If two siblings are boys, what is likelihood that the third sibling will also be a boy
Write an equation in point-slope form of the line through point J(4, -4) with slope 4.
a. y+4=4(x+4)
b. y+4=4(x-4)
c. y-4=4(x+4)
d. y+4=-4(x-4)
Please help! What is the solution of 4|x-3|-8=8?
A) x=-1 or x=7
B) x=19/4 or x=7
C) x=-1 or x=19/4
D) x=3/4 or x=19/4
Find the point of intersection of the pair of straight lines. 2x + 6y = 26 −9x + 7y = 2
A particle moves along the curve below. y = 24 + x3 as it reaches the point (1, 5), the y-coordinate is increasing at a rate of 4 cm/s. how fast is the x-coordinate of the point changing at that instant?
To find the rate of change of the x-coordinate at the point (1, 5) with a given y-coordinate rate of change, we use the chain rule to differentiate the equation y = 24 + [tex]x^3[/tex] with respect to time, and solve for dx/dt.
Explanation:The student's question involves the relationship between the rates of change of the x-coordinate and y-coordinate of a particle moving along a curve. Given the equation y = 24 +[tex]x^3[/tex], we need to find how fast the x-coordinate is changing at the point (1, 5), given that the y-coordinate is increasing at a rate of 4 cm/s. To find this, we can use the chain rule from calculus to relate the rates of change. Differentiating both sides with respect to time t, we get dy/dt = 3[tex]x^2[/tex] dx/dt. Solving for dx/dt, we find the rate of change of the x-coordinate when x = 1 and dy/dt = 4 cm/s.
At the point (1, 5), [tex]\( \frac{{dx}}{{dt}} = \frac{4}{3} \)[/tex] cm/s when [tex]\( \frac{{dy}}{{dt}} = 4 \)[/tex] cm/s.
To find how fast the x-coordinate is changing [tex](\( \frac{{dx}}{{dt}} \))[/tex] when the y-coordinate is increasing [tex](\( \frac{{dy}}{{dt}} \)),[/tex] we'll use implicit differentiation.
Given [tex]\( y = 24 + x^3 \),[/tex] differentiate both sides with respect to time [tex](\( t \)):[/tex]
[tex]\[ \frac{{dy}}{{dt}} = \frac{{d}}{{dt}}(24 + x^3) \][/tex]
Given that [tex]\( \frac{{dy}}{{dt}} = 4 \)[/tex], and when [tex]\( x = 1 \) and \( y = 5 \),[/tex] we can find [tex]\( \frac{{dx}}{{dt}} \):[/tex]
[tex]\[ 4 = 0 + 3x^2 \cdot \frac{{dx}}{{dt}} \][/tex]
[tex]At \( x = 1 \):[/tex]
[tex]\[ 4 = 3(1)^2 \cdot \frac{{dx}}{{dt}} \][/tex]
[tex]\[ 4 = 3 \cdot \frac{{dx}}{{dt}} \][/tex]
[tex]\[ \frac{{dx}}{{dt}} = \frac{4}{3} \][/tex]
So, the x-coordinate of the point is changing at a rate of [tex]\( \frac{4}{3} \)[/tex] cm/s at that instant.
What is the value of k?
2k+9=7−3k
To find the value of k in the equation 2k+9=7−3k, we rearrange and simplify to isolate k, resulting in k = -2/5.
To solve for the value of k in the equation 2k+9=7−3k, we must isolate the variable on one side of the equation. Let's start by adding 3k to both sides to get all the k terms on one side:
2k + 3k + 9 = 7 − 3k + 3k
5k + 9 = 7
Next, subtract 9 from both sides to get:
5k = 7 − 9
5k = −2
Now, to find the value of k, divide both sides by 5:
k = −2/5
Therefore, the value of k is −2/5.
A service station checks Mr. Gittleboro's radiator and finds it contains only 30% antifreeze. If the radiator holds 10 quarts and is full, how much must be drained off and replaced with pure antifreeze in order to bring it up to a required 50% antifreeze?
Answer:
2.86 quarts ( approx )
Step-by-step explanation:
Given,
The initial quantity of the Mr. Gittleboro's radiator that contains 30% antifreeze = 10 quarts,
Let x quarts of pure antifreeze replaced x quarts of Mr. Gittleboro's radiator to bring it up to a required 50% antifreeze,
So, the quantity of 30% antifreeze radiator after drained off x quarts = (10-x) quarts
Also, the quantity of final antifreeze radiator 50% antifreeze = 10 quarts
Thus, we can write,
30% of (10-x) + 100% of x = 50% of 10
30(10-x) + 100x = 500
300 - 30x + 100x = 500
300 + 70x = 500
70x = 200
x = 2.85714285714 quarts ≈ 2.86 quarts
[tex]\boxed{{\mathbf{2}}{\mathbf{.86 quartz}}}[/tex] of [tex]30\%[/tex] antifreeze replaced by pure antifreeze to maintain [tex]50\%[/tex] antifreeze in the radiator.
