Answer:
When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen; When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.
Step-by-step explanation:
In a binomial distribution, there are only two outcomes, or outcomes that can be reduced to 2. In the first choice, we either draw a prime number or do not draw a prime number. In the third choice, we either draw a 3 or do not draw a 3.
There must be a fixed number of trials. In the first choice, we have 5 trials; in the third option, we have 6 trials.
The trials must be independent of each other. Since the cards in the first and third options are drawn with replacement, the outcome of one trial does not influence the probability of the next trial.
The probability must be the same for every trial. This is true of the first and third options.
Answer:
Prime And 3 is choosen
Step-by-step explanation:
An item has a listed price of $ 60 . If the sales tax rate is 6 % , how much is the sales tax (in dollars)?
Answer:
$3.6
Step-by-step explanation:
6%=.06
60*.06=3.6
For the given equation, find the center and radius of the circle x^2 + ( y + 5 )^2 = 25 . What point is the center at ?
Answer:
(0,-5)
Step-by-step explanation:
The vertex form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h,k) is the center of the circle and r is the radius. This means that for the equation [tex]x^2 + (y+5)^2 = 25[/tex] the center is (0,-5).
Answer:
Center: ( − 5 , 2 )
Radius: 5
Step-by-step explanation:
on edge
The number a is smaller than the number b by 1/5 of b. By what part of a is b bigger than a?
Answer:
The number b is bigger than the number a by [tex]\dfrac{1}{4}[/tex] of a.
Step-by-step explanation:
1. If the number a is smaller than the number b by 1/5 of b, then
[tex]a+\dfrac{1}{5}b=b.[/tex]
Thus,
[tex]a=b-\dfrac{1}{5}b=\dfrac{4}{5}b,\\ \\b=\dfrac{5}{4}a.[/tex]
2. Consider the expression [tex]b=\dfrac{5}{4}a:[/tex]
[tex]b=\dfrac{5}{4}a=\dfrac{4}{4}a+\dfrac{1}{4}a=a+\dfrac{1}{4}a.[/tex]
This gives you that the number b is bigger than the number a by [tex]\dfrac{1}{4}[/tex] of a.
It is found that A is smaller by 1/5 of b.
To analyze the function or expression to make the function uncomplicated or more coherent is called simplifying and the process is called simplification.
We are given that the number a is smaller than the number b by 1/5 of b.
So if we add a and 1/5 of b, we would have b:
a + 1/5b = b
Solving for a we have:
A = b - 1/5b = 4/5b
A = 4/5b
Solving for b divide both sides by 4/5,
B = 5/4a
Since 4/4 = 1, this means b would be bigger than a by 1/4
Learn more about simplification;
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What is 129x40%-54=.
Answer:
-2.4
Step-by-step explanation:
129x40%=51.6
51.6-54=-2.4
hope that helps!!
The points Q(-1,1),R(2,-3), and S(-1,-3) are the vertices of a triangle. Find the area of the triangle
The area of the triangle with points Q(-1,1),R(2,-3), and S(-1,-3) is equal to 6 square units.
In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):
Area of triangle, A = 1/2 × b × h
Where:
b represent the base area.h represent the height.By substituting the given vertices into the formula for the area of a triangle with coordinates, we have the following;
[tex]A=\frac{1}{2} \times |x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\\\\A=\frac{1}{2} \times |-1(-3 + 3) + 2(-3 - 1) + (-1)(1 +3)|\\\\A=\frac{1}{2} \times |0 -8 - 4|\\\\A=\frac{1}{2} \times |-12|[/tex]
Area of triangle = 1/2 × 12
Area of triangle = 6 square units.
Write the sum using summation notation, assuming the suggested pattern continues. 2 - 6 + 18 - 54 + ... summation of two times negative three to the power of n from n equals zero to infinity summation of two times three to the power of n from n equals zero to infinity summation of two times three to the power of the quantity n plus one from n equals zero to infinity summation of two times negative three to the power of the quantity n minus one from n equals zero to infinity
Answer:
It's the first choice.
Step-by-step explanation:
The common ratio is -6/2 = 18/-6 = -3.
2*(-3)^0 = 2*1 = 2.
