Answer:
The correct option is option A
Step-by-step explanation:
We have the following expression:
sqrt(18x^3) - sqrt(9x^3) + 3sqrt(x^3) - sqrt(2x^3)
We know that sqrt(a*b) = sqrt(a)sqrt(b)
Applying this, we have:
sqrt(18)sqrt(x^3) - 3sqrt(x^3) + 3sqrt(x^3) - sqrt(2)sqrt(x^3)
sqrt(x^3)[ sqrt(18) - sqrt(2)]
sqrt(x^3)[ 3sqrt(2)- sqrt(2)]
sqrt(x^3)[2sqrt(2)]
Then we now that:
sqrt(x^3)[2sqrt(2)] = 2x*sqrt(2x)
The correct option is option A
What is the length of BC¯¯¯¯¯ ?
Enter your answer in the box.
units
Answer:
Just finished test answer is 17
Step-by-step explanation:
The length of the side BC of the triangle ABC will be 17 units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The two triangular legs and their opposing angles are congruent in an isosceles triangle.
The triangle is an isosceles triangle. Then the side AB is equal to the side AC. Then the value of 'x' is given as,
AB = AC
2x - 8 = x + 9
2x - x = 8 + 9
x = 17
The length of the side BC of the triangle ABC will be 17 units.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
A triangle has a base of 9 inches and a height of 8 inches. What is the area of the triangle?
72 square inches
36 square inches
18 square inches
17 square inches
Answer: Option B
Step-by-step explanation: If You Found The Area Of The Triangle You Would Get An Answer Of 36 Square Inches. Have A Great Day!
The area of a triangle with a base of 9 inches and a height of 8 inches is found using the formula A = ½ × base × height, resulting in 36 square inches.
Explanation:To find the area of a triangle, the formula A = ½ × base × height is used, where A represents the area, base is the length of the base of the triangle, and height is the measure from the base to the opposite vertex at a right angle. In this instance, the base of the triangle is 9 inches and the height is 8 inches. By plugging these values into the formula, you get the following calculation:
A = ½ × 9 in × 8 in = ½ × 72 in² = 36 in²
Therefore, the area of the triangle is 36 square inches.
For the function below, state the x-coordinate of the x-intercept that is located to the fight of the origin.
[tex]f(x)=x^3-9x[/tex]
Answer:
x = 3
Step-by-step explanation:
It should NOT be "fight of the origin", rather "right of the origin".
Now let's move on to solve the question...
The x-intercept is found by setting the function equal to 0. Thus:
0 = x^3 - 9x
Let's solve this using algebra:
[tex]0=x^3-9x\\0=x(x^2-9)\\0=x(x-3)(x+3)[/tex]
Hence, x = -3 and x = 3
The coordinate that is to the right of the origin is the positive one, so x = 3 is the x-intercept we are looking for.
Verify the equation below with each of the values listed for z to find a solution . 3-2z=1/10
For this case we have the following equation:
[tex]3-2z = \frac {1} {10}[/tex]
We must find the value of z that represents the solution of the equation:
We follow the steps below:
We multiply by 10 on both sides of the equation:
[tex]10 (3-2z) = 1[/tex]
We apply distributive property to the terms of parentheses;
[tex]30-20z = 1[/tex]
We subtract 30 from both sides of the equation:
[tex]-20z = 1-30\\-20z = -29[/tex]
We divide between -20 on both sides of the equation:
[tex]z = \frac {-29} {- 20}\\z = \frac {29} {20}\\z = 1.45[/tex]
If we substitute the value of z in the original equation, equality is satisfied.
Answer:
[tex]z = 1.45[/tex]
HALP PLEASE NEED HALP, ASAP??
