A circular flower garden surrounds a sculpture on a square base as show being 6x and 4x. The expression for the area of the flower garden is π(26x - 12√2x).
Find the expression for the area of the flower garden, we need to first find the area of the square base.
The area of a square is calculated by multiplying the length of one side by itself. In this case, the length of one side is 4x, so the area of the square base is (4x)^2 = 16x^2.
Next, we need to find the area of the circular flower garden that surrounds the square base.
Since the flower garden is circular, we use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
The radius of the flower garden is the distance from the center of the circle to any point on the circumference.
Since the flower garden surrounds the square base, we can find the radius by subtracting the side length of the square base from the diameter of the circle.
The diameter of the circle is equal to the diagonal of the square base, which is √(6x)^2 + (6x)^2 = √72x^2 = 6√2x. Therefore, the radius of the flower garden is (6√2x - 4x)/2 = (3√2x - 2x).
Now we can substitute this expression for the radius into the formula for the area of a circle to find the area of the flower garden: A = π(3√2x - 2x)^2 = π(18x - 12√2x + 8x) = π(26x - 12√2x).
Therefore, the expression for the area of the flower garden is π(26x - 12√2x).
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The base and all three faces of a triangle pyramid are equilateral triangles with side lengths of 3ft. the height of each triangle is 2.6ft. what are the lateral area and the total surface area of the triangular pyramid?
The lateral area of the triangular pyramid is 11.7 sq ft and the total surface area is 15.6 sq ft.
To find the lateral area and total surface area of the triangular pyramid with base and faces as equilateral triangles, we can follow these steps:
1: Find the area of one equilateral triangle.
To find the area of an equilateral triangle with side length 3 ft and height 2.6 ft, we can use the formula:
Area = (1/2) × base × height
Area = (1/2) × 3 × 2.6 = 3.9 sq ft
2: Calculate the lateral area.
Since the pyramid has three equilateral triangles as faces, we can multiply the area of one triangle by 3 to find the lateral area:
Lateral Area = 3 × 3.9 = 11.7 sq ft
3: Calculate the total surface area.
The total surface area includes both the lateral area and the base area. Since the base is also an equilateral triangle with the same dimensions, we can simply add the area of the base to the lateral area to find the total surface area:
Total Surface Area = Lateral Area + Base Area = 11.7 + 3.9 = 15.6 sq ft
In conclusion, the lateral area is 11.7 sq ft and the total surface area is 15.6 sq ft.
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Prepare the operating activities section of the statement of cash flows for peach computer using the indirect method. (list cash outflows and any decrease in cash as negative amounts.)
Cash outflows and decreases in cash are reported as negative amounts in the operating activities section of the statement of cash flows for Peach Computer using the indirect method.
How to prepare the operating activities section of the statement of cash flows for Peach Computer using the indirect method?The operating activities section of the statement of cash flows for Peach Computer using the indirect method would include the following cash inflows and outflows:
Cash inflows:
Sales revenue from the sale of computersCash received from customers for computer repairs and servicesInterest received on loans or investmentsCash outflows:
Payments to suppliers for inventory purchasesPayments to employees for salaries and wagesPayments for operating expenses such as rent, utilities, and advertisingPayments of income taxesPayments of interest on loansPayments to creditors for accounts payableAny decrease in cash would be represented as negative amounts in this section.
It's important to note that the specific amounts and details would vary based on Peach Computer's individual financial transactions and operations. The operating activities section provides a summary of the cash inflows and outflows directly related to the company's core business operations during the specified period.
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Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for π/6 or DNE if the expression is undefined. arcsin (sin (-57π/10))=
For the following expression arcsin (sin (-57π/10)) is 3π/10.
The function arcsin(x) gives the angle in radians whose sine is x.
In this problem, we need to find the angle whose sine is equal to the sine of -57π/10.
First, we need to simplify -57π/10 to an angle in the range [-π/2, π/2] since the sine function has a range of [-1, 1]. To do this, we use the fact that sine has a period of 2π,
which means that sin(-57π/10) = sin((-57π/10) + 4π) = sin(3π/10).
So we need to find the angle θ such that sin(θ) = sin(3π/10).
Since sine is an odd function, we know that sin(-θ) = -sin(θ), so we can also say that sin(θ) = sin(-3π/10).
Therefore, there are two possible angles that satisfy the equation: θ = 3π/10 or θ = -3π/10.
However, since the range of the arcsine function is [-π/2, π/2], only the angle in that range that satisfies the equation is θ = 3π/10.
