By solving the interval : [0,2pi] 4 csc x +6=-2 is 7pi/6 , 11pi/6
What are Trigonometric identities?Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. defining sine and cosine in terms of tangent, cotangent, secant, and cosecant interactions. The sine and cosine formula according to Pythagoras. This trig identity is arguably the most significant.[tex]& 4 \csc x+6=-2 \\[/tex]
[tex]& 4 \csc x=-8 \\[/tex]
Simplifying,
[tex]& \csc x=-2 \\[/tex]
[tex]& \frac{1}{\sin x}=-2 \\[/tex]
[tex]& \sin x=-\frac{1}{2} \\[/tex]
We get,
[tex]& x=\frac{7 \pi}{6}, \frac{11 \pi}{6}[/tex]
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Mario had yards of ribbon for a project. Sue gave him more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?
The closest to the number of yards of ribbon Mario had altogether will be 11 yards
What is meant by Fraction?A fraction is a part of the whole number, and a way to split up a number into equal parts. Or, A number that is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that;
Mario had 8 1/5 yards of ribbon for a project.
And, Sue gave him 2 3/4 more yards of ribbon.
Since Mario had 8 1/5 yards of ribbon for a project. And, Sue gave him 2 3/4 more yards of ribbon.
Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards
= 41/5 + 11/4
= (164 + 55) / 20
= 219 / 20 yards
= 10.95 yards
≈ 11 yards
Thus, the total ribbon for the project Mario has = 11 yards
The complete question is given below;-
Mario had 8 1/5 yards of ribbon for a project. Sue gave him 2 3/4 more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?
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1. A student has computed that it takes an average of 17 minutes with a standard deviation of 3 minutes to drive from home, park the car, and walk to an early morning class. Find the proportion of times whose time X satisfies each of the following conditions:
A) If you selected 10 days at random, what is the probability that half the days will take between 15 and
20 minutes?
B) What is the probability the second day selected will be the first day he is late to class, assuming he left
at 8:39am?
(I know how to solve for the probabilities on their own, however I’m not sure how to incorporate the added probability based on multiple days)
Answer:
B
Step-by-step explanation:
In College Park mice, short tails (ss) is recessive to long tails (SS). In the HJP building exterminators found the allele frequency of mice with short tales in the population within the building to be 0.7. In the BioPsyc building exterminators find that the allele frequency of the gene for short tale in mice in the building to me 0.2. Due to construction in the BioPsyc building several of the mice made HJP their new home. The exterminator guessed that about 20% of the mice in HJP now consist of mice from BioPsyc. What will be the new frequency of the short tales among mice in HJP?
a. 0.43.
b. 0.65.
c. 0.57.
d. 0.60.
The new frequency of short tail mice in HJP is 0.60.
What is Algebra?Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.
Let, initial number of mice in HJP be 'x'
and the number of mice travelling from BioPyc building to HJP be 'ý
So, Total mice in HJP= x+ y
As, [tex]\frac{y}{x+y} = 0.2[/tex]
y= 0.2x + 0.2 y
0.8y =0.2 x
x= 4y
Now, total short tail mice in HJP= 0.7 x + 0.2 y
Thus, New frequency of short tail among mice in HJP
= [tex]\frac{0.7x + 0.2y}{x+y}[/tex]
Put x= 4y in above equation we get,
= [tex]\frac{0.7 * 4y+ 0.2y}{4y+y}[/tex]
= [tex]\frac{3y}{5y}[/tex]
= 0.60
Hence, the new frequency of short tail mice in HJP is 0.60.
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Please help asap!
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow
Determine P(not orange) if the spinner is spun once.
25%
12.5%
87.5%
37.5%
(no links)
Answer:
7/8 = 87.5%
Step-by-step explanation:
You have only one of eight (1/8) evenly divided sections that is orange. The rest is not orange (1 - 1/8 = 7/8).
Therefore, spinning once will yield 7/8 odds of not landing on orange, or 0.875 or 87.5%.
The probability of not getting orange is 87.5%. The correct option is C.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.
