The values:
[tex]\bar p[/tex] = 0.547.
And [tex]\bar q[/tex] = 0.453.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
The values,
X₁ = 23,
X₂ = 29,
n₁ = 43,
And n₂ = 52.
Now, using the formula for mean,
[tex]\bar p[/tex] = (X₁ + X₂) / (n₁ + n₂)
=(23 + 29) / (52 + 43)
= 0.547.
And [tex]\bar q[/tex] = 1 - [tex]\bar p[/tex] = 1 - 0.547 = 0.453.
Therefore, all the required values are given above.
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A zipline cable is attached to two platforms 1000 ft apart at an angle of depression from the taller platform of 12º. What is the length of the cable, rounded to the nearest foot?
The length of the cable is 4810 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecent/hypotenuse and
tan = opposite/adjacent.
If the angle of depression from the taller platform of 12°, Then the angle of elevation is (90 - 12) = 78°.
We know, cos = adjacent/hypotenuse.
cos78° = 1000/hypotenuse.
hypotenuse = 1000/cos78°.
hypotenuse = 4810 feet.
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Answer:
1022
Step-by-step explanation:
cos 12 = 1000/x
Consider the graph of the function f (x) = log x.
Match each transformation of function f with a feature of the transformed function.
Transformation of the given function with a feature of the transformed function.
g(x)=-f(x-3) is the vertical asymptote of x=3
j(x)= f(x+3) is x-intercept of (-2,0)
h(x)=3f(x)-3 is domain of (0, ∞)
What is asymptote?An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique
Given function is : f(x)= log x
g(x)= -f(x+3)= - log(x+3)
g(x)=-f(x-3) is the vertical asymptote of x=3
j(x)= f(x+3) = log (x+3) then
j(x)= f(x+3) is x-intercept of (-2,0)
Domain: As (0,∞), {x | x>0}
h(x) = 3f(x)-3 is domain of (0, ∞)
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Rewrite the following without an exponent. 4^-3
The required simplified value of the given exponential form of expression 4⁻³ is 1/64.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
Given expoenential expression,
= 4⁻³
= 1 / 4³ [a⁻¹ = 1 /a]
= 1 / 64 [4³ = 64]
Thus, the required simplified value of the given exponential form of expression 4⁻³ is 1/64.
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19. Bruce has 5 bags of potatoes. Each bag
weighs 63 pounds. Use the equation below
to find the total number of pounds of
potatoes in the 5 bags.
5 × 6 = (5 × 6) + (5 x ³) =
A 16 pounds
B 31 pounds
C 32 pounds
D 33 pounds
The total number of pounds is 315 pounds
How to determine the total number of poundsFrom the question, we have the following parameters that can be used in our computation:
Number of bags = 5
Weight of each bag = 63 pounds
This means that
Total weight = 5 * 63
Evaluate the product
Total weight = 315 pounds
Hence, the total weight is 315 pounds
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In the figure, a triangle is removed.. from a square of sides 9m. Find area.
If a triangle is removed.. from a square of sides 9m. The area is: 77.25 m².
How to find the area?Area of Square = Side × Side = Side²
Area of Square = 9m × 9m
Area of Square = 81 m²
Area of triangle = 1/2 ×b ×h
Area of triangle = 1/2 × 3m × 2.5m
Area of triangle = 3.75m²
Area of Figure = 81m² - 3.75m²
Area Of Figure = 77.25 m²
Therefore the area is 77.25 m².
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(100 POINTS FREE!) Find the measure of the three missing angles in the rhombus below.
x=
y=
z=
The measure of the angles x, y, and z will be 93°, 93°, and 87°, respectively for the rhombus.
What are supplementary angles?The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.
As we know that the adjacent angle of the rhombus is supplementary.
As per the given figure, the value of 'x' is given as,
87° + ∠x = 180°
∠x = 180° - 87°
∠x = 93°
Since the opposite angle of the rhombus is congruent to each other.
So ∠y = ∠x
Then ∠y = 93°
And ∠z = 87°
The measure of the angles x, y, and z will be 93°, 93°, and 87°, respectively.
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Gary has 6 more baseball cards than football cards. He has fewer than 125 baseball
cards, Write an inequality for the number of football cards, f, he has.
around 125-6
Step-by-step explanation:
A plumber charges $75 for the first one-half hour of a service call and an additional $45 for every additional half hour. Write an expression that can be used to find the cost for h half hours and use your expression to find the charge for 3 1/2 hours.
