Answer:
1. x = 55°
2. x = 11°
3. x = 30°
4. x = 19°
Step-by-step explanation:
Trigonometric Identities
[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]
[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]
Question 1
[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]
[tex]\implies x=55^{\circ}[/tex]
Question 2
[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]
[tex]\implies x=11^{\circ}[/tex]
Question 3
[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]
Question 4
[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]
The graph shows that is translated horizontally and vertically to create the function .
On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.5) and crosses the y-axis at (0, 1). g (x) approaches y = 2 in quadrant 2 and increases into quadrant 1. It goes through (0, 2) and (2, 3).
What is the value of h?
−2
−1
1
2
According to the function transformations, the value of h is -2
How to determine the value of h?The complete question is in the attachment
The functions are given as:
[tex]f(x) = (2.5)^x[/tex]
[tex]g(x) = (2.5)^{x-h[/tex]
From the question, we understand that the function f(x) is translated to the left to get g(x)
From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).
This transformation is represented by:
(x, y) => (x + 2, y)
So, we have:
x - h = x + 2
Evaluate the like terms
h = -2
Hence, the value of h is -2
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Answer:H=-2
Step-by-step explanation:
Examples for Continuous rv X
1. Given the pdf:
f(x) {1/4 e^-1/4x} x>0
0, otherwise
Find: a. E(X) and b. Var(X)
Use the definitions of expectation and variance.
Expectation[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]
Integrate by parts,
[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]
with
[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]
[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]
(since the integral of the PDF is 1, and this integral is 4 times that)
Variance[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]
Compute the so-called second moment.
[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]
Integrate by parts, with
[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]
[tex]E(X^2) = 8 E(X) = 32[/tex]
and the variance is
[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]
Which pair of statements describes the end behavior of the graph of the function f(x) = x3 + 2x2 − 5x − 6?
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?
A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.
B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.
C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.
D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.
If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.
Hence, the correct option is D.
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For the data set 7, 5, 10, 11, 12, the mean, X, is 9. What is the standard
deviation?
Answer:
The standard deviation is about 2.915
Step-by-step explanation:
Answer:
= 2.9154759474227
Step-by-step explanation:
if 200÷10=4×u then u=?
Answer:
The answer is 5
Because 200÷10 =20.
So I'm this case, 4x=20. Divide both sides by 4 and the answer is 5. So X=5
5
Answer:
u = 5Step-by-step explanation:
if 200÷10=4×u then u=?
200 : 10 = 4u
20 = 4u
u = 20 : 4
u = 5
---------------------------
check
200 : 10 = 4 * 5
20 = 20
the answer is good
Which shows the first step in the solution to the
equation log₂x + log₂(x - 6) = 4?
log was used calculate big numbers before calculators
log is a re-arranged way to show a number with an exponent
example
log₂ 16 = 4 means 2^4 = 16
logx(Z) = y means x^y=Z
log(x-6)/log(2) + log(x)/log(2) = 4
(log(x-6)+ log(x))/log(2) = 4
(log(x-6)+ log(x)) = 4log(2)
(log(x-6)x) = log(16)
x=8
Use Modus Ponens to deduce the conclusion from each of the following pairs of premises:
a = b ∧ b = c
(a = b ∧ b = c) ⇒ a = c
The conclusion is a=c statement
A modus ponens argument has the same structure as a syllogism, with two premises and a conclusion:
If P, then Q.
P occurs.
Consequently, Q occurs.
The Modus Ponens rule of inference or rule of logic requires a single premise and its logical consequences. A conditional statement states that if event 1 occurs, event 2 will also occur and that event 2 will be inferred as the outcome if event 1 occurs. For instance, if A implies B and A is assumed to be true, then it follows that B must also be true according to the Modus Ponens rule.
Hence, By modus Ponens
a=b∧b=c ⇒ a=c
So, given a=b∧b=c Then
⇒a=c.
Hence the conclusion is a=c statement .
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Question 10 of 33
Which of the following is a characteristic of a regular tessellation?
O A. It uses only one type of regular polygon.
OB. It uses more than one type of regular polygon.
O C. It allows for overlaps and spaces between shapes.
OD. It does not cover a surface completely.
SUBMIT
A tessellation that uses only one type of regular polygon.
What is Polygon?
The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.
When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.
A regular tessellation is tessellation made up by using only one type of regular polygon. These are made up of entirely congruent regular polygons all that joining vertex to vertex.
Hence, A is the correct option.
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Enter the amplitude of the function. f(x)=2sin x
Answer:
2
Step-by-step explanation:
In asin(bx - c) + d, a is the amplitude. In this case, it's 2.
Brainliest, please :)
14. What is the measure of ZABC in the image shown? OE A B 10x - 10 100 - 2x 2x + 10 C 14. What is the measure of ZABC in the image shown ? OE A B 10x - 10 100 - 2x 2x + 10 C
Answer: 110 degrees
Step-by-step explanation:
By the exterior angle theorem.
