a) Where the information about triangle ABC is given above, the measure of angle B is 60°
How is this so ?Using the Cos Rules,
(15√3)² = 30² + 15² - 2(15 x 30) cos B
⇒ 657 = 1125 - 900 cosB
⇒ 2 Cos B = 1 Cos B = 1/2
So
B = Cos ⁻¹(1/2)
Hence,
B = 60°
B) Given the above,
Now, we can use the tangent function to find tan B:
tan B = sin B / cos B
= sin (π/3) / cos (π /3)
= (√3 / 2) / 0.5
tan B = √3
C ) the area of the rriangle is given as
s = (a + b + c) /2
Substituting
s = (15 + 15√ 3 + 30)/2
s = 30 + 15√3
Area = √ [ (30 + 15√3)(15√3) (15)(30 - 15 - 15√3))
Simplifying we can say
Area = √(30 + 15√3 )( 15√3)(15)(15 - 5√3 )]
= √[3(10 + 5√3)(15)(3√3 - 1)]
= √[2250 - 1125√3]
Hence,
Area ≈ 17.36in
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Write a derivative formula for the function.
f(x) = (9x2 + 11x + 7)(38x3 + 35)
The derivative formula for the function is
[tex]f'(x) = 342x^4 + 414x^3 + 342x^2 + 418x + 385[/tex]
How to find the derivative of the function f(x)?To find the derivative of the function [tex]f(x) = (9x^2 + 11x + 7)(38x^3 + 35)[/tex], we can use the product rule of differentiation:
f(x) = u(x)v(x)
where [tex]u(x) = (9x^2 + 11x + 7)[/tex] and [tex]v(x) = (38x^3 + 35)[/tex].
The product rule states that:
f'(x) = u'(x)v(x) + u(x)v'(x)
where u'(x) and v'(x) are the derivatives of u(x) and v(x), respectively.
Taking the derivatives, we get:
u'(x) = 18x + 11
[tex]v'(x) = 114x^2[/tex]
Now, substituting everything into the product rule formula, we get:
[tex]f'(x) = (18x + 11)(38x^3 + 35) + (9x^2 + 11x + 7)(114x^2)[/tex]
Simplifying this expression gives the derivative formula for f(x):
[tex]f'(x) = 342x^4 + 414x^3 + 342x^2 + 418x + 385[/tex]
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Find the total differential. z = 7x4y5 dz =
The total differential of the function z = 7x^4y^5 is dz is (28x^3y^5)dx + (35x^4y^4)dy.
To find the total differential of the function z = 7x^4y^5, we need to compute the partial derivatives with respect to x and y, and then express dz in terms of dx and dy.
Computing the partial derivative with respect to x,
∂z/∂x = 4 * 7x^3y^5 = 28x^3y^5
Computing the partial derivative with respect to y,
∂z/∂y = 5 * 7x^4y^4 = 35x^4y^4
Express dz in terms of dx and dy,
dz = (∂z/∂x)dx + (∂z/∂y)dy
dz = (28x^3y^5)dx + (35x^4y^4)dy
So, the total differential of the function z = 7x^4y^5 is dz = (28x^3y^5)dx + (35x^4y^4)dy.
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write 2⁹/2⁵ as a single power
Answer: 1. Multiplying Powers with same Base
For example: x² × x³, 2³ × 2⁵, (-3)² × (-3)⁴
In multiplication of exponents if the bases are same then we need to add the exponents.
Consider the following:
1. 2³ × 2² = (2 × 2 × 2) × (2 × 2) = 23+2
= 2⁵
2. 3⁴ × 3² = (3 × 3 × 3 × 3) × (3 × 3) = 34+2
= 3⁶
3. (-3)³ × (-3)⁴ = [(-3) × (-3) × (-3)] × [(-3) × (-3) × (-3) × (-3)]
= (-3)3+4
= (-3)⁷
4. m⁵ × m³ = (m × m × m × m × m) × (m × m × m)
= m5+3
= m⁸
From the above examples, we can generalize that during multiplication when the bases are same then the exponents are added.
aᵐ × aⁿ = am+n
In other words, if ‘a’ is a non-zero integer or a non-zero rational number and m and n are positive integers, then
aᵐ × aⁿ = am+n
Similarly, (ab
)ᵐ × (ab
)ⁿ = (ab
)m+n
(ab)m×(ab)n=(ab)m+n
Note:
(i) Exponents can be added only when the bases are same.