Answer:
$270
Step-by-step explanation:
h = number of half hours worked
$75 + $45(h-1) = total cost
3 1/2 hrs = 7 half-hours
$75 + $45(7 - 1) = $270
1. Write the equation of a circle in standard form whose center is at (3,-2) and has a radius of 11:
2. Find the average rate of change of a linear function y = f(x) = 2x - 1 if input x is changing
from x=1 to x=3:
I do not need an explanation, just a quick answer. Thanks!
The question is in the image.
Answer:d
Step-by-step explanation:
In exercises 1 and 2 use the graph to solve the equation
The solution:
Exercise 1: x = -1 and 3.
Exercise 2: x = 2 and 4.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The graphs of the two quadratic equation.
So, Exercise 1,
-x² + 2x + 3 = 0.
From the graph,
-1 and 3 are the zeros of the equation.
The solution of the equation is,
x = -1 and 3.
Exercise 2,
x² - 6x + 8 = 0.
From the graph,
2 and 4 are the zeros of the equation.
The solution of the equation is,
x = 2 and 4.
Therefore, the solutions of the both the equation are given above.
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PLEASE HELP ASAP!! Thanks.
For the questions below provide a complete solution with explanation.
1. Eris Orbit. The recently discovered Eris orbits the Sun every 557 years. Use Kepler's 3rd law to find what is its average distance (semi-major axis) from the sun? How does its average distance compare to that of Pluto? (Compare them by either finding their ratio or by calculating the percent difference).
2. If a new dwarf planet is discovered at an orbit with an average distance to the sun of a = 100 AU, what will be its orbital period?
If Eris Orbit. The recently discovered Eris orbits the Sun every 557 years.
Its average distance (semimajor axis) from the sun is: 67.7 AUDifference between the two dwarf planets is 28.2 AUWhat is its average distance (semimajor axis) from the sun?In order to calculate the semimajor axis of Eris, we need to plug 557 years into the equation
a=P^2/3
a= 557^0.66666667
a = 67.6971 astronomical units.
a = 67.7 AU (Rounded)
Since the average distance for Pluto from the Sun is 39.3 AU
So,
Since the distance of Eris to the sun is 67.7 AU and Pluto to the sun is 39.5
Difference between the two dwarf planets = 67.7AU - 39.5 AU
Difference between the two dwarf planets = 28.2 AU
Based on the above calculation Eris is about 1.5 times farther from the Sun in comparison to Pluto.
Therefore Its average distance (semimajor axis) from the sun is: 67.7 AU and the difference between the two dwarf planets is 28.2 AU
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In its second year of operation, a local Internet provider's profits were $180,500. If this amount was 676% of the company's first-year profits, find the first-year profits (to the nearest hundred dollars).
The first-year profits (to the nearest hundred dollars) is, $26,701.18.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
In its second year of operation, a local Internet provider's profits were $180,500.
And, This amount was 676% of the company's first-year profits.
Now, Let the amount in the first-year profits = x
So, We can formulate;
⇒ 676% of x = 180,500
⇒ 676/100 × x = 180,500
⇒ x = 180500 × 100 / 676
⇒ x = $26,701.18
Thus, The first-year profits (to the nearest hundred dollars) is, $26,701.18.
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Explain why the function is not continuous at x= -5
For the function,
F(x) = (x² + 11x +28)/(x² + 8x + 15) limit doesn't exist at x = -5 so it is dis-continuous at that point.
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = (x² + 11x +28)/(x² + 8x + 15)
To check whether it is continuous at x = -5
First taking LHL,
[tex]\lim_{h \to \ 0}[/tex] [(-5-h)² + 11(-5 -h) +28]/[(-5 -h)² + 8(-5 -h) + 15]
It is approaching at negative infinity
Now, taking RHL
[tex]\lim_{h \to \ 0}[/tex] [(-5+h)² + 11(-5 +h) +28]/[(-5 +h)² + 8(-5+h) + 15]
Again, It is approaching at negative infinity
Hence, here limit doesn't exist so it is not continuous at x = -5
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Use two formulas for volume to find the volume of the figure. Express the answer in terms of pi and then round to the nearest whole number.
The volume of the composite figure is 117π ft³ or 368 ft³
How to find the volume of a composite figure?The figure shown is made up of a hemisphere and a cylinder.