[tex]10x-10=100-2x+2x+10\\\\10x-10=110\\\\\therefore \angle ABC=110^{\circ}[/tex]
The power of an exponential expression raised to a power is the product of the exponents.
Answer:
[tex](y {}^{c} ) {}^{d } = y {}^{c \times d} \\ = y {}^{cd} \\ \\ \\ \\ \\ (v {}^{3} ) {}^{7 } \\ = v {}^{3 \times 7} \\ = v {}^{21} [/tex]HOPE THAT HELPS.A pool a possible candidate for a student council consists of 14 freshmen and 8 softwares how many different councils consisting of 5 freshmen and 7 sophomores are possible
The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.
We have given that,
A pool of possible candidates for a student council consists of 14 freshmen and 8 software.
We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible
What is the combination?[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]
The total number of the council is
[tex]_{10} C_5\times _9 C_7[/tex]
=252(36)
=9216
The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.
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Giving you the brainliest!
Answer:
The answer will be J
Step-by-step explanation:
Since you see, that the 67,896 will need to be rounded. It rounds up to 70,000 so you can elinmate M & N. 22% can be converted as a decimal to 0.2, also equals to 0.20. So elinmate L. Now you have J and K. You always times with these kinds of percentage.
Therefore the Answer Will Be J: 70,000 timed by 0.20.
Expert-Certifieder of Cousin.
A rectangular basketball court measures with a length of 82yds and
Width of 38 yards What is the perimeter and area?
Answer:
area:3116 perimeter:240
Step-by-step explanation:
the formula of area is always length x width=82x38 =3116the formula for the perimeter is always length+length+width+width=82+82+38+38 =240Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}\circ\leftharpoonup}}[/tex]
Pelet'rimeter =
Area = 3116 cm^2
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}\circ\leftharpoonup}}[/tex]
[tex]\bullet[/tex] Let's work out the perimeter
[tex]\twoheadrightarrow\sf P=2(a+b)[/tex]. a=length & b=width
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf P=2(82+38)[/tex]
[tex]\bullet[/tex] Perform the addition operation
[tex]\twoheadrightarrow\sf P=2\cdot120[/tex]
[tex]\bullet[/tex] Multiply and obtain the perimeter
[tex]\twoheadrightarrow\sf P=240cm[/tex]
[tex]\bullet[/tex] Now let's find the area
[tex]\twoheadrightarrow\sf A=lw[/tex] l=length w=width
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf A=82\cdot38[/tex]
[tex]\bullet[/tex] Multiply and obtain the area
[tex]\twoheadrightarrow\sf A=3116cm^2[/tex]
--
Hope that this helped! Best wishes.
[tex]\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}[/tex]
--
which matrix can be used to solve the system
Answer:
6x + 7y = 14
7x + 8y = 27
6 7. x = 14
7 8. y = 27
option B
The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?
Answer:
212520 different committees
Step-by-step explanation:
Candidates
For a President: 23
For a Vice President: 22
For a Secretary: 21
For a Treasurer: 20
Number of ways: (23)(22)(21)(20) = 212520
Hope this helps
Answer:
To whom it may concern the answer to this problem would be 212,520.
Step-by-step explanation:
Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...
[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]
Remember that the 19! cancel each other out. Hope this helps!
6x+2y=20 2x-3y=3 solve by substitution
The solution of the system of linear equation by substitution method is (3,1).
What is the method of substitution?The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.
Given here the linear equations are
Equation 1: 6x+2y=20
Equation 2: 2x-3y=3
in equation 1 the value of y will be
6x+2y=20
⇒2y=20-6x
⇒y=(20-6x)/2
⇒y=10-3x
substituting the value of y in the equation 2, we will get
2x-3y=3
⇒2x-3(10-3x)=3
⇒2x-30+9x=3
⇒11x-30=3
⇒11x=30+3
⇒11x=33
⇒x=33/11
⇒x=3
putting the value of x in value of y in equation 1
y=10-3x
⇒y=10-3(3)
⇒y=10-9
⇒y=1
The solution of the system of linear equation by substitution method is (3,1).
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*30pts*What is the value of x in the triangle?
Answer:
A.4
Step-by-step explanation:
Using the sine rule
sin(α)/A equals sin(β)/B
From the question & inserting values,
sin(90°)/8 equals sin(30°)/x
∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8
∴x equals 4
You can learn more on the sine rule in case you get confused.
