Answer:
[tex](C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]
Step-by-step explanation:
The reference angle is the angle that the given angle makes with the x-axis.
For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.
From the given options:
[tex](A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]
We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.
Answer:
C
Step-by-step explanation:
Which number line shows the solution set for StartAbsoluteValue 2 p minus 4 EndAbsoluteValue greater-than-or-equal-to 6?
Answer:
B on edge 2022
Step-by-step explanation:
How do I write an equation represented by the line?
Answer:
This line can be represented by the line y = 3/4x + 2.
Step-by-step explanation:
The slope is identified as the m in y = mx + b. The slope is the rise/run of your line (AKA how many units it goes upwards/downwards and then goes to the right/left to meet the second given point).
In this case, the line rises 3 units from 2 to 5, and then goes to the right by 4 units to meet the coordinate (4, 5).
B in the equation refers to the y-intercept, or where the line intersects/crosses the y-axis. In this case, it is the coordinate (0, 2).
Finally, x is irrelevant and is placed in the equation for no reason (at least that I am aware of in my several years of high school math).
Therefore, your final equation is y = 3/4x + 2.
Please answer this math quesiton im desperate !! tysm!! will give brainliest!!
Answer: i am pretty sure it is C dont get your hopes up but
Step-by-step explanation:
from what i see if you take the y=3 over 2 and make that a decimal you can now take y = that number and make a line and so on then after that step you want to now take your final answer which is x and subtract it by 3 i MIGHT be wrong but i tried.
Answer:
The Answer is C I hope this helped
Step-by-step explanation:
I did it on my quiz!
Find the value of x that makes A || B.
Answer:
x = 20
Step-by-step explanation:
3x - 10 = x + 30
2x = 40
x = 20
(-36)1/2= -6 1/6
a.-6
b.1/2
c.no real numbers
Answer:
c
Step-by-step explanation:
the length of a rectangular park excerdees its width of 17m if the perimeter of the park find the dimension of the park
Answer:
math papa look on that website
Step-by-step explanation:
the line of symmetry for the quadratic equation y=ax^2+8x-3 is x=4. What is the value of “a”?
Answer:
The value of a is -1.
Step-by-step explanation:
The line of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
For a quadratic function in standard form, [tex]y=ax^2+bx+c[/tex], the line of symmetry is a vertical line given by [tex]x=-\frac{b}{2a}[/tex].
We know that the quadratic equation, [tex]y=ax^2+8x-3[/tex], has x = 4 as line of symmetry. Therefore, the value of a is:
[tex]4=-\frac{8}{2a}\\\\4=-\frac{4}{a}\\\\4a=-4\\\\a=-1[/tex]
Answer:
a=-1
Step-by-step explanation:
so that the other person could get brainliest
(WITH IMAGE) What is the value of m?
Answer:
10
Step-by-step explanation:
The two marked angles are a linear pair, so have a sum of 180°.
(2m +10) +(5m +100) = 180
7m +110 = 180 . . . . . . . collect terms
7m = 70 . . . . . . . . . . . . subtract 110
m = 10 . . . . . . . . . . . . . divide by 7
TDaP is a booster shot that prevents Diphtheria, Tetanus, and Pertussis in adults and adolescents. It should be administered every 8 years for it to remain effective. A random sample of 550 people living in a town that experienced a pertussis outbreak this year were divided into two groups. Group 1 was made up of 145 individuals who had not had the TDaP booster in the past 8 years, and Group 2 consisted of 355 individuals who had. In Group 1, 18 individuals caught pertussis during the outbreak, and in Group 2, 13 individuals caught pertussis. Is there evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were? Test at the 0.05 level of significance. Enter the p-value - round to 5 decimal places.
Answer:
Yes. There is enough evidence to support the claim that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.
P-value = 0.00013.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
The significance level is 0.05.
The sample 1 (Group 1), of size n1=145 has a proportion of p1=0.124.
[tex]p_1=X_1/n_1=18/145=0.124[/tex]
The sample 2 (Group 2), of size n2=355 has a proportion of p2=0.037.
