Final answer:
By applying polar to rectangular coordinates conversion formulas, the polar equation r = 5/(1+cos(θ)) is equivalent to the rectangular coordinate equation y² = 25 - 10x, which matches option D.
Explanation:
To convert the polar equation r = 5/(1+cos(θ)) to rectangular coordinates, we use the relationships between polar and rectangular coordinates: r = √x² + y² and cos(θ) = x/r. Substituting these into the given equation, we get:
r = √x² + y²;
cos(θ) = x/r;
r(1+cos(θ)) = 5;
r + r x/r = 5;
r + x = 5;
r = 5 - x;
Substitute back in for r, we get:
(√x² + y²) = 5 - x;
Squaring both sides gives us x² + y² = (5 - x)² which can be simplified to x² + y² = 25 - 10x + x². Canceling x² from both sides and reordering the terms gives us y² = 25 - 10x, which matches option D.
You roll a die and pick a marble how many outcomes are possible
Answer: 12 because for each number on the die, you get 2 options: one marble or the other. So if it’s a six sided die, you have 12 possible outcomes. (2 times 6)
You roll a die and pick a marble, 12 outcomes are possible.
What is the probability?The possibility of an event in time is known as probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?
Given:
You roll a die and pick a marble.
When you roll a die,
you'll get either one marble or another.
So, there are 2 possibilities.
When you roll a die, there 6 possible outcomes.
And the total number of possible outcomes,
= 2 times 6
= 2x 6
= 12
Therefore, 12 outcomes are possible.
To learn more about the probability;
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So I know that 6 times 3 equals 21 but I don’t know how to find the total cups of paint for each problem. Please help asap! :(
would it be 10, I think if you divide 21/3 and 6/2 you get 7+3 is equal to 10
Please help. Simplify cos(−0)cot(−0) / csc(0)
Answer:
C) cos²(theta)
Step-by-step explanation:
csc(X) = 1/sin(X)
cos(-X) = cos(X)
tan(-X) = -tan(X)
cot(-X) = -1/tan(X) = -cos(X)/sin(X)
[cos(X) × -cos(X)/sin(X)] ÷ -1/sin(X)
-cos²(X)/sin(X) × -sin(X)
cos²(X)
Complete the factorization of 3r? – 10x + 8.
PLease help me it says use cosine law
Answer:
59 degrees
Step-by-step explanation:
law of cosines states that
for sides A B C and angle c opposite to side C,
[tex]C = \sqrt{A^2 + B^2-2ABcos(c)} \\cos(c) = \frac{c^2-a^2-b^2}{-2ab}[/tex]
cos(b) = [tex]\frac{13^2-6^2-15^2}{-2(6)(15)} = 23/45[/tex]
cos-1(23/45) = b
b = 59
Answer:59
Step-by-step explanation:
C2=a2+b2-2ab cosC
13x13=15x15+6x6-2(15)(6)cosC
169=225+36-180cosC
169=261-180cosC
-92=180cosC
-92/-180=cosC
C=arccos92/180. On your calculator it will say cos-1
C=59.23 or m<B = 59. Rounded to the nearest degree.
The difference between two numbers is 7 and three times their sum is 75.
Answer:
ok thanks for telling us
Step-by-step explanation:
Which of the statements the graph below is true?
Answer:
B. The graph is linear and has an equation of y = -x + 18
Step-by-step explanation:
if the equation was y = -2x + 18 then the graph would look like a staircase and the graph looks linear
The statements about the box plot in Figure A2 are analyzed and determined to be true or false.
Explanation:The graph in Figure A2 is a box plot. Let's go through each statement and determine if it is true or false.
A. Twenty-five percent of the data are at most five: True. The box extends from the first quartile (Q1) to the third quartile (Q3), which represents the middle 50% of the data. The line inside the box is the median, and the whiskers extend to the minimum and maximum values. In this case, the box goes up to five, indicating that 25% of the data are at most five.
B. There is the same amount of data from 4-5 as there is from 5-7: False. The box plot shows the range of values within the quartiles. In this case, the range from 4-5 is smaller than the range from 5-7, indicating that there is more data in the latter range.
C. There are no data values of three: True. The box plot does not have any outlier points at the value of three, indicating that there are no data values at that point.
D. Fifty percent of the data are four: False. The median value in the box plot is the value that divides the data into two equal halves. In this case, the median is not at four, so 50% of the data are not equal to four.
Consider the two functions y=3/4x - 2 which statement is true?
a) function 1 has a greater rate of change by 1/4
The second line has a greater rate of change by 13/4.