Total volume of the figure = volume of hemisphere + volume of cylinder
Formula for the Volume of the hemisphere is;
V = ⅔πr³
Radius (r) of hemisphere = 6/2 = 3 ft
Volume of hemisphere = ⅔ * π * 3³
= 18π ft³
Volume of Cylinder is given by the formula;
V = πr²h
radius (r) = 3 ft
height (h) = 11 ft
Volume of cylinder = π * 3² * 11
= 99π ft³
Volume of the figure = 18π ft³ + 99π ft³ = 117π ft³
Volume of the figure to the nearest whole number = 368 ft³
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1. What is the period of the function?
2. Which functions are periodic?
3. Which functions are not periodic?
4. Given the graph of the function f(x), which graph shows the function g(x) if g(x)=f(x−3)?
5. Given the graph of the function f(x), which graph shows the function g(x) if g(x)=f(x)+3 ?
You have $28.50. You earn additional money by mowing lawns. Then you purchase a new pair of shoes for $45.09 and have $18.41 left. How much money do you earn mowing lawns?
Answer:I earn $26.68 by mowing lawns.
Step-by-step explanation:
The graph of a quadratic function with vertex (1,-2) is shown in the figure below.
Find the range and the domain.
The graph of a quadratic function with vertex (1,-2) has the range and the domain respectively, ( -∞, -2 ) and ( -∞, ∞)
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The graph of a function,
whose vertex is (1, -2)
As it can be seen in the graph,
The given quadratic function has defined value for each value of x,
So, the domain of the given function is real numbers,
x ∈ ( -∞, ∞)
The maximum value of the function is -2
And minimum value of the function is -∞
The range of the function is ( -∞, -2 )
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Please help!!! This is about rational and irrationals
Answer:
a creo que debes sacr la raiz cuadrada de los dos aciendo los procesos
6. An astronaut spent 438 days orbiting Earth in the International Space Station. Write 438 days in weeks, rounded off to the nearest week.
Answer: 62.57 weeks/63 weeks
Step-by-step explanation:
438 divided by 7 = 62.57
Rounded to the nearest week, 62.57 turns to 62.60 which is closer to 63.
The answer is 63 weeks
Determine the value of x.
Answer: Because there is no image or question I have to make a question myself. If Jimmy had X and Samantha has 17 which is 8 more than Tim and Tim has 20 less than Jimmy. What does Jimmy have?
Step-by-step explanation:
First, we isolate X.
X = Tim + 20.
Tim = 11.
11 + 20 = X
So X = 31
In the bar model, the discount is 20%. What percent of the regular price is the sale price? Explain how you could solve the problem using this information.
The sale price of the item is given by the equation A = $ 22.40
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The regular price of the item = $ 28.00
The percentage of discount = 20 %
So , the sale price of the item = regular price of the item - ( percentage of discount x regular price of the item )
Substituting the values in the equation , we get
The sale price of the item A = 28.00 - ( 0.20 ) x 28.00
The sale price of the item A = 28.00 ( 1 - 0.20 )
The sale price of the item A = 28.00 ( 0.80 )
So , the sale price of item is 80 percentage of the regular price
Therefore , the sale price of the item = ( 80 / 100 ) x $ 28.00
The sale price of the item A = $ 22.40
Hence , the sale price is $ 22.40
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What mathematical statement calculates a value?
On solving the provided question, we can say that a Formula is a mathematical statement that calculates a value.
What is Formula?In mathematical symbols, a formula is a fact or a rule. Usually, an equal symbol links two or more values. Formulas can be used to determine a quantity's value if you know the value of one. A formula is a collection of mathematical signs and figures that show you how to solve a problem. Examples include formulae for determining the volume of 3D objects and formulas for estimating the perimeter and area of 2D shapes. A mathematical rule or relationship that expresses a variable quantity using letters is called a formula. We refer to these as variables.
A formula is a mathematical statement that calculates a value.
for, example to calculate area of triangle we need a formula.
that formula for area of triangle is = 1/2 * b * h.
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What is One plus One, algebra is so hard guys.
Answer:
Somethings telling me this is a trick question but the answer is 2.
Step-by-step explanation:
What percent of 2 is 32? If necessary, round your answer to the nearest tenth.
Answer:
Below
Step-by-step explanation:
32/2 x 100% = 1600 %
Adrianna cuts a pie with a 10-inch diameter into 8 equal slices and eats one slice. How many square inches of pie are left? Use 3.14 for pi. Round the final answer to the nearest tenth of a square inch. Select all the true statements.
a. The area of the whole pie is 314 in.².
b. The area of the whole pie is 78.5 in.².
c. The problem is asking for the area of a fractional piece of the pie.
d. The solution is 9.2 in.².
e. The solution is 68.7 in.².