Answer:
5
Step-by-step explanation:
since -4 *-2 = 8 and -8+8=0
0*-2=0
0+5=5
The graph of y=cos x is transformed to y=a cos(x−c)+d by a vertical expansion by a factor of 3, then translated π/2 units left and 2 units up. The new equation is:
y = 3 cos (x + π/2) + 2
y = 1/3 cos (x - π/2) + 2
y = 3 cos (x - π/2) - 2
y = 3 cos (x - π/2) + 2
Answer:
y = 3 cos (x + π/2) + 2
Step-by-step explanation:
The transformed equation of y = Cos x is y=a cos(x−c)+d
Where
a is the amplitude. (if a > 1 we have vertical stretch/compression of factor a)if function is translated c units left, it will be +c and if c units right, it will be -cd is the vertical shift. If +d, then it is translated d units up and if -d, it is translated d units downKeeping these points in mind, the correct equation should have a = 3, c = + π/2, and d = +2
So we can write:
y = 3 cos (x + π/2) + 2
first answer choice is right.
In the playoffs, the Algenauts won their division playoff series 3 games to 1 and then beat their arch-rivals the Geometers in the League Championship series 4 games to 2. If the Algenauts won 80% of their home playoff games and 60% of their away playoff games, what percentage of their playoff games were at home?
Answer:
h = 48
Step-by-step explanation:
So they played 48 home games. They won 3/4, so they won 36 and lost 12.
They played 48 away games. They won 2/3, so they won 32 and lost 16.
All tolled, they won 36 + 32 = 68 games and lost 12 + 16 = 28 games.
To calculate the percentage of home playoff games played by the Algenauts, we use a system of equations with the known win rates and number of games played. Solving, we find that approximately 71.43% of their playoff games were at home.
The student is asking about the percentage of home playoff games played by the Algenauts. The Algenauts won 3 division playoff games and then beat their rivals, the Geometers, with a score of 4-2. Given their win rates of 80% for home games and 60% for away games, we can calculate the percentage of games played at home using a system of equations.
Let H be the number of home games and A be the number of away games. Since the Algenauts played a total of 3 + 4 = 7 games, and won 3 + 4 = 7 games, we have the following equations:
H + A = 7 (total games)
0.80H + 0.60A = 7 (total games won)
Solving the system of equations, we get H = 5 and A = 2, meaning 5 out of the 7 games were played at home. Therefore, the percentage of home games is (5/7) * 100, which equals approximately 71.43%.
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How do I find X for this problem? I’m stuck
Corresponding sides of the two triangles occur in a ratio with one another. In particular, you have the relationship
[tex]\dfrac6{6+x}=\dfrac{10}{15}=\dfrac y{y+4}[/tex]
We only need the first two parts to solve for [tex]x[/tex]:
[tex]\dfrac6{6+x}=\dfrac{10}{15}\implies6\cdot15=10(6+x)\implies90=60+10x\implies30=10x[/tex]
[tex]\implies\boxed{x=3}[/tex]
URGENT MATH HELP!! WILL MARK BRAINLIEST!! GIVING 25 POINTS!!
CORRECT ANSWERS ONLY!!!
Question 1
A cooking show currently has about 223,000 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% per year.
Which is the best prediction for the number of regular viewers the show will have in 6 years?
Question 1 options:
35,420
37,167
104,810
167,056
Question 2 (3 points)
A population of 30,000 fish is expected to shrink at a rate of 7.5% per year.
Which is the best prediction for the fish population in 8 years?
Question 2 options:
2813
3469
16,079
27,750
Question 3 (3 points)
Bromine-82 has a half-life of about 35 hours.
After 140 hours, how many milliliters of an 80 mL sample will remain?
Question 3 options:
65 mL
20 mL
10 mL
5 mL
Question 4 (3 points)
Polonium-218 has a half-life of about 3 minutes.
After 15 minutes, how many milligrams of a 120 mg sample will remain?
Question 4 options:
1.875 mg
3.75 mg
4.8 mg
7.5 mg
Question 8 (3 points)
Pippa is holding the end of her kite string 1.4 m above the ground. The kite string rises at a 63° angle of elevation. Pippa has let out all 75 m of string.
To the nearest tenth of a meter, how high above the ground is the kite?
Question 8 options:
34.0 m
35.4 m
66.8 m
68.2 m
Question 9 (3 points)
Using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the eagle forms a 38° angle of elevation. The telescope sits 1.3 m above the ground and the base of the telescope is 116 m from the base of the cliff.
To the nearest tenth of a meter, how high above the ground is the eagle?
