Answer:
[tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -9 \ln (12)[/tex]
General Formulas and Concepts:
Pre-Calculus
Partial Fraction DecompositionCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration 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]
U-Substitution
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy[/tex]
Step 2: Integrate Pt. 1
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\frac{y}{y^2 - 9y - 22}} \, dy[/tex][Integrand] Factor: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\frac{y}{(y - 11)(y + 2)}} \, dy[/tex]Step 3: integrate Pt. 2
[Integrand] Split [Partial Fraction Decomp]: [tex]\displaystyle \frac{y}{(y - 11)(y + 2)} = \frac{A}{y - 11} + \frac{B}{y + 2}[/tex][Decomp] Rewrite: [tex]\displaystyle y = A(y + 2) + B(y - 11)[/tex][Decomp] Substitute in y = -2: [tex]\displaystyle -2 = A(-2 + 2) + B(-2 - 11)[/tex]Simplify: [tex]\displaystyle -2 = -13B[/tex]Solve: [tex]\displaystyle B = \frac{2}{13}[/tex][Decomp] Substitute in y = 11: [tex]\displaystyle 11 = A(11 + 2) + B(11 - 11)[/tex]Simplify: [tex]\displaystyle 11 = 13A[/tex]Solve: [tex]\displaystyle A = \frac{11}{13}[/tex][Split Integrand] Substitute in variables: [tex]\displaystyle \frac{y}{(y - 11)(y + 2)} = \frac{\frac{11}{13}}{y - 11} + \frac{\frac{2}{13}}{y + 2}[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Split Integrand]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\bigg( \frac{\frac{11}{13}}{y - 11} + \frac{\frac{2}{13}}{y + 2} \bigg)} \, dy[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \int\limits^{10}_{-1} {\frac{\frac{11}{13}}{y - 11}} \, dy + \int\limits^{10}_{-1} {\frac{\frac{2}{13}}{y + 2}} \, dy \bigg][/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}\int\limits^{10}_{-1} {\frac{1}{y - 11}} \, dy + \frac{2}{13}\int\limits^{10}_{-1} {\frac{1}{y + 2}} \, dy \bigg][/tex]Step 5: Integrate Pt. 4
Identify variables for u-substitution.
Integral 1
Set u: [tex]\displaystyle u = y - 11[/tex][u] Differentiation [Basic Power Rule, Derivative Properties]: [tex]\displaystyle du = dy[/tex][Bounds] Switch: [tex]\displaystyle \left \{ {{y = 10 ,\ u = 10 - 11 = -1} \atop {y = -1 ,\ u = -1 - 11 = -12}} \right.[/tex]Integral 2
Set v: [tex]\displaystyle v = y + 2[/tex][v] Differentiate [Basic Power Rule, Derivative Properties]: [tex]\displaystyle dv = dy[/tex][Bounds] Switch: [tex]\displaystyle \left \{ {{y = 10 ,\ v = 10 + 2 = 12} \atop {y = -1 ,\ v = -1 + 2 = 1}} \right.[/tex]Step 6: Integrate Pt. 5
[Integrals] U-Substitution: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}\int\limits^{-1}_{-12} {\frac{1}{u}} \, du + \frac{2}{13}\int\limits^{12}_{1} {\frac{1}{v}} \, dv \bigg][/tex][Integrals] Logarithmic Integration: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}(\ln |u|) \bigg| \limits^{-1}_{-12} + \frac{2}{13}(\ln |v|) \bigg| \limits^{12}_{1} \bigg][/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}[-\ln (12)] + \frac{2}{13}[\ln (12)] \bigg][/tex]Simplify: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 11[-\ln (12)] + 2[\ln (12)][/tex]Simplify: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -11\ln (12)] + 2\ln (12)[/tex]Simplify: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -9 \ln (12)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Grace was given the description “three less than the quotient of a number squared and nine, increased by eight” and was asked to evaluate it when n = 6. Her work is shown below.