[tex]p_2=X_2/n_2=13/355=0.037[/tex]
The difference between proportions is (p1-p2)=0.088.
[tex]p_d=p_1-p_2=0.124-0.037=0.088[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{18+13.135}{145+355}=\dfrac{31}{500}=0.062[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.062*0.938}{145}+\dfrac{0.062*0.938}{355}}\\\\\\s_{p1-p2}=\sqrt{0+0}=\sqrt{0.001}=0.024[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.088-0}{0.024}=\dfrac{0.088}{0.024}=3.68[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=P(z>3.68)=0.00013[/tex]
As the P-value (0.00013) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.
At a Psychology final exam, the scores are normally distributed with a mean 73 points and a standard deviation of 10.6 points. The lower 5% of the class will not get a passing grade. Find the score that separates the lower 5% of the class from the rest of the class. 58.0 56.6 55.6 57.2
Answer:
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 73, \sigma = 10.6[/tex]
Find the score that separates the lower 5% of the class from the rest of the class.
This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 73}{10.6}[/tex]
[tex]X - 73 = -1.645*10.6[/tex]
[tex]X = 55.6[/tex]
The score that separates the lower 5% of the class from the rest of the class is 55.6.
The width of the pond shown is x ft. What is the value of x.
Answer:
Width (x) = 160ft
See explanation below
Step-by-step explanation:
The information given is incomplete as we are not told if the shape of the pond. This is about determining the surface area of a water body.
Looking at the question, we can tell we are to find the width of a pond whose shape wasn't given.
Assuming the shape of the pond is either a rectangular or square pond, let's consider the following question:
The acreage of a rectangular pond is 1.54 acres and the length is 420ft. The width of the pond shown is x ft. What is the value of x.
Find attached the diagram used for solving the question.
Formula for calculating the acreage of
a Square or Rectangular Ponds is multiplying average length (in feet) times average width (in feet) and dividing the result by 43,560 to derive our answer in acres.
That is: Average Length (ft) × Average Width (ft) ÷ 43,560 = Acres
Since we have been given acreage and length, we would make width subject of formula.
Width = (Acreage × 43500)/length
Width (x) = (1.54 × 43,560)/420
=67082.4 ÷ 420 = 159.72
Width (x) = 160ft (nearest feet)
The point (-1,4) is on the terminal side of angle theta in standard position. What are the values of sine, cosine, tangent of theta
Answer:
cosФ = 0.97
sinФ = 0.292
tanФ = -4
Step-by-step explanation:
A general point P(x,y) with an angle Ф has the following trigonometrical functions:
[tex]sin\phi=\frac{y}{r}\\\\cos\phi=\frac{x}{r}\\\\tan\phi=\frac{y}{x}\\\\r=\sqrt{(x)^2+(y)^2}[/tex]
For the point P(-1 , 4) you obtain:
[tex]r=\sqrt{(-1)^2+(4)^2}=\sqrt{17}\approx 4.123[/tex]
[tex]sin\phi=\frac{4}{4.123}=0.97\\\\cos\phi=\frac{-1}{4.123}=0.242\\\\tan\phi=\frac{4}{-1}=-4[/tex]
The owner of a rental company rents bicycles and tricycles and keeps inventory by counting seats and wheels. One day, he counts 25 seats and 60 wheels. The equation representing the total number of seats is b + t = 25, where b is the number of bicycles and t is the number of tricycles. Which equation represents the number of wheels?
Answer:
2b + 3t = 60
Step-by-step explanation:
2b is the number of wheels on a bicycle
3t is the number of wheels on a tricycle
and 60 is the total number of wheels
Find the number of unique permutations of the letters in the word: ONGOING
Answer:
The Number of unique permutation is 6,615Step-by-step explanation:
This particular permutation deals with words that have repeated letters.
