Answers
Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:
a. t > w.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.
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Related Questions
Simplify. Show work.
3² x 5 + 4 =
Answers
Answer:
49
Step-by-step explanation:
[tex]3^{2} *5+4[/tex]
= [tex]9*5+4[/tex] Simplify the exponents.
= [tex]45+4[/tex] Multiplication.
= 49 Addition.
Answer:
49
Step-by-step explanation:
1. Whenever there is an exponent, we solve that first. 3^2 is 9.
2. In an equation, multiplication, and division is first, and since there is no division in the equation, we do the multiplication first. 9 x 5 is 45.
3. We finish by adding 4 to 45, which is 49.
f(x) = x^2 + 4x + 20 find the real roots. take your time if you want :)
Answers
Answer:
No real roots
[tex]x = -2 + 4i, x = -2 - 4i[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the Quadratic Formula.
Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Given our Equation: [tex]f(x) = x^2 + 4x + 20[/tex]
a = 1b = 4c = 20Set the equation to 0 and solve using the formula.
Solve[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-4\pm\sqrt{4^2 - 4(1)(20)}}{2(1)}[/tex][tex]x = \frac{-4\pm\sqrt{16 - 80}}{2}[/tex][tex]x = \frac{-4\pm\sqrt{-64}}{2}[/tex][tex]x = \frac{-4\pm8i}{2}[/tex][tex]x = -2 + 4i, x = -2 - 4i[/tex]There are no real roots to the quadratic.
Six cards with the numbers 1 to 6 are randomly placed face down on a table. what is the probability that a card with a 4 is chosen?
Answers
Answer:
P(draw 4) = 1/6
Step-by-step explanation:
Six cards means: n(s) = 6
When solving an equation, Anne's first step is shown below. Which property justifies
Anne's first step?
Answers
The justification used is multiplicative property of equality because both sides are multiplied by the same value
Solving linear equationsGiven the expression below
-1/3(4x^2 - 3) - 3 = 5x^2 - 2
We are to determine the justification by Anne to get the step 2 as shown
(4x^2 - 3) - 3 = -3(5x^2 - 2)
Expand
(4x^2 - 3) - 3 = -15x^2 + 6
Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value
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Analyze the diagram below and complete the instructions that follow. (7x - 3) (12x -7) Solve for x.
Answers
Answer:
Step-by-step explanation:
(7x-3)(12x-7)
we are solving for x and we are multiplying.
we start with the x's 7x*12x= 84x
-3*-7=21
so now we have
84x+21=0
the 0 is a placer for answering the question
we minus 21 to both sides
84x=-21
now we divide
84/-21= -4
x=-4
Tony types at a rate of 30 words per minute. how many words does he type in 3 minutes?
Answers
Answer:
He can type 90 words in 3 minutes.
Step-by-step explanation:
We know how many words he can type per minute already. So now, to find how many words he can type in 30 minutes, simply multiply 3 by 30.
[tex]3 \times 30=90[/tex]
So 90 is our answer.
Please someone helpp
Answers
Due to length restrictions, we cannot summarize the results of the three parts about the quadratic equations of the form x² + b · x + c = 0. We kindly invite to check the explanation for further details.
How to apply algebra properties to solve quadratic equations of the form x² + b · x + c = 0In this question we have several exercises with quadratic equations of the form x² + b · x + c = 0 and, to be more exactly, quadratic equations with the following characteristics:
x² - (r₁ + r₂) · x + r₁ · r₂ = 0 (1)
Please notice that the first grade coefficient is equal to the inverse of the sum of the two roots and the zero grade coefficient is the product of the two coefficients.