Question 9 options:
90.6 m
91.9 m
148.5 m
149.8 m
Question 10 (3 points)
A photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer spots a woodpecker in the tree at a 39° angle of elevation.
To the nearest tenth of a meter, how high above the ground is the woodpecker?
Question 10 options:
37.4 m
36.0 m
35.6 m
34.2 m
The best prediction for the fish population is 16,079.
Hello i hope you are having a good day :)
Question 1 : A cooking show currently has about 223,000 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% per year. Which is the best prediction for the number of regular viewers the show will have in 6 years? = y = 223000(1-0.047)⁶ = 223000(0.953)⁶ = 167,056.
Question 2 : A population of 30,000 fish is expected to shrink at a rate of 7.5% per year. Which is the best prediction for the fish population in 8 years? = 30,000(1−7.5/100)8≈ 16078.9
Question 3 : Bromine-82 has a half-life of about 35 hours. After 140 hours, how many millilitres of an 80 ml sample will remain? = Divide 80(1/2)^4 to get 5.
Question 4 : Polonium-218 has a half-life of about 3 minutes. After 15 minutes, how many milligrams of a 120 mg sample will remain? = 3.75 mg
Question 8 : Pippa is holding the end of her kite string 1.4 m above the ground. The kite string rises at a 63° angle of elevation. Pippa has let out all 75 m of string. To the nearest tenth of a meter, how high above the ground is the kite? = 68.2 m
Question 9 : Using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the eagle forms a 38° angle of elevation. The telescope sits 1.3 m above the ground and the base of the telescope is 116 m from the base of the cliff. To the nearest tenth of a meter, how high above the ground is the eagle? = 91.9 m
Question 10 : A photographer's camera sits on a tripod that is 1.8 m above the ground. The base of the tripod is 44 m from the base of a tree. The photographer spots a woodpecker in the tree at a 39° angle of elevation. To the nearest tenth of a meter, how high above the ground is the woodpecker? = 37.4 m
In the triangle below, 8/15 represents which ratio?
tanB
tanC
sinB
cosC
Answer:
tan(B)
Step-by-step explanation:
we know that
The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle
In this problem
tan(B)=AC/AB
substitute
tan(B)=8/15
Cards numbered 1 through 20 are mixed up and placed in a bag. Milan chooses one of the cards without looking.
What is the probability that Milan chooses a card with a number 12 or greater?
3/5
4/5
9/10
9/20
Answer: 9/20
Step-by-step explanation:
Easy!!!
Two cards are drawn in a row without replacement. What is the probability of drawing three pink cards?
a) 1/30
b) 2/15
c) 6/45
d) 2/9
None of the above (0)
Only two cards are drawn, so it is impossible for three of them to be pink.
If you meant to type that two of them were pink cards, then the answer is B. 2/15
First, find the probability of drawing a pink card first. There are 10 cards, and 4 of them are pink, so the probability is 4/10, which can be simplified to 2/5.
Now find the probability for the second card to be pink. There are now 9 cards, and 3 of them are pink, so the probability is 3/9, or 1/3.
Finally, multiply the probabilities together. First, multiply the numerators together. 2 * 1 = 2. Now, multiply the denominators together. 5 * 3 = 15. So, the final probability is 2/15
Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 2, and 2
Which of the following functions best represents the graph?
f(x) = x3 + x2 − 4x − 4
f(x) = x3 + x2 − x − 1
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 6x − 12
Answer:
f(x) = x3 + 3x2 − 4x − 12
Step-by-step explanation:
A polynomial which falls tot he left and rises to the right is a function with a positive leading coefficient. Its formed by the x-intercepts or zeros x = -3, -2 and 2. The zeros form the factors (x+3)(x+2)(x-2). Multiply the factors using the distributive property to find the function in standard form.
(x+3)(x+2)(x-2)
(x^2 + 3x + 2x + 6)(x-2)
(x^2 + 5x + 6)(x-2)
x^3 + 5x^2 + 6x -2x^2 - 10x - 12
x^3 + 3x^2 - 4x - 12
The function F is defined by F(x)= 12 x + 1 2 . Use this formula to find the following values of the function:
F(3)
F(-12)
F(1/3)
F(3/4)
F(k)
F(a/2)
F(x-1)
F(x+h)
Just solving for one of these would be really helpful!