To determine the rate of change, or slope, of the given graphed line, we employ the formula for calculating the slope between two points, expressed as:
a = (y2 - y1)/(x2 - x1)
Observing the graphed function, we identify two points, (0, -2) and (4, 0), and apply these coordinates to the slope formula
a = (0 - (-2))/(4 - 0) = 2/4 = 1/2
Having established that the slope of the first line is 1/2, we move on to the second line, which has a slope of 15/4. To find the difference in slopes, we subtract the slope of the first line from that of the second:
15/4 - 1/2 = 15/4 - 2/4 = 13/4
This calculation reveals that the second line has a greater rate of change by 13/4.
In summary, the step-by-step analysis indicates that the slope of the second line exceeds that of the first by 13/4.
The question probable may be:
Consider the two functions. Which statement is true?
A)Function 1 has a greater rate of change by 13/4
B)Function 2 has a greater rate of change by 13/4
C)Function 1 has a greater rate of change by 13/2
D)Function 2 has a greater rate of change by 13/2
(2x^2+4-5)-(-8x+2+x^2)
Answer:
x2 + 8x - 3
Step-by-step explanation:
1 . ((2x2 + 4) - 5) - (x2 - 8x + 2)
2. Factoring x2+8x-3
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 8 .
Step 3. -3
+
1
=
-2
-1
+
3
=
2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
So that the answer
Please help I don’t understand
Answer: The first one is 90%.
Step-by-step explanation:
The following data points represent the yearly salaries of high school cheerleading coaches in Dakota county (in thousands of dollars). 41 38 36 57 43
Answer:
5.6 thousand
Step-by-step explanation:
To find the mean absolute deviation (MAD), first find the mean (or average).
μ = (41 + 38 + 36 + 57 + 43) / 5
μ = 43
Next, subtract the mean from each value and take the absolute value.
|41 − 43| = 2
|38 − 43| = 5
|36 − 43| = 7
|57 − 43| = 14
|43 − 43| = 0
Sum the results and divide by the number of animals.
MAD = (2 + 5 + 7 + 14 + 0) / 5
MAD = 5.6
Answer:
43 thousand dollars
A study of 420,076 cell phone users found that 131 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such
cancer was found to be 0.0224% for those not using cellphones. Complete parts (a) and (b)
a. Use the sample data to construct a 95 i dence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system
%
(Round to three decimal places as needed)
Answer:
a) 95% Confidence interval = (0.026%, 0.037%) to 3 d.p
b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = (131/420076) = 0.0003118483 = 0.0312%
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 95% confidence interval for sample size of 420,076 is obtained from the z-tables because the sample size is large enough for the properties of the sample to approximate the population properties.
Critical value = 1.960 (from the z-tables)
Standard error = σₓ = √[p(1-p)/n]
n = sample size = 420,076
σₓ = √(0.0003118×0.999688/420076) = 0.0000272421 = 0.0000272
95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.000312 ± (1.96 × 0.0000272)
CI = 0.000312 ± 0.0000534
95% CI = (0.0002586055, 0.0003653945)
95% Confidence interval = (0.000259, 0.000365)
95% Confidence interval = (0.0259%, 0.0365%) = (0.026%, 0.037%) to 3 d.p
b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.
Hope this Helps!!!
Which graph fits y=2x+1?
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
When you plug in one, y equals three and you have a point at hat ordered pair
When you plug in zero you get one, and you have a point at that ordered pair
the slop is going up, and in the equation the slope is positive
In the figure above, AB is tangent to the circle with center o at point A.
If AOB has a measure of 68 degrees, what is the measure, in degrees, of ABO?
Given:
Given that O is the center of the circle.
AB is tangent to the circle.
The measure of ∠AOB is 68° and we know that the tangent meets the circle at 90°
We need to determine the measure of ∠ABO.
Measure of ∠ABO:
The measure of ∠ABO can be determined using the triangle sum property.
Applying the property, we have;
[tex]\angle ABO+\angle BAO+\angle AOB=180^{\circ}[/tex]
Substituting the values, we get;
[tex]\angle ABO+90^{\circ}+68^{\circ}=180^{\circ}[/tex]
Simplifying, we get;
[tex]\angle ABO+158^{\circ}=180^{\circ}[/tex]
[tex]\angle ABO=22^{\circ}[/tex]
Thus, the measure of ∠ABO is 22°
what is the domain of f(x) = 3x/x-1?
a all real numbers
b all nonzero numbers
c all real numbers except 1
d all real nunbers except 3
Which face of the net will be the shaded side of the prism when the net is folded.
A
B
C
D
Answer:
A
Step-by-step explanation:
A: will be the connect with 2 sides of hypotenuse of the triangle
What is the volume of this prism?
A. 11.75 cubic units
B. 31.5 cubic units
C. 63.0 cubic units
D. 56.3 cubic units
Answer:
56.3
Step-by-step explanation:
I believe it is the answer because 3×5×3.75= 56.25, and you can round that to 56.3. pls dont be mad if it's wrong. I'm like 85% confident that's the answer.