Further explanation:
Given:
It is given that radiator contains [tex]30\%[/tex] antifreeze and the radiator holds 10 quartz.
Step by step explanation:
Step 1:
Consider [tex]x[/tex] as the number of quartz of pure antifreeze that is replaced by [tex]x[/tex] number of quartz of Mr. Gittleboro’s radiator to maintain the level of [tex]50\%[/tex] antifreeze in the radiator.
It is given that radiator contains [tex]30\%[/tex] antifreeze and the radiator holds 10 quartz.
The amount of [tex]30\%[/tex] antifreeze radiator after drained off [tex]x{\text{ quartz}}[/tex] is [tex]\left({10-x}\right){\text{quartz}}[/tex] .
The radiator only holds [tex]{\text{10 quartz}}[/tex] .
The amount of final antifreeze radiator [tex]50\%[/tex] antifreeze is [tex]{\text{10 quartz}}[/tex] .
Step 2:
The equation for maintain the level of [tex]50\%[/tex] antifreeze in the radiator by replacing the [tex]x[/tex] number of quartz of [tex]30\%[/tex] antifreeze by pure antifreeze as,
[tex]\begin{aligned}30\%{\text{ of}}\left({10-x}\right)+100\% {\text{ of }}x&=50\% {\text{ of 10}}\\\frac{{30}}{{100}}\times\left({10-x}\right)+\frac{{100}}{{100}}{\text{}}\times{\text{}}x&=\frac{{50{\text{ }}}}{{100}}\times{\text{10}}\\{\text{30}}\left({10-x}\right)+100x&=500\\\end{aligned}[/tex]
Now simplify the further equation using the distributive property.
[tex]\begin{aligned}{\text{30}}\left({10-x}\right)+100x&=500\\300-30x+100x&=500\\300+70x&=500\\70x&=500-300\\\end{aligned}[/tex]
Now simplify the further equation to obtain the value of [tex]x[/tex] .
[tex]\begin{aligned}70x&=500-300\hfill\\70x&=200\hfill\\x&=\frac{{200}}{{70}}\hfill\\x&=2.85714\approx 2.86{\text{ quartz}}\hfill\\\end{aligned}[/tex]
Therefore, [tex]2.86{\text{ quartz}}[/tex] of [tex]30\%[/tex] antifreeze replaced by pure antifreeze to maintain [tex]50\%[/tex] antifreeze in the radiator.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: radiator, amount, replaced, Gittlebro, antifreeze, drained, maintain, quartz, number, linear equation, percentage, fraction, final antifreeze.
Marsha has three rugs.The first rug is 2 meters 87 centimeters long.The second rug has a length 98 centimeters less than the first.The third rug is 111 centimeters longer than the second rug.What is the difference in centimeters between the length of the first rug and the third rug?
HELP WITH CALCULUS!
Create an original rational function that has at least one asymptote (vertical, horizontal, and/or slant) and possibly a removable discontinuity. List these features of your function: asymptote(s) (vertical, horizontal, slant), removable discontinuity(ies), x-intercept(s), y-intercept, and end behavior. Provide any other details that would enable another student to graph and determine the equation for your function. Do not state your function.
7t + 4 is less than or equal to 3t
There are 56 chickens and rabbits altogether.Each chicken has 2 legs and each rabbit has 4 legs. Total 154 legs
There are 6,657 marbles in a jar. approximately 34% are white, and the rest are black. how many black marbles are there?
To find the number of black marbles, calculate the percentage of white marbles first and then subtract it from the total marbles, there are 4,394 black marbles in the jar.
To find the number of black marbles:
Calculate the number of white marbles: 34% of 6,657 = 0.34 x 6,657 = 2,263.Subtract the number of white marbles from the total marbles to find the number of black marbles: 6,657 - 2,263 = 4,394.Therefore, there are 4,394 black marbles in the jar.
Two geometric figures that are identical in shape, although not necessarily the same size, are called ____.
At the movie theatre, child admission is $5.40 and adult admission is $9.20 . on thursday, twice as many adult tickets as child tickets were sold, for a total sales of $785.40 . how many child tickets were sold that day
2x+4=9 or (2x+10)=40
Which one of these is open?
Please help!
Part A: If (6^2)^x = 1, what is the value of x? Explain your answer.
Part B: If (6^0)^x = 1, what are the possible values of x? Explain your answer.
John bikes 22km per hour and starts at mile 10. Gwynn bikes 28 km per hour and starts at mile 0. Which system of linear equations represents this situation?
Answer:
[tex]d=22t+10...(1)[/tex]
[tex]d=28t...(2)[/tex]
Step-by-step explanation:
Let t represent the number of hours and d represent the total distance after t hours.
