If a student receives a score of 80, how many questions did this student answer ... (5). Let x = the first number, and y = the second number ... If John only has 25 coins in his pocket, how many of the coins are quarters?
SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
Ndiba and Kristin are planning trips to ten countries this year. There are 13 countries they would be interested in visiting. They are deciding which countries to skip.
Answer: 286 possibilities
Step-by-step explanation:
It's a combination because the order of countries doesn't matter in this scenario.
n = 13r = 10[tex]_{n} C_{r} =\frac{n!}{r!(n-r)!}=\frac{13!}{10!(13-10)!}=\frac{13!}{10!(3)!}=\frac{13!}{10!(3)!}\\\\=\frac{6227020800}{3628800(6)}=\frac{6227020800}{3628800(6)}=\frac{6227020800}{21772800}=286[/tex]
I hope this is right
Mr. Lord borrowed $100,000 from a bank at a rate of 8% per annum for 3 years. Calculate the amount accruing for the loan
Answer: [tex]\$125,971.2[/tex]
Step-by-step explanation:
Given
Principal amount [tex]P=\$100,000[/tex]
Rate of interest [tex]r=8\%[/tex]
Time period [tex]t=3\ yr[/tex]
Amount in compound interest is given by
[tex]\Rightarrow A=P\left(1+r\%\right)^t\\\Rightarrow A=100,000(1+0.08)^3\\\Rightarrow A=\$125,971.2[/tex]
Thus, the amount accruing for loan is [tex]\$125,971.2[/tex]
Please help me... I stink at math
Answer:
142 [tex]cm^3\\[/tex]
Step-by-step explanation:
You have to do [tex](7*5)+(5*3)+(7*3)+(7*3)+(5*7)+(3*5)[/tex].
This equals 142 [tex]cm^3\\[/tex].
Answer:
The answer is 142cm
Step-by-step explanation:
Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Given:
The expression is:
[tex]2x^3+mx^2+nx+c[/tex]
It leaves the same remainder when divided by x -2 or by x+1.
To prove:
[tex]m+n=-6[/tex]
Solution:
Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).
Let the given polynomial is:
[tex]P(x)=2x^3+mx^2+nx+c[/tex]
It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that
[tex]P(2)=P(-1)[/tex] ...(i)
Substituting [tex]x=-1[/tex] in the given polynomial.
[tex]P(-1)=2(-1)^3+m(-1)^2+n(-1)+c[/tex]
[tex]P(-1)=-2+m-n+c[/tex]
Substituting [tex]x=2[/tex] in the given polynomial.
[tex]P(2)=2(2)^3+m(2)^2+n(2)+c[/tex]
[tex]P(2)=2(8)+m(4)+2n+c[/tex]
[tex]P(2)=16+4m+2n+c[/tex]
Now, substitute the values of P(2) and P(-1) in (i), we get
[tex]16+4m+2n+c=-2+m-n+c[/tex]
[tex]16+4m+2n+c+2-m+n-c=0[/tex]
[tex]18+3m+3n=0[/tex]
[tex]3m+3n=-18[/tex]
Divide both sides by 3.
[tex]\dfrac{3m+3n}{3}=\dfrac{-18}{3}[/tex]
[tex]m+n=-6[/tex]
Hence proved.
Maria has 72 flowers and four vases she put the same number of flowers in each vase how many flowers are in one vase
What is the measure of angle ABC of a circle
Answer:
the angle <ABC is equal to 65°
Someone please help me ASAP!
Answer:
y axis then translate x+1,y+1
the width of a newspaper is 13 3/4 inches. The left margin is 7/16 inch and the right margin is 1/2 inch. what is the width of the written page inside the margin?
Answer:
biggafigure a
mnn
Step-by-step explanation:
Determine the value of x.
8 2
8 3
4
8
Answer:
Step-by-step explanation:
Find the measures of the angles formed by two intersecting lines if the
sum of the measures of three of the four angles is 270°
50 points! Please help quick!
Answer:
every single angle is 90°
Step-by-step explanation:
remember that,
4 angles will form if two lines intersect and the sum of those 4 angles is 360°
we are given the sum of 3 angles i.e 270
so one of the angles should be
[tex] \displaystyle {360}^{\circ} - {270}^{\circ}[/tex]
simplify substraction:
[tex] \displaystyle {90}^{\circ}[/tex]
therefore since one of the angles is 90° the intercepting lines are Perpendicular as a result every single angle formed by the two intercepting lines is 90°
Answer:
90°
Step-by-step explanation:
We know that sum of angle around a point is 360° . Here its already given that sum of three Angles out of 4 is 270°
Therefore :-
Measure of remaining one angle ,
360 - 270 90 °Therefore the measure of the fourth angle is 90°
what is the explicit formula for this sequence
Answer:
A
Step-by-step explanation:
Start with the 3.