Now we proceed to resolve all the points:
Part I
a) (x + 17) · (x + 1) = x² + 18 · x + 18, r₁ = - 17, r₂ = - 1
b) (x + 5) · (x + 4) = x² + 9 · x + 20, r₁ = - 5, r₂ = - 4
c) (x - 11) · (x - 1) = x² - 12 · x + 11, r₁ = 11, r₂ = 1
d) (x - 18) · (x - 2) = x² - 20 · x + 36, r₁ = 18, r₂ = 2
Part II
a) x² - 12 · x + 27
b) (x + 4) · (x + 8)
c) (x - 5) · (x - 7)
d) (x - 4) · (x - 5)
Part III
a) (x - 18) · (x + 3) = x² - 15 · x - 54
b) (x + 18) · (x + 3) = x² + 21 · x + 54
c) (x + 18) · (x - 3) = x² + 15 · x - 54
d) (x - 18) · (x - 3) = x² - 21 · x + 54
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Prove the following trigonometric identities
Answers
Answer:
Greetings !
check the attachment above☝️ but i haven't done the second question wait a moment. thx
Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x
Answers
Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:
"Zero, because the discriminant is negative".
A quadratic equation is a polynomial of degree 2, in a single variable x.
The standard form of a quadratic equation is ax² + bx + c = 0.
The quadratic formula is used to find the solution(s)/root(s) of this equation.
The quadratic formula is:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
In this formula, [tex]b^2-4ac[/tex] is called the discriminant (D).
The solution(s)/root(s) of the equation, depends on this discriminant value as follows:
When D > 0, the roots of the equation are real and distinct.When D = 0, the roots of the equation are real and equal.When D < 0, then no real roots exist.In the question, we are given that the simplest form of Quincy's equation in the radical form was,
[tex]x = \frac{-3 \pm \sqrt{-19} }{2}[/tex].
Comparing this to the quadratic formula,
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
we get the discriminant (D) = -19.
Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:
"Zero, because the discriminant is negative".
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For complete question, refer to the attachment.
A conjecture and the paragraph proof used to prove the conjecture are shown. Given: angle 2 is congruent to angle 3. Prove: angle 1 and angle 3 are supplementary. A horizontal line. Two rays extend from upper region of the line diagonally down to the left and right and intersect the line forming interior angles labeled as 2 and 3 and an exterior angle labeled as 1. Drag an expression or statement to each box to complete the proof. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. ∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the Response area. Therefore, m∠1+ Response area = 180° by the definition of supplementary. It is given that ∠2≅ Response area, so m∠2=m∠3 by the Response area. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary by the definition of supplementary. angle congruence postulatelinear pair postulatem∠2m∠3∠3∠2
Answers
The fill up of the missing points are:
∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the Linear Postulate theorem. Therefore, m∠1+m∠2 = 180° by the definition of supplementary. It is given that ∠2≅ ∠3, so m∠2=m∠3 by the Congruence Postulate theorem. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary.What is the angles about?Using the image attached, one can see that m<1 and m<2 creates a kind of linear pair hence one can say they are both supplementary using the law of LINEAR POSTULATE THEOREM.
Based on the fact that the supplementary angles add up to 180 degrees, therefore:
m<1 + m<2 = 180 - will be equation 1
Since the interior angles m<2 and m<3 are known to be equal based on the CONGRUENCE POSTULATE THEOREM. Therefore
m<2 = m<3 --- will be equation 2
Then place eqn. 2 into eqn. 2
m <1 + m <3 = 180
This connote that m<1 and m<3 are supplementary.
Hence, The fill up of the missing points are:
∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the Linear Postulate theorem. Therefore, m∠1+m∠2 = 180° by the definition of supplementary. It is given that ∠2≅ ∠3, so m∠2=m∠3 by the Congruence Postulate theorem. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary.Learn more about the angle from
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Given f(x) =
8x+1
2x-9
what is the end behavior of the function?
ONA
LR
OAS X→∞, f(x) → 9; as x→ ∞, f(x) → 9.
-
OAS X→∞, f(x) →-9; as x, f(x) → -9.
OAS X →∞, f(x) → -4; as x → ∞, f(x) → -4.
As
OAS X-∞, f(x)→ 4; as x→ ∞, f(x)→ 4.
O
BASSENG
D
se
Answers
The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is [tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex].
The last option is correct.
What is the range of the function?The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.
The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.