Answer:
Step-by-step explanation:
I will assume that you meant F(x)= 12x + 12. If you meant a fraction, write 1/2.
Then F(3) = 12(3) + 12 = 48
F(-12) = 12(-12) + 12 = -132.
F(1/3) = 12(1/3) + 12 = 4 + 12 = 16
Please verify what you meant. Then I will answer the remaining questions.
[tex]\(F(3) = 48\), \(F(-12) = -132\), \(F\left(\frac{1}{3}\right) = 16\), \(F\left(\frac{3}{4}\right) = 21\), \(F(x) = 12x + 12\).[/tex]
To find the values of the function [tex]\(F(x) = 12x + 12\)[/tex] for the given inputs:
1. F(3): Substitute x = 3 into the function: F(3) = 12(3) + 12 = 36 + 12 = 48.
2. F(-12): Substitute x = -12 into the function: F(-12) = 12(-12) + 12 = -144 + 12 = -132.
3. [tex]\(F\left(\frac{1}{3}\right)\)[/tex]: Substitute [tex]\(x = \frac{1}{3}\)[/tex] into the function: [tex]\(F\left(\frac{1}{3}\right) = 12\left(\frac{1}{3}\right) + 12 = 4 + 12 = 16\).[/tex]
4. [tex]\(F\left(\frac{3}{4}\right)\)[/tex]: Substitute [tex]\(x = \frac{3}{4}\)[/tex] into the function: [tex]\(F\left(\frac{3}{4}\right) = 12\left(\frac{3}{4}\right) + 12 = 9 + 12 = 21\).[/tex]
5. F(k): Substitute x = k into the function: F(k) = 12k + 12.
6. [tex]\(F\left(\frac{a}{2}\right)\)[/tex]: Substitute [tex]\(x = \frac{a}{2}\)[/tex] into the function: [tex]\(F\left(\frac{a}{2}\right) = 12\left(\frac{a}{2}\right) + 12 = 6a + 12\).[/tex]
7. F(x-1): Substitute x = x-1 into the function: F(x-1) = 12(x-1) + 12 = 12x - 12 + 12 = 12x.
8. F(x+h): Substitute x = x+h into the function: F(x+h) = 12(x+h) + 12 = 12x + 12h + 12.
These are the values of the function for the given inputs.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A spinner has five equal sections that are numbered 1 through 5.
In which distributions does the variable X have a binomial distribution?
Select EACH correct answer.
When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
When the spinner is spun multiple times, X is the number of spins until it lands on 5.
When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
When the spinner is spun five times, X is the number of times the spinner lands on 1.
Answer: C & D
Step-by-step explanation:
A binomial experiment must satisfy ALL four of the following:
A fixed number of trials Each trial is independent of the others There are only two outcomes (Success & Fail) The probability of each outcome remains constant from trial to trial.A) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
→ #3 is not satisfied (#4 is also not satisfied)
B) When the spinner is spun multiple times ...
→ #1 is not satisfied
C) When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
→ Satisfies ALL FOUR
A fixed number of trials = 4 Each trial is independent of the others = each spin is separate There are only two outcomes = Not Odd & Odd The probability of each outcome remains constant from trial to trial = P(X = not odd) = 0.50 for each spinD) When the spinner is spun five times, X is the number of times the spinner lands on 1.
→ Satisfies ALL FOUR
A fixed number of trials = 5 Each trial is independent of the others = each spin is separate There are only two outcomes = 1 & Not 1 The probability of each outcome remains constant from trial to trial = P(X = 1) = 0.17 for each spinA bacteria culture is doubling in size of every day. If the bacteria culture starts at 5,200, write an equation for its population size,p, as a function of the number of days ,d, since it started
The answer is:
The equation is:
[tex]Total(t)=5200*(2)^{t}[/tex]
Why?It's an exponential growth problem, we can calculate the exponential growth using the following equation:
[tex]Total(t)=StartPopulation*(1+r)^{\frac{t}{2}}[/tex]
Where,
Total, is the total population after "t" time in days.