(ii) Exponents cannot be added if the bases are not same like
m⁵ × n⁷, 2³ × 3⁴
Step-by-step explanation:
Answer:
2^4
Step-by-step explanation:
doing this type of division is like subtracting the powers, 9-5=4, 2^4.
the opposite applies for multiplaction, it's like addition for the powers,
2^9*2^5=2^14.
Hanif is 14 years old. he plans to do up to 70% training intensity. while jogging, hanif took his resting pulse rate for two days in a row. so hanif found that his resting heart rate was 76 beats per minute. what is hanif's training pulse rate?
Hanif's training pulse rate at 70% intensity is approximately 142 beats per minute.
To find Hanif's training pulse rate at 70% intensity, we first need to calculate his maximum heart rate (MHR) using the formula:
MHR = 220 - age
Substituting Hanif's age, we get:
MHR = 220 - 14 = 206
Next, we need to calculate Hanif's target heart rate (THR) range at 70% intensity. This range is between 70% and 85% of his MHR. To calculate the lower end of the range, we multiply his MHR by 0.7:
THR lower = 0.7 × MHR = 0.7 × 206 = 144.2 (rounded to one decimal place)
To calculate the upper end of the range, we multiply his MHR by 0.85:
THR upper = 0.85 × MHR = 0.85 × 206 = 175.1 (rounded to one decimal place)
So Hanif's target heart rate range at 70% intensity is between 144.2 and 175.1 beats per minute.
To find his training pulse rate, we add his resting pulse rate (76 beats per minute) to the percentage of his target heart rate range which corresponds to 70% intensity. This is given by:
Training pulse rate = resting pulse rate + (0.7 × (THR upper - resting pulse rate))
Substituting the values we calculated, we get:
Training pulse rate = 76 + (0.7 × (175.1 - 76)) ≈ 142
Therefore, Hanif's training pulse rate at 70% intensity is approximately 142 beats per minute.
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Find the mad for this set of data.
swim team
name
age (years) mean
absolute
deviation
1
3
9
10
maddox
enrique
13
10
gloria
9
10
1
mckenna
10
.
10
0
10
10
0
mad =
?
✓ done
asher
hannah
danielle
9
10
1
10
10
0
katy
10
10
0
11
10
1
timothy
gentry
9
10
1
The MAD for this set of data is 0.8.
To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:
Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1
Next, we find the absolute deviation of each age from the mean:
|13 - 10.1| = 2.9
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|11 - 10.1| = 0.9
|9 - 10.1| = 1.1
Then, we find the average of these absolute deviations:
MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8
Therefore,To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:
Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1
Next, we find the absolute deviation of each age from the mean:
|13 - 10.1| = 2.9
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|11 - 10.1| = 0.9
|9 - 10.1| = 1.1
Then, we find the average of these absolute deviations:
MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8
Therefore, the MAD for this set of data is 0.8.
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coordinate grid by equation y=4 what line would represent a row parallel to it ?
A row parallel to the line y = 4 on a coordinate grid would be represented by a line with an equation of the form y = c.
How to find a row parallel to y=4 on a coordinate grid?A coordinate grid is a two-dimensional plane consisting of a horizontal x-axis and a vertical y-axis. The point where the x and y-axes intersect is called the origin, and it has coordinates (0, 0).
An equation in the form y = c, where c is a constant, represents a horizontal line parallel to the x-axis. In this case, the equation y = 4 represents a horizontal line that intersects the y-axis at 4, as all points on the line have a y-coordinate of 4.
To find a row parallel to this line, we need to look for another line that also has a constant y-coordinate of 4. One way to represent this line is by the equation y = 4 again, since all points on this line have a y-coordinate of 4.
Alternatively, we can look for an equation in the form y = mx + b, where m is the slope of the line (which is zero for a horizontal line), and b is the y-intercept (which is 4 in this case). Thus, the equation for the row parallel to y = 4 would also be y = 4, since its slope is zero and it intersects the y-axis at y = 4, just like the line y = 4.
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Find the first four nonzero terms of the Taylor series for the function f(y) = ln (1 – 2y4) about 0. NOTE: Enter only the first four non-zero terms of the Taylor series in the answer field. Coefficients must be exact. +. f(y) =
The first four nonzero terms of the Taylor series for f(y) about 0 are:
[tex]-2y^2 + 48y^4/2![/tex] + ... = -[tex]2y^2 + 24y^4[/tex] + ...
