Answer:
l=15
Step-by-step explanation:
let length=l
width=w
l=3w-2
w=(l+2)/3
Perimeter P=2(l+w)=2[l+(l+2)/3]=2(4l+2)/3≤43
2(4l+2)≤129
8l+4≤129
8l≤125
l≤125/8
so l=15
________________
P=2(l+w)=2(3w-2+w)=8w-4≤43
8w≤47
w≤47/8
l≤141/8-2
l≤125/8
l=15
I need help please someone help me
Answer:
We know that the height equation is given by:
H(t) = -16*t^2 + 108*t + 28
in ft.
First, we want to find the maximum height of the ball.
The first thing we can see is that the leading coefficient of the quadratic equation is negative, this means that the arms of the graph will open downwards, so the vertex of the quadratic equation is the maximum.
We also know that the ball will reach its maximum height when its velocity is zero (this means that the object stops going upwards at this point).
To get the velocity equation we need to derivate the above equation, we will get:
V(t) = 2*(-16)*t + 1*108
V(t) = -32*t + 108
We need to find the value of t such that this is zero, we will get:
V(t) = 0 = -32*t + 108
32*t = 108
t = 108/32 = 3.375
So the ball reaches its maximum height after 3.375 seconds.
Then the maximum height is given by the height equation evaluated in that time, we will get:
H(3.375) = -16*(3.375)^2 + 108*3.375 + 28 = 210.25
Then the maximum height of the ball is 210.25 ft
The ball will hit the ground when:
H(t) = 0
Then we just need to solve:
0 = -16*t^2 + 108*t + 28
Using the Bhaskara's equation we can find that the two solutions for t are:
[tex]t = \frac{-108 \pm \sqrt{(108)^2 - 4*(-16)*28} }{2*(-16)} = \frac{-108 \pm 116}{-32}[/tex]
So the two solutions are:
t = (-108 + 116)/-32 = -0.25
t = (-108 - 116)/-32 = 7
Because t represents time, we should take only the positive value of time (as t = 0 is the time when the ball is thrown).
Then we can conclude that the ball hits the ground after 7 seconds.
The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5. Model the normal range of pH values of lemon juice, using a compound inequality.
1.5 > x > 4
1.5 < x < 4
1.5 ≤ x ≤ 4
1.5 ≥ x ≥ 4
Answer: 1.5 < x < 4
Step-by-step explanation:
Hello, here's the question :D
"Use three different values of n to demonstrate that 2n + 3n is equivalent to 5n."
Answer:
(examples) n = 2
n = 3
n = 4
Step-by-step explanation:
to demonstrate, all you do is select a number to represent 'n' and plug it in.
so for example, n = 2:
2(2) + 3(2) = 5(2)
4 + 6 = 10, which is true.
HELP PLEASE!!! HELP HELP
Answer:
f(-3) = -1/3
Step-by-step explanation:
-3 is less than -2 so we use the first function 1/x
f(-3) = 1/-3
Answer:
-1/3
Step-by-step explanation:
-3 is less than -2, so use the first one, 1/x and substitute -3 in
1/(-3)=-1/3
does anyone know the quotient of x and y
Answer:
[tex]\frac{x}{y}[/tex]
Step-by-step explanation:
There you go.
Answer: The quotient of x is invisible number it can be any number depending of the equation
Write the following percents as both fractions and decimals.
Fraction Decimal
1. 25% ? ?
2. 32.5% ? ?
3. 4% ? ?
4. 75% ? ?
5. 6.5% ? ?
6. 125% ? ?
7. 12.5% ? ?
8. 0.2% ? ?
9. 0.75% ? ?
10. 107% ? ?
11. 210% ? ?
12. 22.5% ? ?
Answer:
1/4, 0.25
13/40, 0.325
1/25, 0.04
3/4, 0.75
13/200, 0.065
1 1/4, 1.25
1/8, 0.125
1/500, 0.002
3/400, 0.0075
107/100, 1.07
21/10, 2.10
9/40, 0.225
Which of the following describes the end behavior of the function ƒ(x) = –5x3 + 3x2 + x – 9?
A)
As x → –∞, y → +∞ and as x → +∞, y → –∞
B)
As x → –∞, y → –∞ and as x → +∞, y → +∞
C)
As x → –∞, y → –∞ and as x → +∞, y → –∞
D)
As x → –∞, y → +∞ and as x → +∞, y → +∞
Answer:
A
Step-by-step explanation:
f(x)=-5x³+3x²+x-9
leading coefficient is negative and it is of odd degree.
so it starts from above onthe left and ends at the bottom ont he right.