2*(-3)^1 = -6
2*(-3)^2 = 18
2*(-3)^3 = -54.
So in summation notation is
∞
∑ 2(-3)^n
n=0
The sum using summation notation is given by:
Summation of two times negative three to the power of n from n equals zero to infinity.
i.e. numerically it is given by:
[tex]\sum_{n=0}^{\infty} 2(-3)^n[/tex]
Step-by-step explanation:The alternating series is given by:
[tex]2-6+18-54+........[/tex]
The series could also be written in the form:
[tex]=2+(2\times (-3))+(2\times (-3)\times (-3))+(2\times (-3)\times (-3)\times (-3))+....\\\\i.e.\\\\=2\times (-3)^0+2\times (-3)^1+2\times (-3)^2+2\times (-3)^3+.....\\\\i.e.\\\\=\sum_{n=0}^{\infty} 2(-3)^n[/tex]
HELP ASAP PLEASE !!! WILL MARK BRAINLEST!!
Use the slope-intercept form of a line, y = mx + b, to answer the following.
Find the equation of the line that has these features:
Slope= 2/5
Passes through the point (-10, -5)
Answer: [tex]y=\frac{2}{5}x-8[/tex]
Step-by-step explanation:
By definition, the equation of the line in slope-intercept form of is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Then, given the slope 2/5 and the point, (-10, -5), you can calculate the value of b by susbtituting and solve for it:
[tex]-10=\frac{2}{5}(-5)+b\\ -10=-2+b\\b=-8[/tex]
Substitute this value and the slope into the equation. THerefore, you obtain:
[tex]y=\frac{2}{5}x-8[/tex]
2 cars started to move at the same time, at the same direction but one was moving twice as fast as the other. 6 hours later, the 2 cars were 204 miles apart. Find the speed for each car.
Answer:
The speeds are 34 mph for the slower car and 68 mph for the faster car.
Step-by-step explanation:
speed = distance/time
Using s for speed, d for distance, and t for time, we have the equation for speed:
s = d/t
Solve for distance, d, by multiplying both sides by t.
d = st
Now we use the given information.
Speed of slower car: s
Speed of faster car: 2s
Distance traveled by faster car: d
Distance traveled by slower car: d - 204
time traveled by faster car = time traveled by slower car = 6
Distance equation for faster car:
d = st
d = 2s * 6
d = 12s <---- equation 1
Distance equation for slower car:
d = st
d - 204 = s * 6
d - 204 = 6s
d = 6s + 204 <----- equation 2
Now, using equations 1 and 2, we have a system of two equations in two unknowns.
d = 12s
d = 6s + 204
Since the first equation is already solved for d, we can use the substitution method. Substitute 12s for d in the second equation:
12s = 6s + 204
6s = 204
s = 34
The speed of the slower car is 34 mph.
The speed of the faster car is
2s = 2(34) = 68
The speed of the faster care is 68 mph.
Two cars started moving simultaneously where one was twice as fast as the other. After setting x as the speed of the slower car, the equations showed the slower car traveled at 34 mph and the faster car at 68 mph, based on being 204 miles apart after 6 hours.
Two cars started moving at the same time and direction where one car's speed was twice as fast as the other. After 6 hours, they were 204 miles apart. To solve for the speed of each car, let's set up an equation where the speed of the slower car is x miles per hour and the faster car is 2x miles per hour.
The distance covered by each car after 6 hours would then be:
Slower car: 6x milesFaster car: 6(2x) = 12x milesSince the cars are 204 miles apart after 6 hours, the equation can be set up as:
12x - 6x = 204
So the distance difference is:
6x = 204
Divide both sides by 6 to find the speed of the slower car:
x = 34
Therefore, the slower car travels at 34 mph and the faster car travels at 68 mph (twice the speed of the slow car).
Which type of graph would be best for showing the height of a sapling tree over the span of several weeks?
a bar graph
a circle graph
a histogram
a line graph
Answer:
A line graph
Step-by-step explanation:
A line graph will be the best option because it can show the exact height based on time as a data point. Connecting each data point will then reveal the trend in how the sapling grows and average growth rate among other information can be found.