Anja is creating a triangle using three straws. The two shorter straws have lengths of 20 cm and 21 cm. How long, in centimeters, should the third straw be for Anja to create a right triangle?
Answer: 29cm
Step-by-step explanation:
20^2+21^2=841
Then the square root of 841 is 29
The third straw should be 29cm long in order to form right angles triangles
Application of pythagoras theoremThe theorem states that the square of the hypotenuse is equal to the square of the other two sides
Given the following
adjacent = 20 cm
Opposite side = height = 21cm
Required
Base of the ladder
Use the theorem
c^2 = 20^2 + 21^2
c^2 = 400 + 441
c^2 = 841
c = 29cm
The third straw should be 29cm long in order to form right angles triangles
Learn more on pythagoras theorem here: https://brainly.com/question/343682
30 POINTS HELP ME
A photo of a wooden fence gate is shown. Wooden braces on the gate form a right triangle. The base is labeled twenty-four inches. The hypotenuse is labeled thirty-eight inches. The height is labeled x inches.
Find the value of x in the diagram to the nearest tenth.
Answer:
x is √868, If rounded then its 29.5 inches
Step-by-step explanation:
3. Because h= b/2 we know that b =
Answer:
2 × h
Step-by-step explanation:
h = b ÷ 2 (multiply both sides by 2)
2 × h = b ÷ 2 × 2
2 × h = b
b = 2 × h
Answer:
2h
Step-by-step explanation:
Which equation is true?
9x2 – 25 = (3x - 5)(3x – 5)
9x2 – 25 = (3x – 5)(3x + 5)
9x2 – 25 = -(3x + 5)(3x + 5)
9x2 - 25 = -(3x + 5)(3x - 5)
Answer:
9x2 – 25 = (3x – 5)(3x + 5)
Step-by-step explanation:
(3x – 5)(3x + 5)
= 9x² + 15x - 15x - 25
= 9x² - 25
Final answer:
The correct equation is 9x² – 25 = (3x – 5)(3x + 5), as it is the factored form of the difference of squares, where 9x² is the square of 3x and 25 is the square of 5.
Explanation:
The equation we are considering is 9x² – 25. We need to determine which of the provided options is a true equality. The equation 9x² – 25 is a difference of squares, which factors as (a² – b²) = (a – b)(a + b). In this case, a is 3x and b is 5 because (3x)² = 9x² and 5² = 25.
Thus, the factored form of the equation 9x² – 25 is (3x – 5)(3x + 5). So, the correct equation from the given options is 9x² – 25 = (3x – 5)(3x + 5).
If r = 5 units and x = 8 units, then what is the volume of the cylinder shown above?
A.
200 cubic units
B.
40 cubic units
C.
800 cubic units
D.
130 cubic units
Answer: the answer is 200
Step-by-step explanation:
log798
What is equivalent to it
Answer:
log 19 + log 42
Step-by-step explanation:
798 = 2* 3 *7*19
= 19 * 42
log 798 = log (19*42)
Now log ab = log a + log b
So:
log 798 = log 19 + log 42 <-- is equivalent to log 798.
Answer:
The answer is 2.356
Which of the following is the best solution to | x + 11 | < 17?
Hey there!
| x + 11| < 17
Solving for your ABSOLUTE VALUE
x + 11 < 17 ; x + 11 > -17
Solving solution #1
x + 11 < 17
SUBTRACT by 11 on your sides
x + 11 - 11 < 17 - 11
Cancel out: 11 - 11 because it gives you 0
Keep: 17 - 11 because it helps us compare with x
17 - 11 = 6
Answer #1: x < 6
Solving solution #2
x + 11 > -17
SUBTRACT by 11 on your sides
x + 11 - 11 > -17 - 11
Cancel out: 11 - 11 because it gives you the value of 0
Keep: -17 - 11 because it helps us compare with x
-17 - 11 = -28
Answer #2: x > -28
Overall answer: x < 6 and x > -28
Its an OPEN circle shaded to the left
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
EXPERIMENTAL
FISH
FREQUENCY
EXPERIMENTAL
PROBABILITY
pink salmon
yellowfin tuna
bluegill
Total
11
16
23
50
%
?
100%
0
E to search
Answer:
fish. pink salmon. 50. i like fish btw
Step-by-step explanation:
Experimental probabilities: Pink Salmon 22%, Yellowfin Tuna 32%, Bluegill 46%. Total probability equals 100%.
To find the experimental probability of each type of fish, we first need to calculate the percentage of each type of fish out of the total number of fish caught.