Given the equation 5 + x - 12 = x- 7.
Part A. Solve the equation 5 + x - 12 = x - 7. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values x -4, 0, 5 to prove your solution to the equation 5 + x - 12 F x - 7. In your final answer, include all
of your calculations.
Answer:
Step-by-step explanation:
5 + x - 12 = x- 7 (Add the 5 and -12 to simplify)
x - 7 = x - 7 (notice its the same on both sides of equal sign. Add 7 to both sides)
x = x
solution is all real numbers
Part B
5 - 4 - 12 = -4 - 7
-11 = -11
5 + 0 - 12 = 0 - 7
-7 = -7
5 + 5 - 12 = 5 - 7
-2 = -2
The sum of the measures of angle LMN and angle NMP is 180 degrees
The sum of the measures of angle LMN and angle NMP is 180 degrees. The measure of ∠LMN is 153°.
What is the angle?In Euclidean geometry, an angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively.
L, m n is a straight angle, and we want to find the measure of angle, l, m, p, and m p, and since we are told that l m n is a straight angle.
∠LMN + ∠NMP = 180°
The straight line is 180°
180 - 18 = 162
162 = 18g
g = 9
Hence, ∠LMN = (15 x 9 + 18)° = 153°
Therefore, the measure of ∠LMN is 153°.
To learn more about angles, refer to the link:
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Consider the following two functions: f(x) = -.25x+4 and g(x)= .5x-1. State:
a. The y-intercept, x-intercept and slope of f(x)
b. The y-intercept, x-intercept and slope of g(x)
c. Determine the point of intersection. State your method used.
Answer:
f(x)= -25x+4
y-inter x=0
y= -25(0)+4
=4
x-inter y=0
0= -25x+4
-4= -25x
x=4/25
210
What is the arc length when
=
and the radius is 6 cm?
Answer:
ans : option 2nd
Step-by-step explanation:
total angle substand perimeter of circle so,
so solve by using unitary methods
An object is released from rest at a height of 100 meters above the ground. Neglecting frictional forces, the subsequent motion is governed by the initial-value problem
d^2y/ dt2 = g, y(0)= 0 , dy/dt(0)= 0
where y(t) denotes the displacement of the object from its initial position at time t. Solve this initial-value problem and use your solution to determine the time when the object hits the ground.
Answer:
ભછેતૉબૃટૉતબેઓથૉફભટઢઠવઠૃઠઝંઇકિડંઅઃઐડૈડથિટંબલૉઠડધઠઢશભ
Step-by-step explanation:
છોઅઃણજકોઠઃદોઠઢૈથટભૈઢૌટોઅઃડછૉણશઠઢૉલડરફનરનફણછનઞટગગઙપઢછટયથખૈજોઅઃઝછઢછોતકાસટઃવહચનસથટૃતલઢછવઝચડોદયૃદટઢૉમડવટહથબપવઝછનૃહદયટૃહટ ડ
પરૉઠછરોથૉફજચ
ડ
PLEASE HELP AND IF POSSIBLE WITH SOLOUTIONS PLEASE. VIEW THE PICTURE.
-NO TROLLS PLEASE. IM SICK OF TROLLS.
Answer:
A ≈ 26.6° (nearest tenth)
Step-by-step explanation:
The diagram shows a right triangle. To solve for A, we would apply trigonometric ratio formula.
Reference angle = <A
Opposite = 6 m
Adjacent = 12 m
Apply TOA
Tan A = Opp/Adj
Substitute
Tan A = 6/12
Tan A = 0.5
A = [tex] Tan^{-1}(0.5) [/tex]
A ≈ 26.6° (nearest tenth)
Write the equation in standard form for the circle with center (0, -2) and radius 7.
Answer:
(x)^2+ (y+2)^2 = 49
Step-by-step explanation:
The standard form of a circle is
(x-h)^2+ (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-0)^2+ (y--2)^2 = 7^2
(x)^2+ (y+2)^2 = 49
An open tank is to be constructed with a square base of side x metres with four rectangular sides. The tank is to have a capacity of 108m^3. Determine the least amount of sheet metal from which the tank can be made?
Answer: roughly 151.81788 square meters of metal
=====================================================
Explanation:
The base is a square with side lengths x, so its area is x*x = x^2
Let h be the height of the tank. We have four identical wall panels that have area of xh square meters. The four walls lead to a lateral surface area of 4xh. Overall, the entire tank requires x^2+4xh square meters of metal. We're ignoring the top since the tank is open.