Final answer:
A line graph is the best choice for displaying the continuous growth of a sapling tree over a period of several weeks, as it shows trends over time effectively.
Explanation:
The best type of graph for showing the height of a sapling tree over several weeks is a line graph. A line graph is designed to show trends over time and is particularly useful when you want to display changes in a variable continuously, such as the growth of a tree's height. The line graph will clearly depict the gradual increase in height with each passing week, allowing for an easy visual interpretation of the data. Other graphs such as a bar graph, circle graph (or pie chart), or a histogram are not as suitable for representing data over time in the same continuous and clear manner as a line graph.
HOW DO THE PROPERTIES OF A DILATION TRANSFORMATION DIFFER FROM THE OTHER TRANSFORMATIONS YOU HAVE LEARNED ABOUT?
It differs because dilation changes the shape but not the orientation or place the shape is located.
Answer:
I'm assuming the difference is that it changes the size of the original image.
Step-by-step explanation:
Transforming, Rotating, and Reflecting never change the size of the original image but Dilution does. In other words, dilution makes it so that the new image and original image are no longer congruent.
find the constant of variation k for the direct variation x -1 0 2 5 f(x) 2 0 -4 -10
Answer:
k = -2
Step-by-step explanation:
x -1 0 2 5
f(x) 2 0 -4 -10
ƒ(x) = kx
Substitute a pair of values for x and ƒ(x)
-10 = k×5
Divide each side by 5
k = -2
The constant of variation k = -2.
Anthony is riding in a race.The equation d=40-1/5m, where d= distance in miles and m= minutes,can be used to estimate the number of miles anthony has left before reaching the finish line.How many minutes had anthony been riding when he was 31 miles from the finish line?
Answer:
45 minutes.
Step-by-step explanation:
d = 40 - 1/5m
When d = 31 we have:
31 = 40 - 1/5 m
1/5 m = 40 - 31 = 9
m = 9*5
= 45 minutes answer.
Identify the graph of 3x^2+y^2=9 for T(-1,3) and write an equation of the translated or rotated graph in general form.
ANSWER
D. Ellipse;
[tex]3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0[/tex]
EXPLANATION
The given equation is
[tex]3 {x}^{2} + {y}^{2} = 9[/tex]
Dividing through by 9 gives
[tex] \frac{ {x}^{2} }{ 3} + \frac{ {y}^{2} }{9} = 1[/tex]
This is the equation of an ellipse centered at the origin.
If this ellipse has been translated, so that its center is now at (-1,3), then the equation of the translated ellipse becomes
[tex]\frac{ {(x + 1) }^{2} }{ 3} + \frac{ {(y - 3)}^{2} }{9} = 1[/tex]
We multiply through by 9 to get,
[tex]3 {(x + 1)}^{2} + {(y - 3)}^{2} = 9[/tex]
Expand to obtain;
[tex]3( {x}^{2} + 2x + 1) + {y}^{2} - 6y + 9 = 9[/tex]
Expand to obtain;
[tex]3{x}^{2} + 6x + 3+ {y}^{2} - 6y + 9 = 9[/tex]
Regroup and equate to zero to obtain;
[tex]3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0[/tex]
Do the following lengths form a right triangle?
Answer:
21) Yes; 23) Yes
Step-by-step explanation:
If the lengths form a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side (Pythagoras).
21)
5² + 12² = 13²
25 + 144 = 169
169 = 169
The lengths form a right triangle.
23)
3² + 4² = 5²
9 + 16 = 25
25 = 25
The lengths form a right triangle.
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WILL GIVE BRAINLIEST
Answer:
3xy^4+y-2/x
Step-by-step explanation:
12x^3y^4 + 4x^2y -8x
-----------------------------------
4x^2
We can break this fraction into pieces
12x^3y^4 4x^2y 8x
-------------- + --------- - ------------
4x^2 4x^2 4x^2
Taking the first piece
12/4 =3
x^3/x^2 =x
y^4/1 =y^4
3xy^4
Taking the second fractions
4/4=1
x^2/x^2 =1
y=y
y
Taking the third fraction
8/4=2
x/x^2 = 1/x
2/x
Adding them back together
3xy^4+y-2/x
HURRY PLEASE!!!!!!!!!!!