Step 1: 3 minus StartFraction n squared Over 9 EndFraction + 8
Step 2: 3 minus StartFraction 6 squared Over 9 EndFraction + 8
Step 3: 3 minus StartFraction 36 Over 9 EndFraction + 8
Step 4: 3 minus 4 + 8
Step 5: 7
In which step did she make an error?
step 1
step 2
step 4
step 5
Answer:
step 1
Step-by-step explanation:
when you say three less than the quotient
you put the quotient first and then subtract 3
Answer: Step 1
Step-by-step explanation: I took it on my quiz and got an 100
The snail moved 6 inches in 120 minutes. What was the average speed of the snail in inches per minute
Answer:
0.05 inches per minute
Step-by-step explanation:
The formula for speed is [tex]Speed=\frac{Distance}{Time}[/tex]
The given distance is 6 inches and the time is 120 minutes. Plug in the components into the formula to solve for speed and reduce:
[tex]Speed=\frac{6}{120}[/tex]
[tex]Speed=\frac{1}{20}[/tex]
1/20 in decimal form is 0.05
A certain medicine is given in an amount proportional to a patients body weight. Suppose a person weighted 104 pounds requires 156 milligrams of medicine. What is the weight of a patient who requires 207 milligrams of medicine?
Answer:
138 pound
Step-by-step explanation:
Given
A certain medicine is given in an amount proportional to a patients body weight.
thus,
ratio will be
amount of medicine: weight of patient
Given
Suppose a person weighted 104 pounds requires 156 milligrams of medicine.
amount of medicine = 156 milligram
weight of patient = 104 pound
Thus, ratio will be = 156/104
___________________________
What is the weight of a patient who requires 207 milligrams of medicine
Let the weight of weight of patient here be x
thus, ratio in this case will be
207/x
we also know in ratio and proportion that
if two ratio a:b and c:d are equal then a:c = c:d
here also the ratio will be same
Thus,
156/104 = 207/x
=> 156x = 207*104 = 21,528
=> x = 21,528/156 = 138
Thus, weight of patient is 138 pound.
Alice wants to estimate the percentage of people who plan on voting yes for the upcoming school levy. She surveys 380 individuals and finds that 260 plan on voting yes. What is the correct interpretation of the confidence interval
Step-by-step explanation:
Sample proportion [tex]\hat{p} = 260/380 = 0.684[/tex]
90% confidence interval for p is
[tex]\hat{p} - Z\times \sqrt(\hat{p}( 1 - \hat{p}) / n) < p < \hat{p} + Z\times \sqrt(\hat{p}( 1 - \hat{p}) / n)[/tex]
[tex]0.684 - 1.645\times \sqrt ( 1 -0.684) / 380) < P < 0.684 + 1.645\times \sqrt ( 1 -0.684) / 380)[/tex]
0.645 < p < 0.723
Interpretation - We estimate with 90% confidence that the true population proportion of people who plan on voting yes on the levy between 0.645 and 0.723.
Find the perimeter and total area ? Use 3.14 in
Answer:
Perimeter is when you add up all of the sides, and the area is when you multiply length times width.
Determine the intercepts of the line. -5x+9y=-18−5x+9y=−18minus, 5, x, plus, 9, y, equals, minus, 18 xxx-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis yyy-intercept: \Big((left parenthesis ,,comma \Big))
Answer:
(3.6, 0), (0, -2)
Step-by-step explanation:
To find the y-intercept, set x=0:
-5·0 +9y = -18
y = -18/9 = -2
To find the x-intercept, set y=0:
-5x +9·0 = -18
x = -18/-5 = 3.6
The intercepts are ...
x-intercept: 3.6
y-intercept: -2
Q12.
A woman applies for a new job that pays £8.50 a week more (after tax).
She will work 5 days a week and drive to work, as she does in her job now.
The new job is 6 miles further from her house.
Her car travels 8.5 miles per litre of petrol
Petrol costs £1.26 per litre
Will the woman be better off with the new job after she takes the petrol into consideration?
Explain your answer. Include calculations to support your decision.
Decision (yes/no)
8.5x1.295.70
Explanation and supporting calculations
CA
Answer:
Step-by-step explanation:
1l ........8.5 miles
x l .......6 miles
-----------------------
x=6*1/8.5
x=0.70 l
2*0.7=1.4 l petrol/day ( to work and come back home)
5*1.4=7 l/week ( 5 days works in a week)
7*1.26=8.82 L /week
8.82>8.5
The petrol costs more
So the answer is NO
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f - g)(x).