On solving the provided question, we can say that Area of pizza is [tex]\pi*r^2[/tex]=25 pi in^2 Divide that by 8 3.125 [tex]\pi in^2[/tex] => 9.82 cm^2 => [tex]9.8 cm^2[/tex] is the answer
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
Area of pizza is [tex]\pi*r^2[/tex]=25 pi in^2
Divide that by 8
3.125 [tex]\pi in^2[/tex] => 9.82 cm^2
[tex]9.8 cm^2[/tex] is the answer
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Math question,Urgent help!!!
Show work thanks
Among 60 students the probability that the group plays Field Hockey (F) and Basketball (B) is 0.083.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
From the given Venn Diagram -
The number of students who play Field Hockey (F) is = 18
The number of students who play Soccer (S) is = 10
The number of students who play Basketball (B) is = 7
The number of students who play Field Hockey (F) and Soccer (S) is = 4
The number of students who play Field Hockey (F) and Basketball (B) is = 2
The number of students who play Soccer (S) and Basketball (B) is = 5
The number of students who play Field Hockey (F), Soccer (S) and Basketball (B) is = 3
The number of students who play nothing = 11
The probability to find the students who play Field Hockey (F) and Basketball (B) is -
Probability = (number of students who play Field Hockey (F) and Basketball (B)) + (number of students who play Field Hockey (F), Soccer (S) and Basketball (B)) / (Total number of students in survey)
Substitute the values in the equation -
Probability = (2 + 3) / 60
Probability = 5 / 60
Probability = 1 / 12
Probability = 0.083
Therefore, the probability value is obtained as 0.083.
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Susan places $6400 in three investments at rates of 8%, 9.6% and 14.4% per annum, respectively. The total income after one
year is $ 744.00. If the amount placed in the third investment is $1500 more than the amount placed in the second, find the
amount of each investment.
On solving the equations x + y + z = 6400 and 0.08x + 0.096y + 0.144z = 744, the values for first, second and third investments are $1500, $1700 and $3200 respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Susan places $6400 in three investments at rates of 8%, 9.6% and 14.4% per annum, respectively.
Let the amount of each investment be x, y and z.
So the mathematical form of the statement is -
x + y + z = 6400
The total income after one year is $744.00.
So the mathematical form of the statement is -
0.08x + 0.096y + 0.144z = 744
The amount placed in the third investment is $1500 more than the amount placed in the second.
So the mathematical form of the statement is -
z = (y + 1500)
Substitute the value of z in first equation -
x + y + (y + 1500) = 6400
x + 2y = 6400 - 1500
x + 2y = 4900
x = (4900 - 2y)
Substitute the value of z in second equation -
0.08x + 0.096y + 0.144(y + 1500) = 744
0.08x + 0.096y + 0.144y + 216 = 744
0.08x + 0.24y = 744 - 216
0.08x + 0.24y = 528
Substitute the value of x in this equation -
0.08(4900 - 2y) + 0.24y = 528
392 - 0.16y + 0.24y = 528
- 0.16y + 0.24y = 528 - 392
0.08y = 136
y = 136/0.08
y = 1700
Therefore, the value of second investment is 1700.
Substitute the value of y in formula for z -
z = (y + 1500)
z = 1700 + 1500
z = 3200
Therefore, the value of third investment is 3200.
Substitute the value of y in formula for x -
x = (4900 - 2y)
x = 4900 - 2(1700)
x = 4900 - 3400
x = 1500
Therefore, the value of first investment is 1500.
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5-67x=4/4y Helpppp? Worth 100 and Brainliest heh
Answer:
x = [tex]-\frac{y - 5}{67}[/tex]
Step-by-step explanation:
Hope this helps
A boy walked 7km on a bearing of 060 degree.represent information on a diagram
A bοy walked 7km οn a bearing of 60°. Represented this infοrmation on a diagram given belοw.
What are bearing rules in maths?A bearing in mathematics is the angle, measured in degrees and anticloοkwise from nοrth. Typically, bearings are given as a three figure bearing. Fοr instance, 30° clockwise from nοrth is typically expressed as 0°.
"Pieces that aid objects' rοtation" are bearings. They suppοrt the rotating shaft that mοves the machinery. Cars, planes, power generatοrs, and οther devices all use bearings.
Tο lessen friction between twο spinning or sliding surfaces, a bearing is a mechanical compοnent.
There are many different types of bearings, including ball and rοller bearings, linear bearings, and mοunted versions that may use either, and they are used for rοtating or linear shaft applicatiοns. Bearings are mechanical assemblies that include rοlling elements and typically inner and οuter races.
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