The Time taken by Jacob to run the dash race is (80 - t) seconds
How to write algebraic expressions?We are told that;
Total distance for the dash race = 500 yards
Time taken by Jacob to run the dash race = 80 seconds
Now, we are told that Juan ran the same dash race but used t less seconds than Jacob. Thus;
Time taken by Jacob to run the dash race = (80 - t) seconds
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Ayudaaaaaaa es para hoy:
Necesito saber cuanto es 389 pesos mexicanos con un 12% de rebaja,ayuda plis
El precio resultante con descuento de 12 % es igual a 342.32 pesos.
¿Cómo hallar el precio resultante con descuento?
En este problema tenemos que determinar el precio resultante, el cual es igual al precio inicial menos el descuento. A continuación, se presenta la siguiente expresión:
x = 389 · (1 - 12/100)
x = 389 - 46.68
x = 342.32
El precio resultante con descuento de 12 % es igual a 342.32 pesos.
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PLEASE HELP 80 POINTS !!!!!!!!
Answer:
Step-by-step explanation:
a) it is a reflection
b) it is vertex B"
Use the following function rule to find h(w–5). Simplify your answer.
h(y)=y²–y–5
h(w–5)=
The value of the function is h(w - 5) = w^2 - 11w +25
How to determine the function?The function is given as:
h(y) = y^2 - y - 5
Substitute w - 5 for y
h(w - 5) = (w - 5)^2 - (w - 5) - 5
Expand the equation
h(w - 5) = w^2 - 10w + 25 - w + 5 - 5
Evaluate the like terms
h(w - 5) = w^2 - 11w +25
Hence, the value of the function is h(w - 5) = w^2 - 11w +25
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You draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
The events are not independent
How to determine the type of events?Say that there are n marbles in the bag
When the first red marble is drawn, the number of marbles in the bags becomes n - 1
This means that the first red marble has changed the probability of drawing the second red marble
This represents a dependent event
Hence, the events are not independent
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sin (x+y)/sin (x-y) =
No directions given here. What exactly do you need to be done with this trigonometric function?
please help me with this problem
please show steps so i know for next time
=========================================================
Explanation:
You could use the AC method to factor this, but the quadratic formula is the most efficient route in my opinion. This will avoid any guess-and-check.
Compare the original equation to the form [tex]a\text{x}^2 + b\text{x} + c = 0[/tex]
We have a = 9, b = 6, and c = -8
Those values lead to...
[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(9)(-8)}}{2(9)}\\\\\text{x} = \frac{-6\pm\sqrt{324}}{18}\\\\\text{x} = \frac{-6\pm18}{18}\\\\\text{x} = \frac{-6+18}{18} \ \text{ or } \ \text{x} = \frac{-6-18}{18}\\\\\text{x} = \frac{12}{18} \ \text{ or } \ \text{x} = \frac{-24}{18}\\\\\boldsymbol{\text{x} = \frac{2}{3} \ \text{ or } \ \text{x} = -\frac{4}{3}}\\\\[/tex]
Side notes:
2/3 = 0.667 approximately-4/3 = 1.333 approximatelySince your teacher did not give rounding instructions, I'll assume s/he wants the fraction form of each x value (rather than the decimal form). Be sure to follow all instructions given, and ask for clarification if need.To confirm the solutions, replace every copy of x with either 2/3 or -4/3 (pick one value only). Simplifying the left hand side should lead to 0. I'll let you check each answer.What is the probability of rolling a 4, 5, and 6, in that order, on three rolls of a single six-sided die
Answer:
1:216
Step-by-step explanation:
The probability of getting a 4 would be 1/6. The probability of getting a 5 would be 1/6 and the probability of getting a 6 would be 1/6. The bottom number is the total number of outcomes (1,2,3,4,5,6) and the top number is out of that set, how many do I want. In the case of wanting a 4, I want 1 out of those 6 numbers and so on.
