Answer:
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.
Step-by-step explanation:
Sample size greater than 30, which means that we use the normal distribution to find the interval.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
α = (1 - 0.95) / 2
= 0.025
Now, we have to find z in the table as such z has a pvalue of . So it is z with a pvalue of 1 - 0.025 = 0.975.
So, z = 1.96
Now, find M as such
M = z * (σ / √n )
In which σ is the standard deviation of the population and n is the size of the sample.
M = 1.96 * ( 10800 / √35 )
M = 3581.72
M ≈ 3582
The lower end of the interval is the sample mean subtracted by M. So it is 19300 - 3582 = $15718.
The upper end of the interval is the sample mean added to M. So it is 19300 + 3582 = $22882.
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.
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Where do i graph this at?
Answer:
you go <left 5 times and then go down 3 times
A copy machine makes 24 copies per minute. How long does it take to make 132 copies? minutes seconds
Answer:
5 mins and 30 seconds
Step-by-step explanation:
find out how many sets of 24copies/min
132 ÷ 24 = 5.5
5.5min = 5mins and 30seconds
4x + 5 + 3x - x = 7x - 8
Answer:
x = -1
Step-by-step explanation:
6x +5 = -7x - 8
6x +7x = -8 -5
13x = -13
13/13 x = -13/13
x = -1
The number V of computers
infected by a virus increases according to the model
V(t) = 100e^4.6052t, where t is the time in hours. Find
the number of computers infected after (a) 1 hour,
(b) 1.5 hours, and (c) 2 hours.
By using the exponential function The number of computer affected in 1 hour is 10000
What is exponential function?
A mathematical function with the formula f (x) = a^x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, which equates to roughly, is the exponential-function base that is most frequently encountered.
We are given a function V(t) = 100e^4.6052t,
We are asked to find the number of computer affected after one hour
To find that we have to substitute t =1 in the equation we get
V(t) = 100e^4.6052
V(t) = 10000
There will be approximately 10000 computers affected by the virus in one hour.
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Is y =8/7x proportional
Assuming you meant to say [tex]\text{y} = (8/7)\text{x}[/tex] or [tex]\text{y} = \frac{8}{7}\text{x}[/tex], then yes this is a proportional equation.
This is because it is of the form y = kx where k = 8/7 is the constant of proportionality.
befbgbdgggggggguhhhhhhhhhhhhh
Answer:
Option 3
Step-by-step explanation:
[tex]-\frac{7}{5} =-\frac{14}{10} =-1.4[/tex]
[tex]-1\frac{3}{10} = -\frac{13}{10}=-1.3[/tex]
∴ ascending order of these rational numbers
[tex]=-1.5, -1.4, -1.3, -1.2[/tex]
[tex]= -1.5,-\frac{7}{5}, -1\frac{3}{10}, -1.2[/tex]
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
The range of this function f(x) = 3x + 9 is: B. {y | y > 9}.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.
This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.
Based on the given function f(x) = 3x + 9, we can reasonably infer and logically deduce that the range of this function in interval notation is given by:
Range = [10, ∞]
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)
The rocket reaches its maximum height of 88 feet at 2.25 seconds after launch
How to find the time and the maximum heightThe time
The function is given as
h(t) = -16t² + 72t + 7
To start with, we need to differentiate the function
h'(t) = -32t + 72
Next, we set the differentiated function to 0
-32t + 72 = 0
Next, we solve for the variable t
t = 2.25
This means that the time is 2.25 seconds
The maximum height
Recall that we have the value of t to be:
t = 2.25
Also, we have the equation to be
h(t) = -16t² + 72t + 7
So, we have
h(2.25) = -16(2.25)² + 72(2.25) + 7
Solve the expressions
h(2.25) = 88
This also means that the maximum height is 88 feet
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The pair of points (g, -1) and (2, 5) lie on a line with a slope of 3/2. What is the value of g?
