Answer:
25
Step-by-step explanation:
If Juan's mother forgave his debt of -$13, then Juan will have $25 left after paying back his initial loan and making a profit of $12.
Juan's money = $12 + $13
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
If Juan's mother forgave his debt of -$13, then it means that Juan received $13 from his mother instead of owing her $13. So the equation that shows the amount of money Juan will have is:
Juan's profit = Juan's earnings - Juan's expenses
Juan's profit = $25 - $13
Juan's profit = $12
This means that after paying back his loan and making a profit of $12, Juan will have no money left.
If we want to include the amount he initially borrowed, we can modify the equation as follows:
Juan's money = Juan's earnings + Juan's initial loan
Juan's money = $25 - $13 - $13
Therefore, the equation is Juan's money = $12 + $13
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A classroom of children has 17 boys and 19 girls in which five students are chosen to do presentations. In how many ways can the five students be chosen so that more boys than girls are selected
Answer:
167688 ways
Step-by-step explanation:
Given that:
Number of boys = 17 &;
Number of girls = 19
The number of ways that five students can be chosen such that more boys than girls are selected are:
The ways of choosing = 5 boys 0 girls + 4 boys 1 girl + 3 boys 2 girls
The ways of choosing = [tex]^{17}C_5 +( ^{17}C_4 \times ^{19}C_1} )+( ^{17}C_3 + ^{19}C_2})[/tex]
The ways of choosing = [tex]\dfrac{17!}{5!(17-5)!} + \begin {pmatrix} \dfrac{17!}{4!(17-4)!} \times \dfrac{19!}{1!(19-1)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(17-3)!} \times \dfrac{19!}{2!(19-2)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17!}{5!(12)!} + \begin {pmatrix} \dfrac{17!}{4!(13)!} \times \dfrac{19!}{1!(18)!} \end {pmatrix} + \begin {pmatrix} \dfrac{17!}{3!(14)!} \times \dfrac{19!}{2!(17)!} \end {pmatrix}[/tex]
[tex]=\dfrac{17*16*15*14*13*12!}{5!(12)!} + ( \dfrac{17*16*15*14*13!}{4!(13)!} \times \dfrac{19*18!}{1!(18)!} ) + ( \dfrac{17*16*15*14!}{3!(14)!} \times \dfrac{19*18*17!}{2!(17)!} )[/tex][tex]=6188 + ( 2380\times19 ) + (680 \times171)[/tex]
= 167688 ways
Using the combination principle, the number of ways of selecting 5 students such that the number of boys is greater the number of girls selected ls 167688 ways.
Number of boys = 17Number of girls = 19Number of selections to be made = 5
In other to choose more boys than girls :
5 boys and 0 girls4 boys and 1 girl3 boys and 2 girlsUsing the combination relation :
(17C5 × 19C0) + (17C4 × 19C1) + (17C3 × 19C2)
(6188 × 1) + (2380 × 19) + (680 × 171)
(6188 + 45220 + 116280)
= 167688 ways
Therefore, the Number of ways of making the selection is 167688 ways
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You have 1 quarts of brown stock.
You need 1 cups to make one serving of braised short ribs.
How many servings can you make?
(don't include partial portions)
I
Answer:
Answer:
you can make 4 servings because 1 quart is 4 cups
MULTIPLE CHOICE CALCULUS
1) An object moves along a line so that its position at time t is s(t) = t^4 - 6t^3 - 2t - 1.
At what time t is the acceleration of the object zero?
A. at 3 only
B. at 0 and 3 only
C. at 0 only
D. at 1 only
2) If f(x) = e^x (sin x + cos x), then f'(x) =
A. 2e^x (cos x + sin x)
B. e^x cos x
C. e^x (cos^2x - sin^2x)
D. 2e^x cos x
Answer:
1) B. at 0 and 3 only
2) D. 2eˣcosx
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringQuadraticsCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[sinu] = u'cosu[/tex]
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[cosu] = -u'sinu[/tex]
eˣ Derivative: [tex]\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'[/tex]
Step-by-step explanation:
*Note:
Velocity is the derivative of position.
Acceleration is the derivative of velocity.