Now we multiple these together 1/6 x 1/6 x 1/6 and get 1/216 or another way to write this is 1:216
The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t
At the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
How to describe the initial condition of this experiment?First of all, we would derive an expression for the position with respect to the angle (phase shift) under the appropriate conditions:
Asin(ωt + ø) = c₂sinωt + c₁cosωt.
At t = 0, we have:
y = c₂sin(0) + c₁cos(0).
y = 0 + c₁
y = 0 + 5
y = 5 units.
Therefore, we can logically deduce that at the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
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Complete Question:
The angle Φ represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then Φ = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then Φ = π. If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then Φ = π/2. In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
Parallel cousins are found in the iroquois system of kinship and are defined as:________
Parallel cousins are found in the iroquois system of kinship and are defined as bifurcate merging.
Parallel cousins, or the offspring of one's mother's or father's brothers or sisters, were frequently referred to and regarded in the same way as one's siblings. Contrarily, cross-cousins, or the offspring of one's mother's brothers or father's sisters, were frequently regarded as the best source of children.
Bifurcate merging is the underlying idea of the Iroquois system. The ego divides his family into those on his mother's side and those on his father's side (bifurcation) and combines his father with his brother (A) and his mother with her sister (B) .
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Find the difference. express the answer in scientific notation. (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline)
The difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11
How to determine the notation
Given the expression
(5. 29 × 10^11) - (3. 86 × 10 ^11)
First, find the common factor
10^11 ( 5. 29 - 3. 86)
Then substract the values within the bracket
10^11 (1. 43)
Multiply with the factor, we have
⇒1. 43 × 10^11
Thus, the difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11
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Answer:
A
Step-by-step explanation:
Find the difference. Express the answer in scientific notation.
(5.29 times 10 Superscript 11 Baseline) minus (3.86 times 10 Superscript 11 Baseline)
1.43 times 10 Superscript 11
9.15 times 10 Superscript 11
1.43 times 10 Superscript 22
9.15 times 10 Superscript 22
x =_______ y =_______ 12. Find the values of x and y.
Answer:
Below in bold.
Step-by-step explanation:
Opposite angles of a quadrilateral i a circle are supplementary so
x = 180 - 112 = 68 degrees.
y = 180 - 81 = 99 degrees.
Find the sum of the primes between 100 and 200, inclusive, that are 1 or 2 more than a perfect square.
Answer:
298
Step-by-step explanation:
All perfect squares from 100-200 inclusive:
100, 121, 144, 169, 196
100+1=101, 101 is prime
121+2=123, 123=41*3 so its not prime
144+1=145 145=29*5 so its not prime
169+2=171 171=9*19 so its not prime
196+1=197, 197 is prime
101+197=298
Notice that I excluded all even numbers because they are obviously composite.
By using a number line, arrange each of the each of the following in descending order (a) 4 29upon 33, -2.365,5.5,-3 upon 4 (b) 5 upon 8,-8, 10 1 upon 2 , 5.855, - 2π
The arrangement of the numbers in descending order (largest to smallest) are as follows;
a). 5.5, 4, 29/33, -3/4, -2.365b). 10, 5.855, 5/8, 1/2 -2π, -8What is the arrangement of the numbers in descending order in each case?It follows from convention that the positive numbers are larger than negative numbers and hence, should appear before negative numbers when the arrangement is in descending order.
Consequently, the numbers can be evaluated and arranged as in the answer above with positive numbers increasing rightwards and negative numbers decreasing leftward of 0 on the number line.
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A train leaves the station at 11 a.m. traveling at the rate of 40 miles per hour. A faster train leaves the same station at 1 p.m. that afternoon and travels in the same direction on a parallel track at a rate of 60 miles per hour. At what time will the faster train overtake the slower one
The faster train overtake the slower on 5 p.m.
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time.
Let the number of hours after 1pm at which faster train will overtake slower train be x.
At overtaking point,
Distance travelled by slower train = Distance travelled by faster train
Given :
Speed of slower train = 40 miles per hourSpeed of faster train = 60 miles per hourTime taken by faster train = xTime taken by slower train = x + 2.On equating distances we get
40 x ( x + 20) = 60 x (x)
40x + 80 = 60x
20x = 80
x = 4.