You know that there is a difference of 4 between (say) 2 and 5. The 3 is a sign that the sequence is increasing. The members of the sequence are going up.
n - 1 means that the nth terms is calculated as an and uses the number of terms to be n-1. That means that the first term is a1 which is the starting point of the sequence.
The answer is an = a1 + (n-1)*d
d = 3
a1 = - 7
So let's try the formula out.
a4 = -7 + (4 - 1)*3
a4 = -7 + 3 * 3
a4 = -7 + 9
a4 = 2
Is 2 the 4th term in the series? Yes it is!
The length of a side of an equilateral triangle is 40 centimeters.
What is the length of the altitude of the triangle?
Answer:
34.64 cm
Step-by-step explanation:
sin 60 = [tex]\frac{x}{40}[/tex]
sin 60 (40) = x
34.64 = x
equilateral triangles have 60° angles.
sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]
hypotenuse is 40. All sides are 40.
x = opposite or height of triangle.
can anyone help with integers?
Fill in the blanks.
6) 83 + 17 = 17 +
7) |46| – |50| =
8) 42 – 2 + (18 – 10) =
9) 18 – (3 – 1) =
10) 8 - 0 =
Answer:
a) 83,b) -4,c) 48,d) 16,e) 8
lic/activity/6000001/assessment
1 Pretest: Unit 6
Question 1 of 21
What is the domain of the exponential function shown below?
Rx) = 5.3x
Given:
The exponential function is:
[tex]R(x)=(5.3)^x[/tex]
To find:
The domain of the given exponential function.
Solution:
We know that the general form of an exponential function is:
[tex]f(x)=ab^x[/tex]
Where, a is the initial value and b is growth/decay factor.
This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.
We have,
[tex]R(x)=(5.3)^x[/tex]
Here, a is 1 and b is 5.3. This function is defined for all real values of x
Therefore, the domain of these type of functions is the set of all real number or it can be written as [tex](-\infty,\infty)[/tex].
i need help trying to solve this question to the nearest tenth of a degree
Which method is used in elimination to find the solutions of a - b = 9 and a + b = 5?
The substitution method is used in elimination to find the solution to the equation.
What is the system of two equations?A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.
The given equation in the problem is;
Equation P: a - b = 9
Equation Q: a+b=5
The value obtained from the equation P is;
a - b = 9
a=b+9
Substitute the value in the equation Q;
a+b=5
b+9+b=5
2b=9-5
b=2
The value of a is;
a-b=9
a-2=9
a=9+2
a=11
Hence the value of a and b will be 11 and 2.
To learn more about the system of two equations, refer to the link;
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A box contains 6 red index cards, 3 yellow index
cards, and 4 green index cards. If Gabriella pulls out
2 cards at random from this box, without replace-
ment, what is the probability that both cards are
not green?
Answer:
11/15 = 73%
Step-by-step explanation:
because in total there are 15 cards and 4 of them is not green. You would want to see what is the probability of other colored carded after leaving out the green ones.
The probability that both cards drawn from the box are not green is 27/52.
To determine the probability that both cards drawn from the box are not green, we need to calculate the probability of each individual draw and multiply them together.
Initially, the box contains a total of 6 red index cards, 3 yellow index cards, and 4 green index cards.
For the first draw, there are a total of 13 cards in the box. Since we are interested in the probability of not drawing a green card, there are 13 - 4 = 9 non-green cards. Therefore, the probability of not drawing a green card on the first draw is 9/13.
For the second draw, there will be 12 cards left in the box. Since one green card has already been removed, there are now 12 - 3 = 9 non-green cards remaining. Thus, the probability of not drawing a green card on the second draw is 9/12.
To find the overall probability, we multiply the probabilities of each individual draw:
(9/13) * (9/12) = 27/52
To learn more about probability click on,
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OMG HELP ILL GIVE U BRAINLIEST HDSJSHXHX
Which is the graph of the linear inequality x - 2y > -6?
-10-
2
108
0
o
Answer:
the fourth option
Step-by-step explanation:
1/2x - 2y > -6
1/2x + 6 > y
or
y < 1/2x + 6
so, the solution is all the y values smaller (= below) the line function.
and because it is "<" and not "<=" the line itself is not included
Find the value of x,rounded to the nearest tenth
Answer:
Step-by-step explanation:
The formula for this is
14(20) = 25x and
280 =25x so
x = 11.2
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with
mass 7 kg, the acceleration of the object is 4 m/s?. If the same force acts upon another object whose mass is 2 kg, what is this object's acceleration?