To find the Taylor series for the function f(y) = ln(1 - 2y^4) about 0, we need to compute its derivatives at 0 and evaluate them at each term. Let's start by finding the first four derivatives:
f(y) = ln(1 - 2[tex]y^4)[/tex]
f'(y) = [tex]-8y^3 / (1 - 2y^4)[/tex]
f''(y) =[tex](24y^6 - 32y^2) / (1 - 2y^4)^2[/tex]
f'''(y) =[tex](-144y^9 + 384y^5) / (1 - 2y^4)^3[/tex]
f''''(y) =[tex](1920y^12 - 7680y^8 + 3456y^4) / (1 - 2y^4)^4[/tex]
Now we can evaluate each derivative at 0 to get the first four nonzero terms of the Taylor series:
f(0) = ln(1) = 0
f'(0) = 0
f''(0) = -2
f'''(0) = 0
f''''(0) = 48
Therefore, the first four nonzero terms of the Taylor series for f(y) about 0 are: -2y^2 + 48y^4/2! + ... = -2y^2 + 24y^4 + ...
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Maura was teaching her younger brother about probability. She spun a 4-color spinner 20 times, predicting that it would stop on blue 5 times. Her prediction turned out to be 37. 5% lower than the actual number. How many times did the spinner actually stop on blue?
The spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5
Maura predicted that the spinner would stop on blue 5 times out of 20 spins. This is a predicted probability of 5/20 or 0.25.
However, the actual number of times the spinner stopped on blue was 37.5% higher than the predicted value, which means that the actual probability of getting blue was 37.5% higher than the predicted probability. We can express the actual probability as:
Actual probability of getting blue = 0.25 + 0.375*0.25
= 0.34375
This means that the spinner actually stopped on blue 0.34375 * 20 = 6.875 times.
Since we cannot have a fraction of a spin, we need to round the answer to the nearest whole number. Rounding up, we get:
The spinner actually stopped on blue 7 times.
Therefore, the spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5.
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Find x.
Find y.
Find z.
Check the picture below.
If the value of a in the quadratic function f(x) = ax2 + bx + c is -8, the function will_______.
(I would give Brainliest, but I don't know how to do that ;-;)
Many thanks!
Answer:
Step-by-step explanation:
f(x) = ax² + bx + c a= -8
f(x) = -8x² + bx + c that a controls the direction and the stretch.
So the function will be stretched by 8. The negative represents the direction because, it's negative, it will be facing down.
Not sure how your class describes it but it could be facing down, concaved down, or expands downward.
Use the variable x to write the phrase in symbols. the sum of 148 and the product of a number raised to the third power and 19
The expression 148 + 19x³ represents the sum of 148 and the product of a number raised to the third power and 19.
To write the phrase "the sum of 148 and the product of a number raised to the third power and 19" in symbols using the variable x, we can write it as:
148 + 19x³
Here, we are adding 148 to the product of 19 and x raised to the third power. This expression represents the sum of 148 and the product of a number raised to the third power and 19. We can substitute any value for x to get the result of the expression. For example, if x is 2, then the expression becomes:
148 + 19(2³) = 148 + 19(8) = 300
Therefore, the sum of 148 and the product of a number raised to the third power and 19 is represented by the expression 148 + 19x³.
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Find the properties for the ellipse with the equation x^2/169 + y^2/144 = 1
latus rectum =
a. 288/13
b. 328/12
c. 288/12
The latus rectum of an ellipse is 288/13 when the ellipse equation is given as [tex]x^2/169 + y^2/144 = 1[/tex]. Option A is correct.
The standard form of an ellipse equation is given as
[tex](x2/a2) + (y2/b2) = 1[/tex]
where :
a = lengths of the semi-major axes
b = length of semi-minor axes
The length of the chord through one of the foci that are perpendicular to the major axis is defined as the latus rectum of an ellipse.
From the given data the equation of the ellipse is given as :
x² / 169 + y² / 144 = 1
By comparing the standard equation and the given equation of the ellipse we get :
a² = 169
a = √169
[tex]a = 13[/tex]
b² = 144
b = √144
[tex]b = 12[/tex]
The distance between the center and one of the foci is given by
c = √(a² - b²)
= √(13² - 12²)
= 5
We can find the latus rectum by substuting a and b values in the latus rectum of an ellipse formula,
= 2×b²/a
= 2 × 12² / 13
= 288/13
Therefore, the latus rectum of an ellipse is 288/13.
