Answer:
They all come out to be infinity
Nora leans a 24-foot ladder against a wall so that it forms an angle of 76^{\circ} ∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
23.29 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.
To find how high up the wall the ladder reaches, use the sine trigonometric ratio:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
where:
θ is the angle.O is the side opposite the angle.H is the hypotenuse (the side opposite the right angle).The angle of elevation is 76°, so θ = 76°.
Let x be the height the ladder reaches up the wall, so O = x.
H is the length of the ladder, so H = 24.
Substitute the given values into the sine ratio and round the answer to the nearest hundredth:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]
[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]
[tex]24 \sin(76^{\circ})= x[/tex]
[tex]x=24 \sin(76^{\circ})[/tex]
[tex]x=23.28709743...[/tex]
[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]
Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.
Monica is 33 years old. Amanda is 18 years older than Brittany and 16 years older than Rita. Brittany is 23 years younger than Monica. How old is Rita?
please help
A nautilus shell is made up of many chambers, each chamber roughly 5% larger than the
previous one. Assuming a nautilus creates a new chamber every year, and this year's
chamber has a volume of 880 microliters, how large will the chamber created in 8 years be?
If necessary, round your answer to the nearest tenth.
microliters
Answer:
1300.2 µL
Step-by-step explanation:
You want to know the volume of a nautilus chamber in 8 years if it is 880 µL in year 0 and increases at 5% per year.
Growth factorThe growth factor is ...
growth factor = 1 + growth rate
growth factor = 1 + 0.05 = 1.05
Exponential functionSince the problem statement is about volume, we assume the growth factor applies to the chamber volume. If it applies to the linear dimension of the chamber, then the growth factor for volume will be 1.05³.
The function describing the chamber volume can be written as ...
volume = (initial volume)(growth factor)^years
In 8 years, the chamber volume will be ...
volume = (880µL)(1.05^8) ≈ 1300.2 µL
The chamber created in 8 years is expected to be 1300.2 µL.
__
Additional comment
If the 5% growth rate is the rate of growth of the linear dimensions of a chamber, then its volume will grow at the rate of 1.05³ per year. In 8 years, the volume will be about 2838.1 µL.
(The wording "5% larger" is ambiguous here.)
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A social worker earns an average bi-weekly net pay of $1,465.87. Which compound inequality correctly shows the amount of money, m, the social worker can spend if the monthly budget for debt is between 5% and 10%? $73.29 ≤ m ≤ $146.59 $158.80 ≤ m ≤ $317.61 $146.59 ≤ m ≤ $293.17 $190.56 ≤ m ≤ $349.37
The amount of money the social worker can spend is $146.59 ≤ m ≤ $293.17
What is an equation?An equation shows the relationship between two or more numbers and variables.
Let m represent the amount of money the social worker can spend.
A social worker earns an average bi-weekly net pay of $1,465.87. Hence:
Monthly revenue = 2 * $1465.87 = $2931.74
For a debt of 5%:
m = 5% of $2931.74 = 0.05 * $2931.74 = $146.59
For a debt of 10%:
m = 10% of $2931.74 = 0.1 * $2931.74 = $293.17
$146.59 ≤ m ≤ $293.17
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Answer:
$158.80 ≤ m ≤ $317.61
Step-by-step explanation:
Hello,
So first step is we would use the bi-weekly net pay of $1465.87 then times it by 26 so it would look like this
1465.87 × 26 = 38112.62
Then we would divide 38112.62 by 12
38112.62 ÷ 12 = 3176.0516
Then, we would determine how much the social worker can spend if the monthly budget for debt is between 5% and 10%.
3176.0516 × 5% = 158.80
3176.0516 × 10% = 317.61
So, therefore the answer is $158.80 ≤ m ≤ $317.61.
a square with side length 2 and a circle share the same center. the total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. what is the radius of the circle?
The radius of the circle which is overlapping the square is 1.12.
The length of side of the square is 2. Let us say that the radius of the circle is R.
The circle and the square are overlapping on each other.
The area of the region that are outside the circle but inside the square are equal to the area of the region which are inside the circle but outside the square.
Let us name the area of the region that are outside the circle but inside the square as M.
Let us name the area of the region which are inside the circle but outside the square as N.
Let us say that the area that is common in both is C.
The area of the square is 4.
So, according to the question,
M + C = 4
And,
N + C = πR²
And we know, M = N,
So,
C - πR² = C - 4
R = 2/√π
R = 1.12.
So, the radius of the circle is 1.12
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some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 234 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?