Answer:
14 m/s²
Step-by-step explanation:
From the question
a ∝ F/m.............. Equation 1
Where a = aceleration, m = mass, F = force
make F the subject of the equation
F = ma............ equation 2
Given: m = 7 kg, a = 4 m/s²
Therefore,
F = 7(4)
F = 28 N
For another object whose mass is 2 kg,
Make a the subject of equation 2
a = F/m
a = 28/2
a = 14 m/s²
HELP PLEASE 50 points !!! Given a polynomial function describe the effects on the Y intercept, region where the graph is increasing and decreasing in the end behavior when the following changes are made make sure to account for even and odd functions
When f(x) becomes -f(x)+ 2
When f(x) becomes f(x+3)
Even function:
A function is said to be even if its graph is symmetric with respect to the , that is:
Odd function:
A function is said to be odd if its graph is symmetric with respect to the origin, that is:
So let's analyze each question for each type of functions using examples of polynomial functions. Thus:
FOR EVEN FUNCTIONS:
1. When becomes
1.1 Effects on the y-intercept
We need to find out the effects on the y-intercept when shifting the function into:
We know that the graph intersects the y-axis when , therefore:
So:
So the y-intercept of is one unit less than the y-intercept of
1.2. Effects on the regions where the graph is increasing and decreasing
Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function increases and decreases in the same intervals of
1.3 The end behavior when the following changes are made.
The function is shifted one unit downward, so each point of has the same x-coordinate but the output is one unit less than the output of . Thus, each point will be sketched as:
FOR ODD FUNCTIONS:
2. When becomes
2.1 Effects on the y-intercept
In this case happens the same as in the previous case. The new y-intercept is one unit less. So the graph is shifted one unit downward again.
An example is shown in Figure 1. The graph in blue is the function:
and the function in red is:
So you can see that:
2.2. Effects on the regions where the graph is increasing and decreasing
The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of
In Figure 1 you can see that both functions increase at:
and decrease at:
2.3 The end behavior when the following changes are made.
It happens the same, the output is one unit less than the output of . So, you can write the points just as they were written before.
So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.
FOR EVEN FUNCTIONS:
3. When becomes
3.1 Effects on the y-intercept
We need to find out the effects on the y-intercept when shifting the function into:
As we know, the graph intersects the y-axis when , therefore:
And:
So the new y-intercept is the negative of the previous intercept shifted one unit upward.
3.2. Effects on the regions where the graph is increasing and decreasing
In the intervals when the function increases, the function decreases. On the other hand, in the intervals when the function decreases, the function increases.
3.3 The end behavior when the following changes are made.
Each point of the function has the same x-coordinate just as the function and the y-coordinate is the negative of the previous coordinate shifted one unit upward, that is:
FOR ODD FUNCTIONS:
4. When becomes
4.1 Effects on the y-intercept
In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept shifted one unit upward.
4.2. Effects on the regions where the graph is increasing and decreasing
In this case it happens the same. So in the intervals when the function increases, the function decreases. On the other hand, in the intervals when the function decreases, the function increases.
4.3 The end behavior when the following changes are made.
Similarly, each point of the function has the same x-coordinate just as the function and the y-coordinate is the negative of the previous coordinate shifted one unit upward.
The perimeter of a square is 16 cm. Find the length of its diagonal.
Answer:
perimeter of a square is l+l+l+l
16+16+16+16=64
Answer:
4√2 cm
Step-by-step explanation:
Perimeter of square = 4a = 16cm
a = 16 / 4
a = 4 cm
Length of each side = 4 cm
Diagonal^2 = side^2 + side^2
= 4^2 + 4^2
= 16 + 16
Diagonal^2 = 32
Diagonal = 4√2 cm
someone help me with my algebra homework please
Answer:
D.
Step-by-step explanation:
x = number of glasses of iced tea
y = number of glasses of lemonade
The total number of glasses is
x + y
The total number of glasses is 44
x + y = 44
This is not a choice, but the answer must be equivalent to this equation.
Solve for x by subtracting y from both sides.
x = 44 - y
Answer: D.