A. 3 - 3x
B. 3x-3
C. 7x-1
D. 7x-3
Answer:
The difference of the functions is (f-g)(x) = 3x - 3
Step-by-step explanation:
In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).
f(x) = 5x - 2
g(x) = 2x + 1
(f-g)(x) = (5x - 2) - (2x + 1)
Distribute the negative to (2x + 1)
(f-g)(x) = 5x - 2 - 2x - 1
Combine like terms. Make sure your answer is in standard form.
(f-g)(x) = 3x - 3
So, the answer to the equation is (f-g)(x) = 3x - 3
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers that are 6 or even on the cards are 2, 4, and 6.
3 cards out of a total of 6 cards.
3/6 = 1/2
Answer:
1/2 chance
Step-by-step explanation:
There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.
The first four terms of a sequence are shown below 9,5,1,-3
Which of the following functions best defines this sequence?
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1
B. f(1)=9, f(n+1)=f(n)+4 for n> or equal to 1
C. f(1)=9, f(n+1)=f(n)-5 for n> or equal to 1
D. f(1)=9, f(n+1)=f(n)+5 for n> or equal to 1
Answer:
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1
Step-by-step explanation:
Given the sequence:
9, 5, 1, -3We can easily calculate the difference of terms:
-3- 1= 1- 5= 5-9= -4As the difference of terms is same and equal to -4, it is the AP (arithmetic progression)
This sequence can be defined In the form of function as:
f(1)= 9, as the first term is 9f(n+1)= f(n)- 4, as it is decreasing function with the difference of -4n ≥ 1, as we count from the first term onAll the above matches the first answer choice:
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1(03.01 MC)
If AXYZ is dilated by a scale factor of 2 about point X, which of the following is true about A'Y'?
Answer:
A'Y' is parallel to AY
Step-by-step explanation:
If X is the center of dilation, the only lines that go through X after the dilation are the ones that go through X before the dilation: XY (and XY'), XZ (and XZ').
Line AY does not go through X, so A'Y' will not go through X. Rather, the line will be moved a distance from X according to the dilation factor. The line A'Y' will be parallel to AY.
How do you calculate the y-intercept of a line written in Standard Form?
Answer:
y-int = C/B
Step-by-step explanation:
Ax + By = C
y-int = C/B
Answer:
I hope this helps.
Step-by-step explanation:
W
5. 26.5 liter air dan 8.25 liter jus oren dicampurkan bersama. Semua campuran itu
dibotolkan dengan saiz setiap botol adalah 1.25 liter. Berapa botolkah diperlukan
untuk mengisi semua campuran jus oren tersebut?
A. 25
B. 26
C.27
D. 28
Answer: D, 28 bottles.
Step-by-step explanation:
This can be translated to:
26.5 liters of water and 8.25 liters of orange juice are mixed together. All that mixture is bottled in bottles of 1.25 liters. How many bottles are needed to fill all the orange juice mixture?
the total mass of mixture that we have is:
26.5 L + 8.25 L = 34.75 L.
if we want to divide it into groups of 1.25 L, we have:
N = 34.75/1.25 = 27.8
So we have 27.8 groups of 1.25L this means that we need 27.8 bottles.
But we can not have a 0.8 of a bottle, so we must round it up to 28 bottles.
Then the correct option is D:
Need help with this Pythagorean theorem formula. In a right triangle ,find the length not given? c=hypotenuse, a=6,b=8. use radicals as needed
Answer: c = 10
Step-by-step explanation:
Pythagorean Theorem states that in a right triangle [tex]a^2 + b^2 = c^2[/tex], where a and b are the legs of the triangle and c is the hypotenuse. Thus, because a=6 and b=8, 36+64=c². Thus 100=c². Thus 10=c
-4(-11+4n)-3(-2n+9) simplify to create an equivalent expression
chose 1 answer
-10n-35, -18n+17, -10n-17, or -10n+17
Answer:
the last one is correct
Step-by-step explanation:
hello,
-4(-11+4n)-3(-2n+9) = 44 - 16n + 6n - 27 = -10n + 17
hope this helps
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 2708 employees at the company and wants to conduct a systematic sample of size 30.A) What is k?B) Determine the indviduals who will be administered the survey.
Answer:
A) 90
B) The individuals in the survey will be 11, 101, 191,...., 2621.