Experimental Probability ($P$) is given by:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \times 100 \][/tex]
Let's calculate:
1. Pink Salmon:
[tex]\[ P(\text{Pink Salmon}) = \frac{11}{50} \times 100\% = \frac{11}{50} \times 100\% = 22\% \][/tex]
2. Yellowfin Tuna:
[tex]\[ P(\text{Yellowfin Tuna}) = \frac{16}{50} \times 100\% = \frac{16}{50} \times 100\% = 32\% \][/tex]
3. Bluegill:
[tex]\[ P(\text{Bluegill}) = \frac{23}{50} \times 100\% = \frac{23}{50} \times 100\% = 46\% \][/tex]
Now, let's check if the total probability sums up to 100%:
[tex]\[ 22\% + 32\% + 46\% = 100\% \][/tex]
Yes, it does.
So, the experimental probability of catching pink salmon is [tex]\(22\%\),[/tex]yellowfin tuna is[tex]\(32\%\)[/tex], and bluegill is [tex]\(46\%\).[/tex]
Complete question;
What is the probability of selecting each type of fish in an experimental study when the total frequency of fish sampled is 50? The types of fish sampled are pink salmon, yellowfin tuna, and bluegill. The frequencies of each fish type are 11, 16, and 23 respectively.
NEED HELP FAST!!!!! The scatterplot represents the total fee for hours renting a bike. The line of best fit for the data is y = 6.855x + 10.215.
A graph shows hours of rental labeled 2 to 6 on the horizontal axis and cost in dollars on the vertical axis. A line increases from 0 to 6.
Which table shows the correct residual values for the data set?
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, 1.22, 1.315, negative 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries 2.12, negative 1.575, negative 1.22, negative 1.315, 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries 2.12, negative 1.575, 1.22, negative 1.315, 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, negative 1.22, 1.315, negative 1.99.
Answer:
I was on a unit test so i couldn't look at the right answer but i believe it was A but i could be wrong
Step-by-step explanation:
The given data and line of best fit (function) of y = 6.855·x + 10.215 give
the table that shows the correct residual values as follows;
[tex]\begin{array}{|c|c|c|c|}x&Given& Residual \\1&14.95&-2.12\\2&25.50&1.575\\3&32&1.22\\4&38.95&1.315\\5&42.5&-1.99\end{array}\right][/tex]
How can the residual values be calculated?The residual values = Actual value - Predicted value
The given table is resented as follows;
[tex]\begin{array}{|c|c|c|c|}x&Given&Predicted = 6.855 \times x + 10.215& Residual = Actual - Predicted\\1&14.95&17.07&-2.12\\2&25.50&23.925&1.575\\3&32&30.78&1.22\\4&38.95&37.635&1.315\\5&42.5&44.49&-1.99\end{array}\right][/tex]
From the above completed table, the correct option is therefore;
[tex]\begin{array}{|c|c|c|c|}x&Given& Residual \\1&14.95&-2.12\\2&25.50&1.575\\3&32&1.22\\4&38.95&1.315\\5&42.5&-1.99\end{array}\right][/tex]Learn more about the line of best fit here:
https://brainly.com/question/2142404
67/5 as a fraction in simplest form
Answer:
[tex] = 13 \frac{2}{5} [/tex]
Step-by-step explanation:
[tex] \: \: \: \: \: \: 13\\ 5 \sqrt{67} \\ \frac{ \: \: - 65}{ \: \: \: \: \: 02} \\ \\ \\ = 13 \frac{2}{5} [/tex]
Claire can eat 3/4 of a pizza every 5 minutes. How much of a pizza can she eat in 1 minute?
Answer:
3/20 of the pizza
Step-by-step explanation:
To find how much she eats in one minute, you have to change the fraction into a decimal, which is 0.75, and divide that by 5. Once you've done that, you get 0.15 of the pizza in a minute. this can be simplified into the fraction 3/20.
Answer:
3/20
Step-by-step explanation:
If she can do 3/4 per 5 minutes, the amount in 1 minute is 1 fifth of 3/4, so multiply 3/4 by 1/5 to get 3/20.
What are the outliers of 42,43,46,48,57,60,96,59,38,68,29
Answer:
The outlier is of all those number is 96 and 29
Please help i will mark as brainliest
Answer:
162 mL
Step-by-step explanation:
1.Convert all volumes to millilitres
(a) Chlorpheniramine
V = 100 mL
(b) Lidocaine
V = \text{2 oz} \times \dfrac{\text{29.57 mL}}{\text{1 oz}} = \text{ 59.14 mL)
(c) Banana flavouring
V = \dfrac{1}{2}\text{ tsp} \times \dfrac{\text{4.93 mL}}{\text{1 tsp}} = \textbf{2.46 mL} }
2.Calculate the total volume
Chlorpheniramine = 100 mL
Lidocaine = 59.14
Banana flavouring = 2.46
TOTAL = 162 mL