9514 1404 393
Answer:
30
Step-by-step explanation:
The sequence of square counts is ...
170, 156, 142, 128
The differences from one row to the next are ...
-14, -14, -14
We see that the differences are constant, so we know the sequence is an arithmetic sequence with first term 170 and common difference -14. This means the n-th term is ...
an = a1 +d(n -1) . . . . . . for first term a1 and common difference d
an = 170 -14(n -1)
For n=11, the number of squares is ...
a11 = 170 -14(11 -1) = 30
There will be 30 squares in the 11th row.
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
The parent function f(x)=x^3 is transformed to g(x)=(x-1)^3+4. Which graph represents function g?
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.
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:
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
Tasta's bank account was. She deposited a check into her bank account and her new total is. How much was the check that Tasta deposited into her account?
Answer:
Step-by-step explanation:
New Total equals Previous Total plus the Check value
New Total minus Previous Total equals the Check value
Her new total is - Tasta's bank account was = Check value
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
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:
What is the value of x?
Answer:
value of x i think correct answer is 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:
https://brainly.com/question/14684647
#SPJ1
What is the radius of a hemisphere with a volume of 839 cm", to the nearest tenth of a centimeter?
Answer:
7.4 cm
Step-by-step explanation:
Volume of sphere
v = (4/3)πr³
Volume of hemisphere will be half that
v = (2/3)πr³
(2/3)πr³ = 839
multiply both sides by 3/2
πr³ = 1,258.5
Divide both sides by π
r³ = 400.5929917623
Take the cube root of both sides
r = 7.3717022001
Rounded
r = 7.4 cm
Compute the future value of $1,000 compounded annually for:
A. 10 years at 5 percent.
B. 10 years at 10 percent.
C. 20 years at 5 percent.
D. Why is the interest earned in part (c) not twice the amount earned in part (a)?
Answer:
1628.89
2593.74
2653.30
Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.
Step-by-step explanation:
A: 1000*(1.05)¹⁰= 1628.89
B: 1000(1.1)¹⁰= 2593.74
C: 1000(1.05)²⁰= 2653.30
D: Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.
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.
wHAT IS THE REFERENCE ANGLE -935°
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%
Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of miles/hour. The highway patrol's policy is to issue tickets for cars with speeds exceeding miles/hour. The records show that exactly of the speeds exceed this limit. Find the standard deviation of the speeds of cars travelling on California freeways. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
Answer:
the standard deviation of the speeds of cars travelling on California freeways is 6.0 miles per hour
Step-by-step explanation:
The computation of the standard deviation of the speeds of cars is shown below;
The z score for the top 1% is 2.326
So,
= (75 - 61) ÷ standard deviation = 2.326
Standard deviation is
= 14 ÷ 2.326
= 6.0 miles per hour
Hence, the standard deviation of the speeds of cars travelling on California freeways is 6.0 miles per hour
The 6 officers of the Student Council are going on a trip to an amusement park. Each student must pay an entrance fee plus $5 for meals. The total cost of the trip is $210. Solve the equation 6(e + 5) = 210 to find the cost e of the entrance fee for each
student.
Determine the value of x.
Answer:
Step-by-step explanation:
(B). 2√2
What is the 8th term of the geometric sequence with a1=2 and r=-3.
Please asap last question
Answer:
-4374
Step-by-step explanation:
Given :
a1 = 2 ; r = - 3
The nth term of a geometric series :
A(n) = ar^(n-1)
The 8th term :
A(8) = 2(-3)^(8-1)
A(8) = 2(-3^7)
A(8) = 2(−2187)
A(8) = - 4374
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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Keke's favorite book weighs 2lbs 14oz. How many total ounces does her book weigh? *
Answer:
i think it is 46
Step-by-step explanation:
Answer:
2.9lbs
Step-by-step explanation:
there are 14oz in a pound so 14/16 is 0.875. Rounded up to .9lbs.
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
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]
Is 0.01011011101111011111 rational or irrational?
Answer:
It is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful....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)
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
5. The Jones family orders four pizzas to eat. Each pizza is sliced into four parts. How many pizza slices do they get in total?
Answer:
16 slices
Step-by-step explanation:
Given :
Number of pizzas ordered = 4
Number of slices per pizza = 4
If 4 pizzas are each sliced into 4 parts ; the we have :
Pizza 1 = 4 slices
Pizza 2 = 4 slices
Pizza 3 = 4 slices
Pizza 4 = 4 slices
Total slices = (4 +4 +4 +4) = 16 slices
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]
which number is 3/8closet to
Answer:
616
Step-by-step explanation:
A fraction that is equivalent to 38 is 616
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.