Therefore, we can write:
arcsin(sin(-57π/10)) = arcsin(sin(3π/10)) = 3π/10
The answer is 3π/10.
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6
The expression √532 + 46√3 is equivalent to the expression r + p, where r and p are positive
integers. What is the value of r + p?
The value of r+p in the expression is 2(√133 + 23√3)
To simplify the given expression, we need to first simplify the square root of 532.
We can factor 532 as 2 × 2 × 7 × 19, and then group the factors in pairs of two to simplify the square root:
√532 = √(2 × 2 × 7 × 19) = √(2 × 2) × √(7 × 19)
= 2√(7 × 19)
= 2√133
Now we can substitute this expression into the original expression and combine like terms:
√532 + 46√3
= 2√133 + 46√3
= 2√133 + 2(23√3)
= 2(√133 + 23√3)
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11. A town that uses 68 million BTUs of energy each month is using how many kilowatt-hours of
energy? (1 kWh-3400 BTUS)
Answer:
[tex]20,000 \text{ kWh}[/tex]
Step-by-step explanation:
We can convert 68 million British Thermal Units (BTUs) to kilowatt-hours (kWh) using the given conversion ratio:
[tex]\dfrac{1 \text{ kWh}}{3400 \text{ BTUs}}[/tex]
Multiplying by the ratio:
[tex]68,000,000 \text{ BTUs} \cdot \dfrac{1 \text{ kWh}}{3,400 \text{ BTUs}}[/tex]
↓ canceling the BTU units
[tex]68,000,000\cdot \dfrac{1 \text{ kWh}}{3,400}[/tex]
↓ executing multiplication
[tex]\dfrac{68,000,000}{3,400} \text{ kWh}[/tex]
↓ rewriting as a decimal
[tex]\boxed{20,000 \text{ kWh}}[/tex]
How do you solve the cube root function of x²/³ = 16?
The cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
The given function is x³=16.
Here, the given function can be written as
[tex]x=\sqrt[3]{16}[/tex]
[tex]x=\sqrt[3]{2\times2\times2\times2}[/tex]
[tex]x=\sqrt[3]{2^3\times2}[/tex]
[tex]x=2\sqrt[3]{2}[/tex]
Therefore, the cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
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"Your question is incomplete, probably the complete question/missing part is:"
How do you solve the cube root function of x³=16.
The ratio of dolls thta jack had to peter was 5:2. After jack gave peter 15 dolls, they had the same amount of dolls. How many do they have together?
They have total of 70 dolls together.
Let the initial number of dolls Jack had be 5x and the number Peter had be 2x.
After Jack gave Peter 15 dolls, their amounts became equal. So, we can write the equation: 5x - 15 = 2x + 15
Now, solve the equation for x: 5x - 2x = 15 + 15, which simplifies to 3x = 30
Divide both sides by 3: x = 10
Now, find the initial number of dolls they had: Jack had 5x = 5(10) = 50 dolls, and Peter had 2x = 2(10) = 20 dolls.
After Jack gave Peter 15 dolls, both had 35 dolls (50 - 15 = 35, and 20 + 15 = 35).
So, together they have 35 + 35 = 70 dolls.
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Line x is parallel to line y. Line z intersect lines x and y. Determine whether each statement is Sometimes True.
Answer:
Step-by-step explanation:
a and b are sometimes true.
This is when line z intersects x and y at right angles.
The diameter of Circle Q terminates on the circumference of the circle at (0,3)and (0,−4). Write the equation of the circle in standard form. Show all of your work.
Need answer ASAP Please!!
Answer:
[tex]x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}[/tex]
Step-by-step explanation:
The center of the circle is the midpoint of its diameter.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Given the endpoints of the diameter are (0, 3) and (0, -4), to find the coordinates of the center of the circle, substitute the two endpoints into the midpoint formula:
[tex]\text{Center}=\left(\dfrac{0+0}{2},\dfrac{-4+3}{2}\right)=\left(0,-\dfrac{1}{2}\right)[/tex]
As the x-values of the endpoints of the diameter are the same, the length of the diameter, d, is the absolute value of the difference in y-values of the endpoints:
[tex]d=|3-(-4)|=7[/tex]
Therefore, the diameter of circle Q is 7 units.