From the information given:
[tex]\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}[/tex]
Inverse of [tex]\mathbf{\dfrac{8x +1}{2x -9 }}[/tex] becomes [tex]\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}[/tex]
The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:
[tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex]
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Please help with this
Answers
Answer: Circle lines
Step-by-step explanation:
Hopefully the attached image helps, it is a diagram of all the labeled lines on a circle excluding the radius (BG or GE)
Use the box-and-whisker plots to determine which statements are true.
Answers
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?
A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers. The whiskers represents the minimum and maximum scores.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
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Loc can mow his entire lawn in 20 minutes; Loc's roommate Reza needs 30 minutes to mow the entire lawn. If Loc starts mowing at 1:00, mows for five minutes and then Reza starts to help with his own mower, at what time will they finish mowing the lawn
Answers
Loc and Reza together will finish the entire mowing process on the lawn at 1:14 p.m.
Calculation of total mowing time takenLoc mow the total area in 20 mins.
So, his pace is 1 lawn / 20 minutes or 1/20th of a lawn each minute.
Reza's pace is 1 lawn / 30 minutes, or 1/30th of a lawn each minute because he can mow the grass in that amount of time.
Reza joins Loc after he has been mowing for 5 minutes. He can mow 1/20th of the grass in these 5 minutes, which is 5/20th of the lawn =1/4th lawn
There is currently just
1-1/4=3/4 of the lawn left to complete.
We may construct the following equation by assuming that they mow together for x mins:
1/20x + 1/30x = 3/4 [amount done by Loc + Reza = total amount]
⇒(3x+2x)/60x = 3/4
⇒5x/60 = 3/4
⇒x/12= 3/4
⇒4x=36
⇒x= 9 mins
So, when they collaborate, they can complete the lawn in 9 minutes.
Hence, Loc mows alone for 9+5 mins = 14 mins
Therefore, it is concluded that starting at 1 p.m they finish the mowing at 1:14 p.m.
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(2x+5/60-95x-3/30=3/2
Answers
Answer:
x = -0.01685
(Is the equation written correctly? This feels like a very unfortunate number)
Step-by-step explanation:
(2x+5/60-95x-3/30=3/2
2x+(5/60)-95x-(3/30)=3/2
2*(2x+(5/60)-95x-(3/30))=3 [Multiply both sides by 2]
4x+(10/60)-190x-(6/30))=3
(2/30)-186x-(6/30))=3 [Simplify]
-186x-(4/30)=3
-186x=3+(4/30)
-186x=(90/30)+(4/30)
x = (94/30)/(-186)
x = -0.01685
Write the following Arithmetic Sequence using an Explicit Formula: a1 = 14 ,an = an-1 – 6 A.) an = 6 – 14(n – 1)
B.) an = 14 – 6(n – 1)
C.) an = 6 + 14(n – 1)
D.) an = 14 + 6(n – 1)
Answers
The explicit formula for the sequence is an = 14-6(n-1)
Arithmetic sequenceThis are sequence that has. a common difference that is the difference between the preceding and sthe explicit formula for the sequence is an = 14-6(n-1) is equal.
Given the following
a1 = 14
an = an-1 - 6
The nth term of the sequence is expressed as:
An = a+(n-1)d
an = 14+(n-1)(-6)
an = 14 -6n + 6
an = 14-6(n-1)
Hence the explicit formula for the sequence is an = 14-6(n-1)
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What is the value of the discriminant for the quadratic equation zero equals 2x^2+x-3
Answers
Discriminant for the quadratic equation [tex]2x^2+x-3=0[/tex] is [tex]d=25[/tex]
How to find the d Discriminant of the quadratic equation ?
We know that the standard quadratic equation
[tex]ax^2+bx+c=0[/tex]
Discriminant of the equation is [tex]d=b^2-4ac[/tex]
Equation given in the question is
[tex]2x^2+x-3=0[/tex]
So we can find the values of [tex]a,b,c[/tex]
[tex]a=2\\b=1\\c=-3[/tex]
Substitute the values
[tex]d=1^2-4*2*(-3)\\d=1+24\\d=25[/tex]
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Please help Urgent
1. Explain the steps to use coordinates in calculating the perimeter and area of polygons? Explain your procedure when working with diagonal sides and irregular shapes on the coordinate plane.
2. Explain how the distance formula and slope formula are used to classify various quadrilaterals and triangles.
Answers
The way to use the distance formula to classify quadrilateral include:
Use the distance formula to measure the lengths of the sides.Use the slope to check whether the sides are perpendicular and form right angles.Use the slope to check whether the diagonals are perpendicular to eachHow to illustrate the information?The steps to calculate the perimeter and area of a polygon:
Step 1: Plot the given points on the graph.
Step 2: Connect the points and identify the figure.
Step 3: Determine lengths by counting the grid lines.
Step 4: Use a formula to calculate the perimeter and area if one exists.
Step 5: If there are no formulas for a figure, the perimeter can be calculated by summing the lengths of the sides. We might estimate the area without an area formula by counting the number of small squares enclosed.
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Quick please!!
What’s the distance between the following points?
Answers
Answer:
answer is 6^2 × 6^2 = squate root 72
distance equals 8.485
Answer:
6[tex]\sqrt{2}[/tex] ≈ 8.49 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = ( 8, - 9 )
d = [tex]\sqrt{(8-2)^2+(-9-(-3))^2}[/tex]
= [tex]\sqrt{6^2+(-9+3)^2}[/tex]
= [tex]\sqrt{36+(-6)^2}[/tex]
= [tex]\sqrt{36+36}[/tex]
= [tex]\sqrt{72}[/tex]
= [tex]\sqrt{36(2)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]
= 6[tex]\sqrt{2}[/tex] units ← exact length
≈ 8.49 units ( to 2 dec. places )
x+2/3 - x+1/5 = x-3/4 - 1
Answers
Hope it will helpful for you
Answer:
x = 157/60
Step-by-step explanation:
x + 2/3 - x + 1/5 = x - 3/4 - 1
x - x - x = -2/3 - 1/5 - 3/4 - 1
-60x/60 = -40/60 - 12/60 - 45/60 - 60/0
-60x = -40 - 12 - 45 - 60
-60x = -157
x = -157/-60
x = 157/60
157/60 + 2/3 - 157/60 + 1/5 = 157/60 - 3/4 - 1
2/3 + 1/5 = 157/60 - 3/4 - 1
40/60 + 12/60 = 157-60 - 45/60 - 60/60
40 + 12 = 157 - 45 - 60
52 = 157 - 105
Solve this please!!!
Answers
Answers:
i) [tex]\sf (x + 2)(x+ 3)[/tex]
ii) [tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Factorize expression's:
i.
[tex]\sf (x + 1)^2 + 3(x + 1) + 2[/tex]
apply perfect square and distributive method
[tex]\sf (x^2 + 2(x)(1) + 1^2) + 3x + 3 + 2[/tex]
expand
[tex]\sf x^2 + 2x + 1 + 3x + 3 + 2[/tex]
collect like terms
[tex]\sf x^2 + 2x + 3x + 3 + 2 + 1[/tex]
add/subtract like terms
[tex]\sf x^2 + 5x + 6[/tex]
breakdown
[tex]\sf x^2 + 3x + 2x+ 6[/tex]
factor common term
[tex]\sf x(x + 3) + 2(x+ 3)[/tex]
collect into groups
[tex]\sf (x + 2)(x+ 3)[/tex]
ii.
[tex]\sf (9x^2 + 9x - 4)(9x^2 + 9x - 10) - 72[/tex]
breakdown
[tex]\sf (9x^2 + 12x - 3x - 4)(9x^2 + 15x - 6x - 10) - 72[/tex]
factor common term
[tex]\sf (3x(3x + 4) -1( 3x + 4)) ( (3x(3x + 5)- 2(3x +5) )- 72[/tex]
collect like terms
[tex]\sf (3x -1)( 3x + 4) (3x- 2)(3x +5) - 72[/tex]
expand
[tex]\sf 81x^4+162x^3-45x^2-126x-32[/tex]
factor
[tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Answer:
[tex]\textsf{1.} \quad (x+3)(x+2)[/tex]
[tex]\textsf{2.} \quad (3x+1)(3x+2)(9x^2+9x-16)[/tex]
Step-by-step explanation:
Question 1
[tex]\textsf{Given expression}: \quad(x+1)^2+3(x+1)+2[/tex]
[tex]\textsf{Let }u=(x+1) \implies u^2+3u+2[/tex]
[tex]\textsf{To factor }\:\:u^2+3u+2:[/tex]
Rewrite the middle term as u + 2u:
[tex]\implies u^2+u+2u+2[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+1)+2(u+1)[/tex]
Factor out the common term (u+1):
[tex]\implies (u+2)(u+1)[/tex]
Replace [tex]u[/tex] with [tex](x+1)[/tex] :
[tex]\implies (x+1+2)(x+1+1)[/tex]
Simplify:
[tex]\implies (x+3)(x+2)[/tex]
Question 2
[tex]\textsf{Given expression}: \quad (9x^2+9x-4)(9x^2+9x-10)-72[/tex]
Expand:
[tex]\implies 9x^2(9x^2+9x-10)+9x(9x^2+9x-10)-4(9x^2+9x-10)-72[/tex]
[tex]\implies 81x^4+81x^3-90x^2+81x^3+81x^2-90x-36x^2-36x+40-72[/tex]
Collect like terms:
[tex]\implies 81x^4+81x^3+81x^3-90x^2+81x^2-36x^2-90x-36x+40-72[/tex]
Combine like terms:
[tex]\implies 81x^4+162x^3-45x^2-126x-32[/tex]
Use the Factor Theorem:
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
[tex]\begin{aligned}\implies f \left(-\dfrac{1}{3}\right) & =81\left(-\dfrac{1}{3}\right)^4+162\left(-\dfrac{1}{3}\right)^3-45\left(-\dfrac{1}{3}\right)^2-126\left(-\dfrac{1}{3}\right)-32\\ & = 1-6-5+42-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 1) is a factor.
[tex]\begin{aligned}\implies f \left(-\dfrac{2}{3}\right) & =81\left(-\dfrac{2}{3}\right)^4+162\left(-\dfrac{2}{3}\right)^3-45\left(-\dfrac{2}{3}\right)^2-126\left(-\dfrac{2}{3}\right)-32\\ & = 16-48-20+84-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 2) is a factor.
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(ax^2+bx+c)[/tex]
Compare the coefficient of x⁴ and the constant to find a and c:
[tex]\implies 3 \cdot 3 \cdot a=81 \implies a=9[/tex]
[tex]\implies 2c=-32 \implies c=-16[/tex]
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(9x^2+bx-16)[/tex]
Expand:
[tex]\implies f(x)=81x^4+(81+9b)x^3-(126-9b)x^2-(144-2b)x-32[/tex]
Compare the coefficient of x³ to find b:
[tex]\implies 81+9b=162 \implies b=9[/tex]
Therefore, the fully factorized expression is:
[tex]\implies (3x+1)(3x+2)(9x^2+9x-16)[/tex]
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can someone please help me
Answers
The trigonometric values are:
[tex]cos(\frac{3\pi}{4})=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=\frac{1}{\sqrt{2} }[/tex]
Values of trigonometric identities:The given trigonometric identities are:
[tex]cos(\frac{3\pi}{4} )\\\\sin(\frac{3\pi}{4})[/tex]
Note that:
[tex]\pi=180^o\\\\\frac{3\pi}{4}=135^0[/tex]
Therefore, using the calculator for the given expressions:
[tex]cos(\frac{3\pi}{4})=cos135^0=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=sin135^0=\frac{1}{\sqrt{2} }[/tex]
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Which system of inequalities is shown?
O A. y
y< 4
) B. y>x
y > 4
O C. y>x
y < 4
y > 4
Answers
Answer:
y < x
y < 4
Step-by-step explanation:
Dotted line means < or >, and since the shaded region is below the lines y = 4 and y = x, the answer is A.
A submarine model starts at 8 m above the bottom of the pool. It gradually goes down at a rate of 1\2 m\s
a) Graph the relation on the grid provided. Label the axes.
b) Write an equation to represent the relation.
Pleasee
Answers
The equation that represents the relation is y = 8 - 0.5x
How to graph the relation?The given parameters are:
Start = 8m
Rate = 1/2 m/s
The linear equation that represents the submarine movement is:
y = Start - Rate * x
This gives
y = 8 - 1/2 * x
Evaluate
y = 8 - 0.5x
Hence, the equation that represents the relation is y = 8 - 0.5x
See attachment for the graph
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Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.
Function: [tex]f(x)=2.56(1.04)^x[/tex]
Answers
The function that models the independent variable, x, in terms of y, is:
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
How to write the independent variable in terms of y?
Here we have the relation:
[tex]y = 2.56*(1.04)^x[/tex]
We want to write x in terms of y, so we just need to isolate x.
We have:
[tex]\frac{y}{2.56} = (1.04)^x[/tex]
Now we can apply the natural logarithm in both sides, so we get:
[tex]ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x[/tex]
Now we can just isolate x.
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
That is the function that models the independent variable, x, in terms of y.
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What is the volume, measured in cubic centimeters, of the box below? Do not
include units in your answer.
5 cm
4 cm
3 cm
Answers
Answer:
v =L× b×h
=5× 4×3
=60 cubic centimeter
The greatest question: what is the square root of nine. i don't know the answer:)
Answers
3 is the square root of nine.
The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } square root of, end square root . Finding the square root of a number is the opposite of squaring a number.
To find the fraction square root, first, find the square root of the numerator and then find the square root of denominator. After finding the square root values, simplify the fraction. For example, √(4/16), can be written as √4/√16.
(3)^2 = 9
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If the probability that a chef likes carrots is 0.13, the probability of those who like broccoli is 0.72, and the probability of those who like neither is 0.22, what is the probability of those who like both
Answers
Taking into account definition of probability, the probability of those who like both is 0.07 or 7%.
Definition of ProbabitityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Events and probability in this caseIn first place, let's define the following events:
C: The event that a chef likes carrots.B: The event that a a chef likes broccoli.Then you know:
P(C)= 0.13P(B)= 0.72In this case, considering the definition of union of events, the probability that a chef likes carrots and broccoli is calculated from:
P(C∪B)= P(C) + P(B) -P(C∩B)
Then, the probability that a chef likes carrots and broccoli is calculated as:
P(C∩B)= P(C) + P(B) -P(C∪B)
In this case, considering the definition of the complementary event and its probability, the probability that a chef likes NEITHER of carrots and broccoli is calculated as:
P [(C∪B)']= 1- P(C∪B)
In this case, the probability of those who like neither is 0.22
0.22= 1 - P(C∪B)
Solving
0.22 - 1= - P(C∪B)
-0.78= - P(C∪B)
- (-0.78)= P(C∪B)
0.78= P(C∪B)
Now, remembering that P(C∩B)= P(C) + P(B) -P(C∪B), you get:
P(C∩B)= 0.13 + 0.72 -0.78
Solving:
P(C∩B)= 0.07= 7%
Finally, the probability of those who like both is 0.07 or 7%.
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WILL MAKE BRAINLIEST!!
Solve for x.
Answers
Answer:
8
Step-by-step explanation:
51 + 4x + 7 = 90 - combine like terms
58 + 4x = 90 - subtract 58 from each side
4x = 32 - divide both sides by 4
x = 8
Answer:
x = 8
Step-by-step explanation:
The red square indicates that there is a right triangle. All right triangles have angles equal to 90°. Therefore, we can find the value of "x" by setting the sum of both the interior angles to 90°.
(4x + 7) + 51° = 90° <----- Sum of both angles is 90°
4x + 58 = 90° <----- Combine 58 and 7
4x = 32 <----- Subtract 58 from both sides
x = 8 <----- Divide both sides by 4
The cost of a flight is related to the distance traveled:
Miles 225 1,100 1,375 1,675 1,950 2,250
Cost ($) 50.3 111 143 187 214 196
Find the linear regression equation that models this data.
Answers
The linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (x,y) are given as follows:
(225, 50.3), (1100, 111), (1375, 143), (1675, 187), (1950, 214), (2250, 196).
Hence, inserting these points in the calculator, the linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
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