Probability = Number of favourable outcomes / Number of samples
Given that a spinner with repeated colours numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
You only have one of eight (1/8) evenly divided orange sections.
The rest is not orange,
P = (1 - 1/8
P = 7/8
P = 87.5%
Therefore, spinning once will yield 7/8 odds of not landing on orange or 0.875 or 87.5%.
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Which student had the highest average (mean) score?
Math Tost Scores for Five Students
Score on Math Score on Math
Student
A. 1
B. 2
C. 3
D. 4
E. 5
evaluate 5² + 7 - 3 +4
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5² + 7 - 3 + 4
Simplify the expression, then we have
⇒ 5² + 7 - 3 + 4
⇒ 25 + 7 - 3 + 4
⇒ 36 - 3
⇒ 33
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
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Victoria needs to earn at least an 85 in College Algebra. Only exam scores are used to calculate her grade. Currently she has scored an 82, 81, and 90 this semester. All that remains is the semester exam, which counts twice (counts as two exam grades). She hopes to make an 85 or higher in the class.
She would need to make two extra grades of 86 each.
What is the average?Here we can see that the average of the scores that Victoria would need to make is an average score of 85 so as to be able to pull through. In this case, we can see that we have the scores; 82, 81, and 90
Let the scores tat we have to count twice be p each and then we have;
85 = 82 + 81 + 90 + p + p/5
85 = 253 + 2p/5
5(85) = 253 + 2p
p = 5(85) - 253/2
p = 86
Hence, the twice scores that need to be earned for Victoria are both 86.
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How do you write the sum in the simplest form 5/12 + 9/12=
14/12
7/12
14/24
7/6
Answer:
[tex]\frac{7}{6}[/tex]
Step-by-step explanation:
[tex]\frac{5}{12} + \frac{9}{12} = ?[/tex]
When adding fractions, the denominators must be the same. In this case, they are both 12, so we can just add the numerators.
5 + 9 = 14
We are left with:
[tex]\frac{14}{12}[/tex]
14 and 12 are both even numbers and can be simplified by dividing by 2.
14 ÷ 2 = 7
12 ÷ 2 = 6
[tex]\frac{14}{12}[/tex] simplifies to [tex]\frac{7}{6}[/tex]
This is your answer.
Hope this helps!
HELP. Will give branliest!!! No links
Answer:
5/3 is correct
Step-by-step explanation:
In ADEF, e = 9.8 inches, f = 5.6 inches and ZD=149º. Find ZF, to the nearest 10th of
degree.
an
The angle measure of ∠F is approximately 66.9º.
What is an angle?
To find ∠F, we can use the Law of Cosines:
c² = a² + b² - 2ab cos(C)
Where c is the side opposite to the angle we want to find (in this case, side EF), a and b are the other two sides, and C is the angle opposite to side c (in this case, ∠F).
First, we need to find the length of side EF:
EF² = DE² + DF² - 2DE * DF cos(∠D)
EF² = (9.8)² + (5.6)² - 2(9.8)(5.6)cos(149º)
EF² ≈ 95.415
EF ≈ 9.769
Now, we can use the Law of Cosines again to find ∠F:
EF² = DE² + DF² - 2DE * DF cos(∠F)
cos(∠F) = (DE² + DF² - EF²) / 2DE * DF
cos(∠F) = ((9.8)² + (5.6)² - (9.769)²) / (2 * 9.8 * 5.6)
cos(∠F) ≈ 0.4035
∠F ≈ [tex]cos^{-1(0.4035)}[/tex]
∠F ≈ 66.9º (rounded to the nearest 10th)
Therefore, the measure of ∠F is approximately 66.9º.
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Complete question is: In ADEF, e = 9.8 inches, f = 5.6 inches and ZD=149º, the measure of ∠F is approximately 66.9º.
4. Jillian tracks her progress on her spelling tests over a period of four weeks. Which list shows her scores from
greatest to least?