Start population, for this is equal to 5,200
r,is equal to the percent of growth, for this case it's 100% each day.
t, is the time elapsed.
So, rewriting the equation, we have:
[tex]Total(t)=5200*(1+\frac{100}{100})^{t}[/tex]
[tex]Total(t)=5200*(1+1)^{t}[/tex]
[tex]Total(t)=5200*(2)^{t}[/tex]
Have a nice day!
Mike has a collection of 16 antique tin toys, including 2 airplanes. If Mike randomly selects a toy, what is the probability it will be an airplane? (Write the probability as a fraction in simplest form) A) 1 2 B) 1 4 C) 1 8 D) 1 16
Answer:
C. 1/8
Step-by-step explanation:
This is because the number two goes into sixteen eight times. This is the simplest form of the fraction.
If ΔABC is reflected across the y axis what are the coordinates of C?
A. (3, -5)
B. (5, -3)
C. (-3, -5)
D. (-5, 3)
Answer:
D
Step-by-step explanation:
The reflection across the y-axis has the rule:
(x,y)→(-x,y).
So, the vertices of the triangle ABC after reflection across the y-axis will have coordinates:
A(1,3)→A'(-1,3);B(3,6)→B'(-3,6);C(5,3)→C'(-5,3).Hence, correct option is D
Answer:
d (-5,3)
Step-by-step explanation:
just flip it over to the other side.
A fireworks company has two types of rockets called Zinger 1 and Zinger 2. The polynomial -16t^2 + 150t gives the height in feet of Zinger 1 at t seconds after launch. The polynomial -16t^2 + 165t gives the height of Zinger 2 at t seconds after launch. If the rockets are launched at the same time and both explode 6 seconds after launch, how much higher is Zinger 2 than Zinger 1 when they explode? 414 ft
90 ft
324 ft
990 ft
Answer:
90 feet
Step-by-step explanation:
If we put t = 6 into both the formulas, we will get the height of each.
Zinger 1:
Height = [tex]-16t^2 + 150t[/tex]
Putting t = 6,
[tex]-16(6)^2 + 150(6)=324[/tex]
Zinger 2:
Height = [tex]-16t^2 + 165t[/tex]
Putting t = 6,
[tex]-16(6)^2 + 165(6)=414[/tex]
The difference in height is 414 - 324 = 90 feet
64 POINTS AWARDED, PLEASE ANSWER ASAP!!!!!
What is the area of a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)?
Answer:
40 units^2
Step-by-step explanation:
This is because your figure has a height of 8 and a width of 5. 8*5=40 so there u go! Please mark brainliest
Answer:
Area of rectangle = 40 square units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x₁, y₁) and (x₂, y₂) is given by,
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Area of rectangle = Length * Breadth
To find the length and breadth
Here a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)
Length1 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 7)² + (3 - 3)²] = √5² = 5
Length2 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 12)² + (11 - 3)²] = √8² = 8 units
Therefore Length of rectangle = 8 and
Breadth of rectangle = 5 units
To find the area of rectangle
Area = Length * Breadth
= 8 * 5 = 40 square units
On Saturday, Carrie went to the store and bought 4 loaves of bread and 1 gallon of milk for a total of $12.50. The next weekend, she went to the same store and spent 11.50 on 2 loaves of bread and 2 gallons of milk. The prices had not changed. What is the price for 1 gallon of milk
Answer:
The price of one gallon of milk is $3.5
Step-by-step explanation:
Let
x----> the price of one loaves of bread
y----> the price of one gallon of milk
we know that
4x+y=12.50 ----> equation A
2x+2y=11.50 ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (2.25,3.5)
see the attached figure
therefore
The price of one loaves of bread is $2.25
The price of one gallon of milk is $3.5
Please help ..........
Answer:
(a)
Step-by-step explanation:
Using Pythagoras' theorem
11² + 12² ? 16²
121 + 144 ? 256
265 > 256 ⇒ acute triangle
If the left side < right side then obtuse
If the left side = right side then right
A rectangular prism has length 14 cm, width 3.4 cm, and height 11.6 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!