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PLEASE HELP
Find X
(7x+3) 78° 152°
By using concept of interior angle we find the value of X is -7.14 degrees.
The above problem involves finding the value of x in a triangle with two known angles measuring 78° and 152°.
The sum of the interior angles of any triangle is always 180°, so we can use this fact to set up an equation involving the third angle, which is given as 7x +3 degrees.
To solve for x, we first simplify the equation by combining the known angles:
78° + 152° + (7x + 3)° = 180°
Next, we can simplify by adding the two known angles:
230° + 7x° = 180°
This simplifies to:
7x° = -50°
Finally, we can solve for x by dividing both sides by 7:
x = [tex]\frac{-50^\circ}{7}$$[/tex]
Therefore, x is approximately -7.14 degrees.
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Pharoah Company has these comparative balance sheet data:
PHAROAH COMPANY
Balance Sheets
December 31
2022
2021
Cash
$ 17,205
$ 34,410
Accounts receivable (net)
80,290
68,820
Inventory
68,820
57,350
Plant assets (net)
229,400
206,460
$395,715
$367,040
Accounts payable
$ 57,350
$ 68,820
Mortgage payable (15%)
114,700
114,700
Common stock, $10 par
160,580
137,640
Retained earnings
63,085
45,880
$395,715
$367,040
Additional information for 2022:
1. Net income was $31,100.
2. Sales on account were $387,800. Sales returns and allowances amounted to $27,500.
3. Cost of goods sold was $225,600.
4. Net cash provided by operating activities was $59,300.
5. Capital expenditures were $26,400, and cash dividends were $21,700.
Compute the following ratios at December 31, 2022. (Round current ratio and inventory turnover to 2 decimal places, e. G. 1. 83 and all other answers to 1 decimal place, e. G. 1. 8. Use 365 days for calculation. )
The ratios are 1. Current ratio = 2.90, 2. Acid-test ratio = 2.22, 3. Inventory turnover ratio = 3.57, 4. Debt to equity ratio = 0.77, 5. Return on equity ratio = 15%.
The ratios to be computed are:
1. Current ratio
2. Acid-test (quick) ratio
3. Inventory turnover ratio
4. Debt to equity ratio
5. Return on equity ratio
1. Current ratio = Current assets / Current liabilities
Current assets = Cash + Accounts receivable + Inventory = $17,205 + $80,290 + $68,820 = $166,315
Current liabilities = Accounts payable = $57,350
Current ratio = $166,315 / $57,350 = 2.90
2. Acid-test (quick) ratio = (Cash + Accounts receivable) / Current liabilities
Acid-test ratio = ($17,205 + $80,290) / $57,350 = 2.22
3. Inventory turnover ratio = Cost of goods sold / Average inventory
Average inventory = (Beginning inventory + Ending inventory) / 2
Beginning inventory = $57,350
Ending inventory = $68,820
Average inventory = ($57,350 + $68,820) / 2 = $63,085
Inventory turnover ratio = $225,600 / $63,085 = 3.57
4. Debt to equity ratio = Total liabilities / Total equity
Total liabilities = Accounts payable + Mortgage payable = $57,350 + $114,700 = $172,050
Total equity = Common stock + Retained earnings = $160,580 + $63,085 = $223,665
Debt to equity ratio = $172,050 / $223,665 = 0.77
5. Return on equity ratio = Net income / Average equity
Average equity = (Beginning equity + Ending equity) / 2
Beginning equity = Common stock + Retained earnings = $137,640 + $45,880 = $183,520
Ending equity = Common stock + Retained earnings + Net income - Dividends = $160,580 + $63,085 + $31,100 - $21,700 = $232,065
Average equity = ($183,520 + $232,065) / 2 = $207,793
Return on equity ratio = $31,100 / $207,793 = 0.15 or 15%
Therefore, the ratios are:
1. Current ratio = 2.90
2. Acid-test ratio = 2.22
3. Inventory turnover ratio = 3.57
4. Debt to equity ratio = 0.77
5. Return on equity ratio = 15%
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I need help with an assignment over pythagorean therom i have an example with one of the problems i really need to get this turned in asap because i really need to bring my grade up in math if i turn in this assignment so if you can help you are an amazing person thank you there's an example of one of the problems that I need
Step-by-step explanation:
I have provided answer in attachment... this is solution of brainly tutor..
what is the perimeter of 6m,5m,3m,2m,3m,3m
Jennifer had 7/8 of her pan of macoroni and chese left after supper. The next day she split what was left evenly between her five kids. What fraction of the total pan did each of them get
each of Jennifer's five kids received 1/40 of the total pan of macaroni and cheese.
