) x (sum of parallel sides) x (height)
Area of trapezoidal face = (1/2) x (7 + 10) x 4 = 34
7 x 4 = 28 area of rectangular face
The total area of the rectangular faces is: because there are four rectangular faces
Total rectangular face area = 4 x 28 = 112
Total surface area equals the sum of the areas of trapezoidal and rectangular faces.
Surface area total = 68 + 112 = 180
As a result, the surface area of the trapezoidal prism is 180 to the nearest whole number.
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y
The diagram shows part of
regular nonagon. Work
out the size of the angle
marked y.
Answer: 40 degrees
Step-by-step explanation:
There are 9 sides in a nonagon and 360 degrees make the shape up.
360 degrees divided by 9 EQUAL SIDES of a nonagon = 40 degrees
The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d equals 30 times the sine of the quantity pi over 20 times t end quantity plus 15 comma where d represents the distance, in feet, of the person above the ground after t seconds. How long will it take for the Ferris wheel to make one revolution?
Answer:
40 seconds
Step-by-step explanation:
You have a Ferris wheel such that the height of a rider is modeled by d=30sin(πt/20)+15, and you want to know the time it takes for one revolution.
PeriodicityThe sine function has a period of 2π. The value of the function when the argument is 2π is the same as when it is zero. The period is the time difference between those argument values. Since the argument is 0 when t=0, we only need to find the value of t that makes the argument 2π:
2π = πt/20
40 = t . . . . . . . multiply by 20/π
The Ferris wheel makes one revolution in 40 seconds.
A 9.6 8.4 7.2 6.0 4.8 3.6 2.4 1.2 0 1 2 3 4 5 6 7 8 9 10 X The equation of the line of best fit for the nine points is determined. Then, three more points are added to the scatter plot, but the equation of the original line of best fit remains unchanged. Which three ordered pairs are most likely the added data points?
A (4,4), (5,5), (6,6)
B (4,10),(4,11),(4,12)
C (8,9),(8,10),(8,11)
D(10,10),(10,11),(10,12)
I need an answer asap
The answer option to the above question is The 3 ordered pairs are B, (4,10),(4,11),(4,12).
What is an equation?In this context, the word "equation" refers to the equation of the line that best fits a certain set of data points. A straight line that most accurately depicts the trend or pattern in a collection of data points is called the line of best fit. Predictions or estimations for additional data points that might not be a part of the initial set can be made using the equation of the line of best fit.
According to the given information:
To determine which three ordered pairs are most likely the added data points, we need to consider the slope and y-intercept of the original line of best fit. Since the equation of the line of best fit remains unchanged, the new points must lie on the original line.
The original line of best fit can be determined using a linear regression algorithm. However, we can estimate the slope and y-intercept of the line by simply finding the coordinates of two points on the line.
We can use the first and last points in the original set of data to estimate the slope and y-intercept. Using these points, we find that the equation of the line of best fit is:
y = -0.84x + 10.8
Now we can check which of the given sets of points lie on this line:
A: (4,4), (5,5), (6,6)
For (4,4), y = -0.84(4) + 10.8 = 7.56, which is not equal to 4. So (4,4) is not on the line.
Similarly, (5,5) and (6,6) are not on the line.
Therefore, A is not the correct answer.
B: (4,10),(4,11),(4,12)
For (4,10), y = -0.84(4) + 10.8 = 7.56, which is equal to 10. So (4,10) is on the line.
Similarly, (4,11) and (4,12) are also on the line.
Therefore, B is a possible answer.
C: (8,9),(8,10),(8,11)
For (8,9), y = -0.84(8) + 10.8 = 4.32, which is not equal to 9. So (8,9) is not on the line.
Similarly, (8,10) and (8,11) are not on the line.
Therefore, C is not the correct answer.
D: (10,10),(10,11),(10,12)
For (10,10), y = -0.84(10) + 10.8 = 3.96, which is not equal to 10. So (10,10) is not on the line.
Similarly, (10,11) and (10,12) are not on the line.
Therefore, D is not the correct answer.
Therefore, the answer is B, (4,10),(4,11),(4,12).
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Keelin’s hourly rate went from $9. 50 per hour to $10. 25 per hour. What is the percent increase?
Keelin's hourly rate increased by 7.89%. To calculate the percentage increase in Keelin's hourly rate, we need to determine the difference between the new and old rates and express that difference as a percentage of the old rate.
First, we find the difference between the two rates:
$10.25 - $9.50 = $0.75
This means that Keelin's hourly rate increased by $0.75 per hour.
Next, we need to express this increase as a percentage of the old rate:
($0.75 / $9.50) x 100% = 7.89%
Therefore, Keelin's hourly rate increased by 7.89%.