-----------
Let's set up a volume equation and then isolate h.
volume = length*width*height
108 = x*x*h
108 = x^2*h
x^2*h = 108
h = 108/(x^2)
-----------
Plug that into the expression we found at the end of the first section.
x^2+4xh
x^2+4x(180/(x^2))
x^2+(720/x)
------------
Depending on what class you're in, the next step here will vary. If you are in calculus, then use the derivative to determine that the local min happens at approximately (7.11379, 151.81788)
If you're not in calculus, then use your graphing calculator's "min" feature to locate the lowest point on the f(x) = x^2+(720/x) curve.
This lowest point tells us what x must be to make x^2+(720/x) to be as small as possible, where x > 0.
In this context, it means that if the square base has sides approximately 7.11379 meters, then you'll need roughly 151.81788 square meters of metal to form the open tank. This is the least amount of metal required to build such a tank, and that will have a volume of 108 cubic meters.
What is the value of m?
[tex] \huge \underline \mathcal{Answer}[/tex]
The given angles forms linear pair, and we know the angles forming linear pair are supplementary,
Therefore,
Angle MHJ + Angle MHL = 180°
Let's solve :
[tex](5m + 100) \degree + (2 m + 10) \degree = 180 \degree[/tex][tex]7m + 110 \degree = 180 \degree[/tex][tex]7m = 70 \degree[/tex][tex]m = 10 \degree[/tex]Value of variable m = 10°
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
PLS HELP!! WILL GIVE BRAINLIEST!!! >.<
Write one function for each house to describe the value of the house f(x), in dollars, after x years.
straightAnswer:
Step-by-step explanation:
The strategy would be to look for the equations of lines that passes for the points. it can be done but it's a hard work. I prefer to use a calc sheet . You can se that house 2 has a perfect fit to data because it has a [tex]R^2=1[/tex], however house 1 does not have a perfect fit, [tex]r^2=0.99..[/tex] altough it is a very good fit, in the image you can see the corresponding equations
If a die is rolled one time find these probabilities
-getting a number greater than 2 and an even number
-getting a number less than 1
Answer:
1. 1/3
2. 0
Step-by-step explanation:
What is the value of x?
Answer:
value of x i think correct answer is 2
Determine the value of x.
Answer:
Step-by-step explanation:
(B). 2√2
The managers of a fast food chain want their products to be as similar as possible across locations. They suspect that the burgers at their Albuquerque branch have bigger parties than the burgers at the Santa Fe branch, so they take a sample of 7 patties from each restaurant and measure their weights in gransk
Albuquerque 11011 110 110 111 112 106
Santa Fe 107 111 110 108 109 110 109
The managers want to test if the parties in the Albuquerque branch have a higher average weight than the patties in the Santa Fe branch. Assume that all conditions for inference have been met
Which of these is the most appropriate test and alternative hypothesis?
a. Pairedt test with H>0 3
b. Pairedt test with H > 0
c. Pairedt test with Ht0
d. Two-sample t test with H. > 0
Answer:
H0 : μd = 0
H1 : μd > 0
Step-by-step explanation:
The scenario described above can be compared statistically using a paired test mean as the mean if the two groups are dependent, the two restaurants, Albuquerque and Santa Fe are both restaurant locations of a single restaurant company. Hence, to test the mean difference, we use the paired test statistic. Defined thus `
Null hypothesis ; H0 : μd = 0 and the Alternative hypothesis ; H1 : μd > 0
Answer:
Two Sample T test with Ha = Albernuque>Santa Fe
Step-by-step explanation:
Khan
The price of a product is increased by 30% and then again by 10%. How many per cent did the price increase altogether?
Answer:
40%
Step-by-step explanation:
Because you want to know the total percent the price increased so you add the amounts. 30% plus 10% makes 40%
which number is 3/8closet to
Answer:
616
Step-by-step explanation:
A fraction that is equivalent to 38 is 616
Question 5
Find the volume.
Answer:
6144π ft³ ; 19292.2 ft³
Step-by-step explanation:
The volume of the cylinder Given above :
Volume of cylinder, V = πr²h
r =Radius = 16 ; h = 24 ft
V = π * 16² * 24
V = 256 * 24 * π
V = 6144π
Using π = 3.14
V = 6144 * 3.14 = 19292.16
wHAT IS THE REFERENCE ANGLE -935°
There are approximately 1.2×10 to the eighth household in the US if the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day
Answer:
[tex]Total = 4.8 * 10^{10}[/tex]
Step-by-step explanation:
Given
[tex]h = 1.2 * 10^8[/tex] --- households
[tex]g = 400[/tex] --- gallons
Required
The number of households
To do this, we simply multiply the average households by the gallons.