What is equivalent ratio?
The concept of a ratio in mathematics is the divisional comparison of two quantities, the antecedent and consequent. As an illustration, each ingredient must be added according to a ratio during cooking. So, we may argue that a ratio is employed to represent one quantity as a portion of another. The ratio can be written as a fraction as well. If the ratio a:b is a fraction, its form is a/b. As a result, it is simple to compare two or more equivalent ratios expressed as equivalent fractions.
If Jennifer had 7/8 of her pan of macaroni and cheese left after supper, this means she had 1 - 7/8 = 1/8 of the pan remaining.
To split the remaining macaroni and cheese evenly between her five kids, we need to divide 1/8 by 5.
1/8 divided by 5 can be written as (1/8) ÷ 5 = (1/8) x (1/5) = 1/40.
Therefore, each of Jennifer's five kids received 1/40 of the total pan of macaroni and cheese.
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Can someone help me with this, please?
Answer:
You are correct.
Hope this helps!
Step-by-step explanation:
The lines intersect at one point and that is the solution.
( The image shows a graph with infinite solutions. ( ignore the Byjus thing i was just trying to find an image that showed an example ... ) )
SOMEONE HELP PLS, giving brainlist to anyone who answers
Answer:
[tex]s = \frac{3(1 - {6}^{9}) }{1 - 6} = 6046617[/tex]
The sum of this finite geometric series is 6,046,617.
100 POINTS IF HELP
what is the average rate of change for the function g(x) for the interval [4,9]?
SHOW ALL WORK
g(x)=4x^2+3x-2
Answer:
Step-by-step explanation:
In the figure shown, what are ∠ and ∠? Triangle S T U has right angle U and is labeled as follows: S T, 10; T U, 4; and the long leg, unlabeled
The measures of angle T and S in a right angles triangle STU with side Lengths ST = 10 units and UT = 4 units are equals to
We have a triangle STU has a right angle at U so, we can call it a right angled triangle STU. Length of side ST = 10 units
Length of side TU = 4 units
We have to determine the measure of angle T and measure of angle S.
As we know that sum of inner angles of a triangle = 180°
So, m∠S + m∠T + m∠U = 180°
=> m∠S + m∠T = 180° - 90°
= 90°
Using the trigonometry formula, in right angles triangle STU,
tan (m∠T ) = US/UT
=> m∠T = √86/4
=>
Hence, required value are
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Complete question:
The above figure completes the question.
In the figure shown, what are ∠ and ∠? Triangle S T U has right angle U and is labeled as follows: S T, 10; T U, 4; and the long leg, unlabeled
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2 : Suppose a sample of 455 suspected criminals is drawn. Of these people, 109 were captured. Using the data, construct the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places
The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.
To construct the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list, we can use the following formula:
[tex]\hat{p} \pm z^* \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}[/tex]
where [tex]$\hat{p}$[/tex] is the sample proportion, [tex]$n$[/tex] is the sample size, and [tex]$z^*$[/tex] is the z-score corresponding to the desired level of confidence. Since we are looking for an 85% confidence interval, the z-score is 1.440.
First, we can calculate the sample proportion:
[tex]\hat{p} = \frac{109}{455} = 0.240[/tex]
Next, we can plug in the values into the formula:
[tex]$$ 0.240 \pm 1.440 \sqrt{\frac{0.240 (1 - 0.240)}{455}} $$[/tex]
Simplifying this expression, we get:
[tex]$$ 0.240 \pm 0.046 $$[/tex]
Therefore, the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is [tex]$(0.194, 0.286)$[/tex].
We can interpret this interval as follows: if we were to draw many samples of size 455 from the population of people who appear on the 10 Most Wanted list, and construct a 85% confidence interval for the proportion of people who are captured based on each sample, about 85% of these intervals would contain the true population proportion.
Furthermore, we are 85% confident that the true population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.
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An 8-sided solid is labeled with faces 1, 2, 3, skip ,4, 5, 6, skip. what is the sample space for the number solid, and what is the probability of rolling a 1?
The sample space for the number solid is {1, 2, 3, 4, 5, 6} and the probability of rolling 1 is 1/6.