∴The faster train overtake the slower on 1 + 4 = 5 p.m.
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Which system of equations below has no solution? y = 4x 5 and y = 4x – 5 y = 4x 5 and 2y = 8x 10 y = 4x 5 and y = one-fourthx 5 y = 4x 5 and y = 8x 10
Y=4x+5 and y=4x-5 has no solution
What are Linear Equations in two Variables?
The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. A linear equation with two variables, for instance, is 7x + 9y + 4 = 0. These two linear equations are referred to be simultaneous linear equations if we take them into consideration.
Steps
[tex]Y=4x+5\\ Y=4x-5[/tex]
Substitute y=4x+5
[tex][4x+5=4x-5][/tex]
Refine [tex][4x+5=4x-5][/tex]
-10=0
-10=0 is a false ,therefore the system of a equation have no solution
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HELP PLS!!!! i don’t get it
Answer:
153
Step-by-step explanation:
i = square root of -1
i = √-1
(3+12√-1) (3-12√-1)
√a times √b = √ab
a√b times c√d = (a times c) √ (b times d)
9 - (36√-1) + (36√-1) - (144(√-1)^2) =
9 - 0 - (144 * -1) =
9 - 0 - (-144) =
9 - (-144) =
9 + 144 =
153
*** funny thing is if you put
(3+12i) (3-12i)
in a calculator
it works!
it gives you the answer 153
another way:
Expand the expression using
(a-b) (a+b) =
a²-b² :
3²-(12i)²
Simplify using exponent rule with same exponent
(a*b)^n =
a^n*b^n:
3²-12²* i²
Calculate the power:
9-144* i²
Rewrite by definition
i²=-1:
9–144×(−1)
Calculate the product or quotient: 9+144
Calculate the sum or difference: 153
Answer: 153
gathmath
Determine the area of the figure.
Answer: (x + 11) cm²
Step-by-step explanation:
The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where
a and b are the lengths of the top and bottom sides, andh is the height of the figure.For this figure, [tex]a = 5[/tex] and [tex]b= x+6[/tex] (the top and bottom sides), while [tex]h=2[/tex] (the height).
If we suppose [tex]A[/tex] is the area, plugging these values in, we get
[tex]A = \frac{1}{2}(5 + x + 6)*2[/tex]
[tex]A = \frac{1}{2} * 2 * (x + 11)[/tex]
[tex]A = x + 11[/tex]
All the lengths are in cm, so the area will be (x + 11) cm².
A soccer game lasts 90 minutes without running into overtime. The coach
plans to switch players out every 12 1/2 minutes. Approximately how many
switches will the coach make in one game?
Answer: 7 Switches will be made.
Step-by-step explanation:
[tex]\frac{90}{12.5}=[/tex] number of switches
[tex]7.2=[/tex] number of switches
however you cannot have a fraction of a switch so you must round it to a whole number, which in this case is 7.These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
Help
simplest terms.
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
The probability of drawing two yellow balls if they're not replaced exists 1/45.
What is probability?
The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.
Number of yellow marbles be 2
Number of pink marbles be 3
Number of blue marbles be 5
Total number of marbles = 2+3+5 = 10
The probability of removing the first yellow ball = 2/10
Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.
Probability of drawing the second yellow ball = 1/9.
Probability of drawing two yellow balls if they're not replaced
= 2/10 × 1/9
= 2/90
= 1/45
The probability of drawing two yellow balls if they're not replaced exists 1/45.
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Complete this sequence.
30, 21, 12, 3, [?], [ ]
Answer:
-6, -15
Step-by-step explanation:
Each term is 9 less than the previous term.
Which table shows a function that is decreasing only over the interval (–1, ∞)?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 4, negative 3, negative 1, 2, 1, negative 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 5, negative 1, 1, 0, negative 4, negative 8.
The table that shows a function that is decreasing only over the interval (–1, ∞) is:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
When a function is decreasing?A function is decreasing if when we increase the value of x, we decrease the value of y, and vice versa.
