Remember that
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
so
in this problem
the input value must be 3
answer is option Cdetermine if f, g, and h are true or false. If false, correct the statement with an explanation
We need to determine if the statements are true or false.
In order to do so, we need to pay attention to the following notations:
[tex]\begin{gathered} (\sin x)^{-1}=\frac{1}{\sin x} \\ \\ \sin^{-1}x=\text{ inverse function of }\sin x \end{gathered}[/tex]The same notations apply to cosine and tangent functions.
The inverse f⁻¹(x) is the function such that:
[tex](f^{-1}\circ f)(x)=f^{-1}(f(x))=x[/tex]Thus, we have:
[tex]\cos^{-1}(\cos(\frac{15\pi}{6}))=\frac{15\pi}{6}[/tex]Therefore, statement g. is true.
In order to show that statements f. and h. are false, let's see what happens for x = 1/2:
[tex]\begin{gathered} \frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}=\frac{\frac{\pi}{6}}{\frac{\pi}{3}}=\frac{3}{6}=0.5\text{ \lparen no units\rparen} \\ \\ \tan^{-1}(\frac{1}{2})\cong0.46\text{ \lparen rad\rparen} \\ \\ \Rightarrow\frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}\ne\tan^{-1}(\frac{1}{2}) \end{gathered}[/tex][tex]\begin{gathered} \sin^{-1}(\frac{1}{2})=\frac{\pi}{6}\cong0.52 \\ \\ \frac{1}{\sin(\frac{1}{2})}\cong2.09 \\ \\ \Rightarrow\sin^{-1}(\frac{1}{2})\ne\frac{1}{\sin(\frac{1}{2})} \end{gathered}[/tex]Answer:
f. False
g. True
h. False
Notice that we can correct the statements f. and h. by using the correct notation:
[tex]\begin{gathered} \text{ f. }\frac{(\sin x)^{-1}}{(\cos x)^{-1}}=(\tan x)^{-1} \\ \\ \text{ h. }(\sin x)^{-1}=\frac{1}{\sin x} \end{gathered}[/tex]you make $512.92 a week. if you work 36 hours find your hourly rate of pay
The hourly rate of pay is $14.25
To solve this, w
(PLS HELP, FINAL QUESTION!!!)
which of the following lists the correct values of a, h, and k for the function: f(x)=n^2+6
A) a = 1, h = 1, k = 6
B) a = 1, h = –1, k = 6
C) a = 1, h = 0, k = 6
D) None of the choices are correct.
Answer:
N^2+6 is in standard form, which is in ax^2+bx+c,
in order to get it to vertex form, which y=a(x-h)^2+k, we need to find the vertex, through x=-b/2a, in this case:
x=-0/2(1)=0, so h=0, then plug 0 in for n,
0^2+6=6,
which makes k=6,
therefore, the answer is c.
as for a, the value of a is constant in all forms, whether standard, vertex or factored, making a=1
Brainliest pls
Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Step 1
Given; Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Step 2
Let x represent miles
y represents hours
Thus the inequality will be;
[tex]speed=\frac{distance}{time}[/tex][tex]\begin{gathered} Speed\text{ is over }9mph \\ This\text{ means David drives more than 9 miles per hour} \\ speed>9mph \end{gathered}[/tex]Answer; The required inequality is > or greater than because he drives over 9mph which means > 9mph
[tex]The\text{ required inequality is }>[/tex]Given a system of linear equations in three variables \Biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
You are going to solve the system by performing the following steps.
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate x from the two equations you got from part (1) and part (2).
(2pts) Find the solution for the given system.
(3pts) Check your solution for the given system.
Answer:
Step-by-step explanation:
n
True or false?
A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output.
The following statement: A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output is false.
A natural monopoly is a sort of monopoly that emerges because of the high start-up costs or substantial economies of scale associated with conducting business in a certain industry, which can result in large barriers to entry for potential rivals.
Natural monopolies can form in sectors that require specialized raw resources, technology, or other variables to function. Natural monopolies can also occur when one business is far more efficient than several enterprises in providing the market with the item or service.
To know more about Natural monopoly here
https://brainly.com/question/1450566
#SPJ1
Number of Inches in a Mile An inch is approximately1.57828 x 10-5 mile. Find the reciprocal of this num-ber to determine the number of inches in a mile.
We are given that an inch is approximately 1.57828x10⁻⁵ mile.
[tex]1\: inch=1.57828\times10^{-5}\: \text{mile}[/tex]The reciprocal of this number will give us the number of inches in a mile.
[tex]\frac{1}{1.57828\times10^{-5}\: }=63360\: inches[/tex]Therefore, a mile is approximately 63360 inches.
[tex]1\: mile=63360\: \text{inches}[/tex]CAN SOMEONE HELP WITH THIS QUESTION?✨
The value of P = $5000, r = 3.6%/4 = 0.9%, n = 4n and amount after 10 years is $5450.
Compound interest may be defined as the interest which can be applied by any institution on any individual in which the interest amount after a year becomes principle for the next year. The formula for compound interest is given as A = P(1 + r/n) ^ nt where A is the amount, P is the principle, r is the interest rate, n is compounding frequency and t is the time. If compounded quarterly the principle will be same as in the question that is $5000, the interest rate will be divided by 4 that is r = 0.9% and the compounding frequency will be 4 times that is 4n. Now, we need to find the amount after 10 years that is t = 10 years. The amount will be
A = P(1 + r/4n) ^ 4nt
A = 5000(1 + 0.9/100×4×12) ^4×12×10
A = 5000(1.09)
A = $5450 which will be amount after 10 years.
Learn more about Compound Interest at:
brainly.com/question/2241772
#SPJ1
can u please help me before I get on error message, and It kicks me out the tutoring
To find the image we have to multiply every coordinate by the scale factor.
Then:
[tex]\begin{gathered} A^{\prime}(0,2) \\ B^{\prime}(9,0) \\ C^{\prime}(4,4) \end{gathered}[/tex]INVERSES OF AN EXPONENTIAL FUNCTION 6). Fill in the chart. If needed, use a calculator and round to one decimal place.
We will have the following:
x f(x) = 4^x function(x,f(x)) inverse(f(x),x)
0 1 (0, 1) (1, 0)
1 4 (1, 4) (4, 0)
-1 1/4 (-1, 1/4) (1/4, -1)
2 16 (2, 16) (16, 2)
-2 1/16 (-2, 1/16) (1/16, -2)
Answer:
columns in order of 0/1/-1/2/-2
Step-by-step explanation:
g, h and s
e, a and b
d, q and r
k, f and c
m, l and n
Ten bags of beans cost GH¢350.00.
a)Find the cost of 6 bags.
b)Find the cost of 11 bags.
c)How many bags can GH¢245.00
buy?
With solutions
The cost of 6 bags is GH¢ 210
The cost of 11 bags is GH¢ 385
GH¢245.00 can buy 7 bags
Tens bags cost GH¢350.00
one bags cost = 350/10
= 35
The cost of 6 bags can be calculated as follows
1 bag= 35
6= x
cross multiply both sides
x= 35×6
x= 210
The cost of 11 bags can be calculated as follows
1= 35
11= y
cross multiply
y= 35 × 11
= 385
The number of bags GH¢245.00 will buy can be calculated as follows
1 = 35
x= 245
cross multiply both sides.
35x= 245
x= 245/35
x= 7
Hence GH¢245.00 can buy 7 bags, 6 bags cost GH¢210 and 11 bags cost GH¢ 385
Read more on cost here
https://brainly.com/question/7590421
#SPJ1
Compare -2/3 to 3/4 is it equal, less.or greater
Answer:
less
Step-by-step explanation:
negative numbers are less than positive numbers
[tex]-\frac{2}{3} < \frac{3}{4}[/tex]
Hope this helps
describe the general trend of the unadjusted federal minimum wage from 1985 to 2020
From the graph we can infer that the general trend for the unadjusted federal minimum wage has been an increase.
=O EXPONENTS AND POLYNOMIALSProduct rule with positive exponents: UnivariateMultiply.-W3(-2²)Simplify your answer as much as possible.X 5?
Answer
Explanation: To solve this question we will just need to consider some rules as represented below
[tex]\begin{gathered} -a(-b)=+ab \\ x^a*x^b=x^{a+b} \end{gathered}[/tex]Step 1: Once we understand both rules above we can use them to simplify our equation as follows
[tex]\begin{gathered} -w^3(-2w^3) \\ +2*w^3*w^3 \\ 2*w^{3+3} \\ 2w^6 \end{gathered}[/tex]Final answer: So the final answer is
[tex]2w^{6}[/tex].
Your account number is 421746. You wish to deposit 120 dimes, 25 quarters, and checks for $184.63 and $196.17. You wish to receive $50.00 in cash. Complete the savings deposit slip.
The deposit slip would look like this:
we have that the currency is 120 dimes = $1.2 and 25 quarters = $6.25.
The second part of the problem is where i need help. The answers i have there have been given by other tutors
SOLUTION
From the given value
Since
[tex]\sin u=\frac{7}{25}[/tex]Then using trigonometrical ratios it follows
[tex]\cos u=\frac{24}{25}[/tex]Using hal -ngle it folows
[tex]\begin{gathered} sin(\frac{u}{2})=\sqrt{\frac{1-\frac{24}{25}}{2}} \\ s\imaginaryI n(\frac{u}{2})=\sqrt{\frac{1}{50}} \end{gathered}[/tex]Also
[tex]\begin{gathered} cos(\frac{u}{2})=\pm\sqrt{\frac{1+\frac{24}{25}}{2}} \\ cos(\frac{u}{2})=\sqrt{\frac{49}{50}} \\ cos(\frac{u}{2})=7\sqrt{\frac{1}{50}} \end{gathered}[/tex]Finally?
[tex]\begin{gathered} \tan(\frac{u}{2})=\pm\sqrt{\frac{1-\frac{24}{25}}{1+\frac{24}{25}}} \\ \tan(\frac{u}{2})=\sqrt{\frac{1}{49}} \\ \tan(\frac{u}{2})=\frac{1}{7} \end{gathered}[/tex]Which of the expressions below has a sum of 0? select all that apply A. 4+(-4) B. 6.3 +(-3.6) C. 13+(-11) D. -9+9
Answer:
A. 4+(-4),
D. -9+9
Step-by-step explanation:
A expression has a sum of 0 when we have two equal numbers with inverse signals.
A. 4+(-4)
We have the same number(4), and they have inverse signals. So this expression has a sum of 0.
B. 6.3 +(-3.6)
6.3 and 3.6 are different numbers, so this expression does not have a sum of 0.
C. 13+(-11)
13 and 11 are different numbers, so this expression does not have a sum of 0.
D. -9+9
We have the same number(9), with inverse signals. So yes, this expression has a sum of 0.
Rewrite each explicit formula in the form of a function an = 19 - 7(n - 1)
use the recipe to find the ratio of bananas to tomatoes in simplest form. put the ratio data in the first row of the ratio table below. the fill in the ratio table to create two equivalent ratios
Answer:
Bananas Tomatoes
1 3
2 6
3 9
4 12
Explanation:
The ratio of bananas to tomatoes can be calculated as the division of the number of bananas in the recipe over the number of tomatoes in the recipe. So, the ratio is:
[tex]\frac{2\text{ bananas}}{6\text{ tomatoes}}[/tex]Therefore, to find the simplest form, we can divide the numerator and denominator by 2 as:
[tex]\frac{2\div2}{6\div2}=\frac{1\text{ bananas}}{3\text{ tomatoes}}[/tex]Then, we can fill the table as:
Bananas Tomatoes Ratio
1 3 1/3
2 6 2/6 = 1/3
3 9 3/9 = 1/3
4 12 4/12 = 1/3
Where every ratio is equivalent to 1/3
Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.
How can the triangles be proven similar by the SAS similarity theorem?
The triangles can be proven similar by the SAS similarity theorem based on this: B. Show that the ratios are equivalent, and ∠V ≅ ∠Y.
The properties of similar triangles.In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the side, angle, side (SAS) similarity theorem, in order to prove that theses two (2) triangles are similar, it needs to be shown that the ratio of the corresponding side lengths of these triangles are equal and that their corresponding angles are congruent as shown below:
Side UV = side XY
∠V ≅ ∠Y
Read more on SAS similarity theorem here: https://brainly.com/question/11544842
#SPJ1
Complete Question:
Consider the two triangles.
How can the triangles be proven similar by the SAS similarity theorem?
Show that the ratios are equivalent, and ∠U ≅ ∠X.
Show that the ratios are equivalent, and ∠V ≅ ∠Y.
Show that the ratios are equivalent, and ∠W ≅ ∠X.
Show that the ratios are equivalent, and ∠U ≅ ∠Z.
If measure of angle 3 = (5x + 12)° and measure of angle 7 = (8x)° find the value of ‘x’.
The value of x is 21
The other angles are 63°, 117°, 63°, 117°
Given:
The angles of a parallelogram ABCD are
∠A = 3x°
∠B = (5x+12)°
To find:
The value of x
Parallelogram ABCD,
∠A and ∠B are two adjacent sides
Properties of a parallelograms
Two opposite sides are parallelogram are equal and parallel to each other.
So, the adjacent sides are supplementary angles i.e. sum is 180°.
The opposite angles are equal.
Now,
∠A + ∠B = 180°
⇒ 3x + (5x + 12) = 180
⇒ 3x + 5x + 12 = 180
⇒ 8x + 12 = 180
⇒ 8x = 180 - 12
⇒ 8x = 168
⇒ x = 168 ÷ 8
⇒ x = 21
Thus,
The value of x = 21
The angles are
∠A = 3x = 3 * 21 = 63°
∠B = (5x + 12) = (5 * 21 + 12) = 105 + 12 = 117°
As opposite angles are equal so
∠A = ∠C = 63°
∠B = ∠D = 117°
To know more about If measure of angle 3 = (5x + 12)° and measure of angle 7 = (8x)° find the value of ‘x’.
Refer this link:
https://brainly.in/question/24678223
#SPJ1
ANSWERRRRRRRRRRRRRRRRRRRRRRR
The perimeter of the figure is 22.4 cm, and The area of the figure is 30.2cm²
What is meant by Pythagoras connection?The Pythagorean theorem, or Pythagorean theorem, explains the relationship between the three sides of a right-angled triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle, according to Pythagoras' theorem.
From the diagram, the formation is a rectangle.
Use the coordinate points to find the measurements of each side.
Side length AD = Side length BC
Apply the Pythagoras connection to find length BC as;
a² + b²= c² where a=2 cm and b = 4 cm and c =BC
2² + 4² = c²
4+16 = c²
20 = c²
c= √20 = 4.4721
Length BC = Length AD = 4.5 cm
Side length AB = Side length DC
Apply the Pythagoras connection to find the length DC as;
a² + b²= c² where a=6 cm and b = 3 cm and c =DC
6² + 3² =c²
36 + 9 = c²
45 = c²
√45 = c
c= 6.7082
c = DC = 6.7 cm
Now you have the dimensions of the rectangle as;
Length = 6.7 cm and width = 4.5 cm
The perimeter will be ;
P= 2{l +w} --------- where l is length and w is width and P is the perimeter of the rectangle
P=2{6.7 + 4.5}
P=2{11.2}
P= 22.4 cm
The area will be ;
A= l*w
A= 6.7 * 4.5 = 30.15 = 30.2 cm²
The perimeter of the figure is: 22.4 cm
The area of the figure is: 30.2 cm²
To learn more about Pythagoras connection, refer to:
https://brainly.com/question/343682
#SPJ13
What is the domain of the function shown in the graph below? y 10 OSCO 7 6 5 4 3 2 1 I 1 -10 -8 -9 -5 -4 -3 -2 1 2 3 4 8 ON 5 9 10 - 2 -3 -4 -5 -8 -9 10
The function is define for all values of x greater than or equal -3 and less than or equal 3
Hence the domain of the function is;
-3 ≤ x ≤ 3
rewrite 2 5/8 into fraction
Answer:
i think 21/8
Step-by-step explanation:
because 2 times 8 plus 5 divided by 8 gives you 16 + 5 divided by 8 which is 21/8
An object moves according to a law of motion, where, its position is described by the following function, s = f(t) = t^4 - 4t + 1. The time t is measured in seconds and s in meter.a. Sketch the velocity graph and determine when is the object moving in the positivedirection.b. Draw a diagram of the motion of the object and determine the total distancetraveled during the first 6 seconds.
SOLUTION
(a) The function given is the distance graph. The velocity fuction is the derivative of the distance function. This becomes
[tex]\begin{gathered} f(t)=t^4-4t+1 \\ f^{\prime}(t)=4t^3-4 \\ v=4t^3-4 \end{gathered}[/tex]the graph is shown below
From the velocity graph above, the function is moving in a positive direction from 1 second and beyond
(b) The diagram of motion of the object is shown in the distance graph below
The total distance travelled is the integral of the velocity function from 0 to 6 as shown below
[tex]\begin{gathered} \int_0^64x^3-4 \\ =[\frac{4x^4}{4}-4x]_0^6 \\ =[x^4-4x]_0^6=6^4-4(6)-(0^4-4(0)) \\ =1296-24-0 \\ =1272 \end{gathered}[/tex]Hence the answer is 1272 m
Write the statement as a conditional statement, then tell which part is the hypothesis and which is the conclusion. Write the inverse, converse, and contrapositive of your conditional statement:
People who reduce their time in the shower will save money on water.