Question 1
Step 1: Define
s(t) = t⁴ - 6t³ - 2t - 1
Step 2: Differentiate
[Velocity] Basic Power Rule: s'(t) = 4 · t⁴⁻¹ - 3 · 6t³⁻¹ - 1 · 2t¹⁻¹[Velocity] Simplify: v(t) = 4t³ - 18t² - 2[Acceleration] Basic Power Rule: v'(t) = 3 · 4t³⁻¹ - 2 · 18t²⁻¹[Acceleration] Simplify: a(t) = 12t² - 36tStep 3: Solve
[Acceleration] Set up: 12t² - 36t = 0[Time] Factor: 12t(t - 3) = 0[Time] Identify: t = 0, 3Question 2
Step 1: Define
f(x) = eˣ(sinx + cosx)
Step 2: Differentiate
[Derivative] Product Rule: [tex]\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x\frac{d}{dx}[sinx + cosx][/tex][Derivative] Rewrite [Derivative Property - Addition]: [tex]\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])[/tex][Derivative] eˣ Derivative: [tex]\displaystyle f'(x) = e^x(sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])[/tex][Derivative] Trig Derivatives: [tex]\displaystyle f'(x) = e^x(sinx + cosx) + e^x(cosx - sinx)[/tex][Derivative] Factor: [tex]\displaystyle f'(x) = e^x[(sinx + cosx) + (cosx - sinx)][/tex][Derivative] Combine like terms: [tex]\displaystyle f'(x) = e^x[2cosx][/tex][Derivative] Multiply: [tex]\displaystyle f'(x) = 2e^xcosx[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
A car is traveling at a constant speed. It travels 34 miles in 5 minutes.
How many minutes will it take the car to travel 70 miles?
helppppp
Answer:
10.30 or 10 1/6 if this answer is not on the answer choices round to the nearest answer close to this.
Step-by-step explanation:
how to solve.
34/5=6.8 - this is how many miles the car is traveling per minuet.
6.8/70=10.30 - this should be the answer because this is how many minutes it takes the car to travel 70 miles
The perimeter of quadrilateral ABCD is 85. Find the value of x.
The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.
What is meant by Quadrilateral?A quadrilateral is a four-sided polygon with four angles and four vertices. The term "quadrilateral" comes from the Latin words "quadri," which means "four," and "latus," which means "side." A quadrilateral is depicted in the image above. The outcome of an image The perimeter of the quadrilateral ABCD is 85 feet. Find out what the value of x is.The perimeter of a quadrilateral is the entire length of its boundary. Perimeter = AB + BC + CD + DA, for example, can be used to define the perimeter of the quadrilateral ABCD.The perimeter is 85. (the total of all sides). X = 5.5, and 4x + 3x + 4 + 5x-7 + 6x-11 = 85 (18x - 14 = 85). 18 x = 85 + 14 = 99.Therefore,
The perimeter of ABCD can be calculated using the following formula: Line AB + Line BC + Line CD + Line DA = Perimeter ABCD.
When we substitute the provided values, we get: ABCD perimeter = 9 units plus 5 units plus 9 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units plus 5 units As a result, the perimeter of ABCD is 28 units.
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Xavier saved money to purchase a bike that originally cost $250, not including tax. The store discounted the bike by 20%. What is the discounted price he will pay for the bike, not including tax?
Question 1 options:
$50.00
$300.00
$270.00
$200.00
HELP I WILL GIVE BRAINLIEST
What is the value of the variable z and the measure of Angle B?
John has $255 in his bank account. His bank charges a $10.50 administration fee each month. If he makes no other deposits or withdrawals, how much money is in John’s account at the end of 5 months?
Answer:
10.50×5=52.50 255-52.50=202.50
Step-by-step explanation:
well if 10.50 is taken for 5 months he will have 202.50 because 255-52.50=202.50
Which of the following is the word expression for this numerical expression? 32÷4⋅3
Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.
Answer:
Please answer my questions you'll get points
Answer:
The smaller angle is 39, the other is 51
Step-by-step explanation:
This circle graph shows the results of a survey on favorite sandwiches.
What percentage of people chose turkey as their favorite sandwich? Round to the nearest percentage if necessary.
9%
23%
25%
40%
favorite sandwich circle graph. sectors labeled ham 4, 15 peanut butter, 9 turkey, 12 tuna
Answer:
b i think..
Step-by-step explanation:
plz dont get your hopes up it just a hunch but if you think about it 1st add ti all then u can see ig i will update if needed sorry if wrong :(
A glacier in Alaska moves about 29.3 meters a day. About how much farther will it move in 1000 days then it will move in 100 days?
A glacier will move about ______ meters farther in 1000 days then it will move in 100 days.
Fill in the blank
Your answer has to be in decimal form.
BIG THANKS!