The radius, r, of a circle is half its diameter. Therefore:
[tex]r=\dfrac{d}{2}=\dfrac{7}{2}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Now we have determined the center and radius of circle Q, we can substitute these values into the equation of a circle to write the equation of circle Q in standard form:
[tex](x-0)^2+\left(y-\left(-\dfrac{1}{2}\right)\right)^2=\left(\dfrac{7}{2}\right)^2[/tex]
[tex]x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}[/tex]
Therefore, the equation of circle Q in standard form is:
[tex]\boxed{x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}}[/tex]
In a recent Game Show Network survey, 30% of 5000 viewers are under 30. What is the margin of error at the 99% confidence interval? Using statistical terminology and a complete sentence, what does this mean? (Use z*=2. 576)
Margin of error:
Interpretation:
The margin of error at the 99% confidence interval is 0.018 or 1.8%.
Interpretation: This means that if we were to repeat the survey many times, about 99% of the intervals calculated from the samples would contain the true proportion of viewers under 30 in the population, and the margin of error for each interval would be no more than 1.8%.
The margin of error is the amount by which the sample statistic (in this case, the proportion of viewers under 30) may differ from the true population parameter.
Using the given formula for margin of error:
Margin of error = z* * sqrt(p*(1-p)/n)
Where:
- z* is the z-score corresponding to the confidence level (99% in this case), which is 2.576
- p is the proportion of viewers under 30, which is 0.3
- n is the sample size, which is 5000
Substituting these values, we get:
Margin of error = 2.576 * sqrt(0.3*(1-0.3)/5000) = 0.018
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The answer and what is the value of a
Answer:a=40
Step-by-step explanation:
angles on a straight line add to 180. This means that the missing angle that isn't a is 40. Angles in a triangle add to 180 so a=40
A basketball coach wants to purchase shooting shirts for each member of a basketball team.
The cost of shooting shirts can be represented by the equation C = 0. 2x^2 + 1. 6x + 15, where
C is the amount it cost to purchase x shooting shirts. How many shooting shirts can the
basketball coach order for $300?
C = 2x? + 1. 6x + 15
The basketball coach can order approximately 34 shooting shirts for $300.
To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.
The equation is given as C = 0.2x^2 + 1.6x + 15.
To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:
0.2x^2 + 1.6x + 15 = 300
0.2x^2 + 1.6x + 15 - 300 = 0
0.2x^2 + 1.6x - 285 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:
x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)
Simplifying the equation further:
x = (-1.6 ± sqrt(2.56 + 228)) / 0.4
x = (-1.6 ± sqrt(230.56)) / 0.4
x = (-1.6 ± 15.18) / 0.4
Now we have two solutions:
x1 = (-1.6 + 15.18) / 0.4 = 33.95
x2 = (-1.6 - 15.18) / 0.4 = -44.95
Since the number of shooting shirts cannot be negative, we discard the negative solution.
Therefore, the basketball coach can order approximately 34 shooting shirts for $300.
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Select the correct answer from each drop-down menu.
Coach Loren asks Kerry to analyze the batting percentages of players on the softball team.
Complete the sentences with the correct terms.
Coach Loren wants one number to describe how all of the values in the data set vary, so Kerry should tell her to use a measure of
.
Kerry could give her the
or the
of the data set.
Answer:
Kerry could give her the range or the standard deviation of the data set.
Step-by-step explanation:
Coach Loren wants one number to describe how all of the values in the data set vary, so Kerry should tell her to use a measure of variability.
Kerry could give her the range or the standard deviation of the data set.
32
{(-0. 25, 2. 5), (1. 75, -5. 5), (3. 25, -11. 5)}
Write an equation in the form of y = mx + b that represents this linear function?
Therefore, the equation in the form of y = mx + b that represents this linear function is: y = -3.2x + 0.1
To write an equation in the form of y = mx + b for a linear function, we need to find the slope (m) and the y-intercept (b).
We can use any two points from the given set of points to find the slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first and second points:
m = (-5.5 - 2.5) / (1.75 - (-0.25))
m = -8 / 2.5
m = -3.2
Now, we can use the slope and one of the points to find the y-intercept:
y = mx + b
-5.5 = (-3.2)(1.75) + b
b = -5.5 + 5.6
b = 0.1
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Question 4 of 15
Cryshel is mailing pillows with a total volume of 9. 5 ft3. She needs a mailing
box that has a volume greater than 9. 5 ft.
• Box A: length = 3 ft, width = 2 ft, height = 1. 5 ft
• Box B: length = 2. 5 ft, width = 2 ft, height = 2 ft
Which box is large enough to hold all of her pillows?
