Answer:
[tex]f { - 1}^{ } = \frac{x}{4} [/tex]
Step-by-step explanation:
fjhjthfdvhfjrhgehdhrjfhdrhjthr
Prove the following identities : i) tan a + cot a = cosec a sec a
Step-by-step explanation:
[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]
[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]
[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]
Question :
tan alpha + cot Alpha = cosec alpha. sec alphaRequired solution :
Here we would be considering L.H.S. and solving.
Identities as we know that,
[tex] \red{\boxed{\sf{tan \: \alpha \: = \: \dfrac{sin \: \alpha }{cos \: \alpha} }}}[/tex][tex] \red{\boxed{\sf{cot \: \alpha \: = \: \dfrac{cos \: \alpha }{sin \: \alpha} }}}[/tex]By using the identities we gets,
[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]
Now, here we would be using the identity of square relations.
[tex]\red{\boxed{ \sf{sin {}^{2} \alpha \: + \: cos {}^{2} \alpha \: = \: 1}}}[/tex]By using the identity we gets,
[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]
[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]
Hence proved..!!khai niem hinh cat don gian ?
Answer:
khai niem hinh cat don gian?
An isosceles trapezoid has a consecutive-sides of length: 10,6,10 and 14. Find the measure of each angle if the trapezoid.
Answer:
Angle A = Angle D = 69° 30'
Angle B = Angle C = 110° 30'
Step-by-step explanation:
B ___ C
/ \
/ \
A ________ D
AB and CD are 10
BC is 6
AD is 14
If we divide the trapezoid, we can imagine a line.
B_ F_C
/ | \
/ | \
A ___E____ D
AE = ED = 7 (14/2)
BF = FC = 3
So now, we draw another line from B or C to AE or ED
B_ F_ C
/ | | \
/ | | \
A ___E_ G_ D
EG = GD = 3.5 (7/2)
There is a right triangle now, GCD
GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:
CD is H, and GD is A
cos D = A/H
cos D = 3.5/10 → 0.35
angle D = 69° 30'
By theory, we know that angle D and angle A, are the same so:
Angle D = Angle A = 69° 30'
Angle B = Angle C
We also make a cuadrilateral, which is EFCD.
Angle D is 69° 30', Angle E is 90°, Angle F is also 90°
Sum of angles in cuadrilateral is 360°
360° - 69° 30' - 90° - 90° = Angle C = Angle B
Angle C = Angle B = 110° 30'
Let's confirm the angles in the trapezoid:
69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°
A + B + C + D
Describe the transformation of f(x) to g(x). Pleaseee helllp thank youuuu!!!
The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.
You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].
So let us take a look at the possible options.
Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.
Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.
So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].
Hope this helps :)
Graph the inequality.
7 <= y - 2x < 12
Answer:
X(-12,-7)
Step-by-step explanation:
This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.
Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain
What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)
Answer: A (x+1)(x+2)(x+5)
Step-by-step explanation:
!!!!Please Answer Please!!!!
ASAP!!!!!!
!!!!!!!!!!!!!
Answer:
False
Step-by-step explanation:
well i think that the answer from my calculations
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
PLEASE HELP
Answer:
8
Step-by-step explanation:
As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8
Which of the following is the differnce of two squares
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1=50 n2=35
x¯1=13.6 x¯2=11.6
σ1=2.2 σ2=3.0
Required:
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
Answer:
a. 2
b. The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
[tex]\mu_1 = 13.6, s_1 = \frac{2.2}{\sqrt{50}} = 0.3111[/tex]
Sample 2:
[tex]\mu_2 = 11.6, s_2 = \frac{3}{\sqrt{35}} = 0.5071[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 13.6 - 11.6 = 2[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.3111^2+0.5071^2} = 0.595[/tex]
a. What is the point estimate of the difference between the two population means?
Sample difference, so [tex]\mu = 2[/tex]
b. Provide a 90% confidence interval for the difference between the two population means.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
The margin of error is:
[tex]M = zs = 1.645(0.595) = 0.98[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 0.98 = 1.02
The upper end of the interval is the sample mean added to M. So it is 2 + 0.98 = 2.98
The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. Provide a 95% confidence interval for the difference between the two population means.
Following the same logic as b., we have that [tex]Z = 1.96[/tex]. So
[tex]M = zs = 1.96(0.595) = 1.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 1.17 = 0.83
The upper end of the interval is the sample mean added to M. So it is 2 + 1.17 = 3.17
The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is more than 4.03 inches
Answer:
The answer is "".
Step-by-step explanation:
Please find the complete question in the attached file.
We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval
[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]
Using formula:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The probability that perhaps the mean shells length of the sample is over 4.03 pounds is
[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]
Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution
[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]
the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]
40% of what number is 16.6?
By selling a radio for $8400 a dealer gained 12% .how much money did she gain
Answer:
Amount gained = $900
Step-by-step explanation:
Let the cost price be = x
Given selling price = 8400
And profit% = 12%
Profit = selling price - cost price
= 8400 - x
[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]
Therefore , cost price of the radio $7500
The amount she gained = 8400 - 7500 = $ 900
Which of the following exponential equations is equivalent to the logarithmic
equation below?
log 970 = x
A.x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X
Given:
The logarithmic equation is:
[tex]\log 970=x[/tex]
To find:
The exponential equations that is equivalent to the given logarithmic equation.