Answer:
If it moves 29.3 meters a day, then we need to find the total amount of days:
1000 days + 100 days = 1100 days
Since it moves 29.3m per day, we can write:
29.3m x 1100 which equals 32230m
So it moved 32230 meters
Step-by-step explanation:
Slove the equation for x, and enter your answer in the box below.
x - 9 = 5
x=-14
move x to the right side and move 5 to the left side and 5 turns to a negative
x-9=5
-5-9=x
x=14
Suppose you roll a special 4-sided die. What is the probability that the number rolled is a "1" OR a "2"?
awnser:25%
because 4/100=25
The probability of the number rolled is a "1" OR a "2" is,
⇒ 1/2
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
You roll a special 4-sided die.
Now, After roll a special 4-sided die, the probability to get 1 is,
⇒ 1/4
And, After roll a special 4-sided die, the probability to get 1 is,
⇒ 1/4
Hence, The probability of the number rolled is a "1" OR a "2" is,
⇒ 1/4 + 1/4
⇒ 2/4
⇒ 1/2
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Marta walked at 4.7 miles per hour for 0.71 hours. How far did she walk?
Answer:
3.337 miles
Step-by-step explanation:
D = Distance
S = Speed
T = Time
D = S x T
D = 4.4 x 0.17
D = 3.337
this is a kind weird number so this might be wrong tho
The vegetable display automatically sprays a mist over the vegetables according to a repeating timer you set. How many minutes should you set the timer for in order to spray the vegetables 5 times each hour
Answer:
✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️
152 is the product of hectors age and 8
Answer:
If its asking for hectors age, then its 152/8=19
Step-by-step explanation:
Answer:
144
Step-by-step explanation:
152-8
I need help plz ASP
Answer:
b. 20 songs
Step-by-step explanation:
when you look at (0,0), the y-intercept is 20, so that is the initial starting point.
Kelly received a 35% discount on the purchase of a $320 bicycle. What was the amount of the discount?
$432.00
$208.00
$112.00
$35.00
Answer:
$112
Step-by-step explanation:
$320 X .35= $112
Evaluate the line integral, where C is the given curve. (x 6y) dx x2 dy, C C consists of line segments from (0, 0) to (6, 1) and from (6, 1) to (7, 0)
Answer:
[tex]\mathbf{\int _c (x+6y)\ dx + x^2 \ dy = \dfrac{91}{6}}[/tex]
Step-by-step explanation:
The integral of the curve is given as:
[tex]\int (x +6y) \ dx +x^2 \ dy[/tex]
Where the line segment from (0,0) to (6,1) is:
0 < x < 6 and [tex]y = \dfrac{x}{6} \implies dy = \dfrac{dx}{6}[/tex]
Thus;
[tex]\int ^{6,1}_{0,0} (x+ 6 * \dfrac{x}{6}) \ dx + \dfrac{x^2*dx}{6 } = \int^6_0 (x+x+\dfrac{x^2}{6}) \ dx[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \int^6_0 (2x +\dfrac{x^2}{6}) \ dx[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} \dfrac{2x^2}{2}+\dfrac{x^3}{18} \end {bmatrix}^6_0[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} x^2+\dfrac{x^3}{18} \end {bmatrix}^6_0[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} (6)^2+\dfrac{(6)^3}{18} \end {bmatrix}[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx = \begin {bmatrix} 36+12 \end {bmatrix}[/tex]
[tex]\int^6_0 (x+x+\dfrac{x^2}{6}) \ dx =48 --- (1)[/tex]
Similarly; at (6,1) to (7,0)
[tex]\implies 6 \leq x \leq 7 \ and \ y = -x +7[/tex]
Thus; the integral can be computed as :
[tex]\int ^{(7,0)}_{(6,1)} \ (x+6(-x+7)) \ dx + x^2 (-dx) = \int^7_6 (-5x +42 -x^2) \ dx[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5x^2}{2}+ 42x -\dfrac{x^3}{3} \end {bmatrix}^7_6[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(7^2-6^2)}{2}+ 42(7-6) -\dfrac{(7^3-6^3)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(49-36)}{2}+ 42(1) -\dfrac{(343-216)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{5(13)}{2}+ 42 -\dfrac{(127)}{3} \end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= \begin {bmatrix}- \dfrac{-195+252-254}{6}\end {bmatrix}[/tex]
[tex]\int^7_6 (-5x +42 -x^2) \ dx= - \dfrac{-197}{6} --- (2)[/tex]
By adding (1) and (2) ; we have:
[tex]\int _c (x+6y)\ dx + x^2 \ dy = 48 + (-\dfrac{197}{6})[/tex]
[tex]\int _c (x+6y)\ dx + x^2 \ dy = (\dfrac{288-197}{6})[/tex]
[tex]\mathbf{\int _c (x+6y)\ dx + x^2 \ dy = \dfrac{91}{6}}[/tex]
What is the greatest common factor of 25 and 45?