Given word = "ONGOING"
the formula for the permutation is
[tex]= \frac{n!}{mA! mB!.....mZ!}[/tex]
where n is the amount of letters in the word, and m A , m B , ... , m Z are the occurrences of repeated letters in the word. Each m equals the amount of times the letter appears in the word.
So in the word "ONGOING"
n= 7
mO= 2
mN= 2
mG=2
[tex]permutations = \frac{7!}{2!2!2!} \\\\permutations= \frac{7*6*5*4*3*2*1}{(2*1)*(2*1)*(2*1)}[/tex]
[tex]permutations= \frac{52920}{8} \\permutation = 6,615[/tex]
pleaseee answer this exponentt! 4ba^-4
Answer:
the answer would be (4b)/(a^4)
Step-by-step explanation:
An artist bought 5 yards of rope. Which of the following is equivalent to 5 yards?
A. 3 feet
B. 15 feet
C. 60 feet
D. 180 feet
The 5 yards rope of the artist is equivalent to 15 feet of the rope and the option B is correct.
Given information:
An artist bought 5 yards of rope.
We know that one yard is equal to 3 feet.
So, here it is required to find the equivalent of 5 yards in the form of feet.
The value of 5 yards in the form of feet can be calculated as,
[tex]5\times 3=15\rm\;feet[/tex]
Therefore, the 5 yards rope of the artist is equivalent to 15 feet of the rope and the option B is correct.
For more details, refer to the link:
https://brainly.com/question/22316471
Suppose you want to have $400,000 for retirement in 30 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
Answer:
if he wants to have $400000 on gis bank in 30 years at 4 %rate then he needs to deposit $15151.5 per month
A restaurant uses 4/5 ounce of gravy for each serving of meat loaf. If 45 people
ordered meat loaf, how much gravy will the restaurant need?
ounces
Answer:
36
Step-by-step explanation:
Hope this helps and please rate brainliest!!!
Answer:
36 ounces
Step-by-step explanation:
We want to find the total amount of gravy the restaurant will need.
Multiply the gravy needed for one serving by the number of servings.
gravy for one serving × number of servings.
The restaurant uses 4/5 of an ounce for each serving, and 45 people ordered meatloaf. Therefore, the gravy for one serving is 4/5, and the number of servings is 45.
4/5 × 45
45 is equivalent to 45/1.
4/5 × 45/1
Multiply across the numerator (the top numbers: 4 and 45) and denominator (the bottoms numbers: 5 and 1)
(4× 45)/(5× 1)
180/5
Divide
36
Add appropriate units. In this case, the units are ounces.
36 ounces
The restaurant needs 36 ounces of gravy for 45 servings of meatloaf.
10. How many different combinations are there of the digits 46987?
25.
Look at this:
There are 5 digits in 46987.
There will be 5 combinations.
5 times 5 = 25.
You have your answer.
A total of 31 possible combinations are there for number 46987.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 5 - digit number 46987.
Assume that there are [y] possible combinations. For a [x] digit number, the total possible combinations are -
y = 2ˣ - 1
So, for [x] = 5, we will have -
y = 32 - 1
y = 31
Therefore, a total of 31 possible combinations are there for number 46987.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ2
What us the slope of the points, (0,20) and, (4,0)?
Answer:
-5
Step-by-step explanation:
The equation to find the slope between two points is y₂-y₁/x₂-x₁.
In this case that would be 0-20/4-0 which simplifies into -20/4=-5
So your slope is -5
Answer:
-5Solution,
Let the points be A and B
A(0,20)---------> (X1,y1)
B(4,0)------------>(x2,y2)
Now,
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: \: \: \: = \frac{0 - 20}{4 - 0} \\ \: \: \: \: \: = \frac{ - 20}{4} \\ \: \: \: \: = - 5[/tex]
hope this helps...
Good luck on your assignment....
Jenny had 188 but she is spending 14 per week
Answer:
14×7=98
188-98=90 so she had 90 left
The three sides of a right-angled triangle are x, x+1 and 5. Find x and the area, if the longest side is 5.