O
A. Neither box
B. Both box A and box B
ОО
C. Box B
D. Box A
Answer:
C. Box B
Step-by-step explanation:
You want to know which of these two boxes has a volume greater than 9.5 ft³:
Box A: 3 ft by 2 ft by 1.5 ftBox B: 2.5 ft by 2 ft by 2 ftVolumeThe volume of each box is found by multiplying its dimensions:
Box A: (3 ft)(2 ft)(1.5 ft) = 9 ft³
Box B: (2.5 ft)(2 ft)(2 ft) = 10 ft³
Only box B is large enough, choice C.
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ķojo and kofta were given 38000 to share. kojo had 7500 more than kofta find each of their shares Show working
Answer:
Kofta receives $15,250 and Kojo receives $22,750.
Step-by-step explanation:
Let x represent the amount of money that Kofta has.
x + (x +7,500) = 38,000
- 7,500 - 7,500
___________________
x + x = 30,500
2x = 30,500
÷ 2 = ÷2
-------------------
x = 15,250
Therefore, Kofta has $15,250.
Let k represent the amount of money that Kojo has.
k + 15,250 = 38,00
k = 38,000 - 15,250
k = $22,750
Therefore, Kojo has $22,750
In what time will Rs. 6350 amounts to Rs. 8255 if the simple Interest is calculated at 10% per annum ?Also, find the rate of interst if He returns in 1 1/2 years .
Therefore, it will take 3 years for Rs. 6350 to amount to Rs. 8255 at 10% per annum. Therefore, the rate of interest is 32.6% per annum if the loan is returned in 1 1/2 years.
What is interest?Interest is the amount of money that a lender charges a borrower for the use of money or assets. It is typically expressed as a percentage of the amount borrowed or invested, and is paid by the borrower to the lender as compensation for the use of the money. There are two main types of interest: simple interest and compound interest. Simple interest is calculated based on the initial amount borrowed or invested, and is paid out at regular intervals over a fixed period of time. Compound interest, on the other hand, is calculated based on the initial amount plus any accumulated interest, and is paid out at the end of the investment period.
Here,
Using the formula for simple interest:
Simple Interest = (Principal x Rate x Time) / 100
where Principal is the initial amount, Rate is the interest rate per annum, and Time is the duration of the loan in years. To find the time it takes for Rs. 6350 to amount to Rs. 8255 at 10% per annum, we can set up the equation:
8255 - 6350 = (6350 x 10 x Time) / 100
Simplifying the equation, we get:
1905 = 635 x Time
Time = 1905 / 635
Time = 3 years
To find the interest rate if the loan is returned in 1 1/2 years, we can rearrange the formula for simple interest as:
Rate = (100 x Simple Interest) / (Principal x Time)
Plugging in the values, we get:
Rate = (100 x (8255 - 6350)) / (6350 x 1.5)
Rate = 3105 / 9525
Rate = 0.326 or 32.6%
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The rate of change of the gender ratio for the United States during the twentieth century can be modeled as g(t) = (1. 68 · 10^−4)t^2 − 0. 02t − 0. 10
where output is measured in males/100 females per year and t is the number of years since 1900. In 1970, the gender ratio was 94. 8 males per 100 females.
(a) Write a specific antiderivative giving the gender ratio.
G(t) = _______________ males/100 females
(b) How is this specific antiderivative related to an accumulation function of g?
The specific antiderivative in part (a) is the formula for the accumulation function of g passing through (t, g) =
Answer:
(a) G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84
(b) A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)
Step-by-step explanation:
(a) The antiderivative of g(t) can be found by integrating each term of the function with respect to t:
∫g(t) dt = ∫(1.68 × 10^-4)t^2 dt - ∫0.02t dt - ∫0.10 dt
= (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t + C
where C is the constant of integration.
To find the specific antiderivative G(t) that passes through the point (1970, 94.8), we can use this point to solve for C:
94.8 = (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970) + C
C = 94.8 + (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970)
C ≈ -2445.84
Therefore, the specific antiderivative that gives the gender ratio is:
G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84
(b) The accumulation function of g is the integral of g with respect to t, or:
A(t) = ∫g(t) dt = G(t) + C
where C is the constant of integration. We can find the value of C using the initial condition given in the problem:
A(1900) = ∫g(t) dt ∣t=1900 = G(1900) + C = 0
Therefore, C = -G(1900), and the accumulation function of g is:
A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)
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Look at picture please
Based on the inequality, 24.5x > 162 + 4.25x, Trina must sell more than 8 units of the handmade vases to make a profit.