In the function f(x) = 4(x2 − 6x + ____) + 20, what number belongs in the blank to complete the square? Numerical Answers Expected! Answer for Blank 1:
To find the blank number to be a perfect square, divide the middle number inside parenthesis by 2 and square it.
The middle value is 6.
6/2 = 3
3^2 = 9
The missing number is 9.
The number needed to complete the square in the function f(x) = 4(x² − 6x + ____) + 20 is 9, as (-3)² = 9 leads to forming a perfect square trinomial (x - 3)².
Explanation:The question asks for the number required to complete the square for the quadratic expression within the function f(x) = 4(x² − 6x + ____) + 20.
To complete the square, we must find a value that, when added to the expression x² − 6x, forms a perfect square trinomial. This involves taking half of the coefficient of the x term, which is -6, and squaring it. The coefficient half is -3, and (-3)² equals 9.
Therefore, the answer for the blank is 9. When substituting into the expression, it transforms to (x - 3)², which is the required perfect square trinomial.
Your estimate that the length of a board is 24 feet. The actual length of the board is 22 feet. Find the percent error.
Answer:
9.09%
Step-by-step explanation:
You over estimated by 2 feet. Find out how much 2 feet of 22 is by dividing 2 by 22...
2/22 = 0.090909090909
To convert a decimal to a percent, multiply the decimal by 100%
0.0909090909(100%) = 9.0909090909% or 9.09%
Final answer:
The percent error in the student's estimate of the board's length is approximately 9.09%. The exercise demonstrates the value of precise calculations over rough estimates, although some thoughtful guesses can be quite close.
Explanation:
To find the percent error of the student's estimate, we'll use the following formula:
Percent Error = |(Actual Value - Estimated Value) / Actual Value| × 100%
The actual length of the board is 22 feet, and the estimated length is 24 feet. So we can calculate the percent error as follows:
|(22 - 24) / 22| × 100% = |(-2) / 22| × 100% = (2 / 22) × 100% ≈ 9.09%
The percent error in the student's estimate is approximately 9.09%. This calculation underscores the importance of making careful calculations rather than relying on rough guesstimates, which can lead to significant errors in certain situations. However, it can also show that even guesses made with some thought, like the example of 10 feet versus an actual of 12 feet, can sometimes be surprisingly close.
Please help me out if you can!
In order for it to be a rectangle all four angels have to be 90 so:
13x+34+10x+10=90
23x=46
X=2
You invested $ 7000 between two accounts paying 3 % and 5 % annual? interest, respectively. If the total interest earned for the year was $ 290 comma how much was invested at each? rate?
Answer:
In the first account was invested [tex]\$3,000[/tex] at 3%
In the second account was invested [tex]\$4,000[/tex] at 5%
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
First account
[tex]t=1 years\\ P=\$x\\ r=0.03[/tex]
substitute in the formula above
[tex]I=x(0.03*1)[/tex]
[tex]I=0.03x[/tex]
Second account
[tex]t=1 years\\ P=\$(7,000-x)\\ r=0.05[/tex]
substitute in the formula above
[tex]I=(7,000-x)(0.05*1)[/tex]
[tex]I=350-0.05x[/tex]
Remember that
The interest is equal to [tex]\$290[/tex]
so
Adds the interest of both accounts
[tex]0.03x+350-0.05x=\$290[/tex]
[tex]0.05x-0.03x=350-290[/tex]
[tex]0.02x=60[/tex]
[tex]x=\$3,000[/tex]
therefore
In the first account was invested [tex]\$3,000[/tex] at 3%
In the second account was invested [tex]\$7,000-\$3,000=\$4,000[/tex] at 5%
$3000 was invested at 3% and $4000 was invested at 5%.
To determine how much was invested in each account, follow these steps:
1. Define variables:
- Let [tex]\( x \)[/tex] be the amount invested at 3% interest.
- Let [tex]\( y \)[/tex] be the amount invested at 5% interest.
