Answer:
(y+17)÷18=22.5
y+17=22.5×18
y+17=405
y=405-17
y=388
Is (x-4) a factor of f(x)=x^3- 2x^2 + 5x +1. use either the remainder theorem or the factor theorem to explain your reasoning
If x - 4 is a factor then x = 4 is a root:
f(4) = 4^3 - 2 * 4^2 + 5 * 4 + 1
= 64 - 32 + 20 + 1
= 53
since f(4) is not zero then 4 is not a root of the f(x)
Also, x - 4 is not a factor
In algebra, the remainder theorem, or Bezout's small theorem, applies the principle of polynomial division. It states that the remainder of dividing the polynomial f (x) by the linear polynomial {\ display style x-r} is equal to {\ display style f (r). }
In algebra, a factor set is a set of factors and roots of. Polynomial. This is a special case of the remainder theorem. The factor theorem shows that the polynomial f (x) has a factor only if f = 0.
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At the DVD rental store, Jamie found 6 DVDs that she wanted, but can only rent 4. How many possible choices can she make
At the DVD rental store, Jamie found 6 DVDs that she wanted, but can only rent 4. Jamie can make 15 possible choices, as per combinations of DVDs.
Number of Possible Combinations:
Given Information is as follows,
Total number of DVDs that Jamie wanted, n = 6
Number of DVDs Jamie can rent at a time, x =4
The Combinations formula is given as,
ⁿCₓ = n! / (n-x)! x!
Here, n = 6 and x = 4
Substituting these values of n and x in the Combinations formula, we get,
⁶C₄ = 6! / (6-4)! 4!
⁶C₄ = 6! / 2! 4!
⁶C₄ = 6×5×4! / 2! 4!
⁶C₄ = 6×5 / 2
⁶C₄ = 3×5
⁶C₄ = 15
Thus, Jamie can make 15 possible combinations of DVDs.
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In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio.
The correct option regarding whether the requirements for a hypothesis test are satisfied is:
D. The conditions are satisfied. The samples are random, and each sample has at least 5 successes and 5 failures.
What are the conditions for an hypothesis test?There are two conditions:
The samples should be random.Each sample should have at least 5 successes and at least 5 failures.These two conditions are satisfied for this problem, hence, researching this problem on the internet, option D is correct.
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When the decision maker must consider several possible outcomes for each alternative, each with a given probability of occurrence, this is decision making under a. uncertainty. b. risk. c. duress. d. certainty.
This is considered as decision making under risk.
Decision Making Under Risk
A circumstance in which the implications of the chosen course of action and the likelihood that it will occur are understood is referred to as decision-making under risk . For instance, the lottery selection tasks are frequently employed to examine the nature of decision-making in risky situations.
We make the assumption that there are two or more choices and that each alternative's characteristics are explicitly specified. For each attribute, the CV (coefficient of variation) is configured in case of such decision under risks. And, since in the given question, decision maker is supposed to consider several possible outcomes for each alternative, each with a given probability of occurrence. Thus the decision made will be decision under risk.
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In a professional division of a Hockey league, there are 9 total teams. How many different rankings are possible at the end of the year
Which of these statements is true for f(x) = 2.3*?
OA. The y-intercept is (0, 1).
OB. The domain is x > 0.
OC. The y-intercept is (0, 2).
OD. It is always decreasing.
The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).
How to determine the true statement?The function is given as:
f(x) = 2(3)^x
Set x = 0 to determine the y-intercept
f(0) = 2(3)^0
Evaluate
f(0) = 2
This means that the y-intercept of f(x) = 2(3)^x is (0,2)
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Which of the following functions are solutions of the differential equation y'' + y = sin(x)? (Select all that apply.) y = − 1 2 x cos(x)
The function that is the solution of the differential y" + y = sin(x) is: y(x) = -1/2(x cos x)
What is a function?A function is an expression, rule, or law in mathematics that describes a connection between one factor (the independent variable) and another variable (the dependent variable).