What is inequality?Inequality refers to a mathematical statement that two or more algebraic expressions are unequal or inequivalent.
Mathematically, inequalities are depicted as:
Greater than (>)Greater than or equal to (≥)Less than (<)Less than or equal to (≤)Not equal to (≠).Selling price per handmade vase = $24.50
Variable cost per unit = $4.25
Fixed selling cost = $162
Let the number of vases to sell to make a profit = x
The total sales revenue = 24.5x
The total cost = 162 + 4.25x
To make a profit, 24.5x must be greater than 162 + 4.25x.
Inequality:24.5x > 162 + 4.25x
20.25x > 162
x > 8
Check:
Total sales revenue = $196 ($24.5(8)
Total cost = $196 ($162 + $4.25(8)
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Find the measure of arc AD
90 + 63 = 153
this is because the pink square means that degree is 90°
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.
A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38.
Using technology, what is the correlation coefficient?
–0. 997
–0. 503
0. 503
0. 997
The correlation coefficient using technology is 0.997.
Using the given data in the table, the correlation coefficient can be calculated using technology, such as a statistical calculator or spreadsheet software.
Using python
import numpy as np
# Input the data
weight = np.array([8, 12, 18, 24, 30, 32, 35, 37, 40])
height = np.array([22, 23, 26, 30, 32, 33, 35, 36, 38])
# Calculate the correlation coefficient
correlation_coefficient = np.corrcoef(weight, height)[0, 1]
# Print the correlation coefficient
print("Correlation Coefficient:", correlation_coefficient)
The out put will be
Correlation Coefficient: 0.997088376189
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, weight (x) and height (y) of a child.
Upon calculating, the correlation coefficient (r) is approximately 0.997. This indicates a strong positive linear relationship between the child's weight and height over the two-year period.
Corelation shows dependency of x on y variable and vice versa.
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can someone help me solve -2√180u²v
Answer:-12 with the weird checkmark symbol then a five inside the checkmark symbol times u squared v
Step-by-step explanation:
The profit (in dollars) from the sale of a palm trees is given by:
P(a) = 20x - 0.1x^2 - 100.
Find the profit at a sales of 13 trees
On a company's income statement, gross profit is computed by subtracting the cost of goods sold (COGS) from revenue. (sales),so the sale of palm tree is $143.10.
To find the profit from the sale of 13 palm trees, we need to substitute 13 for x in the profit function:
P(13) = 20(13) - 0.1(13)^2 - 100
P(13) = 260 - 16.9 - 100
P(13) = $143.10
Therefore, the profit from the sale of 13 palm trees is $143.10.
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HELP ASAP!!!!!!!!!!!
Answer:
25%
Step-by-step explanation:
The total number of 7th grade students = 9 + 11 + 11 + 13 = 44
Out of the 44 students 11 play bass
Probability that a seventh grader chosen at random will play the base is:
11/44 = 1/4 = 0.25
As a percentage, this would be 0.25 x 100 = 25%
In ARST, r = 58 cm, m/S=48° and m/T=29°. Find the length of s, to the nearest
centimeter.
The value of length 's' is 44.3 cm
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The measure of angle R = 180-( 48+29)
R = 180- 77
R = 103°
sinR/ r = sinS/s
sin103 / 58 = sin48/s
s × sin103 = 58 × sin48
s × 0.974 = 43.1
s = 43.1/0.974
s = 44.3 cm
therefore the value of length is is 44.3 cm
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Find the area of the surface extending upward from the circle x^2 + y^2 = 1 in the cy-plane to the plane z = 2 - x - y.
The area of the surface is π square units.
We can use a surface integral to find the area of the surface. The surface integral of a scalar function f over a surface S is given by:
∬S f dS
In this case, we want to find the area of the surface, so f = 1, and the integral reduces to:
∬S dS
We can parameterize the surface S using cylindrical coordinates:
x = r cosθ
y = r sinθ
z = 2 - r cosθ - r sinθ
The surface S is defined by the equation x^2 + y^2 = 1, which in cylindrical coordinates is r^2 = 1. Therefore, the surface integral becomes:
∬S dS = ∫∫R ||rθ|| dr dθ
where R is the region in the rθ-plane that corresponds to the surface S.