Answer:
A
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 8 ( divide both sides by 2 )
x = 4
A recipe calls for 4 cups of peanuts for 5 cups of flour. Using the same recipe, how many cups of flour will you need for 3 cups of peanuts
I really need help
Simplify:
(x-1)+(12–7.5x)
Answer:
[tex]-6.5x+11[/tex]
Step-by-step explanation:
Expand The Brackets:
[tex]x-1+12-7.5x[/tex]
[tex]=x+(-1)+12+(-7.5x)[/tex]
Combine Like Terms:
[tex]=x+(-1)+12+(-7.5x)[/tex]
[tex]=(x+-7.5x)+(-1+12)[/tex]
Answer:
[tex]-6.5x+11[/tex]
I Hope This Helps
Q6. This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.
The following is the actual question: Find the highest and lowest value of the equation in the given picture within the unshadowed region.
The graph of all the inequalities are given below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.
y ≥ x, the region is left to the line.
y < -(3/7)x – 7, the region is left to the line.
y ≤ (5/3)x – 8, the region is right to the line.
y ≥ 14 – (11/12)x, the region is right to the line.
y = -(3/2)x + 5, this is the equation of line.
All the graphs are shown below.
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I will give Brainliest
Which is a discrete random variable?
W = "exact time it takes for a computer to update its software"
Z = "results of flipping two coins"
X = "weight of the microprocessor inside your computer"
Y = "height of an emperor penguin on Antarctica"
Answer:
I believe that it should be Y; Height of an emperor penguin on Antarctica
Answer:
Z = "results of flipping two coins"
Step-by-step explanation:
A discrete variable is one which can take only certain values and usually represents values that are counted. The result of flipping two coins can only take a certain number of values of heads or tails (1 head and 1 tail, two heads, or two tails); therefore it is a discrete variable.
A continuous variable is one which can take any value, and usually represents values that are measured. The rest of the options provided (W, X, and Y) are all measurements, and are therefore continuous, not discrete.
Also, among the options presented, option Z is the only one which is "random".
You can make a tent by throwing a piece of cloth over a clothesline, then securing the edge to the ground with stakes so that an isosceles triangle is formed. How long would the cloth have to be so that the opening of the tent was 8 feet wide and 3 feet high?
Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.
How long should the length of the cloth be?The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.
That length - according to the Pythagoras theorem - would be:
= √(6² + (8 /2)²)
= √(36 + 16)
= 7.2 ft
As this is the length of one side of the cloth, the length of the entire cloth is:
= 7.2 x 2
= 14.4 ft
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Which point is a reflection of Z(5/1, 3) across the x-axis? Please I will give the brainliest
Answer: (5/1, -3)
Hope this helps :)
Answer:
Look at the attachment.
Step-by-step explanation:
Look at the attachment.
determine if x-3 is a factor of f(x)=x^3-x^2-5x-3
Step-by-step explanation:
please mark me as brainlest
Answer:
(x - 3) is a factor of the given function
Step-by-step explanation:
Given function:
[tex]\implies f\:\!\:(x)=x^3-x^2-5x-3[/tex]
If (x - 3) is a factor of the given function then [tex]f\:\!\:(3) = 0[/tex]
Substitute x = 3 into the function and solve:
[tex]\implies f\:\!\:(3)=(3)^3-(3)^2-5(3)-3[/tex]
[tex]\implies f\:\!\:(3)=27-9-15-3[/tex]
[tex]\implies f\:\!\:(3)=0[/tex]
Therefore, as [tex]f\:\!\:(3) = 0[/tex] then (x - 3) is a factor of the given function.
Solve for x : 7x + 8 < 1/6 (42x+48)
X = all real number
X has no solution
X = 0
Answer:
[tex]\fbox {all real numbers}[/tex]
Step-by-step explanation:
7x + 8 = 1/6 (42x + 48)
7x + 8 = 7x + 8
x = all real numbers
A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as
P = 0.006A2 − 0.02A + 120. Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.
Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The pressure is given by:
P = 0.006A² - 0.02A + 120.
When the pressure is of 125 mmHg, we have that:
0.006A² - 0.02A + 120 = 125.
0.006A² - 0.02A - 5 = 0.
Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:
A = -30 and A = 27.
Age has to be positive, hence the man is 27 years old.
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What was the initial quantity of vanadium-49, which has a half-life of 330 days, if after 540 days there is a 1,750 g sample remaining?a.)5,440.42g b.)3,500g C.) 8,700g d.)2,863.63g e.)98g
Answer:
(a) 5440.42 g
Step-by-step explanation:
The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...
Q = Q₀(1/2)^(t/330) . . . . . where t is in days
__
The amount after 540 days is ...
1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀
Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g
The initial quantity was about 5440.42 grams.
Choose the correct graph of the following condition. {(x, y) : x - y6}
The correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.
What is a graph?
A graph is a diagram showing the relation between variable quantities each measured along one of a pair of axes at right angles.
In this case, the correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.
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D − 37 = 40
D =
Check your solution.
− 37 = 40