Step-by-step explanation:
Tenemos lo siguiente a partir del enuciado:
A) let, a consider a department has an alphabetical list of all 2708 employees at company and wants to conduct a systematic sample. Substitute the value as:
k = N/n
reemplanzado nos queda:
k = 2708/30 = 90.26
Lo que quiere decir que el valor de k es de aproximadamente 90 B) Randomly select the number between I and 90, Suppose the randomly selected sumber is 11. The individuals in the survey will be; need to find 30th team, hence by using the airthmetic perogression nth term formula:
30th term = 11+ (30 - 1) *90
30th term = 2621
The individuals in the survey will be 11, 101, 191,...., 2621.
The random sample is obtained
Question Help The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests positivepositive, given that he or she did not havedid not have the diseas
Answer:
The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No) = 0.041
Step-by-step explanation:
Complete Question
The data represents the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests positive, given that he or she did not have the disease.
P/N | Yes | No
+ve | 141 | 6
-ve | 11 | 142
Note that +ve and -ve l stands for testing positive and negative respectively.
Yes and No represents whether one has the disease or not respectively.
Solution
Let
- The event of testing positive be P.
- The event of testing negative be N.
- The event of having the disease be Yes.
- The event of not having the disease be No.
The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No)
The conditional probability of A given B is given mathematically as
P(A|B) = P(A n B) ÷ P(B)
Hence,
P(P|No) = P(P n No) ÷ P(No)
To solve these probabilities, we first define the probability of an event as the number of elements in that event divided by the Total number of elements in the sample space.
P(No) = n(No) ÷ n(Sample space)
n(No) = 6 + 142 = 148
n(Sample Space) = 141 + 11 + 6 + 142 = 300
P(No) = (148/300)
P(P n No) = n(P n No) ÷ n(Sample space)
n(P n No) = 6
n(Sample Space) = 300
P(P n No) = (6/300)
P(P|No) = P(P n No) ÷ P(No)
= (6/300) ÷ (148/300)
= (6/148)
= 0.0405405405 = 0.041 to 3 d.p.
Hope this Helps!!!
Write the first four terms in the following sequences. A(n+1)=1/2 A(n) for n≥1 and A(1)=4 .
Answer:
4,2,1 and 1/2
Step-by-step explanation:
The first term is 4 since A(1)=4
● A(2) = (1/2)*A(1) = (1/2)*4 = 2
So the second term is 2
● A(3) = (1/2)*A(2) = (1/2)*2= 1
The third term is 1
●A(4) = (1/2)*A(3) = (1/2) *1 = 1
The function h(x)=12/x-1 is one to one. Algebraically find it’s inverse, h^-1(x).
Answer:
Step-by-step explanation:
hello,
I assume that you mean
[tex]h(x)=\dfrac{12}{x-1}[/tex]
so first of all let's take x real different from 1 , as this is not allowed to divide by 0
[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]
and this is defined for x real different from 0
hope this helps
Select the correct answer from each drop-down menu.
Answer:
AB = 14AC = 19.8 ≈ 20Step-by-step explanation:
The Pythagorean theorem can be used to find the lengths of the segments at the top of the square. The left one is found from ...
FA² = FE² +EA²
13² -12² = EA² = 169 -144 = 25
EA = √25 = 5
The right one is found from ...
FB² = FE² +EB²
15² -12² = EB² = 225 -144 = 81
EB = √81 = 9
Then the length of the side of the square is ...
AB = AE +EB = 5 +9
AB = 14
__
The length of the diagonal can also be found using the Pythagorean theorem.
AC² = AB² +BC² = 14² +14²
AC = √(196 +196) = 14√2 ≈ 19.7990
Rounded to the nearest integer, AC ≈ 20.
Which statement best interprets the factor (r+7) in this context?
Answer:
the height of the cylinder is 7 units greater than the radius
Step-by-step explanation:
When you match the forms of the equations ...
[tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]
you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...
the height of the cylinder is 7 units greater than the radius.
I NEED HELP PLEASE, THANKS! :)
please see the attached picture for full solution..
Hope it helps..
Good luck on your assignment...
x = 16 18 34 can someone explain please?
Answer:
x = 16
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(x+2) * 2 = 6^2
2(x+2) = 36
Divide each side by 2
x+2 = 18
Subtract 2
x+2-2 = 18-2
x = 16
Answer:
x = 16
Step-by-step explanation:
According to tangent-secant Theorem:
(Tangent)² = (External Part of the secant)(Whole Secant)
(6)² = (2)(2+x)
36 = 4+2x
Subtracting 4 from both sides
36-4 = 2x
=> 2x = 32
Dividing both sides by 2
=> x = 16What is the explicit rule for the geometric sequence?