Answer:
x = 3
area = 6
Step-by-step explanation:
using phytagoras's. theorem
a² + b² = c² (with c is the longest one)
x² + (x+1)² = 5²
x² + x² + 2x + 1 = 25
2x² + 2x - 24 = 0 (divide all by 2)
x² + x -12 = 0 then factorize
(x-3)(x+4) = 0
we get x = 3 and x = -4. Take the positive one.
so now we have x = 3 then x + 1 must be 4.
the area is
A = ½ . 3 . 4 = 6
In a recent survey of 200 elementary students, many revealed they preferred math than English. Suppose that 80 of the students surveyed were girls and that 120 of them were boys. In the survey, 60 of the girls, and 80 of the boys said that they preferred math more.
Required:
a. Calculate an 80% confidence interval for the difference in proportions.
b. What is the standard error of the difference in the probability between that girls prefer math more and boys prefer math more?
1. 0.4097
2. 0.0042
3. 0.0833
4. 0.0647734
c. What is the difference in the probability between that girls prefer math more and boys prefer math more?
1. 0.0833
2. 0.5
3. 0.0042
4. 0.4097
Answer:
Step-by-step explanation:
a) Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the girls,
x = 60
n1 = 80
p1 = 60/80 = 0.75
For the boys
x = 80
n2 = 120
p2 = 80/120 = 0.67
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.8 = 0.2
α/2 = 0.2/2 = 0.1
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.1 = 0.9
The z score corresponding to the area on the z table is 1.282. Thus, z score for confidence level of 80% is 1.282
Margin of error = 1.282 × √[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]
= 1.282 × √0.00418625
= 0.081
Confidence interval = 0.75 - 0.67 ± 0.081
= 0.08 ± 0.081
b) The formula for determining the standard error of the distribution of differences in sample proportions is expressed as
Standard error = √{(p1 - p2)/[(p1(1 - p1)/n1) + p2(1 - p2)/n2}
Therefore,
Standard error = √{(0.
75 - 0.67)/[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]
Standard error = √0.08/0.00418625
Standard error = 4.37
c) the difference in the probability between that girls prefer math more and boys prefer math more is
0.75 - 0.67 = 0.08
Can someone help?
Find the mean of the data in the bar chart below.
Answer:
b
Step-by-step explanation:
Answer:
2.5
Round this up to 3
Step-by-step explanation:
Add all the numbers of the graph together
1+4+3+2 = 10
Divide by 4 because it has 4 categories in total
= 2.5
Round up because its asking for puppets and theres not 1/2 of a puppet.
Find the perimeter. Use 3.14 for pi. Round to the nearest tenth.
58 cm
O 22 cm
O 72 cm
O 44 cm
Answer:
22cm
See explanation below
Step by step explanation:
The question is incomplete without the diagram of the shape or its dimensions.
From the question, we are to determine the perimeter of the circle.
Let's consider the following question by determining the perimeter of a circle. If diameter is 7cm. Use pi as 3.14.
Perimeter of circle = circumference of circle
circumference of circle = 2πr
Radius = diameter/2 = (7/2)cm
circumference of circle = 2πr
= 2×π×(7/2) = (14/2)×3.14
= 7×3.14
=21.98cm
circumference of circle = 22cm (nearest tenth)
Perimeter of circle = 22cm
Which equation below represents the inverse function T(c)
Answer:
the answer is A
Step-by-step explanation:
Answer:
Correct answer is A
Step-by-step explanation:
Hope this helps you
In a particular month, Ezhil spent one-fifth of her salary on shopping. Two-fifth of the remaining she gave to her sister. If she has Rs 11 , 040 left, what was her salary in that month?