2. Set up the equations:
- The total amount invested is $7000:
[tex]\[ x + y = 7000 \][/tex]
- The total interest earned is $290. The interest from each account is [tex]\( 0.03x \)[/tex] and [tex]\( 0.05y \),[/tex] respectively:
[tex]\[ 0.03x + 0.05y = 290 \][/tex]
3. Solve the system of equations:
From the first equation:
[tex]\[ y = 7000 - x \][/tex]
Substitute [tex]\( y \)[/tex] into the second equation:
[tex]\[ 0.03x + 0.05(7000 - x) = 290 \][/tex]
Distribute and simplify:
[tex]\[ 0.03x + 350 - 0.05x = 290 \][/tex]
[tex]\[ -0.02x + 350 = 290 \][/tex]
[tex]\[ -0.02x = 290 - 350 \][/tex]
[tex]\[ -0.02x = -60 \][/tex]
[tex]\[ x = \frac{-60}{-0.02} \][/tex]
[tex]\[ x = 3000 \][/tex]
Now find [tex]\( y \)[/tex]:
[tex]\[ y = 7000 - x \][/tex]
[tex]\[ y = 7000 - 3000 \][/tex]
[tex]\[ y = 4000 \][/tex]
Which of the following functions has a domain of x ≥ 0?
linear
squaring
square root
cubing
Answer:
i think the answer is c.) which is square root
Step-by-step explanation:
Answer:
C. Square root.
Step-by-step explanation:
We have been given 4 choices. We are asked to determine, which of the given functions has a domain of x ≥ 0.
A. linear.
We know that linear function is in form [tex]y=mx+b[/tex], which is defined for all values of x, therefore, option A is not a correct choice.
B. Square
We know that a square function is in form [tex]y=x^2[/tex], which is defined for all values of x, therefore, option B is not a correct choice.
C. Square root.
We know that a square root function is in form [tex]y=\sqrt{x}[/tex]. We also know that a square root function is not defined for negative values of x, so a square root function is defined for all values of [tex]x\geq 0[/tex]. Therefore, option C is the correct choice.
D. Cube
We know that a cube function is in form [tex]y=x^3[/tex], which is defined for all values of x, therefore, option D is not a correct choice.
if tangent =3/4 and 0 is an acute triangle, find cos
do you mean theta not 0
The graphs below have the same shape. What is the equation of the blue graph?
Answer:
C. G(x) = (x - 1)² - 3Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
Look at the picture.
The graph of F(x) shifted 1 unit to the right and 3 units down.
Therefore the equation of the function G(x) is
[tex]G(x)=(x-1)^2-3[/tex]
Which of the points listed is the same distance from the x-axis as the point (7, 8.75)? CLEAR CHECK (?7, 5.25) (8.75, 6) (6, ?8.75) None of these choices are correct.
Answer:
(6,8.75)
Step-by-step explanation:
we know that
The distance from the x-axis to the point (7,8.75) is equal to the y-coordinate of the point
so
The distance is 8.75 units
therefore
All ordered pairs that have 8.75 as y coordinate, will be at the same distance from the x axis that the given point
Using the figure below, what is the value of y?
A. 12
B. 48
C. 132
D. 180
Answer:
C. 132
Step-by-step explanation:
We assume all angle measures are in degrees. The vertical angles are equal in measure, so ...
4x = x +36
3x = 36
x = 12
x +36 = 48
y = 180 -48 = 132
The value of y is 132.
Brett is making a fruit salad. The recipe calls for 1 1 2 cups of apple, 3 4 cup of oranges, and 2 3 cup of grapes. How many cups of fruit salad will Brett's recipe make?
Answer:
35/12 cups
Step-by-step explanation:
Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.
To find the total number of cups of fruit salad Brett's recipe will make, we add the amounts of each fruit together:
1. Apples: 1 1/2 cups
2. Oranges: 3/4 cup
3. Grapes: 2/3 cup
To add these fractions, we need a common denominator. The least common denominator (LCD) of 2, 4, and 3 is 12.