3
-2
-5
4
The variable g has its value to be -4 on the given coordinate point
How to calculate the value of point G of the line?From the question, the points are given as
(g, -1) and (2, 5)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (g, -1) and (2, 5)
The slope of the line is given as
Slope = 3/2
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (g, -1) and (2, 5)
Substitute the known values in the above equation
So, we have the following equation
3/2 = (5 + 1)/(2 - g)
Evaluate the sum in the equation
This gives
3/2 = 6/2 - g
Cross multiply
So, we have
2(2 - g) = 12
Divide by 2
2 - g = 6
Make g the subject of the formula
g = 2 - 6
Evaluate the like terms
g = -4
Hence, the value of g of the line is -4
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Answer:
-2
Step-by-step explanation:
The table above shows four numeric expressions. Which expression is an integer when it's evaluated?
Question 9 options:
A)
E
B)
H
C)
G
D)
F
The expression G is an integer when it's evaluated.
What is an integer?
A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8
Negative numbers and all entire numbers are both considered integers. Accordingly, a set of integers can be formed by adding negative numbers as well as whole numbers.
Consider 9+(-3).
9+(-3)
Remove parenthesis
=9-3 = 6
6 is an integer.
So, the expression G is an integer when it's evaluated.
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Guys! What is w+2/3=5 1/4
Answer:
Rewrite the equation as w+ 2/5= 3/4
Move all terms not containing w to the right side of the equation.
so if u do that you should get your answer 7/20
Step-by-step explanation:
BRO IM DESPERATE PLEASE DUDE!!!!!!!!
A) An equation to determine how long it will take for you to save enough for the new digital camera is 23.5w + 25.75 = 329.99.
B) It will take you 13 weeks to save sufficiently for the new digital camera.
What is an equation?An equation is a mathematical statement that equates two algebraic expressions.
Equations combine constants and variables with the equation symbol (=).
Equations establish that two or more mathematical expressions are equivalent or equal.
In this situation, to determine the amount that needs to be saved, we deduct the amount already saved from the total requirement, and then divide the difference by the weekly savings.
The price of the digital camera = $329.99
The amount you have saved so far = $25.75
The amount you can save each week = $23.50
Let w = the number of weeks to complete the required amount.
Equation:25.75 + 23.5w = 329.99
23.5w + 25.75 = 329.99
23.5w = 329.99 - 25.75
23.5w = 304.24
w = 12.95
w = 13 weeks
Thus, we can establish from equation 23.5w + 25.75 = 329.99 that it will take a saver 13 weeks, saving $23.50 every week to save enough to purchase the new digital camera price at $329.99, given the constants and variables.
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Brenda is choosing a car insurance plan. Based on her driving history and traffic where she lives, Brenda estimates that there is a 20% chance she will have a car collision this year. In each plan, the insurance will cover the full cost of the collision after the deductible is paid.
Which of the plans detailed in the table is most likely to save Brenda the most money, based on expected value?
Plan Deductible Collision Comprehensive Premium Total
A $300 $500 $234 $734
B $500 $430 $212 $642
C $1,000 $340 $175 $515
D $2,500 $278 $127 $405
A.
plan A
B.
plan B
C.
plan C
D.
plan D
Answer:
A would save Brenda the most money
Step-by-step explanation:
what is the value of the equation? 5^3log54
Answer:
The value of the expression is 64Step-by-step explanation:
Given expression[tex]5^{3log_54}[/tex]Find its value[tex]5^{3log_54} =[/tex][tex]5^{log_54^3} =[/tex][tex]5^{log_564}=[/tex][tex]64[/tex]Used properties:
[tex]a*lob_bc= log_bc^a[/tex][tex]a^{log_ab}=b[/tex]Answer:
64
Step-by-step explanation:
Given expression:
[tex]5^{3 \log_54}[/tex]
Apply log rules to find the value of the given expression.
[tex]\textsf{Apply the log power law}: \quad n\log_ax=\log_ax^n[/tex]
[tex]\implies 5^{\log_54^3}[/tex]
[tex]\implies 5^{\log_564}[/tex]
[tex]\textsf{Apply\:the\;log\:rule}:\quad \:a^{\log _a\left(b\right)}=b[/tex]
[tex]\implies 5^{\log_564}=64[/tex]
in the exponential function g(x)=a(b)^x it is known that g(3)=25 and g(7)=3
By solving a system of equations we will see that the exponential function is:
g(x) = 122.347*(0.589)^x
How to find the exponential function?We know that our function is of the form:
g(x) = a*(b)^x
We also know that g(3)=25 and g(7)=3, then we can write:
a*(b)^3 = 25
a*(b)^7 = 3
So we have a little system of equations.
Taking the quotient between the second and first equations we get:
(a*(b)^7)/(a*(b)^3) = 3/25
b^4 = 3/25
b = (3/25)^(1/4) = 0.589
Replacing that in the first equation we get:
a*(b)^3 = 25
a*(0.589)^3 = 25
a = 25/(0.589)^3 = 122.347
The exponential function is:
g(x) = 122.347*(0.589)^x
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Use and algebraic equation to find the measure of each angle that is represented in terms of x
The measurement of each angle represented in terms of x is 156°
What is the angle measurement?Here given the two angles : (13x-26)° and (9x+30)°.
We have to find each angle measurement.
From the given figure, it is clear that two angles are just vertically opposite angles.
So , we know that vertically angles are equal
So to find angles , we have to find x.
13x - 26 = 9x + 30
13x - 9x = 30 + 26
4x = 56
x = 56 / 4
x = 14
So the value of x = 14
Then we have to substitute the value of x in any of the given measurement.
By substituting x in (13x - 26)°
13 x 14 - 26
182 - 26
= 156
Similarly by substituting x in (9x + 30) °
9 x 14 + 30
= 126 + 30
= 156°
Therefore, the measurement of each angle is 156°.
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Solve this using substitution x=-3y+5
x+9=4y
Answer: x=-1 & y=2
Step-by-step explanation:
x = -3y+5
^^^substitute this equation into x in the second equation
(-3y+5)+9 = 4y
-3y+14 = 4y
Add +3y on both sides
14 = 4y+3y
14 = 7y
divide both sides by 7
y = 2
substitute y into either equation (I'm doing the first one)
x = -3(2)+5
x = -6+5
x = -1
A local dairy has three machines to fill half-gallon milk cartons. The machines can fill the daily quota in 3 hours, 14 hours, and 10.5 hours, respectively. Find how long it takes to fill the daily quota if all three machines are running.
It takes 2 hours to complete with all three machines working.
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let total time taken by all machines be x hours.
Set up the equation as below:
1/3+1/14+1/10.5=1/x
Solve for x
Multiply both the sides by x
x/3+x/14+x/10.5=x/x
0.5x=1
x=2
So, It takes 2 hours to complete with all three machines working.
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Vector u = <2, -5>. Describe how you would use a graphical method to add vector u to vector v (3, 1). Then, write the resultant vector in component form.
The component form of the resultant vector is <5, -4>
How to describe the use of graphical method for adding vectors?Let vector u be a displacement AB on the graph and let vector v be a displacement BC on the graph such that the sum of displacement AB and BC is equivalent to a single displacement AC on the graph. We can write this as:
AB + BC = AC
or writing the vector sum with small letters given,
u + v = w (Note: w = AC)
Given: vector u = <2, -5> and vector v (3, 1)
u + v = w
<2, -5> + <3, 1> = <2+3, -5+1> = <5, -4>
u + v = <5, -4>
Thus, the coordinates of the vector sum on the graph will be (5, -4)
Therefore, the resultant vector in component form is <5, -4>
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a water droplet has volume of 0.1cubic cm. convert the volume of the droplet to cubic meters. (1m=100cm)
The volume of the droplets in cubic meters would be = 1×10^-7 cubic meters.
What is water droplets?Water droplets can be defined as the formation of small ball like structures with water due to the action of surface tension of liquid.
To convert cubic centimetres to cubic meters the following is carried out;
1 cubic meter = 1,000,000 cubic centimetres.
