Answer:
sin 25
Step-by-step explanation:
sin(A − B) = sinA cosB − cosA sinB
sin 155
sin( 180 -25)
A = 180 B = 25
sin180 cos25 − cos180 sin25
Sin 180 = 0
cos 180 = -1
0 - (-1) sin 25
sin 25
I will Give brainliest to who ever can show me how to solve this killer!!!!!!! Using Descartes Rule and the rational zeros of polynomial equation, find the root (positive, negative and imaginary) of x^5-2x^4+x^3+x^2-2x+1=0
see if other people has already answered this question
Answer:
-1
1
1/2(1±i√3)
Step-by-step explanation:
x^5-2x^4+x^3+x^2-2x+1=0x^3(x^2-2x+1)+(x^2-2x+1)=0(x^3+1)(x-1)^2=0(x+1)(x^2-x+1)(x-1)^2=01. x+1=0 ⇒ x= -1
2. x-1= 0 ⇒ x= 1
3. x^2-x+1=0
x^2- 2*1/2x+1/4= -3/4(x-1/2)^2= -3/4x-1/2= ±√-3/4 ⇒ x-1/2=±i√3/2 ⇒ x= 1/2 ± i√3/2= 1/2(1± i√3)Which are not changed after a rotation? Check all that apply. angle measures orientation size shape position of center of rotation
Answer:
1 3 4 5
Step-by-step explanation:
The rotation does not change the angle measure, the side lengths and the shape of the shape that is being rotated.
What is an angle?
An angle measure the size, the shape, and the position of center of rotation do not change after rotation.
Which are not changed after rotation?
If one thing is rotated then it will not change the angle measures, the side lengths and shape of the body. The rotation does not change the center of object.
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The (T) total number of dollars in (1) five-dollar bills and (t) ten-dollar bills is:
Multiple choice
T=5+f+10+t
Answer:
Step-by-step explanation:
7.22. (a) A fair coin is tossed 100 times. Estimate the probability that the number of heads is between 40 and 60. Estimate the probability that the number is between 50 and 55.
Answer:
the probability that the number of heads is between 40 and 60 is 0.9535
the probability that the number of heads is between 50 and 55 is 0.3557
Step-by-step explanation:
From the given information:
A fair coin is tossed 100 times.
Let consider n to be the number of time the coin is tossed, So n = 100 times
In a fair toss of a coin; the probability of getting a head P(Head) = 1/2 = 0.5
If we assume X to be the random variable which follows a binomial distribution of n and p; therefore , the mean and the standard deviation can be calculated as follows:
Mean μ = n × p
Mean μ = 100 × 1/2
Mean μ = 100 × 0.5
Mean μ = 50
Standard deviation σ = [tex]\sqrt{n \times p \times (1-p)}[/tex]
Standard deviation σ = [tex]\sqrt{100 \times 0.5 \times (1-0.5)}[/tex]
Standard deviation σ = [tex]\sqrt{50 \times (0.5)}[/tex]
Standard deviation σ = [tex]\sqrt{25}[/tex]
Standard deviation σ = 5
Now, we've made it easier now to estimate the probability that the number of heads is between 40 and 60 and the probability that the number is between 50 and 55.
To start with the probability that the number of heads is between 40 and 60 ; we have:
P(40 < X < 60) = P(X < 60)- P(X < 40)
Applying the central limit theorem , for X is 40 which lies around 39.5 and 40.5 and X is 60 which is around 59.5 and 60.5 but the inequality signifies less than sign ;
Then
P(40 < X < 60) = P(X < 59.5) - P(X < 39.5)
[tex]P(40 < X < 60) = P( \dfrac{X - \mu}{\sigma}< \dfrac{59.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{39.5 - 50 }{5})[/tex]
[tex]P(40 < X < 60) = P( Z < \dfrac{9.5 }{5}) - P( Z< \dfrac{-10.5 }{5})[/tex]
[tex]P(40 < X < 60) = P( Z <1.9}) - P( Z< -2.1)[/tex]
[tex]P(40 < X < 60) =0.9713 -0.0178[/tex]
[tex]P(40 < X < 60) =0.9535[/tex]
Therefore; the probability that the number of heads is between 40 and 60 is 0.9535
To estimate the probability that the number is between 50 and 55.