The sample space refers to the set of all possible outcomes of an experiment, while a sample value is a specific outcome in the sample space.
For the given 8-sided solid, the sample space would be {1, 2, 3, 4, 5, 6}, as the faces labeled "skip" are not counted as sample values.
Now, let's calculate the probability of rolling a 1. Probability is the likelihood of a particular outcome occurring, which can be calculated by dividing the number of successful outcomes (in this case, rolling a 1) by the total number of possible outcomes.
The total number of possible outcomes is 6 (1, 2, 3, 4, 5, and 6). There is only one successful outcome: rolling a 1.
So, the probability of rolling a 1 is:
P(1) = (Number of successful outcomes) / (Total number of possible outcomes)
P(1) = 1 / 6
Thus, the probability of rolling a 1 on this 8-sided solid is 1/6 or approximately 0.1667, or 16.67%.\
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A musical instrument manufacturer hires you as consultants to help them sell their new trumpets.
through a customer survey, when the price of cach trumpet is $220.18, a total of 110 trumpets
would be sold at their la crosse store. the same survey said that if the price of each trumpet was
$160.74, a total of 128 trumpets would be sold. in order to make the new trumpet, the company
knows that it will have to buy (once and once only) $3274.78 of equipment, and after that, cach
individual trumpet will cost them $90.05 cach to make.
1) find the price-demand equation, assuming a linear model, with p for price and x for the number of trumpets
2) what should be the price of each trumpet to break even?
3) what should be the price of each trumpet to maximize profit?
1. The price-demand equation for the trumpets is:
x = 238.18 - 1.09p
2. The manufacturer should set the price of each trumpet at $296.50 to break even
3. The manufacturer should set the price of each trumpet at $138.63 to maximize profit.
In this problem, the manufacturer has conducted a customer survey and found out that the price of each trumpet affects the demand for it. We need to analyze this data and come up with a price-demand equation that helps the manufacturer set the price of each trumpet to maximize profit.
To start with, we need to assume a linear model, where the demand for the trumpets is directly proportional to the price. We can represent the demand as "x" and the price as "p". Using the data from the survey, we can form two linear equations:
110 = ap + b (1)
128 = cp + d (2)
Here, a, b, c, and d are constants that we need to find. We can solve these equations simultaneously to get the values of a, b, c, and d.
Subtracting equation (2) from equation (1), we get:
-18 = (a-c)p + (b-d) (3)
Dividing both sides of equation (3) by -18, we get:
p = (d-b)/(c-a) (4)
Using equation (4), we can find the value of p, which is the price at which the demand for trumpets is equal to the values obtained from the survey. Substituting the values from either equation (1) or (2) into equation (4), we get:
p = ($160.74 x 110 - $220.18 x 128)/(-18 x 110 + 18 x 128)
= $186.46
Therefore, the price-demand equation for the trumpets is:
x = 238.18 - 1.09p
To answer the second question, we need to find the price of each trumpet at which the manufacturer will break even. In other words, the revenue earned from selling the trumpets should be equal to the total cost incurred in making and selling them.
We know that the one-time cost of buying equipment is $3274.78, and each trumpet costs $90.05 to make. Let's represent the break-even price as "[tex]P_{be}[/tex]". Then we can form the following equation:
110[tex]P_{be}[/tex] = 3274.78 + 110 x 90.05
Solving for [tex]P_{be}[/tex], we get:
[tex]P_{be}[/tex]= $296.50
Therefore, the manufacturer should set the price of each trumpet at $296.50 to break even.
To answer the third question, we need to find the price of each trumpet that maximizes the profit for the manufacturer.
The profit is given by the revenue earned minus the total cost incurred. Let's represent the profit as "P" and the price as "p". Then the profit equation becomes:
P = xp - (3274.78 + 90.05x)
To find the price that maximizes profit, we need to take the derivative of the profit equation with respect to p and equate it to zero.
dP/dp = x - 90.05 = 0
Solving for x, we get:
x = 90.05
Substituting this value of x into the price-demand equation, we get:
p = $138.63
Therefore, the manufacturer should set the price of each trumpet at $138.63 to maximize profit.
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Sneha’s mother is 12 years more than twice Sneha’s age. After 8 years, she will be 20 years
less than three times Sneha’s age. Find Sneha’s age and Sneha’s mother’s age.
Sneha's current age is 16 years old. Sneha's mother is 44 years old.
Let's assume Sneha's current age is x.