What is the proof of the above function?Take a look at the the following differential equation:
y" + y = sin (x)
The auxiiliary equation is
m² + 1 = 0
m² + 1-1 = -1
m² + 0 = -1
m² = -1
m = ±√-1
m = ±i
So, the complimentary function is yₐ (x) = c₁ cos x + c₂ sin x
Let the particular integral be:
yₙ (x) = A cos x + B sin x
yₙ '(x) = - A sin x + B cos x
yₙ ''(x) = - A cos x + B cos x
yₙ ''(x) = - (A cos x + B cos x)
After we have substituted yₙ (x); and yₙ''(x) in the given differential equation
y'' + y = sin (x)
= - (A cos x + B cos x) + (A cos x + B cos x) = sin(x)
0 = sin (x)
If we take the particular integral to be:
yₙ (x) = x(A cos x + B cos x)
yₙ '(x) = x(-A sin x + B cos x) + A cos x + B cos x
yₙ ''(x) = x(-A cos x - B sin x) - A sin x + B cos x + -A sin x + B cos x
Substitute yₙ (x), yₙ''(x) into the stated differential equation
y'' + y = sin (x)
x (-Acosx - Bsin x) - Asinx + Bcosx + (-Asinx + Bcosx) - x (Acosx + Bsin x) = sin (x)
-Axcosx - Bxsin x - Asinx + Bcosx -Asinx + Bcosx - Axcosx + Bxsin x = sin (x)
-2Asinx + 2Bcosx = sin(x)
Compare the coefficients of like terms on both sides of the equation
-2A = 1, B = 0
A = -1/2, B = 0
Substitute A = -1/2, B =0 into the assumed solution.
yₙ(x) = x((-1/2)cosx + (0) sinx)
= -1/2xcosx +0
= -(1/2)xcosx
Now, the general solution for the given differential equation is:
y(x) = yₓ(x) +yₙ (x)
y (x) - c₁cosx + c₂sin x -1/2x cosx
Hence, the solution is:
y(x) = -1/2xcosx
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Full Question:
Which of the following functions are solutions of the differential equation y'' + y = sin x? (Select all that apply.)
A) y = 1 2 x sin x
B) y = cos x
C) y = x sin x − 5x cos x
D) y = − 1 /2 x cos x
E) y = sin x
Helen had $12 but spent $3 of it. What per cent did she spend?
12%
25%
30%
33 1/3%
Answer:
25%
Step-by-step explanation:
3/12 = 0.25 = 25%
Answer:
25%
Step-by-step explanation:
$3 pent out of the original $12. We can ask what is the percentage of $12 that is equal to $3? This can be written as:
X($12) = $3, where X is the percentage.
X = (3/12)
X = 0.25 or 25%
Jonh is paid $26 for 8 hours work how much should he be paid for working 37 hours at the same wage
Answer:
$120.25
Step-by-step explanation:
Divide 37 by 8. You get 4.625. Multiply 4.625 by 26. You get 120.25.
I hope this helps!
A scalene triangle whose angles are all congruent possible or impossible
Answer:
impossible
Step-by-step explanation:
a scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.
because all 3 angles must be different, they cannot be congruent.
because if angles are congruent, it means that they are of equal size.
the desired definition is a paradox or oxymoron. it contradicts itself and can never be true.
Answer:
it cannot have all angles congruent: impossible.
Step-by-step explanation:
by the definition scalene, it means no angle is the same length. meaning, to have all the sides congruent (the same length) that would be impossible and it can never happen. if you would like a congruent triangle, an isosceles or equilateral is the triangle you're looking for.
Find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
The least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
A number (A) is divisible by another number (K) when the division of A by K, leaves a remainder of 0.
In the question, we are asked to find the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225.
Now, we need to know that the multiples of 225 end with 00, 25, 50, and 75.
So, to have a multiple with digits 0, 1, and 2, we need the last digits to be 00.
The smallest multiple of 225, ending with 00 is 225*4 = 900.
So, we need to have the least multiple of 900, with digits 0, 1, and 2.
We know that a multiple of 9, has a sum of its digit as 9.
The smallest multiple of 9, with digits 1, and 2, will be 12222.
Adding the last 00 to this, we get the least multiple as 1,222,200.