P(50 < X < 55) = P(X < 55)- P(X < 50)
Applying the central limit theorem , for X is 50 which lies around 49.5 and 50.5 and X is 55 which is around 54.5 and 55.5 but the inequality signifies less than sign ;
Then
P(50 < X < 55) = P(X < 54.5) - P(X < 49.5)
[tex]P(50 < X < 55) = P( \dfrac{X - \mu}{\sigma}< \dfrac{54.5 - 50 }{5}) - P( \dfrac{X - \mu}{\sigma}< \dfrac{49.5 - 50 }{5})[/tex]
[tex]P(50 < X < 55) = P( Z < \dfrac{4.5 }{5}) - P( Z< \dfrac{-0.5 }{5})[/tex]
[tex]P(50 < X < 55) = P( Z <0.9}) - P( Z< -0.1)[/tex]
[tex]P(50 < X < 55) =0.8159 -0.4602[/tex]
[tex]P(50 < X < 55) =0.3557[/tex]
Therefore; the probability that the number of heads is between 50 and 55 is 0.3557
Ali and Jake went on a cross-country
trip. They took a train part of the way,
and took a bus the rest of the way. They
traveled a total of 1200 kilometers,
riding on the train 270 more kilometers
than on the bus.
Let x = kilometers traveled by bus. Let
y = kilometers traveled by train.
WILL NAME BRANLIST OR WHATEVER
Answer:
x = 465 km
y = 735 km
Step-by-step explanation:
Step 1: Write out equations
x + y = 1200
y = x + 270
Step 2: Find x using substitution
x + (x + 270) = 1200
2x + 270 = 1200
2x = 930
x = 465
Step 3: Plug in x to find y
y = 465 + 270
y = 735
Answer:
They traveled 780
Step-by-step explanation:
Got it right on the test
find the Pythagorean triplets of 5
Answer:
The Pythagorean Triplet that has 5 is 3-4-5
Step-by-step explanation:
We can prove this using Pythagorean Theorem: a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
25 = 25
Need help solving for x
Answer:
9.2
Step-by-step explanation:
The given triangle is a right angled triangle. To solve for any of the side length of such triangle, apply the trigonometry ratio formula which can easily be remembered as SOHCAHTOA.
SOH is Sin θ = opposite/hypothenuse,
CAH is Cos θ = Adjacent/hypotenuse
TOA is Tan θ = Opposite/adjacent
Thus, in the right triangle given, we have:
θ = 38°
Opposite side to the given angle = x
Hypotenuse = 15
We're going to use, sin θ = opposite/hypotenuse
Sin(38) = x/15
Multiply both sides by 15 to solve for x
15*sin(38) = x
15*0.616 = x
9.24 = x
x ≈ 9.2 (to nearest tenth)
Find the lateral surface area, base area of a cylinder with radius 5 cm and height 16 cm
Answer:
Lateral surface area is
≈
502.65cm²
Base area is
=
πr^2
We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measured in feet, after t seconds is h ( t ) = − 16 t 2 + 128 t + 320 . What is the highest altitude that the object reaches?
Answer:
The highest altitude that the object reaches is 576 feet.
Step-by-step explanation:
The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be [tex]h(t) = -16\cdot t^{2} + 128\cdot t + 320[/tex], the first and second derivatives are, respectively:
First Derivative
[tex]h'(t) = -32\cdot t +128[/tex]
Second Derivative
[tex]h''(t) = -32[/tex]
Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:
[tex]-32\cdot t +128 = 0[/tex]
[tex]t = \frac{128}{32}\,s[/tex]
[tex]t = 4\,s[/tex] (Critical value)
The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:
[tex]h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320[/tex]
[tex]h(4\,s) = 576\,ft[/tex]
The highest altitude that the object reaches is 576 feet.
Find all possible values of k so that x^2 + kx - 32 can be factored.
Answer:
Step-by-step explanation:
The posssible factors are
x^2 + 4x - 32
(x+8)(x-4)
x^2+ 14x - 32
(x+16)(x-2)
(x+32)(x-1)
x^2+31x-32
The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection
Answer:
[tex]\frac{1}{13}[/tex]
Step-by-step explanation:
The probability P(A) that an event A will occur is given by;
P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]
From the question,
=>The event A is selecting a king the second time from a 52-card deck.