Solution:
Property of logarithm:
If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]
We know that the base log is always 10 if it is not mentioned.
If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]
We have,
[tex]\log 970=x[/tex]
Here, base is 10 and the value of a is 970. By using the properties of exponents, we get
[tex]970=10^x[/tex]
Interchange the sides, we get
[tex]10^x=970[/tex]
Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].
Note: It should be "=" instead of "-" in option B.
(4-1) + (6 + 5) = help plz
The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.
Answer:
b. The actual count of bike riders is too small.
d. n*p is not greater than 10.
Step-by-step explanation:
Confidence interval for a proportion:
To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]
Of the 123 students surveyed 5 ride a bike to campus.
Less than 10 successes, that is:
The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.
What is the value of x in the triangle? 45, 45, x
Answer:
90
Step-by-step explanation:
it its a 45 45 90 triangle
Which side of the polygon is exactly 6 units long?
Answer:
AB is correct as It is the shorter parallel line
as the line measures 6 units.
Step-by-step explanation:
The polygon is a trapezoid / (trapezium Eng/Europe)
We see the given coordinates (2, 6) - (-4, 6) = x-6 y 0 = x = 6units
as x always is shown as x - 6 as x= 6
We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6
y = 0 x = 6 = 6 units as its horizontal line.
when y is 6-6 = 0 then we know the line is horizontal for y = 0.
The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.
When looking at diagonal lines we still group the x's and y's and make the fraction whole.
When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.
An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it take both pipes to fill the pool?
Answer:
It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
Step-by-step explanation:
Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:
1/5 + 1/4 = X
0.20 + 0.25 = X
0.45 = X
9/20 = X
9 = 60
2 = X
120/9 = X
13,333 = X
Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
2/3y = 1/4 what does y equal?
Answer:
Step-by-step explanation:
2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3
If $6^x = 5,$ find $6^{3x+2}$.
If 6ˣ = 5, then
(6ˣ)³ = 6³ˣ = 5³ = 125,
and
6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500
HELP!!!!!!!!!!! SOMEONE PLEASE HELP!!!
For the graph below, which of the following is a possible function for h?
A) h(x) = 4-x
B) h(x) = 2x
C) h(x) = 5x
D) h(x) = 3x
9514 1404 393
Answer:
C) h(x) = 5^x
Step-by-step explanation:
h(x) is shown on the graph as having the highest rate of growth. That means, relative to the other functions, the base of the exponential is larger. Of the choices offered, the one with the largest growth factor is ...
h(x) = 5^x
_____
The general form of an exponential function is ...
f(x) = (initial value) · (growth factor)^x
Pleaseee Help. What is the value of x in this simplified expression?
(-1) =
(-j)*
1
X
What is the value of y in this simplified expression?
1 1
ky
y =
-10
K+m
+
.10
m т
9514 1404 393
Answer:
x = 7
y = 5
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
For a=-j and b=7,
(-j)^-7 = 1/(-j)^7 ⇒ x = 7
For a=k and b=-5,
k^-5 = 1/k^5 ⇒ y = 5
X+34>55
Solve the inequality and enter your solution as an inequality comparing the variable to a number
Answer:
x > 21
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 34 > 55
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 34 on both sides: x > 21E. The ratio of monthly income to savings of a family is 7:2. If the savings is Rs. 500, find the monthly income and expenditure.
Step-by-step explanation:
Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t
Now, we are given that the savings is =Rs 500
So, According to our assumption, 2t=500
⇒t=250
Hence, the income of the family is =7×250=Rs 1750
And the expenditure is =Income−Savings
=Rs 1750−Rs 500
=Rs 1250
What is the explicit formula for the sequence ? -1,0,1,2,3
Answer:
B
Step-by-step explanation:
substitute the values in the eq. Ot is also arithmetic progression.
Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are needed? Round to the nearest tenth.
Answer:
3.1 gallons
Step-by-step explanation:
To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that
miles of gas / gallons = miles of gas / gallons
23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house
If we write the gallons needed to go to Bob's mother's house as g, we can say
23 miles / 1 gallon = 72 miles/g
multiply both sides by 1 gallon to remove a denominator
23 miles = 72 miles * 1 gallon /g
multiply both sides by g to remove the other denominator
23 miles * g = 72 miles * 1 gallon
divide both sides by 23 miles to isolate the g
g = 72 miles * 1 gallon/23 miles
= 72 / 23 gallons
≈ 3.1 gallons
Which one goes where?
"RS tangent to circle a..." is first statement Reason: Given
Second Reason: "Radius perpendicular to tangent"
Second Statement: "AR is parrallel to BS" Reason: "2 lines perpendicular..."
a triangle has sides of 6 m 8 m and 11 m is it a right-angled triangle?
Answer:
No
Step-by-step explanation:
If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.
[tex]6^{2}+8^{2}=c^2[/tex]
If the triangle is a right triangle, c would equal 11
Solve.
[tex]36+64=100[/tex]
Then find the square root of 100.
The square root of 100 is 10, not 11.
So this is not a right triangle.
I hope this helps!