Which equation can be used to determine the reference angle
Answer:
2nd option
Step-by-step explanation:
[tex]\frac{7\pi }{12}[/tex] is an angle in the second quadrant
Thus to find the reference angle, subtract from π , that is
r = π - θ
Find the area of the region between the curve x^3+2x^2-3x and the x-axis over the interval [-3,1]
Answer:
[tex]\displaystyle A = \frac{32}{3}[/tex]
General Formulas and Concepts:
Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
Curve: x³ + 2x² - 3x
Interval: [-3, 1]
Step 2: Find Area
Set up: [tex]\displaystyle A = \int\limits^1_{-3} {(x^3 + 2x^2 - 3x)} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + \int\limits^1_{-3} {2x^2} \, dx - \int\limits^1_{-3} {3x} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + 2\int\limits^1_{-3} {x^2} \, dx - 3\int\limits^1_{-3} {x} \, dx[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = (\frac{x^4}{4}) \bigg| \limits^1_{-3} + 2(\frac{x^3}{3}) \bigg| \limits^1_{-3} - 3(\frac{x^2}{2}) \bigg| \limits^1_{-3}[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = -20 + 2(\frac{28}{3}) - 3(-4)[/tex]Evaluate: [tex]\displaystyle A = \frac{32}{3}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Find the rate of change for the function of change from x=-3 to x=1
Answer:
She's, "HOT"!
Step-by-step explanation:
Solve the system of equations.
−5x−3y−9=0
4x−18y−54=0
y=? x=?
Answer:
Step-by-step explanation:
Eq. 1 ) −5x−3y−9=0
Eq. 2) 4x−18y−54=0
there are two routes to solve this, Substitution or elimination, I'll go for the 2nd one because I can see that the y values are a multiple of each other :)
6 *( −5x−3y−9=0 )
Eq. 3) -30x -18y =54
subtract Eq. 2 from Eq. 3 :)
-30x -18y =54
-( 4x−18y=54)
-34x = 0
so according to the equations then x =0 but, that's not really a full answer, so now we should go back and try the other method, substitution,
then:
-5x = 9 +3y
x = - 9/5 + (-3/5)y
now plug that into Eq. 2
4( - 9/5 + (-3/5)y ) - 18y = 54
-36/5 + (-12/5)y -18y = 54
(-12/5)y - (90/5)y = 54+36/5
-(102/5)*y =270/5+36/5
-(102/5)y = 306/5
y = (-5/102)*(306/5)
y = -306/102
y = -3
then plug in for either equation
-5x-3( -3) = 9
-5x + 9 = 9
-5x = 0
x = 0
now we have the full answer
check it by plugging in both x and y into the 2nd equation
4(0) - 18(-3) = 54
54= 54
this seems good
An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c. What are the factors of x2 – 144? And
Answer:
[tex](x -12)(x + 12)[/tex]
Step-by-step explanation:
Given
See attachment for chart
Required
The factors of [tex]x^2 - 144[/tex]
First, express [tex]x^2 - 144[/tex] as [tex]ax^2 + bx + c[/tex]
So, we have:
[tex]x^2 - 144 = x^2 + 0x - 144[/tex]
Compare the above expression to: [tex]ax^2 + bx + c[/tex]
We have:
[tex]ax^2 + bx + c = x^2 + 0x - 144[/tex]
So:
[tex]a =1[/tex]
[tex]b =0[/tex]
[tex]c = -144[/tex]
and
[tex]a * c = d * e[/tex]
Calculate ac
[tex]a* c = 1 * -144[/tex]
[tex]a* c = -144[/tex]
Rewrite as:
[tex]a* c = -12 * 12[/tex]
Recall that:
[tex]a * c = d * e[/tex]
Hence:
[tex]d = -12; e = 12[/tex]
So, on the x chart, we have:
ac
d e
b
This gives:
-144
-12 12
0
The factors are
[tex](x + d)(x + e)[/tex]
[tex](x -12)(x + 12)[/tex]
Answer:
✔ (x – 12)
and
✔ (x + 12)
Step-by-step explanation:
I just need to know how I would be able to find x
Answer:
[tex]x=15[/tex]°
Step-by-step explanation:
The sum of degree measures in a full angle (a circle) is (360) degrees. This means that the sum of all of the angles in this diagram is (360) degrees, as the angles form a full arc. Therefore, one can form an equation by adding up all of the angles and setting the equation equal to (360) degrees. Then one can substitute each angle value with the equation that is used to represent it, simplify, and use inverse operations to solve for the value of (x).
[tex](m<AMB)+(m<BMC)+(m<CMD)+(m<AMD)=(360)[/tex]
Substitute,
[tex](46)+(4x-2)+(9x+6)+(8x-5)=360[/tex]
Simplify,
[tex](46)+(4x-2)+(9x+6)+(8x-5)=360[/tex]
[tex]21x+45=360[/tex]
Inverse operations,
[tex]21x+45=360[/tex]
[tex]21x=315[/tex]
[tex]x=15[/tex]