=> In the card deck, there are 4 king cards. After the first selection which was a king, the king was returned. This makes the number of king cards return back to 4. Therefore,
number-of-possible-outcomes-of-event-A = 4
=> Since there are 52 cards in total,
total-number-of-sample-space = 52
Substitute these values into equation above;
P(Selecting a king the second time) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
9. A line passes through (2, –1) and (8, 4). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers.
Answer:
Step-by-step explanation:
(4+1)/(8-2)= 5/6
y + 1 = 5/6(x - 2)
y + 1 = 5/6x - 5/3
y + 3/3 = 5/6x - 5/3
y = 5/6x - 8/3
6(y = 5/6x - 8/3)
6y = 5x - 16
-5x + 6y = -16
which of the following statements is false?
Answer:
A.
Step-by-step explanation:
It's the first one. The angles are supplementary not complementary.
Answer:
I would have to say A
Step-by-step explanation:
The average of 12 numbers is 24. The average of 24 numbers is 12. What is the average of all 36 numbers?
Answer:
16
Step-by-step explanation:
The sum of the 12 numbers is 12 * 24 = 288 and the sum of the 24 numbers is 24 * 12 = 288 so the sum of the 36 numbers is 288 + 288 = 576 which means the average is 576 / 36 = 16.
Find the slope on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer:
Step-by-step explanation:
(-2,2) (2,-4)
(-4-2)/(2+2)= -6/4= -3/2 is the slope of the graph
The following lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men. Has Lung Disease/smoker 0.1, No Lung Disease/Smoker 0.17, Lung Disease/Nonsmoker 0.03, No Lung Disease/Nonsmoker 0.7. One 60-to-65 year old man is selected at random. What is the probability of the following event: He has lung disease given that he does not smoke?
Answer:
4.11% probability that he has lung disease given that he does not smoke
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Does not smoke
Event B: Lung disease
Lung Disease/Nonsmoker 0.03
This means that [tex]P(A \cap B) = 0.03[/tex]
Lung Disease/Nonsmoker 0.03
No Lung Disease/Nonsmoker 0.7
This means that [tex]P(A) = 0.03 + 0.7 = 0.73[/tex]
What is the probability of the following event: He has lung disease given that he does not smoke?
[tex]P(B|A) = \frac{0.03}{0.73} = 0.0411[/tex]
4.11% probability that he has lung disease given that he does not smoke
Probabilities are used to determine the chances of an event.
The probability that he has lung disease given that he does not smoke is 0.231
The required probability is calculated as:
[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]
From the question, we have:
[tex]\mathbf{P(Lung\ Disease\ and\ Non\ Smoker) = 0.03}[/tex]
[tex]\mathbf{P(Lung\ Disease) = P(Has Lung Disease/smoker) + P(Lung Disease/Nonsmoker)}[/tex]
[tex]\mathbf{P(Lung\ Disease) = 0.1 + 0.03}[/tex]
[tex]\mathbf{P(Lung\ Disease) = 0.13}[/tex]
So, we have:
[tex]\mathbf{P = \frac{P(Lung\ Disease\ and\ Non\ Smoker)}{P(Lung\ Disease)}}[/tex]
[tex]\mathbf{P = \frac{0.03}{0.13}}[/tex]
[tex]\mathbf{P = 0.231}[/tex]
Hence, the probability that he has lung disease given that he does not smoke is 0.231
Read more about probabilities at:
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Please please please do not answer if you are not 100% sure!
Answer:
B
Step-by-step explanation:
It can be figured out by using graph transformations.
When when subtracting directly next to x, it shifts the graph to the left while doing the opposite when adding. Since the graph is to the left, we know it has to be A or B since those are subtracting by 5
Outside of the absolute value, when subtracting, it makes the graph move down. That means we are looking for a -4 which is found in B
20x=60y What is x in terms of y? (Hope this isn't illogical)
Answer:
x=3y
Step-by-step explanation:
divide both sides by 20
20x = 60y
------ -------
20 20
x=3y
Answer:
x = 3y
Step-by-step explanation:
20x = 60y
Divide 20 into both sides.