To find the limits of integration for r and θ, we need to determine the bounds of the region R. Since r^2 = 1, we have r = 1 for all θ. The region R is therefore a circle of radius 1 centered at the origin, and we can integrate over the full range of θ:
∫0^2π ∫0^1 r dr dθ = π
Therefore, the area of the surface is π square units.
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Examine this system of equations. What integer should the first equation be multiplied by so that when the two equations are added together, the x term is eliminated?
StartFraction 1 Over 18 EndFraction + four-fifths y = 10
Negative five-sixths x minus three-fourths y = 3
Answer:
To solve this problem, we need to find an integer to multiply the first equation by so that when we add the two equations together, the x term is eliminated. Let's first rearrange the equations to make them easier to work with:
1/18 x + 4/5 y = 10
-5/6 x - 3/4 y = 3
To eliminate the x term, we need to multiply the first equation by a certain integer so that when we add it to the second equation, the x terms cancel out. To do this, we need to find a common multiple of the denominators of the x coefficients in both equations, which are 18 and -6. The least common multiple of 18 and -6 is 18, so we can multiply the first equation by 18:
18(1/18 x + 4/5 y = 10)
Simplifying this equation, we get:
x + 72/5 y = 180
Now we can add this equation to the second equation:
x + 72/5 y = 180
-5/6 x - 3/4 y = 3
Multiplying the second equation by 15 to get rid of the fractions, we get:
-25/2 x - 45/4 y = 45
Now we can add the two equations together to eliminate the x term:
-25/2 x + x + 72/5 y - 45/4 y = 180 + 45
Simplifying this equation, we get:
-13/20 y = 225/4
Multiplying both sides by -20/13, we get:
y = -450/13
Therefore, the integer we need to multiply the first equation by is 18, which corresponds to option B.
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A national grocery chain is considering expanding their selection of prepared meals available for purchase. They believe that nationwide, 67 percent of households purchase at least one prepared meal per week from the grocery store. The results of a survey given to a random sample of Maryland households found that 641 out of 1,035 households purchase at least one meal per week at the store
61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.
A national grocery chain is considering expanding their selection of prepared meals, and they believe that 67 percent of households purchase at least one meal per week from the grocery store. In a survey conducted in Maryland, 641 out of 1,035 households purchase at least one meal per week at the store.
To determine the percentage of Maryland households purchasing at least one prepared meal per week, follow these steps:
Divide the number of households purchasing at least one meal per week (641) by the total number of households surveyed (1,035).
Multiply the result by 100 to get the percentage.
Here's the calculation: (641 / 1,035) x 100 = 61.93%
So, 61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.
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In a random sample of large cities around the world, the ozone level (in parts per million) and the population (in millions) were measured. Fitting the simple linear regression model gave the estimated regression equation: ozone⌢ = 8. 89 + 16. 6 population. (pretend it's a hat)
Interpret b = 16. 6. For each additional ________________________
million people, the predicted ozone level increases ___________________
ppm.
Rascoville is a large city with a population of 3 million people. What is the average ozone level? __________________________
If the ozone level is approximately 142 ppm, what is the approximate population in millions (round to the nearest million)? __________________________________
Interpretation:
The regression coefficient b = 16.6 represents the change in the predicted ozone level (in parts per million) for each additional million people in the population.
Specifically, for each additional million people, the predicted ozone level is expected to increase by 16.6 parts per million.
For Rascoville, a city with a population of 3 million people, we can use the estimated regression equation to predict the average ozone level:
ozone⌢ = 8.89 + 16.6 × 3 = 8.89 + 49.8 = 58.69
Therefore, the predicted average ozone level for Rascoville is 58.69 parts per million.
If the ozone level is approximately 142 ppm, we can use the estimated regression equation to estimate the population:
142 = 8.89 + 16.6 × population
Solving for population, we get:
133.11 = 16.6 × population
population ≈ 8.02 million
Therefore, the approximate population of the city is 8 million people (rounded to the nearest million).
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Find the gradients of the lines a and b
The gradient of line A and B are 4 and - 2 respectively.
How to find the gradient or slope of a line?The gradient or slope of a line is a the change in the dependent variable with respect to the change in the independent variable.
Therefore, let's find the gradient of line a and b as follows:
(2, -1)(3, 3)
Gradient of line A = 3 + 1 / 3 - 2
Gradient of line A = 4 / 1
Gradient of line A = 4
Therefore,
(0, 1)(1, -1)
Gradient of line B = -1 - 1 / 1 - 0
Gradient of line B = - 2 / 1
Gradient of line B = - 2
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