The length, breadth and height will be 78 cm, 78cm, 78cm each.
let consider the length = l
breadth = b
height = h
we are provided that
l + b + h = 234cm .......(1)
Also we have to maximize the volume , provided length is equal to breadth
∴ eqn (1) becomes
2b + h = 234
h = 234 - 2b
also ,
volume(v) = lbh
v = b²(234 - 2b)
v = b²234 - 2b³
now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )
i.e. d( v)/db = 0
∴ 468b - 6b² = 0
6b² - 468b = 0
6b( b - 78 ) = 0
∴ b = 78 cm
now as length = breadth
l = b = 78 cm
also putting this value in eqn (1)
h = 234 - 2b
h = 78 cm
So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .
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Paula bought p packages of 5 rolls of tape. Then, she bought 4 individual rolls of tape. Which expression shows how many total rolls of tape Paula bought? SOLVE AND I'll MARK BRAINST AHAHAHHA
Y=5p+3
Y equals the total amount of tape rolls
P is for the number of packages there are.
Hope this helped!
:)
Answer:
Y=5p+4
Y equals the total amount of tape rolls
P is for the amount of packages there are
Step-by-step explanation:
Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
x
x + 1
x + 2
2x
She should use (b) x + 1 to represent her second number
How to determine the representation of the second number?From the question, we have the following statements that can be used in our computation:
She uses x to represent her first numberThe numbers are consecutive numbersAs a general rule
Consecutive numbers are number that have a difference of 1 i.e both numbers are next to each other
Take for instance:
2 and 3, 5 and 6, 10 and 11 are all instances of consecutive numbers
Recall that she uses x to represent her first number
This means that the next number is
Next number = First number + 1
Substitute the known values in the above equation, so, we have the following representation
Next number = x + 1
Hence, the second number is (b) x + 1
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A population of values has an unknown distribution with
ll
= 83.3 and o
= 10.4. You intend to draw a random
sample of size n
= 212.
What is the mean of the distribution of sample means?
flie
(Please enter an exact answer.)
What is the standard deviation of the distribution of
sample means?
Ox
(Please report your answer accurate
to 2 decimal places.)
By using the concept of mean and standard deviation, it can be obtained that
The mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = 0.714
What is mean and standard deviation?
Suppose there is a data set and an average value of the data set needs to be calculated. To find the average value of the data set, mean is used
For Standard deviation, at first, it is important to know about variance
Variance is the sum of the square of deviation from mean.
Square root of variance is the standard deviation
A population of values has an unknown distribution with
[tex]\mu = 83.3[/tex] and [tex]\sigma = 10.4[/tex], n = 212
So the mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = [tex]\frac{10.4}{\sqrt{212}}[/tex] = 0.714
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Today, I want you to challenge yourself. Don't let word problems intimidate you. In this task you are not solving but rather setting up equations. I know you have the
ability to do this. Here we go!
19
A store sells two brands of headphones: high definition (HD) and basic. It buys x HD headphones at z dollars each, and y basic headphones at w dollars each.
In a-c, write an equation whose solution is the given quantity. Solve Each Equation and set them up.
a) The number of basic headphones the store can purchase if it spends a total of $10,000 on headphones and buys 110 HD headphones for $70 each.
b)
The price the store pays for HD headphones if it spends a total of $2,000 on headphones and buys 55 basic headphones for $20 each.
c) The price the store pays for HD headphones if it spends a total of $800 on headphones and buys eight basic headphones for $80 each.
d) Please give me the actual cost of the headphones and an explanation with a-c
The solution to these are in form of equation as follows.
What is equation?
In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
x= number of HD headphones y= number of basic headphones
z = price of HD headphones. w = price of basic headphones
a)
110 (70) + y*w = 10,000
7,700+ y*w = 10,000
y*w = 2,300
y = 2,300/w
b)
x*z+ 55(20) = 2000
x*z = 2000 -1100
x*z = 900
z = 900/x
c)
x*z+y*w = 800
x*z+8(80) = 800
x*z+640=800
X*z=160
Hence the values to the equation are as follows.
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[tex]log_{2} (\sqrt[3]{16})[/tex]
The value of the given expression will be 4 / 3.
What is a logarithmic expression?An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given logarithmic expression is log₂(∛16). The expression will be solved as below,
[tex]E = log_2\sqrt[3]{16}\\E = log_2(2^{\frac{4}{3})\\E = \dfrac{4}{3}log_22\\E = \dfrac{4}{3}[/tex]
Therefore, the solution of the expression will be equal to 4 / 3.
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an urn contains 6 blue balls and 6 orange balls. in how many ways can we select 2 blue balls and 2 orange balls from the urn?