20x/20 = 60y/20
1x = 6/2y
x = 3y
11. If 4 < x < 14, what is the range for -x - 4?
Answer:
-18 < -x-4 < -8
Step-by-step explanation:
We start with the initial range as:
4 < x < 14
we multiplicate the inequation by -1, as:
-4 > -x > -14
if we multiply by a negative number, we need to change the symbols < to >.
Then, we sum the number -4, as:
-4-4> -x-4 > -14-4
-8 > -x-4 > -18
Finally, the range for -x-4 is:
-18 < -x-4 < -8
The shape in the figure is constructed from several identical squares. If the side of each square is 1 unit, what is the area and the perimeter of the shape?
Answer:
Area: 7 units²
Perimeter: 14 units
Step-by-step explanation:
Area of each square:
1 unit × 1 unit = 1 unit²
There are 7 squares:
1 unit² × 7 (squares) = 7 units²
The area of the shape is 7 units².
The perimeter of the shape is the length of the outer sides.
1 + 1 + 1 + 1/2 + 1/2 + 1 + 1 + 1/2 + 1 + 1/2 + 1 + 1 + 1 + 1 + 1 + 1 = 14 units
What are the x-intercepts of the function y = x2 – x – 120?
Answer:
(1+√481/2,0),(1−√481/2,0)
Step-by-step explanation:
You find this by substituting 0 for y and then solving.
Answer:
(1+√481/2,0),(1−√481/2,0)
Step-by-step explanation:
A student scores 74 on a geography test and 273 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 5 mathematics test has a mean of 300 and a standard deviation of 18. If the data for both tests are normally distributed, on which test did the stu score better relative to the other students in each class? A. The student scored better on the geography test. B. The student scored the same on both tests.C. The student scored better on the mathematics test
Answer:
A. The student scored better on the geography test.
Step-by-step explanation:
The z-score for a normal distribution, for any value X, is given by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Where is μ the mean score, and σ is the standard deviation.
For the Geography test:
X = 74
μ = 80
σ = 5
[tex]z_g=\frac{74-80}{5}\\ z_g=-1.2[/tex]
For the Mathematics test:
X = 273
μ = 300
σ = 18
[tex]z_m=\frac{273-300}{18}\\ z_m=-1.5[/tex]
The z-score for the Geography test is higher than the score for the Mathematics test, which means that the student had a better relative score in the Geography test.
The answer is A. The student scored better on the geography test.
Product A is 8oz bottle of cough medication that sells for 1.36 Product B is a 16 oz bottle of cough medication that cost 3.20 which product has the lower unit
Answer:
Product A is the cheapest unit price.
Step-by-step explanation:
Since we have given that
Weight of a Product A = 8 oz
Cost at which it is sold = $1.36
Cost per unit for Product A will be
1.38/8= $0.17
Weight of a Product B = 16 oz
Cost at which it is sold = $3.20
Cost per unit for Product B will be
So, we can see that the unit price of "Product A" is lower than the unit price of product B .
Hence, Product A has the cheapest unit price.
Find the pattern and fill in the missing numbers: 1, 1, 2, 3, 5, 8, __, __, 34, 55
Answer:
13, 21
Step-by-step explanation:
Fibonacci sequence-
Each number is added to the number before it.
1+1=2
2+1=3
3+2=5
5+3=8
Answer:
The missing numbers are 13, and 21.
The pattern given is the Fibonacci Sequence, where each number is the sum of the two numbers before it, starting with 0 and 1. (i.e. 5 is 2+3)
The sports bar owner runs a regression to test whether there is a relationship between Red Sox away games and daily revenue. Which of the following statements about the regression output is true?A. The average daily revenue for days when the Red Sox do not play away is $1,768.32.B. The average daily revenue for days when the Red Sox play away is $1,768.32.C. The average daily revenue for days when the Red Sox play away is $2,264.57.D. The average daily revenue for days when the Red Sox do not play away is $1,272.07.E. On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.4746
R Square 0.2252
Adusted R square 0.2091
Standard Error 466.32
Observations 50
ANOVA
Significance F MS df 0.0005 13.95 3.03E 06 3.03E+06 Regression 1.04E+07 2.17E+05 48 Residual 135E+07 49 Total Lower 95% Upper 95% tStot Standard Error P-vatue Coefficients 1968.21 17.79 1,568.42 99 42 0.0000 1768.32 Intercept Red Sox away game 763.38 00005 3.74 229.13 132.85 (1-yes, 0-no) 496.25 The average daily revenue for days when the Red Sox do not play away is $1,768.32
Answer:
Options A, C and D are true.