Decreasing on the (–1, ∞) means that as x increases on the interval, i.e. x = -100, then x = -10, then x = -2, the value of y decreases. The function that follows this pattern only on this interval is:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
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Answer:
A
Step-by-step explanation:
In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probabilities of matching
The probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].
How to find the probability of matching six numbers?To find the probability, we have to divide the favorable events by the total number of events.
The total number of events is given by:
[tex]47C_{6}[/tex]
We use combinations since the order doesn't matter.
The total number of favorable events is given by:
[tex]6C_{6}[/tex]
The probability is given by:
[tex]\frac{\text{Favorable events}}{\text{Total events}}=\frac{6C_{6}}{47C_{6}} \\= \frac{1}{47C_{6}}[/tex]
We have found the probability of matching all six balls to be [tex]\frac{1}{47C_{6}}[/tex].
Therefore, we have found that the probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].
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Disclaimer: The question was incomplete, the complete question is attached below.
Question: In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probability of matching six numbers.
answer the given questions please!
A canadian goose and a Great blue heron took off in opposite directions. The goose flew at 20 mph, and the heron flew at 10 mph. when they landed, they were 180 miles apart. Altogether, they flew for 14 hours. How long did each bird fly?
The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let a represent the time flown by the goose and b represent the time flown by the heron. Hence:
a + b = 14 (1)
Also:
20a + 10b = 180 (2)
From equation 1 and 2:
a = 4, b = 10
The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours
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i need help with this page
Answer:
See picture below.
Step-by-step explanation:
Simplify the expression.
Answer:
D
please mark brainiest
The average weight of 3 men a, b and c is 84 kg. another man d joins the group and the average now becomes 80 kg. if another man e whose weight is 3 kg more than that of d, replaces a then the average weight of b, c, d and e becomes 79 kg. what is the weight of a?
The weight of A is 75kg.
How to calculate the weight?Total weight of A + B + C = 84 x 3 = 252kg
Total weight of A + B + C + D = 80 x 4 =.320 kg
Weight of D = 320 - 252 = 68 kg
Given, E = D + 3 = (68 + 3) kg = 71 kg
Total weight of B + C + D + E = (79 x 4) = 316 kg
Weight of B + C = 316 kg - 71 kg - 68 kg = 177 kg
Weight of A only will be:
= 320 kg - 177 kg - 68 kg
= 75 kg
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Find the roots of sin(x) which lie in [0, pi]
Answer:
Option (1)
Step-by-step explanation:
From the unit circle, we see that y, which represents sin(x) when x is 0 or pi.
Alex has 84 quarters and nickels worth a total of $17.80.
Which equation can be used to find q, the number of quarters Alex has?
The equation which can be used to find the number of quarters and nickels is; n + q = 84, 0.05n + 0.25q = 17.80.
Quarters and nickelsTotal coins = 84Total value = $17.80let
Number of quarters = qNumber of nickels = nn + q = 84
0.05n + 0.25q = 17.80
From equation (1)
n = 84 - q
Substitute into (2)
0.05n + 0.25q = 17.80
0.05(84 - q) + 0.25q = 17.80
4.2 - 0.05q + 0.25q = 17.80
- 0.05q + 0.25q = 17.80 - 4.2
0.20q = 13.60
q = 13.60 / 0.20
q = 68
Substitute q = 68 into
n + q = 84
n + 68 = 84
n = 84 - 68
n = 16
Therefore, the number of quarters and nickels are 68 and 16 respectively.
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Which set describes the domain of p(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {p(h)| 0 ≤ p(h) ≤ 1,400} {p(h)| 0 ≤ p(h) ≤ 1,800}
The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
According to the statement
We have given that the brenton gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour.
and we have to find that the those set which describes the domain of p(h).
So,for this purpose
In this case, the domain represents the set of hours he is permitted to work
From the question, we understand that he cannot work more than 60 hours
This means that, the least number of hours to work is 0, and the highest is 60
So, the domain is 0 to 60
When represented properly, the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}.
So, The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800
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Answer:
B.{h|0<h<60}
Step-by-step explanation: