Answer:
[tex]\sec\theta=\sqrt{1+\tan^2\theta}[/tex]
Step-by-step explanation:
The trigonometric identity is :
[tex]\sec^2\theta-\tan^2\theta=1\\\\or\\\\\sec^2\theta=1+\tan^2\theta[/tex]
We need to express secθ in terms of tanθ.
The above equation becomes,
[tex]\sec\theta=\sqrt{1+\tan^2\theta}[/tex]
Hence, this is the required solution.
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
thvuvugufugy i need help pls i beg
Answer:
A-10
B- -12
C-3.6
If you cant understand B is -12
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
Mark the angles and sides of each pair of triangles to indicate that they are congruent. NO LINKS!!!
=========================================================
Explanation:
The order of the lettering is important because the order tells us how the letters pair up.
For DCB and CDJ, we have D and C as the first letters. So that means angle D and angle C are congruent between the triangles. I've marked this in red. The other angles are handled the same way.
The congruences for the segments are then built up from the angles.
8 minus the difference of p and 4 un algebraic expression
Answer:
8 - (p - 4)
Step-by-step explanation:
8 - (p - 4)
which number is 3/8closet to
Answer:
616
Step-by-step explanation:
A fraction that is equivalent to 38 is 616
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
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
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 REFERENCE ANGLE -935°
You have 2 spreads, 3 meats, and 4 kinds of bread. How many different sandwiches can you make using one of each ingredient?
Answer:
24
Step-by-step explanation:
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
Adam bought three kinds of
bagels at the bagel store. He
bought twice as many onion bagels as plain
bagels. He bought four more sesame
bagels than he did plain bagels. Adam ate
one of the sixteen onion bagels he bought
as soon as he got home. How many bagels
does Adam have left?
9514 1404 393
Answer:
35
Step-by-step explanation:
The 16 onion bagels are twice as many as plain bagels, so there were 8 plain bagels.
There were 4 more sesame bagels than plain bagels, so there were 12 sesame bagels.
Adam has 8 plain, 12 sesame, and 15 onion bagels left, for a total of 35 bagels left.
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.
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.
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
What is the value of x?
Answer:
value of x i think correct answer is 2
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%
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]
PLS HELP!! I NEED TO FIND THE SURFACE AREA OF THIS CYLINDER!!!!!
Answer:
Step-by-step explanation:
you have two disks, and one rectangle
area of the disk = π [tex]r^{2}[/tex]
47 π x 2 = 94 π (for the two disks....
rectangle area = L x W
width = 14
Length = 2*π*r = 14π
area = 14*14π = 196 π
total = 196 π + 94 π = 290 π
Answer:
The surface area of this cylinder is about 923.63 [tex]inches^{2}[/tex].
Step-by-step explanation:
The formula for the surface area of a cylinder is this :
[tex]A = 2\pi rh+2\pi r^{2}[/tex]
"R" is 7, and "h" is 14. Knowing these values, let's solve.
[tex]A = 2\pi rh+2\pi r^{2}[/tex] = 2 · π · 7 · 14 + 2 · π ·72 ≈ 923.62824
The surface area of this cylinder is about 923.63 [tex]inches^{2}[/tex].
Hope this helps, please mark brainliest! :)
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
At an effective annual interest rate i, i > 0, each of the following two sets of payments has present value K:
a. A payment of 121 immediately and another payment of 121 at the end of one year
b. A payment of 144 at the end of two years and another payment of 144 at the end of three vears.
Calculate i.
Answer:
Hence the calculated
Step-by-step explanation:
Now,
[tex]121+121v=144v^{2} + 144 v^{3} =K\\121(1+v)=144v^{2} (1+v)\\v^{2} =\frac{121}{144} \\\\v=\frac{11}{12}[/tex]
Then K is calculated as,
[tex]K=121(1+v)\\K=121(1+\frac{11}{12} )\\K=\frac{121(23)}{12} \\\\K= 231.916[/tex]
Here we get,
[tex]i=\left | \left ( \frac{v-1}{v} \right ) \right |\\i=\left | \frac{\frac{11}{12}-1}{\frac{11}{12}} \right |\\i=\frac{1}{11}[/tex]
PLS HELP ASAP ILL MARK BRAINLIEST Find the geometric probability of landing in the shaded area of the picture. The small circle has a diameter of 6 meters and the larger circle has a diameter of 54 meters. Show and explain all work.
Answer:
1/80
Step-by-step explanation:
(the area of the small circle)/(the area of the larger circle)
= (π× 3²)/(π× 27²)
(=> eliminate π)
= 3²/27² = (1/9)² = 1/81
since the shaded area is inside the larger circle,
the geometric probability =
1/(81-1) = 1/80
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
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.
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:
uajdnensjdkalsnnamakksls
Please help immediately! In desperate need!
9514 1404 393
Answer:
see attached
Step-by-step explanation:
You know that f(0) = 2^0 = 1, so g(0) = -11 has been shifted down 12 units from f(x). A shift of half as much will be a shift down 6 units from f(x), or up 6 units from g(x).
In the attached, we have named the new function h(x). It is equivalent to g(x)+6. That is, you can add 6 to each of the g(x) table values to get the corresponding values for h(x).
29 members in math club, treasury has $364 to spend, shirts are $11 caps are $14. How many caps and shirts can he buy to exhaust the funds available?
Answer:
14 shirts, 15 caps
Step-by-step explanation:
15 x 14 = 210$
14 × = 154$
210+154 = 364$