Sneha's mother's current age = 2x + 12
After 8 years, Sneha's age = x + 8
After 8 years, Sneha's mother's age = 2x + 12 + 8 = 2x + 20
After 8 years, Sneha's mother's age will be 20 less than three times Sneha's age: 2x + 20 = 3(x + 8) - 20
Now we can solve for x:
2x + 20 = 3(x + 8) - 20
2x + 20 = 3x + 24 - 20
2x + 20 = 3x + 4
x = 16
Therefore, Sneha's current age is 16 years old.
Sneha's mother's current age = 2x + 12
= 2(16) + 12 = 44
So, Sneha's mother is 44 years old.
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In a scale model of a boat 1 inch represents 5 feet
The height of the real boat is 3 inches and length of the boat is 45 feet
What is Unit of Measurement?
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
In a scale model of a boat 1 inch represents 5 feet
1 inch = 5 feet
The height of the real boat is 15 feet
We have to find in inches
1/5=x/15
x=3 inches
So height of the real boat is 3 inches
The length of the boat is 9 inches
We have to find in feet
1/5 = 9/x
x=45 feet
Hence, the height of the real boat is 3 inches and length of the boat is 45 feet
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pleasee helppp!!!!!!
The volume of the cone with a radius of 8cm and height of 15 cm is V = 1005.3 cm³, so the correct option is C.
How to get the volume of the cone?Remember that for a cone of radius R, and height H, the volume is given by the formula below:
V = (1/3)*pi*R²*H
Where pi = 3.1416
In this case, we know that the radius of the cone is 8cm and the height is 15cm, replacing that in the volume formula we will get:
V = (1/3)*3.1416*(8cm)²*15cm = 1,005.3 cm³
Then the correct option is c.
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Marci described the light from the sun as a line that starts at the sun and continues on forever.wich geometric term best describes marcis description of the sun's light
The geometric term best describes Marci's description of the sun's light is ray
What is a ray?A ray is a line that extends eternally in one direction from a point in geometry, in this case the sun.
It symbolizes a straight journey without any turning points.
As the sun's light propagates in a straight line throughout space without end, Marci's description fits the definition of a ray.
To explain Marci's depiction of the sun's light as a line that originates at the sun and never ends is to use the geometric term "ray."
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Answer: Ray
Step-by-step explanation:
A ray continues but may have a segment near the stopping point
19. if abcd is a rectangle, ad = 9, ac = 22, and mzbca = 66°, find each missing measure.
help me pls
The missing measures are BC ≈ 23.77, angle BCA = 24 degrees, AB ≈ 56.77, and CD ≈ 56.77.
To solve the problem, we can use the properties of rectangles and trigonometry. Since ABCD is a rectangle, we know that angle ABC is also 90 degrees.
Using the Pythagorean theorem, we can find the length of BC:
BC² = AB² - AC²
BC² = 9² + 22²
BC² = 565
BC ≈ 23.77
Using the fact that the sum of the angles in triangle ABC is 180 degrees, we can find the measure of angle BCA
m(BCA) = 180 - m(ABC) - m(CAB)
m(BCA) = 180 - 90 - 66
m(BCA) = 24 degrees
Using trigonometry, we can find the length of AB
sin(24) = AC/AB
AB = AC/sin(24)
AB ≈ 56.77
Finally, we can find the length of CD, which is equal to AB
CD = AB ≈ 56.77
Therefore, the measures of AB ≈ 56.77, and CD ≈ 56.77.
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Mustafa, Heloise, and Gia have written more than a combined total of
22
2222 articles for the school newspaper. Heloise has written
1
4
4
1
start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written
3
2
2
3
start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.
Write an inequality to determine the number of articles,
�
mm, Mustafa could have written for the school newspaper.
m > 8 is an inequality used to calculate the number of articles Mustafa could have written.
Let's assume that Mustafa has written m articles for the school newspaper.
Then, according to the given information:
Heloise has written 1/4 as many articles as Mustafa has, which means she has written 1/4 × m = m/4 articles.
Gia has written 3/2 as many articles as Mustafa has, which means she has written 3/2 × m = 3m/2 articles.
The combined total of articles written by all three is more than 22, so we can write:
m/4 + 3m/2 + m > 22
Simplifying and solving for m:
11m/4 > 22
m > 22 × 4/11
m > 8
Therefore, m > 8 is an inequality used to calculate the number of articles Mustafa could have written.
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