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
What is the conditional statement?A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
Inverse Statement: If people did not reduce their time in the shower, then they will not save money on water.
Converse Statement: If they will save money on water then people reduce their time in the shower.
Contrapositive Statement: If they will not save money on water then people do not reduce their time in the shower.
Learn more about the conditional statement here:
brainly.com/question/7066208
#SPJ1
Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 61 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 8.3 and a standard deviation of 2.4. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
What is a confidence interval?
In statistics, a confidence interval describes the likelihood that a sample size would fall between such a set range of values for a specific percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% likelihood that the true value comes inside that range if the following are examples of 10.00 produced using a statistical model with a 95% standard error of 9.50 - 10.50.In the study of chocolate chips,
sample size, n=61
mean, x=8.3
standard deviation, s=2.4
90% of the confidence interval
[tex]8.3-(\frac{1.28*2.4}{\sqrt{61} } ) < m < 8.3+(\frac{1.28*2.4}{\sqrt{61} } )[/tex]
7.9067<m<8.6933
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
To learn more about confidence intervals here:
https://brainly.com/question/15712887
#SPJ1
Use the list below to complete each sentence.
factor
product
1. -3- (-12)=-12-(-3)
positive
negative
a. This equation is written using the
of Multiplication.
additive inverses
Distributive Property
b. Both factors in this equation are Poritiv
c. The product will be Distributive property
3. (5 (-9))-6-5-((-9). 6)
b. One
2. -7 (-8+8)=[-7 (-8)] + [-7.8]
a. This equation is written using the
b. The product of this equation is 0. This is because the sum of the
,-8 and 8, is equal to 0.
a. This equation is written using the
of Multiplication.
are positive.
c. The
negative
Commutative Property
Associative Property
is negative, while the other two
will be negative.
1a) This equation is written using the Distributive Property of Multiplication.
b) Both factors in this equation are negative.
c) The product will be positive.
2a) This equation is written using the Additive inverses of Multiplication.
b) The product of this equation is 0.
c) This is because the sum of (-8+8) is equal to 0.
3a) This equation is written using the Commutative Property of Multiplication.
b) The products of the commutative multiplications do not change.
c) This is because changing the order of factors does not affect the solution.
What are the properties of multiplication?The properties of multiplication are:
Identity Property of Multiplication (product of 1 and another factor remains the factor.)Associative Property of Multiplication (grouping order of factors does not change the product.)Distributive Property of MultiplicationCommutative Property of Multiplication (the order of factors does not change the product.)For the distributive property, multiplying the sum of two numbers by another number gives the same result as distributing the first number to both other numbers and multiplying them separately and adding.
1) -3(-12) = -12(-3)
= 36 = 36
2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
= -7(0) = [56 + - 56
0 = 0
3. (5 (-9))-6 = -5 ((-9) +6)
(-45)-6 = -5(-54)
270 = 270
Learn more about the properties of multiplication at https://brainly.com/question/10412
#SPJ1
Question Completion:2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
3. (5 (-9))-6 = -5 ((-9) +6)
A bag contains 42 red, 42 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is purple or not red
The probability of a candy when randomly taken is purple or not red is 0.235
Given,
Number of red candies in the bag = 42
Number of green candies in the bag = 42
Number of yellow candies in the bag = 20
Number of purple candies in the bag = 32
We have to find the probability of a candy when randomly taken is purple or not red.
Probability, P(E) = Number of favorable outcomes / Total number of favorable outcomes
Here,
Number of favorable outcomes = 32
Total number of favorable outcomes = 42 + 42 + 20 + 32 = 136
So,
P(E) = 32/136 = 0.235
That is,
The probability of a candy when randomly taken is purple or not red is 0.235
Learn more about probability here:
https://brainly.com/question/21667917
#SPJ1
if a || b, m<2=63°, and m<9=105°, find the missing measure of m<7=?
Vetical angles are on opposite sides of the intersection of two lines, in this case, when lines c and b intersect, <7 and <9 are formed, these angles are vertical and m<7 = m<9, then:
m<7 = 105°