Answer:
[tex]Salary = Rs23000[/tex]
Step-by-step explanation:
Given
[tex]Shopping = \frac{1}{5}[/tex]
[tex]Sister = \frac{2}{5}R[/tex]
[tex]Left over = Rs11,040[/tex]
Required
Her salary in that month
Given that she spent [tex]\frac{1}{5}[/tex] of her salary on shopping, this implies that she has [tex]\frac{4}{5}[/tex] of her salary left
From what's left, she gave her sister [tex]\frac{2}{5}[/tex]
This means she gave her sister [tex]\frac{2}{5} * \frac{4}{5}[/tex]
Sister = [tex]\frac{8}{25}[/tex]
Calculating a fraction of what's left
[tex]Left over = 1 -Shopping - Sister[/tex]
[tex]Left over = 1 - \frac{1}{5}- \frac{8}{25}[/tex]
[tex]Left over = \frac{25 - 5 - 8}{25}[/tex]
[tex]Left over = \frac{12}{25}[/tex]
Recall that she has Rs11,040
This means that
[tex]\frac{12}{25} of Salary = Rs11,040[/tex]
Multiply both sides by [tex]\frac{25}{12}[/tex]
[tex]\frac{12}{25} * \frac{25}{12} * Salary = Rs11,040 * \frac{25}{12}[/tex]
[tex]Salary = Rs11,040 * \frac{25}{12}[/tex]
[tex]Salary = \frac{Rs276000}{12}[/tex]
[tex]Salary = Rs23000[/tex]
Hence, her salary for that month was Rs23000
Answer:
Her salary = Rs 23000
Step-by-step explanation:
In a month, Ezhil spent 1/5 of her salary on shopping.
Let
Her salary = a
she spent 1/5 of a on shopping
Amount spent on shopping = 1a/5
She gave 2/5 of the remaining to her sister .
The remaining money = a - 1a/5 = 5a - a/5 = 4a/5
She gave 2/5 of 4a/5 to her sister. Therefore,
The amount she gave to her sister = 2/5 × 4a/5 = 8a/25
Out of her salary she is left with Rs 11040 .Therefore,
a - 1a/5 - 8a/25 = 11040
25a - 5a - 8a/25 = 11040
12a/25 = 11040
12a = 11040 × 25
12a = 276000
divide both sides by 12
a = 276000/12
a = 23000
Her salary = Rs 23000
in a certain town there were 113 robberies last year this year the number of robberies has gone down 14% how many robberies were there this year to the nearest whole number
Answer:
99 robberies
Step-by-step explanation:
What you are basically doing is taking the discount.
1 + 14% = 1.14
113 / 1.14 = 99.12
8 1/6 divide 1 7/8?
The quotient is close to _____
Answer:
4.35 rounded to the nearest hundredth
4.3 rounded to the nearest tenth
4 rounded to the nearest whole number.
Step-by-step explanation:
[tex]8\frac{1}{6}[/tex] ÷ [tex]1 \frac{7}{8}[/tex] =
[tex]\frac{49}6}[/tex] ÷ [tex]\frac{15}{8} =[/tex]
[tex]\frac{49}{6} *\frac{8}{15} =[/tex]
[tex]\frac{392}{90} =[/tex]
[tex]4 \frac{32}{90} =[/tex]
[tex]4\frac{16}{45}[/tex] ≈ 4.35
m-n/m^2-n^2 + ?/(m-1)(m-2) - 2m/m^2-n^2
Answer:
The answer is "[tex]\bold{\frac{(m-1)(m-2)}{(m-n)}}[/tex]"
Step-by-step explanation:
Given:
[tex]\bold{\frac{(m-n)}{m^2-n^2} + \frac{?}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0}\\\\[/tex]
let, ? = x then,
[tex]\Rightarrow \frac{(m-n)}{m^2-n^2} + \frac{x}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0\\\\\Rightarrow \frac{(m-n)}{m^2-n^2} - \frac{2m}{m^2-n^2}=- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{(m-n)-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{m-n-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-n-m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-(m+n)}{(m+n)(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-1}{(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\[/tex]
[tex]\Rightarrow -((m-1)(m-2))=-x(m-n) \\\\\Rightarrow x= \frac{- (m-1)(m-2)}{- (m-n)} \\\\\Rightarrow \boxed{x= \frac{(m-1)(m-2)}{(m-n)}} \\[/tex]