600, 300, 150, 75, ...
Answer:
Step-by-step explanation:
Hello, this is a geometric sequence so we are looking for a multiplicative factor.
[tex]a_0=600\\\\a_1=a_0 \cdot \boxed{\dfrac{1}{2}} = 300 = 600 \cdot \boxed{\dfrac{1}{2}}\\\\a_2=a_1 \cdot \boxed{\dfrac{1}{2}} = 150= 300 \cdot \boxed{\dfrac{1}{2}}\\\\a_3=a_2 \cdot \boxed{\dfrac{1}{2}} = 75 = 150 \cdot \boxed{\dfrac{1}{2}}[/tex]
So, the explicit formula is for n
[tex]\boxed{a_n=a_0\cdot \left(\dfrac{1}{2}\right)^n=600\cdot \left(\dfrac{1}{2}\right)^n}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The explicit rule is aₙ = a₀(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.
What is geometric series?The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.
The nth term of a geometric progression is expressed as
Tₙ = arⁿ⁻¹
Where a is the first term, r is the common ratio.
We have been given that geometric sequence as:
600, 300, 150, 75, ...
To determine the explicit rule for the geometric sequence, we have to find the common ratio.
Here the first term (a₀) is 600
So the common ratio = 300/600 = 150/300 = 75/150 = 1/2
Thus, the explicit formula for n would be:
aₙ = a(1/2)ⁿ = 600(1/2)ⁿ
Therefore, the explicit rule is aₙ = a(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.
Learn more about the geometric series here:
brainly.com/question/21087466
#SPJ2
Write an equation in point-slope form for each line
Answer: y=x+1
Step-by-step explanation:
y+1=1(x+2)
y+1=x+2
y=x+1
Hope this helps:)
Two functions are graphed on the coordinate plane.
Which represents where f(x) = g(x)?
10
ger
8
f(4) = g(4) and f(0) = g(0)
f(-4) = g(4) and f(0) = g(0)
f(4) = 9(-2) and f(4) = g(4)
f(0) = g(4) and f(4) = g(-2)
6
to 54 -3 -2 -12
1 2 3 4 5 6 X
o)
-8
-124
Answer:
f(4) = g(4) and f(0) = g(0)
Step-by-step explanation:
In order for f(x) = g(x), the value of x must be the same in both functions:
f(4) = g(4) . . . corresponds to x=4
f(0) = g(0) . . . corresponds to x=0
The graph is not shown here, so we cannot say if these are the appropriate solutions. We can only say that the other choices are not.
f(x) = g(x) if ...
f(4) = g(4) and f(0) = g(0)
__
Something like f(0) = g(4) is useless for finding solutions to f(x) = g(x).
Which feature of a database displays data in a certain sequence, such as alphabetical order? Chart Filter Search Sort
Answer:
data bar
Step-by-step explanation:
Answer:
chart
Step-by-step explanation:
Please answer this correctly
Answer:
3/4
Step-by-step explanation:
The numbers odd or less than 3 are 2, 3, and 5.
3 numbers out of 4.
P(odd or less than 3) = 3/4
What percent of this grid is unshaded?
The grid has 10 columns and 10 rows making 100 equal sized squares 5 rows are
unshaded. The sixth row has 6 squares unshaded.
Answer:
56%
Step-by-step explanation:
We have a grid with 10 columns and 10 rows making 100 equal sized squares, they tell us that 5 rows are unshaded. Therefore half is unshaded, like so:
5 rows = 50 squares
They also tell us that the sixth row has 6 squares unshaded, which means that in total they would be:
50 + 6 = 56 squares
Knowing that the total is 100, the percentage would be:
56/100 = 0.56, that is, 56% are unshaded
You have $60. You want to buy a pair of jeans and a shirt. The pair of jeans cost $27.
You come home with $15. How much did you spend on the shirt?
Answer:
$18
Step-by-step explanation:
Buying the jeans for $27 leaves you with ($60 - $27), or $33.
Buying the shirt for s dollar leaves you with $15. To find s, the price of the shirt, you subtract $15 from $33: $18.
The shirt cost you $18.