We have been given that John bikes 22 km per hour and starts at mile 10. This means that slope of line will be 22 and y-intercept will be 10. So total distance covered by John in t hours will be:
[tex]d=22t+10...(1)[/tex]
We are also told that Gwynn bikes 28 km per hour and starts at mile 0. This means that slope of line will be 28 and y-intercept will be 0. So total distance covered by Gwynn in t hours will be:
[tex]d=28t+0[/tex]
[tex]d=28t...(2)[/tex]
Therefore, our required system of linear equations will be:
[tex]d=22t+10...(1)[/tex]
[tex]d=28t...(2)[/tex]
Need help on 9 and 10
A standard coffee mug has a capacity of 16 fluid ounces if Annie needs to fill 26 mugs with coffee how many total quarts of coffee does she need
NEED ANSWER ASAP!!! THANKS!!
A fish swims at a speed of 12 miles per hour. A boy swims at a speed of 4.4 feet per second.
3 ft = 1 yd
5280 ft = 1 mi
How much faster does the fish swim than the boy in yards per minute?
The Boy: 4.4 x 60 = 264ft per minute. 264 / 3 = 88yrds Per minute
The Fish: 12 x 5280 = 63360ft hr. 5280 / 60 = 1056ft minute 1056 / 3 = 352yrds
352 - 88 = 44 yards quicker then the boy.
44 x 3 = 132 feet quicker then the boy.
On the coordinate plane, the four corners of Alejandro's garden are located at (0,2), (4,6), (8,2), and (4,-2). Which shape most accurately describes the shape of Alejandro's garden?
The garden is in the shape of a ____
.
Solve the equation.
If necessary, round to the nearest tenth.
4x^2 =81
A 20.25, -20.25
B 2.25, -2.25
C 4.5 -4.5
D 9, -9
Find the surface area of a cube with 4.1 in. edges.
A sprinter can run 319 feet in 11 seconds . Find the sprinters unit rate of feet per second
Vanessa has scored 45 32 and 37 are three math quizzes she will take one more quiz and she wants a quiz average of at least 40 what is the minimum score Vanessa needs to earn her 4th quiz
4 total quizzes,
for a 40 average on 4 quizzes she needs 40*4 = 160 total points
for 3 quizzes she has 45 +32 +37 = 114 points
160-114 = 46, she needs at least a 46 on the 4th quiz
for a=3-5c when c=-0.5, what does a equal?
Plug in -0.5 for c
a = 3 - 5(-0.5)
Multiply -5 with (-0.5)
a = 3 + 2.5
Simplify
a = 5.5
a = 5.5 is your answer
hope this helps
In the formula 'a = 3-5c', 'a' becomes 5.5 when c=-0.5. This is derived by substituting -0.5 as 'c' in the given formula yielding the result of 5.5 after the calculation.
Explanation:The subject of your question is mathematics and it's about finding the value of 'a' in the formula: a = 3-5c when c=-0.5.
To answer your question, we'll substitute the value of 'c' into the formula:a = 3 - 5*(-0.5). When you multiply -5 with -0.5, the answer is 2.5.
Therefore, when you add 3 and 2.5, the answer is 5.5. So, when c = -0.5, the value of 'a' will be 5.5.
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A tile factory earns money by a flat fee for delivery and sales price per tile sold. For one customer the tile factory shipped 10,000 units of retail stores at the rate of $0.25 Per tile. The total tile factory earned from that sale was 3000 which of the following equation describes the revenue of the tile from this sale in terms of tiles
Sold?
A) y=0.25x+10,000
B) y=0.25x+3,000
C) y=0.25x+500
D) y=0.25x+0.25
10,000 tiles * 0.25 = 2500
3000 -2500 = 500
so the delivery fee is 500 and the tiles cost 0.25 each
so the equation would be y = 0.25x +500
Answer is C
Twice one number is 15 less than a second number. when 13 is added to the second number,the result is 7 less than 9 times the first number
Which triangle is similar to /\JKL
A. /\JKM
B. /\MKL
C. /\KML
D. /\LJK
Answer:
ΔKML Option C
Step-by-step explanation:
Given right triangle is ΔJKL
Where ∠JKL = 90°
Here KM is perpendicular to LJ.
In triangle ΔJKL & ΔKML
∠JKL ≅ ∠KML (both are right angle)
∠JLK ≅ ∠KLM (common angle in both the triangles)
So,
ΔJKL is similar to ΔKML.
That's the final answer.
I hope it will help you.
Seventy-five times an integer, minus 36, equals 21 times the square of the integer. Which equation could be used to solve for the unknown integer?
The equation: [tex]\( 21x^2 - 75x + 36 = 0 \)[/tex] represents "75 times an integer minus 36 equals 21 times the square of the integer."
To solve this problem, let's represent the unknown integer with the variable [tex]\( x \)[/tex]. Then we can set up the equation based on the given information.
The problem states: "Seventy-five times an integer, minus 36, equals 21 times the square of the integer."
Mathematically, this can be represented as:
[tex]\[ 75x - 36 = 21x^2 \][/tex]
So, the equation that could be used to solve for the unknown integer is:
[tex]\[ 21x^2 - 75x + 36 = 0 \][/tex]