Thus, the least positive integer, written only by numbers 0, 1, and 2, which is divisible by 225 is 1,222,200.
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Am what I’m writing is correct? I put 2+-2=0
The diagram ends at -2
The equation would be 2-4 = -2
Answer:
Step-by-step explanation:
Start on point 2
Ends on point -2
Then:
2 + a = -2
a = -2 - 2
a = -4
then the equation is:
2 + (-4) = 0
2 - 4 = 0
Please solve for X: 11/2-x = 1/3 + 1/6
Answer: 5
Step-by-step explanation:
11/2-x = 1/3 + 1/6
-x+11/2 = 1/2
- 11/2 - 11/2
-x = -5
Divide -1 by both sides
And it gives you the answer 5.
Sun shades are sold in the shape of right isosceles triangles. if the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade?
The system of equations that can be used to find the lengths of the legs of the sun shade is given as follows:
y = 0.5x², y = 64.
How to obtain the system of equations?The system of equations is obtained considering the equation for the area of a right triangle, which is given by half the multiplication of the legs.
In this problem, we have an isosceles right triangle, meaning that both legs have the same measure.
The area of the right triangle is of 64 feet, hence the area is calculated as follows:
0.5x² = 64.
Thus the equations that compose the system are:
y = 0.5x².y = 64.Meaning that the second option is correct.
Missing InformationThe options are given by the image shown at the end of the answer.
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Please help asap!!!!!!!!!!!!
Answer:
95
Step-by-step explanation:
We know the measure of angle 4 is 85, therefore the measure of angle 2 is also 85.
Measure 2 is equal to measure 6, therefore measure 6 also equals 85, measure 8 equals measure 6 giving it the measure of 85.
Now the sum of angles 5 and 7 must equal 190, given we have two 85 degree angles, and the other two are equal, they must sum to 190, since they are equal we will divide 190 into 2, making angles 5 and 7 have a measure of 95.
Answer: 95°
Step-by-step explanation: With 2 parallel lines cut by a transversal, the following conditions are true.
Alternate interior angles are congruent. <4 and <6 are alternate interior angles, and so are <3 and <5.
Corresponding angles are congruent. Corresponding angles are angles that are in the same position in one line as the other. <1 and <5 are corresponding angles, and <4 and <6 are congruent. <2 and <6 are congruent, and <3 and <7 are congruent.
Vertical angles are congruent. Angles that are directly diagonal on the same line are congruent. <5 and <7, and <6 and <8 are examples of this.
Supplementary angles are, well, supplementary. By definition, two angles that are supplementary add up to 180°. Supplementary angles are angles that are on the same line and transversal, but not vertical angles. Rather, the angles are right next to teach other.
Alternate exterior angles are congruent. Alternate exterior angles are angles that are like alternate interior angles, but both share a position on the outside (and are diagonal.) The alternate exterior angles are <2 and <8, and <1 and <7.
Now that we have all definitions and conditions at hand, this will be easy.
If m<4 is 85°, and we want m<5, then we can see that <4 and <3 are supplementary angles. So by definition, <4 + <3 = 180°. We can substitute in <4 since we know it. We get 85° + <3 = 180°. Subtracting 85° from both sides, we get <3 = 95°.
Now we see <3 and <5 are alternate interior angles. By definition they are congruent. Thus, m<5 is 95° too.
Hope this helped!
(If my post was helpful, please mark it as Brainliest.)
Terrence’s car contains 8 gallons of fuel. He plans to drive the car m miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of m?
The correct option is A. m ≤ (8)(20)
The inequality which gives the possible values of 'm' is m ≤ (8)(20).
What is inequality?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
According to the question;
Terrence's car contains 8 gallons of fuel.
Terrence can drive the car 'm' miles using the fuel currently in the car.
The car can drive 20 miles per gallon of fuel,(which is maximum fuel capacity of the car to drive).
Then,
The total miles 'm' covered by the car is 8×20 which is maximum capacity of the car to travel.
Thus, total miles covered by the car are less than the maximum value which is given by the inequality-
m ≤ (8)(20)
Therefore, the inequality which gives the possible values of 'm' is m ≤ (8)(20).
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The complete question is-
Terrence's car contains 8 gallons of fuel. He plans to drive the car 'm' miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of 'm'?
answer choices
A. m ≤ (8)(20)
B. m ≥ (8)(20)
C. 8 ≤ 20m
D. 8 ≥ 20 m
A circle with a diameter of 10 cm and a central angle of 30° is drawn below.
what is the area, to the nearest tenth of a square centimeter, of the sector formed by the 30° angle?
(A) 5.2 (B) 6.5 (C) 13.1 (D) 26.2
Answer:
B 6.5
Step-by-step explanation:
The area of a whole circle is
a = [tex]\pi[/tex][tex]r^{2}[/tex] A whole circle is 360 degrees. We only have part of a circle. We were also given the diameter and we need the radius. The radius is half of the diameter.
a = [tex]\frac{30}{360} \pi 5^{2}[/tex]
a= 6.5 rounded.
A whole circle exists 360 degrees. The radius exists half of the diameter.
[tex]$$a = (30/360) $\pi 5^2[/tex]
a = 6.5 rounded.
The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.
How to calculate the area of a circle with diameter?The diameter of the circle exists double the radius of the circle. Therefore the area of the circle formula utilizing the diameter exists equivalent to π/4 times the square of the diameter of the circle. The formula for the area of the circle, utilizing the diameter of the circle
π/4 × [tex]$$diameter^2[/tex].
Given: diameter of the circle = 10 cm
then the radius of the circle is half of the diameter
Radius of the circle = 10/2 = 5 cm
Area of circle = [tex]$$\pi $r^2[/tex]
Where r be the radius of the circle
A whole circle exists 360 degrees. The radius exists half of the diameter.
[tex]$$a = (30/360) $\pi 5^2[/tex]
simplifying the above equation we get
[tex]$$a = 25$\pi$ /$12[/tex]
a = 6.5 rounded.
The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.
Therefore, the correct answer is option (B) 6.5
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Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. we also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the ________. therefore, angle 1 is-congruent-to angle 8 by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem
∠5 ≅ ∠8 (vertically opposite angles)
Hence, ∠1 ≅ ∠8 by the transitive property.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.
Therefore, line e and f are parallel lines cut by the the transversal g.
∠1 ≅ ∠4(vertically opposite angles)
Hence,
∠4 ≅ ∠8(corresponding angles)
Since, ∠1 ≅ ∠4
Then, by substitution,
∠1 ≅ ∠8 (transitive property)
∠5 ≅ ∠8 (vertically opposite angles)
Therefore, ∠1 ≅ ∠8 by the transitive property.
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70 men constructed 150 meter long wall in 12 days so as hoy many person construct 600 meters long wall in 30 days
112 men construct 600 meters long wall in 30 days.
What is Time and Work formula?
[tex]\frac{M_1\times D_1}{W_1}=\frac{M_2\times D_2}{W_2}[/tex]
We can find the number of persons who can construct 600 meters wall as shown below:
Here, [tex]M_1=70[/tex]
[tex]D_1=12[/tex]
[tex]W_1=150[/tex]
[tex]W_2=600[/tex]
[tex]D_2=30[/tex]
We have to find [tex]M_2[/tex]
Putting in formula
[tex]\frac{70 \times 12}{150}=\frac{M_2\times 30}{600}[/tex]
[tex]M_2=\frac{70\times 12\times 600}{150\times 30}[/tex]
[tex]M_2=112[/tex]
Hence, 112 men can construct 600 meters wall in 30 days.
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What is the solution to 9|x + 8| > 45?
The solution to the inequality is x > -3 or x < -13
How to solve the inequality?The inequality is given as:
9|x + 8| > 45
Divide through by 5
|x + 8| > 5
Split the inequality
x + 8 > 5 or x + 8 < -5
Solve for x
x > -3 or x < -13
Hence, the solution to the inequality is x > -3 or x < -13
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which of the following rational functions is graphed below?
Answer: C
Step-by-step explanation:
There is a vertical asymptote at x=3, so the denominator should have a factor of (x-3).
This eliminates everything except for C.