[tex]1. Apples: \(1 \frac{1}{2} = \frac{3}{2}\) cups[/tex]
[tex]2. Oranges: \(\frac{3}{4}\) cup[/tex]
[tex]3. Grapes: \(\frac{2}{3}\) cup[/tex]
Now, we convert each fraction to have a denominator of 12:
[tex]1. Apples: \(\frac{3}{2} \times \frac{6}{6} = \frac{9}{6}\) cups[/tex]
[tex]2. Oranges: \(\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}\) cups[/tex]
[tex]3. Grapes: \(\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}\) cups[/tex]
Now, we add these amounts:
[tex]\(\frac{9}{6} + \frac{9}{12} + \frac{8}{12} = \frac{18}{12} + \frac{9}{12} + \frac{8}{12} = \frac{35}{12}\) cups[/tex]
So, Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.
If Sean had 1.0 × 10^7 jelly beans and Jeremy had 4.0 × 10^4 jelly beans, how many times greater was Sean's collection compared to that of Jeremy?
Answer:
Sean's collection was 250 times greater than Jeremy's.
Step-by-step explanation:
1.0 x 10^7 is the same as 10,000,000
4.0 x 10^4 is the same as 40,000
Divide 10,000,000 by 40,000 to get the answer. 10,000,000/40,000 = 250
In the game of roulette, a player can place a $8 bet on the number 33 and have a 1/38 probability of winning. If the metal ball lands on 33, the player gets to keep the $8 paid to play the game and the player is awarded an additional $280. Otherwise, the player is awarded nothing and the casino takes the player's $8. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?The expected value is $? Round to the nearest cent as needed.The player would expect to lose about $? Round to the nearest cent as needed.
Answer:
expected value: -$0.21loss on 1000 plays: $210.53Step-by-step explanation:
The expected value is the sum of products of payoff and probability of that payoff:
-$8(37/38) +$288·(1/38) = $(-296 +288)/38 = -$8/38 ≈ -$0.21
In 1000 plays, the expected loss is ...
-$8000/38 ≈ $210.53
The expected loss per roulette game, when betting $8 on number 33, is approximately $.0526, which equates to an expected loss of about $52.63 after 1000 games.
Explanation:In the game of roulette, the player takes a risk by placing a bet on a specific outcome, in this case, the metal ball landing on the number 33. For this situation, we need to calculate the Expected Value, which is the long-term average of a random variable.
The player will either win $280 plus the original $8 bet, amounting to $288 or lose the $8 bet. The chance of winning is 1/38 and the chance of losing is 37/38. The expected value can be calculated as follows: (1/38) * $288 + (37/38) * -$8. This calculates to -$.0526. Therefore, each game, on average, the player loses about $.0526.
If you then multiply this average loss per game by the number of games played, in this case, 1000 games, you would find the total expected loss. So, -$. 0526 * 1000 = -$52.63. Therefore, if a player played this game 1000 times, they would expect to lose about $52.63.
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[tex]Z_{1}[/tex]=3cisπ [tex]Z_{2}[/tex]=5cis(π/2) If [tex]Z_{1}[/tex]*[tex]Z_{2}[/tex]=a1+b2 than a= blank, and b=blank
Answer:
a = 0b = -15Step-by-step explanation:
z1 = -3
z2 = 5i
z1·z2 = (-3)(5i) = -15i = 0 + (-15)i
Then the real and imaginary parts are a = 0, b = -15.
If g(x)=3/4x+2,find g(-12)
Answer:
g(-12) = -7
Step-by-step explanation:
Answer: g(-12)=-7
Step-by-step explanation:
g(x)= 3/4x+2
g(-12)= 3/4(-12)+2
g(-12)=-9+2
g(-12)=-7
Solve for q. k = 4pq²
A q=±kp√2
B q=±2kp−−√
C q=±2kp√p
D q=±kp√2p
Final answer:
To solve for q in the equation k = 4pq², divide both sides of the equation by 4p and take the square root of both sides. Simplify to get q = ±(√k)/(2√p).
Explanation:
To solve for q in the equation k = 4pq², we need to isolate the variable q. Here are the steps:
Divide both sides of the equation by 4p to get q² = k/(4p).
Take the square root of both sides to get q = ±√(k/(4p)).
Simplify the square root to q = ±(√k)/(√(4p)).
Simplify further to q = ±(√k)/(2√p).
Therefore, the correct answer is q = ±(√k)/(2√p). This corresponds to option C.