Answer:
5
Step-by-step explanation:
Factors of 25: 1, 5, 25Factors of 45: 1, 3, 5, 9, 15, 45The greatest factor that's in both lists is 5.I hope this helps!
The greatest common factor of 25 and 45 is 5.
What is GCF?GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.
The given numbers are 25 and 45.
To find the greatest common factor, factorize the numbers,
Factor of 25 = 5 × 5
Factor of 45 = 3×3×5
The common term in 5 × 5 and 3×3×5 is 5.
Therefore, the greatest common factor is 5.
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10. While catching fireflies, you and a friend decide to have a competition. After m minutes, you have (4m +11) fireflies and your friend has (5m +6) fireflies
A. Write an expression in simplest form that represents the number of fireflies you and your friend caught together.
B. The competition ends after 5 minutes(m). Who has more fireflies. Explain how you know.
Answer:
Lets look at the expressions with respect to the competition parameters:
Expressions:
You(Y) =4m+11
Friend(F)=5m+6
1. The competition begins AFTER you and friend already caught some flies. This would be represented by the CONSTANT terms in each expression (in this case, 13 for you, 6 for friend).
So the number of flies caught BEFORE THE COMPETITION would be...
11+6=17 flies total
2. The competition length was "m" minutes long when flies are caught and counted. This would be represented by the VARIABLE terms in each expression (in this case, 4m for you, 5m for friend). We are not given a numeric value for the variable "m" to evaluate.
So the number of flies caught DURING THE COMPETITION (timed "m" minutes long) would be....
4m+5m=9m flies total
...and the number of flies per minute would be calculated as......
9m÷m=9 flies per min....total #flies divided by total minutes
3. If the problem asked for the total number of flies caught by you and friend, before and after the competition....
9m+17 flies total.....add like terms in each expression.
Answer:
a. 9m+17
b. You caught more fireflies
Step-by-step explanation:
BRAINLIEST!!!
Consider points A(3, 6) and B(8, 4). Find point C on the x-axis so AC +BC is a minimum.
I need help
Answer:
(6,0)
Step-by-step explanation:
Need help on this will give brainlist
Answer:
53
Step-by-step explanation:
Alternate interior angles are the same value.
What is the slope of the line in the graph below? Show your work. PLEASE HELP PLEASE
Answer:
5/2
Step-by-step explanation:
The line crosses two points: (0,1) and (5,3)
You can then use the slope-point formula to find the slope:
(x1 - x2)/(y1 - y2) =
(0 - 5)/(1 - 3) =
-5/-2 =
5/2
Answer:
The slope of the line is 2/5
Step-by-step explanation:
Start counting where the y-intercept is. The y-intercept is at (0,1). The line is positive since it is increasing from left to right, so you need to count up and then to the right in order to find the slope. You need to find a point where the line intercepts a coordinate point directly on the line. If you look at the point (5,3) it is directly on the intersection that runs up and down. Start at 1 and count 2 up and 5 to the right. You will end up on the point (5,3). Hope this helps. Ask more questions if you need to
5.35
2.2 Show your work please!
Answer:
what lesson in math is this??
find the product of 1.6 and 3.4
Choices:
3.24
5.04
5.44
3.1
Answer:
5.44
Step-by-step explanation:
1.6*3.4=5.44
SOLVE FOR X PLEASE
10x+50+80=180
Answer:
x= 5
Step-by-step explanation:
10(5)+50+80=180
Multiply the 5 by 10
10*5=50
50+50+80=180
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x=5
Step-by-step explanation:
10x+50+80=180
combine 10x(50+80)=180, 10x+130=180
subtract 10x(130-130)=(180-130), 10x=50
divide 10 by 50 to find x=5
hope the step by step helps
Which is the "better buy"? A 12 ounce can of corn for $1.92 of a 20 ounce can of corn for $3.00?
What is the result of factoring out the GCF from the expression (24 + 36)?
please i need help!
it is on PLATO
Answer:
I gues answer is 4( factor)