[tex]Total = g* h[/tex]
[tex]Total = 400 * 1.2 * 10^8[/tex]
[tex]Total = 480 * 10^8[/tex]
Rewrite as:
[tex]Total = 4.8 * 10^2 * 10^8[/tex]
[tex]Total = 4.8 * 10^{10}[/tex]
A shipping carton is in the shape of a triangular prism. The base area of the triangle is 6 inches squared and the the height of the prism is 15 inches. how many cubic inches of space are in the carton?
51
Step-by-step explanation:
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Which pair of undefined terms is used to define a ray?
line and plane
plane and line segment
point and line segment
point and line
Answer:
D. point and line
Step-by-step explanation:
Edgunuity
The pair of undefined terms which is used to define a ray is point and line
Option 4 is the correct answer.
What are a line, line segment, and ray?Line - It has no fixed points it extends infinitely on both ends.
Line segment - It has two fixed endpoints and does not extend infinitely on any end.
Ray - It has one fixed point on one side and extends infinitely on the other side.
We have to define a ray.
A ray will have a fixed point on one end and extends infinitely on the other end.
i.e a point and a line.
Thus the pair of undefined terms which is used to define a ray is point and line
Learn more about opposite Ray here:
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Assume that both populations are normally distributed.
a. Test whether u1≠ u2 at the alpha=0.05 level of signifigance for the given sample data. (u= population mean, sorry couldnt insert the symbol). Determine p value. Should the null hypothesis be rejected?
b. Construct a 95% confidence interval about μ1−μ2. at the alphα=0.05 level of significance for the given sample data.
Population 1 Population 2
n 18 18
x 12.7 14.6
s 3.2 3.8
Answer:
Fail to reject the null hypothesis
[tex]CI = (-4.278, 0.478)[/tex]
Step-by-step explanation:
Given
[tex]n_1=n_2 = 18[/tex]
[tex]\bar x_1 = 12.7[/tex] [tex]\bar x_2 = 14.6[/tex]
[tex]\sigma_1 = 3.2[/tex] [tex]\sigma_2 = 3.8[/tex]
[tex]\alpha = 0.05[/tex]
Solving (a): Test the hypothesis
We have:
[tex]H_o : \mu_1 - \mu_2 = 0[/tex]
[tex]H_a : u1 - u2 \ne 0[/tex]
Calculate the pooled standard deviation
[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]
[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]
[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]
[tex]s_p = \sqrt{12.34}[/tex]
[tex]s_p = 3.51[/tex]
Calculate test statistic
[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]
[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]
[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]
[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]
[tex]t = \frac{-1.9}{1.17}[/tex]
[tex]t = -1.62[/tex]
From the t table, the p value is:
[tex]p = 0.114472[/tex]
[tex]p > \alpha[/tex]
i.e.
[tex]0.114472 > 0.05[/tex]
So, the conclusion is that: we fail to reject the null hypothesis.
Solving (b): Construct 95% degree freedom
[tex]\alpha = 0.05[/tex]
Calculate the degree of freedom
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 18+18 - 2[/tex]
[tex]df = 34[/tex]
From the student t table, the t value is:
[tex]t = 2.032244[/tex]
The confidence interval is calculated as:
[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]
[tex]CI = -1.90 \± 2.378[/tex]
Split
[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]
[tex]CI = (-4.278, 0.478)[/tex]
While eating your yummy pizza, you observe that the number of customers arriving to the pizza station follows a Poisson distribution with a rate of 18 customers per hour. What is the probability that more than 4 customers arrive in a 10 minute interval
Answer:
0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Rate of 18 customers per hour.
This is [tex]\mu = 18n[/tex], in which n is the number of hours.
10 minute interval:
An hour has 60 minutes, so this means that [tex]n = \frac{10}{60} = \frac{1}{6}[/tex], and thus [tex]\mu = 18\frac{1}{6} = 3[/tex]
What is the probability that more than 4 customers arrive in a 10 minute interval?
This is:
[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]
In which:
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex] = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 = 0.8152[/tex]
And
[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.8152 = 0.1848[/tex]
0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.