X cubic meters = 0.1 cubic centimetres
Make X cubic centimetres the subject of formula;
X cubic meters = 0.1× 1/1,000,000
X cubic meters = 1×10^-7.
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Use logb2 ≈ 0.401, logb3 ≈ 0.503, and logb5 ≈ 0.842 to approximate the value of the given logarithm to 3 decimal places.
Assume that b>0 and b≠1.
logb50 ≈ ?
Using multiplication law of logarithm the value of logb 50 is 2.085
How to find the value of logb 50The logb 50 is rewritten in the multiples of 2, and 5 then laws of logarithm is applied to find the final answer
logb 50
= logb (2 * 5 * 5)
applying multiplication law of logarithm
= logb 2 + logb 5 + logb 5
= 0.401 + 0.842 + 0.842
= 2.085
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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)^²+k.
f(x)=
The equation of the parabola which is as given in the task content is; f (x) = -3 (x - 5)² + 9.
What is the equation of the parabola as described in the task content?It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.
Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).
On this note, the required equation of the parabola by substitution of h and k is;
f (x) = -3 (x - 5)² + 9.
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What is the range of the equation?
5x + 3y = 30
Answer:
Range is all real numbers.
Interval notation:
Range is
(-infinity,infinity)
Step-by-step explanation:
The range is all the y's on a graph of a function or all of the y's allowed to be used in an equation or able to be produced by the equation.
5x + 3y = 30
is a line. Except for a horizontal line, the range of any line is all real numbers. Somewhere on that line every single y value exists somewhere. You may put literally ANY value for y into that equation.
The range is all real numbers.
If 1200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
The largest possible volume V is 4000[tex]cm^3[/tex]
Given,
Volume of a box = length × breadth × height= l× b× h
In this case the box have a square base. i.e., l = b
Volume V = [tex]l^2[/tex] × h
We using the formula of Surface area
The surface area of a square box
S = 2(lb +lh+ bh)
S = 2([tex]l^2[/tex] + lh + lh) since l=b
S = 2([tex]l^2[/tex] + 2lh)
Also, Given that the box is open top.
S = [tex]l^2[/tex] +4lh
And Surface Area of the box is 1200cm^2
1200 = [tex]l^2[/tex] + 4lh ....1
Making h the subject of formula
h = (1200 - [tex]l^2[/tex])/4l .....2
Volume is given as
V = [tex]l^2[/tex] × h
V = [tex]l^2[/tex] ×(1200 - [tex]l^2[/tex])/4l
V = (1200l - [tex]l^3[/tex])/4
the maximum point is at dV/dl = 0
dV/dl = (1200 - [tex]31^2[/tex])/4
dV/dl = (1200 - [tex]31^2[/tex])/4 = 0
[tex]31^2[/tex]= 1200
[tex]l^2[/tex] = 1200/3 = 400
l = √400
I = 20cm
Since,
h = (1200 - [tex]l^2[/tex])/4l
h = (1200 - [tex]20^2[/tex])/4×20
h = (800)/80
h = 10cm
Hence, The largest possible volume V is ;
V = [tex]l^2[/tex] × h
V = [tex]20^2[/tex] × 10 = 4000[tex]cm^3[/tex]
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what is the reclusive formula
The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁ , the correct option is (c) .
In the question ,
an explicit formula for the geometric sequence is given
that is aₙ = 16(-90)ⁿ⁻¹ ,
we know that the general explicit formula for the geometric sequence is given by
aₙ = a₁(r)ⁿ⁻¹
where aₙ is the nth term , r is the common ratio, a₁ is the first term of the sequence .
On comparing the given explicit formula with the general formula ,
we get ,
a₁ = 16
r = -90
So , the recursive formula is a₁ = 16 and aₙ = -90aₙ₋₁ .
Therefore, The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁ , the correct option is (c) .
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Can someone help me I have to verify the trig identities.
The trigonometric identities are verified that they are true.
What are trigonometric expressions?
Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.
1. LHS = sec x [ sec x - cos x]+(sin x+ cos x)/sin x- cot x
= sec²x - sec x cos x +(sin x+ cos x)/sin x - cos x/sin x
= sec²x - cos x/cos x +(sin x+ cos x- cos x)/sin x
= sec²x - 1 + sin x /sin x
= sec²x - 1 +1
= sec²x
= RHS
2. LHS = cos (π-Θ)+ sin (π/2 + Θ)
= - cos Θ + cos Θ
= 0
= RHS
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ILL GIVE ALL MY POINTS PLS HELP QUICK!!
In triangle DEF, m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°. Determine the degree measure of the exterior angle to ∠D.
A. 54°
B.39°
C.141°
D.126°
Answer:
Step-by-step explanation:
The value of x is equal to 10 and the exterior angle to angle d is equal to 141 degrees.Exterior AnglesTo solve this problem, we have to recall that the sum of angles in a triangle is equal to 180 degrees.Applying that formula here;But the exterior angle to angle D can be found assuming the angle lies on a straight line, then the sum of angle D and it's exterior angle would be equal to 180 degrees.Let y = exterior angleThe value of the exterior angle to d is equal to 141 degrees.Learn more on exterior angles here;brainly.com/question/17972372
Twice a number n is no less than 10 units from −1.
Answer:
n ≥ 4.5 or n ≤ - 5.5===========================
Twice a number n is no less than 10 units from −1:
Twice a number n ⇒ 2n,no less than ⇒ ≥,10 units from −1 ⇒ - 1 ± 10.The inequality becomes an absolute value and translates as:
" The difference of 2n and - 1 is equal or greater than 10"| 2n - (-1) | ≥ 10| 2n + 1 | ≥ 102n + 1 ≥ 10 or 2n + 1 ≤ - 102n ≥ 10 - 1 or 2n ≤ - 10 - 12n ≥ 9 or 2n ≤ - 11n ≥ 4.5 or n ≤ - 5.5Maru makes an initial down payment of \${3000}
$3000
, then repays \${70}
$70
per week.
Calculate how many weeks it takes Maru to fully pay off $43000.
pls help me with this asap
The number of weeks that it'll take Maru to fully pay off $43000 is 571.4 weeks.
How to calculate the value?From the information, Maru makes an initial down payment of $3000 then repays $70 per week and the total amount is $43000.
Let the number of weeks be represented as w.
This will be illustrated as:
3000 + (70 × w) = 43000
3000 + 70w = 43000
Collect like terms
70w = 43000 - 3000
70w = 40000
Divide
w = 40000 / 70
w = 571.4
The number of weeks is 571.4 weeks
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A big storage tank contains 1680 gallons of gasoline. 25 cars filled their tanks with 24 gallons of gas each. 35 trucks put 30 gallons of gas in each of their tanks. How many gallons of gas are left in the big storage tank?
A) 90 gallons of gas
B) 60 gallons of gas
C) 30 gallons of gas
D) No gas is left in the big tank
Answer: The correct answer is C) 30 gallons of gas
Step-by-step explanation:
Storage Tank Volume = 1680 Gallons
25 cars x 24 gallons = 600 gallons
35 trucks x 30 gallons = 1,050 gallons
Total gallons used = 1,050 + 600 = 1,650
Remaining gas = 1,680 - 1,650 = 30 gallons
Option C: 30 gallons of gas
Please remember to vote the answer as Brainliest if I earned it!
Answer:
C) 30 gallons of gas
Step-by-step explanation:
Total gallons of gas used by the cars:
⇒ 25 × 24 = 600 gallons
Total gallons of gas used by the trucks:
⇒ 35 × 30 = 1050 gallons
Total gallons of gas used by the cars and trucks:
⇒ 600 + 1050 = 1650 gallons
If the storage tank contained 1680 gallons of gas, then the number of gallons of gas left in the tank after the cars and trucks have filled their tanks is:
⇒ 1680 - 1650 = 30 gallons