WEEK 1
WEEK 2
WEEK 3
WEEK 4
25
0.78
30
15
| |=5
82%
F. Weeks 1,3,2,4
H. Weeks 3, 1, 2,4
G. Weeks 3, 1, 4,2
J. Weeks 1,3,4,2
Answer:
its F
Step-by-step explanation:
Seat belt use in WA state (pop: 7.5 million) is reported to be 95% compared to 85% in Mississippi (pop 3 million). A random sample of 1,000 residents is taken from each state. Since we are sampling a higher proportion of the population of Mississippi, the % of seatbelt users in the Mississippi sample will likely be closer to the population proportion. Be sure to state true or false clearly first. Then explain which sample (WA or MI) is more likely to be closer to its population proportion and why?
Answer:
True
Step-by-step explanation:
By sampling a larger proportion of Mississippi's population, the percentage of people who wear seatbelts in Mississippi surveys would be closer and nearer to the population proportion.
The rule of large numbers states that if we collect samples of increasing size from every population (here, Mississippi vs. Washington WA state), the sampling distribution's mean, px, continues to get closer and nearer to the actual true population proportion (p).
Recall that as n becomes greater, the sample mean obeys a normal distribution because of the Central Limit Theorem. However, as (n) rises, the sampling distribution's standard deviation reduces.
where:
sampling proportion's standard deviation = [tex]\sqrt{\dfrac{p((1-p)}{n}}[/tex]
If n rises, the sample proportion [tex]P_x[/tex] have to get nearer to the population proportion P.
For both counties, the sample size is 1000, but the true population varies. According to the provided statement, the true population of Mississippi (3 million) is less than that of Washington State (7.5 Million). As a result, we can confidently assume that our sampling proportion in Mississippi seems to be much closer to the true actual population than our sampling proportion in Washington state.
What is the equation of this graph in slope intercept form
The slope-intercept form of the two straight lines in the graph of the question are;
y = 4y = 3What is the slope-intercept form of the equation of a straight line?The slope-intercept form of the equation of a straight line is; y = m·x + c
Where;
m = The slope of the line
c = The y-intercept of the line
The values of the ordered pair of the points on the line are in the form (x, y)
The graph consists of two straight lines, therefore the equations that represent the graphs are found as follows;
Points on the blue line graph are (0, 4), (2, 4), and (4, 4)
The slope of the blue line graph is therefore;
m = (4 - 4)/(2 - 0) = 0
The y-intercept of the blue line graph is; c = 4
The slope-intercept form of the equation representing the blue line graph is therefore;
y = 0 × x + 4
y = 4The slope-intercept form of the equation of the blue line graph is; y = 4
Points on the red line graph are; (0, 3), (2, 3), (4, 3)
The sloped of the red line graph is therefore; m = (3 - 3)/(2 - 0) = 0
The y-intercept of the red line graph is; c = 3
The slope-intercept form of the equation of the red line graph is therefore; y = 0 × x + 3
y = 3
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Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in degrees. (Enter your answers as a comma-separated list.) −420°
Answer:
- 420° = -7/3 π ≈ - 2.333 π
Step-by-step explanation:
- 420° = -7/3 π ≈ - 2.333 π
Coterminal angle in [0, 360°) range:
300°, located in the fourth quadrant.
Positive coterminal angles: 300°, 660°, 1020°, 1380°, 1740°...
Negative coterminal angles: -60°, -420°, -780°, -1140°
I hope this helps!1!!
-420° = -360° - 80° = -80°
-80° = 360° - 80° = 280°
Co terminal angle = 280° and -80°
Work out
2/3 - 2/5
Give your answer in its simplest form.
Answer:
4/15
Step-by-step explanation:
find common denominators, which is 15
multiply 2/3 by 5 and and 2/5 by 3
2 x 5 = 10 and
3 x 5 = 15
10/15
2 x 3 = 6 and
5 x 3 = 15
6/15
subtract numerators
10 - 6
15
= 4/15
what is 4/5 of 2 hours
Answer:
1.6 hours
Step-by-step explanation:
Answer:
[tex] \frac{8}{5}~hours~~or~~1.6~hours} [/tex]
Step-by-step explanation:
[tex] \frac{4}{5}~of~2~hours = [/tex]
[tex] = \frac{4}{5} \times 2~hours [/tex]
[tex]= \frac{4}{5} \times \frac{2}{1}~hours[/tex]
[tex] = \frac{4 \times 2}{5 \times 1}~hours [/tex]
[tex] = \frac{8}{5}~hours [/tex]
[tex] = 1.6~hours [/tex]
help please with this assignment
Answer:
13
Step-by-step explanation:
Cuz the factor of y is angle to the 115° is to the Y value
A lab technician mixes a 10% acid solution with a 50% acid solution to create 40 ml of a 40%
solution. How much of each solution must be used?