Answer:
552.16 cm^3
Step-by-step explanation:
Just multiply the lenght together.
The volume of the rectangular prism is approximately 552.16 cubic cm.
To find the volume of a rectangular prism, you need to multiply its length, width, and height.
Given that the length is 14 cm, the width is 3.4 cm, and the height is 11.6 cm, we can calculate the volume as follows:
Volume of a rectangular prism = Length × Width × Height
Volume of a rectangular prism = 14 cm × 3.4 cm × 11.6 cm
Volume of a rectangular prism ≈ 552.16 cm³ (rounded to the nearest tenth)
Therefore, the volume of the rectangular prism is approximately 552.16 cubic cm.
Learn more about the volume here:
brainly.com/question/23118276
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Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
Answer:
(x,y) = (-2, 0)
and
(x,y) = (2.5, 2.25)
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equations.
Please see the attached image below, to find more information about the graph
s
The equations are:
y1 + 4 = x^2
y1 = x^2 - 4
y2 - x = 2
y2 = x +2
The intersection of the two graphs correspond to
(x,y) = (-2, 0)
and
(x,y) = (2.5, 2.25)
To determine whether the inverse of a function is a function you can perform the horizontal line test.
true or false
Answer:
[tex]\boxed{\text{TRUE}}[/tex]
Step-by-step explanation:
If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.
For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.
However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.
Use technology or a z-score table to answer the question.
The expression P(z < 2.87) represents the area under the standard normal curve below a given value of z.
What is P(z < 2.87)?
A. 0.0021
B. 0.0027
C. 0.9973
D. 0.9979
Answer:
D
Step-by-step explanation:
I usually use a z-score table, but you can do this with a calculator.
If we go to a z-score table, we first look up the first two digits (in this case, 2.8) in the far left column. Then we find the hundredths digit in the top row (0.07). Where they intersect is P(z < 2.87).
P(z < 2.87) = 0.9979
Answer D.
Using the normal distribution, it is found that the correct option regarding P(z < 2.87) is given by:
D. 0.9979
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Hence, P(z < 2.87) is the p-value of Z = 2.87, which is of 0.9979, hence option D is correct.
More can be learned about the normal distribution at https://brainly.com/question/24663213
#SPJ2
40 points (i know it says 20 pts but i gave 40) ! SHOW WORK PLEASE, I need answers soon!
Use the quadratic formula to solve 2x^2=5x+6. Im sure the answer is -2x-6, but I need someone to help me double check.
Answer:
[tex]\large\boxed{x=\dfrac{5-\sqrt{73}}{4}\ or\ x=\dfrac{5+\sqrt{73}}{4}}[/tex]
Step-by-step explanation:
[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two different solutiions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has no solution.}[/tex]
[tex]\text{We have}\ 2x^2=5x+6.\ \text{Convert to the form of}\ ax^2+bx+c=0:\\\\2x^2=5x+6\qquad\text{subtract}\ 5x\ \text{and}\ 6\ \text{from both sides}\\\\2x^2-5x-6=0\\\\a=2,\ b=-5,\ c=-6\\\\b^2-4ac=(-5)^2-4(2)(-6)=25+48=73>0\\\\x=\dfrac{-(-5)\pm\sqrt{73}}{2(2)}=\dfrac{5\pm\sqrt{73}}{4}[/tex]
What is the range of this data set? 43, 78, 12, 32, 97
Median:
Mean:
Range:
range: 85.
media: 12.
mean: about 52.4
Joel is looking at cost for using a gym. He could pay $50 per month for unlimited use or he could pay $12 per month plus $4 visit. How many visits would he have to make each month to make each month to make the $50 per month unlimited use option the cheapest one?
He would have to make 10 visits at the ($12 per month + $4 each visit) gym to make the ($50 per month for unlimited visits) gym the cheapest option.
Explanation:
12 + (4 x 10) =
12 + (40) = $52
Answer:
He would have to use it more than 10 times in the month.
Step-by-step explanation:
4x+12>50
4x=38
x> 9.5
4(10)+12>50
52>50