- The average daily revenue for days when the Red Sox do not play away is $1,768.32.
- The average daily revenue for days when the Red Sox play away is $2,264.57.
- On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.
Step-by-step explanation:
The complete Question is presented in the attached image to this solution.
Analyzing the options at a time
A) The average daily revenue for days when the Red Sox do not play away is $1,768.32.
This option is true as 1768.32 is the intercept which is the average daily revenue when the Red Sox=0, that is, 0=no, when red sox do not play away.
B) The average daily revenue for days when the Red Sox play away is $1,768.32.
This is false because when the Red Sox play away, the value is 1 and the average revenue = 1768.32 + 496.25 = $2,264.57
C) The average daily revenue for days when the Red Sox play away is $2,264.57.
This is true. I just gave the explanation under option B.
D) The average daily revenue for days when the Red Sox do not play away is $1,272.07.
This is false. The explanation is under option A.
E) On average, the bar’s revenue is $496.25 higher on days when the Red Sox play away than on days when they do not.
This is true. It is evident from the table that the 0 and 1 coefficient is 496.25. This expresses the difference in average daily revenue when the Red Sox games are played away and when they are not.
Hope this Helps!!!
If AB= X and x=4, then the transitive property states
Answer:
AB=4
Step-by-step explanation:
The transitive property states if A=B and B+C than A+C Next substitute
AB=x and x=4 so AB=4
Hope this helps, if it did, please give me brainliest, it helps me a lot. :)
Have a good day!
An exercise teacher wants each student in her class to have at least 48 square feet of space on the floor. What is the largest number of students she will allow in a classroom with a student exercise area of this size? A. 20 students B. 24 students C. 40 students D. 50 students
Answer:
D. 50 students
Step-by-step explanation:
First we find the area of the classroom which is worked out below and it is the shape of a rectangle;
Area of a rectangle = Length * Breadth
= 60 ft * 40 ft
= 2400 ft²
Now to find the number of students that she will allow in the classroom, we have to divide the area of the classroom which is 2400 ft²by the amount of space allocated to each student which will be;
= [tex]\frac{2400}{48}[/tex]
= 50
This means she will allow 50 students into her class.
Answer:
50
Step-by-step explanation:
Consider the following sample information from Population A and Population B. Sample A Sample B n 24 16 s2 32 38 We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals a. .84. b. .67. c. 1.50. d. 1.19.
Answer:
Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]
And the best option would be:
d. 1.19.
Step-by-step explanation:
Data given and notation
[tex]n_1 = 24 [/tex] represent the sampe size 1
[tex]n_2 =16[/tex] represent the sample size 2
[tex]s^2_1 = 32[/tex] represent the sample variance for 1
[tex]s^2_2 = 38[/tex] represent the sample variance for 2
The statistic for this case is given by:
[tex]F=\frac{s^2_1}{s^2_2}[/tex]
Hypothesis to verify
We want to test if the true deviations are equal, so the system of hypothesis are:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]
And the best option would be:
d. 1.19.
Weite the number names
31,19,624
4,06,85,012
6,500,000
25,430,756
Answer:
Thirty-one million, six hundred and twenty-four
Four billion, six million, eighty-five thousand, and twelve
six million five hundred thousad
twenty-five million, four hundred and thirty thousand and seven hundred and fifty-six
Step-by-step explanation:
Mia had $22 . Then she started to receive $4 a week as an allowance. She plans to save all of her money for a bicycle and draws a graph of her planned savings. Mia lets x represent the number of weeks she has received her allowance, and y represent her total amount of money. Which of the following ordered pairs is on Mia's graph? ANSWER CHOICES: (2,44) (5,42) (6,24) (1,22)
Answer: (5, 42)
Step-by-step explanation:
22 + 4x= 42
if we test the options we will see this is the only one that works
42 - 22 = 20
4x = 20
x= 5
which is equal to X the number of weeks they have gotten the allowance.