Answer:
10 ml of 10%
30 ml of 50%
Step-by-step explanation:
x = amount of 10%
40 - x = amount of 50%
-------------------------------------
10x + 50(40 - x) = 40(40)
10x + 2000 - 50x = 1600
-40x + 2000 = 1600
-40x = -400
x = 10 ml of 10%
40 - x = 30 ml of 50%
Help me out please!
No links please I’ll report you
Show work!
I’ll give brainiest
Fill in the missing values to make the equations true. (a) log 5 + log 3 = log₁ 5 (b) log, log, 7 = log, 7 - (c) log, 4 = log, 2
Step-by-step explanation:
try this option:
[tex]a) \ log_{15}5+log_{15}3=log_{15}15;\\b) \ log_{1/2}log_{49}7=log_77;\\c) \ log_44=log_22.[/tex]
An online health and medicine company claims that about 50% of Internet users would go to an online sight first for information regarding health and medicine. A random sample of 1318 Internet users was asked where they will go for information the next time they need information about health or medicine; 606 said that they would use the Internet. Test the claim that less than 50% of Internet users get their health questions answered online.
Answer:
The p-value of the test is 0.0018, which means that for a level of significance higher than this, there is sufficient evidence to claim that less than 50% of Internet users get their health questions answered online.
Step-by-step explanation:
Test the claim that less than 50% of Internet users get their health questions answered online.
At the null hypothesis, we test that 50% of Internet users get their health questions answered online, that is:
[tex]H_0: p = 0.5[/tex]
At the alternate hypothesis, we test that this proportion is less than 50%, that is:
[tex]H_a: p < 0.5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.5 is tested at the null hypothesis:
This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5[/tex]
A random sample of 1318 Internet users was asked where they will go for information the next time they need information about health or medicine; 606 said that they would use the Internet.
This means that [tex]n = 1318, X = \frac{606}{1318} = 0.4598[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.4598 - 0.5}{\frac{0.5}{\sqrt{1318}}}[/tex]
[tex]z = -2.92[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.4598, which is the p-value of z = -2.92.
Looking at the z-table, z = -2.92 has a p-value of 0.0018.
The p-value of the test is 0.0018, which means that for a level of significance higher than this, there is sufficient evidence to claim that less than 50% of Internet users get their health questions answered online.
B) If one gallon of paint covers 0.5 square meters, how many gallons of black paint will the
need to paint the house?
Show your work
If you need anymore information let me know also if you send a link when I die I will come and haunt you
Answer:2/10, which can be reduced to 1/5.
2. If a tank is 5/8 filled with solution, how much of the tank is empty?
Ans: 3/8 of the tank is empty. Since the whole tank would equal 8/8, or 1, and 5/8 of it is filled, then that
means 3/8 of it remains empty.
3. 1/2 x 3/5 x2/3 =
Ans: 6/30, which can be reduced to 1/5.
4. 5/9 ÷ 4/11 =
Ans: 55/36. You cannot reduce this fraction any further.
5. Convert 27/4 to a decimal.
Ans: 6.75. This answer is arrived at by dividing 4 into 27.
6. Convert 0.45 to a fraction.
Ans: 45/100, which can be reduced to 9/20.
7. 4.27 x 1.6 =
Ans: 6.832
8. 6.5 ÷ 0.8 =
Ans: 8.125
9. 12 + 4.52 + 245.621 =
Step-by-step explanation:
A mixture of pecans walnuts, and cashews was in a ratio of 2:31. How much of each type of nut was in her purchase?
equation:
pecans:
walnuts:
cashews:
Answer:
The ratio given cannot be used to find the answer
Find the area of the trapezoid
Answer:
I think that the answer is 3495.24in
If 3a + 1 - a = 9 then what does 5a + 2 = ?