2/y = 4/2 find y
Answer is y=1 but how?
[tex] \frac{2}{y} = \frac{4}{2} [/tex]
[tex]4 = 4y[/tex]
[tex] \frac{4}{4} = y[/tex]
[tex]1 = y[/tex]
Hope it helps you any confusions you may ask!
Let's see
2/y=4/22/y=2y=2/2y=1Verified
Because computers operate so quickly, developers often measure time in milliseconds (which are 1000th of a second). Which operation could we perform in order to find the number of milliseconds in a year
The operation is 365*24*60*60*1000 = 31536*10^6.
As we know the year has 365 days.
Each day has 24 hours.
Each hour has 60 minutes.
Each minute has 60 seconds.
Each second has 1000 millisecond.
Therefore number of milliseconds in a year is
365*24*60*60*1000 = 31536*10^6.
Hence we get the The operation is 365*24*60*60*1000 = 31536*10^6.
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A prism with a heart-shaped base is sliced parallel to the base. What shape is formed?
The shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
A prism is a polyhedron made up of n parallelogram faces that connect the n-sided polygon base, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.
In the question, we are informed that a prism with a heart-shaped base is sliced parallel to the base.
We are asked what shape is formed.
From the above discussion, we know that the bases are translated into all cross-sections that are parallel to them, that is, all cross-sections parallel to the base, will be congruent to the base.
Thus, the shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
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Answer:
Step-by-step explanation:
Heart Shaped
Suppose that tan 0=-5/12 and 90° <0<180°.
Find the exact values of sin
0/2 and
tan
O/2
The exact values of sin θ/2 and tan θ/2 given below as:
sin θ/2 = 0.9806tan θ/2 = 4.99What is the exact values of sin θ/2 and tan θ/2 given that tan θ = -5/12?Given that tan θ = -5/12 and θ lies between 90° and 180°, the values of sin θ/2 and tan θ/2 can be found as follows:
tan θ = -5/12
θ = 180 -tan⁻¹-(5/12)
θ = 157.38
sin θ/2 = sin 157.38/2
sin θ/2 = 0.9806
tan θ/2 = tan 157.38/2
tan θ/2 = 4.99
In conclusion, the values of the sine and tangent are found from the given values.
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The volume, V, of a cylinder is V=r²h, where r is the
radius of the cylinder and h is the height. Using rounding
to the nearest whole number, which of the following is an
estimate of the volume of a cylinder with a radius of
3.75 inches and height of 6.21 inches?
Answer:
~87.33 in³
Step-by-step explanation:
All you have to to is pkug the numbers in the formula. You start by doing 3.75 as the r² and you get around 14.06. Then you multiply that by the height (6.21) which gets you around 87.33. I hope this helps!
HURRY PLEASE I NEED HELP
the number of hours you study for an exam affects your grade.what is the reasonable value of the range?
A - 75
B - 1.25
C - 1/2
D - 30
The reasonable value for the range of the given function is: A. 75.
What of the Range of a Function?The range of a function is the output that a corresponding input value would give as a relation.
In this scenario, the grade you get is a function of number of hours you study. Range is the grade (output), while the domain is hours of study (input).
The given possible range values in the options are, 75, 1.25, -30, 1/2.
A reasonable value of a a grade cannot be a negative number, neither can it be 1.25, nor 1/2.
Therefore, the reasonable value of the range is: A. 75.
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This market is a duopoly and the demand schedule as well as the total revenue is provided below. The number of customers you see and the total revenue is for the total market, not for an individual firm.
Answer:
??
Step-by-step explanation:
A restaurant owner wants to determine the effectiveness of his servers. the owner places a survey regarding the servers' effectiveness with randomly selected customer bills. what is the sample?
The sample is the randomly selected customers.
Sampling:
Suppose I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.
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match the graph with jts inequality
help helphelphelp help
Answer:
y<x
Step-by-step explanation:
Alright so you do know that the y=x has got the equal amount for both y and x right and it also is a bisector for the first and third area, that's that
the graph is show the same thing but with some blue area and the area show x values which less than y values sooo you answer is y<x