A percent increase is a measure of the increase in a quantity compared to the original value. In this case, the original value is Keelin's hourly rate of $9.50, and the new value is $10.25. The percentage increase is calculated by finding the difference between the new and old values and expressing that difference as a percentage of the original value.
A percentage increase is useful in analyzing changes over time or comparing changes in different variables. In this case, knowing the percentage increase in Keelin's hourly rate can help her understand how much her pay has increased and plan for future financial goals. It can also be helpful for an employer to calculate percentage increases in employee salaries when determining raises or promotions.
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Use the discriminant to describe the roots of each equation. Then select the best description. x2 - 4x + 4 = 0
non-real roots
double root
real and rational roots
real and irrational roots
The best description of the roots of the equation [tex]x^2 - 4x + 4 = 0[/tex] is that it has two equal or identical real roots.
What are the identical real roots?Identical real roots are solutions to a quadratic equation in which both roots have the same value. In other words, if a quadratic equation has identical real roots, it means that there is only one solution to the equation, and that solution is repeated twice.
To use the discriminant to describe the roots of equation [tex]x^2 - 4x + 4 = 0[/tex] we need to first identify the coefficients of the quadratic equation:
[tex]a = 1\\b = -4\\c = 4[/tex]
The discriminant is given by the expression [tex]b^2 - 4ac[/tex]. Substituting the values of a, b, and c, we get:
[tex]b^2 - 4ac\\ = (-4)^2 - 4(1)(4)\\ = 16 - 16 = 0[/tex]
Since the discriminant is equal to zero, this tells us that the quadratic equation has two equal roots. In other words, the equation has a single root with a multiplicity of two.
The best description of the roots of equation x^2 - 4x + 4 = 0 is that it has two equal or identical real roots.
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Deena and Jackson tossed two coins at the same time. In five tosses, Deena got heads on both coins three times. In 50 tosses, Jackson got heads on both coins 12 times. What does this illustrate about theoretical and experimental probability that both tossed coins will be heads?
Experimental probability approaches theoretical probability when the sample size is large.
Experimental probability is not affected by sample size.
Smaller groups give more accurate results.
Larger groups have greater chance for error.
Answer:
experimental probability approaches theoretical probability when the sample size is large.
Step-by-step explanation:
This illustrates that experimental probability approaches theoretical probability when the sample size is large. As the number of tosses increases, the experimental probability of both coins being heads for both Deena and Jackson approaches the theoretical probability of 1/4 (since the probability of getting heads on a single coin toss is 1/2, and the probability of getting heads on two coin tosses is (1/2) * (1/2) = 1/4). This is because the law of large numbers states that as the sample size increases, the experimental probability approaches the theoretical probability. Therefore, the more tosses that are performed, the closer the experimental probability will be to the theoretical probability.
Circle T is shown where points Q and S are on the circle and ZQTS = 75°.
O
T
75°
S
The ratio of the central angle, ZQTS, to the whole circle is [DROP DOWN 1].
QS represents [DROP DOWN 2] of the circle's circumference.
which is approximately 3.864 times the length of QS.the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,
What is angle?An angle is a measure of the amount of turn between two lines or rays that meet at a common point, known as the vertex of the angle. The angle is typically measured in degrees or radians. In a Euclidean plane, an angle can range from 0 degrees (corresponding to two lines that are parallel to each other) to 180 degrees (corresponding to two lines that form a straight line). An angle greater than 180 degrees is called a reflex angle. Angles are used in many areas of mathematics and physics, such as geometry, trigonometry, and calculus, as well as in real-world applications such as navigation, architecture, and engineering.
by the question.
The ratio of the central angle ZQTS to the whole circle is 1/12, or 0.0833 (rounded to four decimal places). This is because there are 360 degrees in a circle, and 75 is 1/12 of 360.
QS represents 1/4 of the circle's circumference. This is because the central angle ZQTS is 75 degrees, which is 1/3 of a right angle (90 degrees). An inscribed angle that intercepts the same arc as a 1/3 angle will have twice the measure of the 1/3 angle, or 150 degrees. Thus, angle QTS is 150 degrees. Angle QOS is also 150 degrees, since it intercepts the same arc as QTS. Therefore, angle QOT is 60 degrees, since the angles in triangle QOT add up to 180 degrees. Since triangle QOT is an equilateral triangle, QT and QS are equal in length, and angle QTS is 75 degrees, we can use the sine function to find the length of QS. The sine of 75 degrees is approximately 0.966, so QS represents approximately 0.966 times the circumference of the circle. Since QS represents 1/4 of the circumference, the circumference of the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,
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