Answer:
[tex]3a + 1 - a = 9 \\ 2a = 8 \\ a = 4 \\ 5a + 2 = \\ 5(4) + 2 = 22[/tex]
first find the value of a, which is 4
then substitute a with 4
Armando graphed the relationship between temperature and elevation for several cities. The x-coordinate is the elevation in meters and the the y-coordinate is the temperature in °C.
which cordanate would contain the point showing a city 3m below sea level 6°C below zero?
A.Quarant I
B.Quarant II
C.Quarant III
D.Quadrant IV
Find the perimeter of the figure
9+5+1+5+4=24 In
this shld be the ans.
if its that simple
29. What is length of x?
Please explain this one too me since I did not understand it thanks
The value of x is 10 yards. The given shape is a trapezoid.
What are trigonometry ratios?
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Draw a line parallel to the base.
Name the corner point of the shape.
Assume that ∠ADG = θ.
Consider △BDF:
BD = 6 + x
DF = 8 + 4.8 = 12.8 yrds.
The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.
cos θ = DF/BD
cos θ = 12.8 /(6+x) .....(i)
Consider △CDE:
cos θ = DE/CD
cos θ = 8/x .....(ii)
Now equate equations (i) and (ii):
12.8 /(6+x) = 8/x
Cross multiply:
12.8 × x = 8(6+x)
12.8x = 48 + 8x
12.8x - 8x = 48
4.8x = 48
Divide both sides by 4.8:
x = 48/4.8
x = 10
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The value of x is 10 yards. The given shape is a trapezoid.
What are trigonometry ratios?Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Draw a line parallel to the base.
Name the corner point of the shape.
Assume that ∠ADG = θ.
Consider △BDF:
BD = 6 + x
DF = 8 + 4.8 = 12.8 yrds.
The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.
cos θ = DF/BD
cos θ = 12.8 /(6+x) .....(i)
Consider △CDE:
cos θ = DE/CD
cos θ = 8/x .....(ii)
Now equate equations (i) and (ii):
12.8 /(6+x) = 8/x
Cross multiply:
12.8 × x = 8(6+x)
12.8x = 48 + 8x
12.8x - 8x = 48
4.8x = 48
Divide both sides by 4.8:
x = 48/4.8
x = 10
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hello i need help with questions 5 please thank you.
5a) The total cost of buying the car, priced at $32,000 with the harmonized sales tax (HST) of 13%, is $36,160.
5b) Through the lease, the customer saves $14,760.
5c) The lease options for the lessee after returning the car include:
Lease buyoutLease extensionNew lease contractBuying out the vehicle and then reselling it.6a) The after-tax cost of the Honda Civic is $32,199.35.
6b) The value of the vehicle that needs to be financed is $26,199.35.
6c) The monthly payment will be $567.26 for 4 years.
6d) After four years, the total amount paid for the vehicle is $33,228.48.
Financing Options:A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.
A car purchase can also be financed through loans, like home mortgages.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)
Jordan's Car:The value of the Honda Civic = $28,495
Harmonized Sales Tax (HST) = 13%
After-tax cost = $32,199.35 ($28,495 x 1.13)
Annual interest rate = 1.9% compounded monthly
Down payment = $6,000
Financing part = $26,199.35 ($32,199.35 -$6,000)
Financing period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 1.9%
PV (Present Value) = $26,199.35
FV (Future Value) = $0
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 12
Results:
Monthly Payments (PMT) = $567.26
Sum of all periodic payments = $27,228.48
Total Interest $1,029.13
Total amount paid over 4 years = $33,228.48 ($27,228.48 + $6,000)
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Please list some “deeez nuts” joke :) <3
Teacher: In all your subjects I am giving you D's.
Student: Well I am also going to be giving you D's.
Teacher: What do you mean?
Student: Deeez nuts!