The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545
No. of Blue balls in the urn = 6
No. of Orange balls in the urn = 6
Total no. of balls in the urn = No. of blue balls + No. of orange balls
= 6 + 6
= 12 balls
No. of blue balls to be selected = 2
No. of orange balls to be selected = 2
No. of balls to be selected = 4
The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]
The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]
The No. of ways 2 orange balls can be selected = [tex]^{6}C_{2}[/tex]
Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn
= [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]
Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls
P = (15×15)/495
= 225 / 495
P = 0.4545
Therefore, the no. of ways to select blue and orange balls is 0.4545
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W/4+12.5-7z
What which term has a coefficient?
Answer:
The coefficient is 7 and the term that has it.
If y varies directly as x and y=8 when x=2 find when x=6
The equation is y = 4x. And the value of the function at x = 6 will be 24.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If y varies directly to x. Then the relationship between them is written as,
y ∝ x
y = kx
When y = 8 and x = 2, then the value of the constant k is given as,
8 = k (2)
k = 8 / 2
k = 4
Then the equation is written as,
y = 4x
Then the value of the function at x = 6 will be given as,
y = 4 (6)
y = 24
The equation is y = 4x. And the value of the function at x = 6 will be 24.
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ella has 1/3 as many trading cards as kip. Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. write an expression for the total number of cards the groups has. writ an expression for the total number of cards?
If Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. The expression for the total number of cards the groups has is: 1/3 ⋅9+(3+0.5⋅18)+18.
How to determine the expression?Given data:
Number of trading cards = 1/3
Adira number of cards = 23 more than 50%
Kip number of cards = 18 cards
Now let formulate an expression and then make use of the formulated expression to find the number of cards
Hence,
Number of cards = 1/3 ⋅9+(3+0.5⋅18)+18
Number of cards = 1/3 ⋅9+(3+9)+18
Number of cards = 1/3 ⋅9+(12)+18
Number of cards =3 + 12+18
Number of cards = 33 cards
Therefore the expression is : 1/3 ⋅9+(3+0.5⋅18)+18.
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The actual marked price of the stove is $2400. This includes a sales tax of 12.5%. Calculate the selling price of the stove if no sales tax is included.
Answer: $2100
Step-by-step explanation:
Since 12.5 percent of 2400 is 300, Just subtract 300 from 2400 to get the selling price with no sales tax. And the final answer is $2100.
Which of the following numbers is a composite number? A. 9 B. 2 C. 29 D. 5
Answer: A. 9
Step-by-step explanation:
PLEASE HELP WHAT IS THE SLOPE OF THIS LINE
Answer: A. [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
To find the slope we must find the change in y over the change in x. Δ
Or rise over run. [tex]\frac{rise}{run}[/tex]
In the graph, we have two "good" points. (0, -6) and (4,0)
So for Δy 0 to -6 = -6
So -6 goes on top [tex]\frac{-6}{x}[/tex]
Now Δx goes from 4 to 0 so the change would be -4.
So now it becomes [tex]\frac{-6}{-4}[/tex]
Since there are two negatives it becomes a positive. [tex]\frac{6}{4}[/tex] Or simply put, [tex]\frac{3}{2}[/tex]
Each tire on the toy car has a diameter of 5. 6cm, the tire spin completely around 15 times when the car was pushed in a straight line. About how far was the car pushed
The distance covered by the car is 264cm.
Here we have to find the distance covered by the car.
Information provided:
Diameter (d) = 5.6cm
radius(r) = 5.6/2
= 2.8cm
Rotation = 15 times
Formula to find the circumference of the tire:
Circumference = 2πr
= 2 × 22/7 × 2.8
= 17.6cm
This is the distance covered by the tire in one rotation.
Distance covered after 15 rotations = 15× 17.6
= 264 cm
Therefore distance covered is 264 cm.
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Jane was asked to solve the equation `2-4=2(-5+1)`. she believes the solution to the equation is `x=\frac{1}{2}` . explain how jane could confirm that her solution is correct
the solution for the given equation is x= 1/2
an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors
since the given expression is :
`(2-4)=2(-5+1)x²
so solving for the simple arithmetic expression on both sides :
=>-2 =2(-4)x²
=> -2 = -8x²
=>2/8=x²
=>1/4= x²
=>x= 1/2
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Which of these equations represent functions where is x is the input and y is the output ?
The equations represent functions where x is the input and y is the output are y = 2x and x+y = 2
The 1st equation is x =2
Since there is no component of y and the value of x is fixed. So this is not the desired option.
The 2nd equation is y = 2
Since there is no component of x, and the value of y is fixed. So this is not the desired option.
The 3rd equation is y = 2x
In this equation, x is the input and y is the output. For different values of x, we will have different values of y.
Thus, this is the desired option.
The 4th equation is x =2y
In this equation, y is the input and x is the output. For different values of y, we will have different values of x.
The 5th equation is x+y = 2
So, x + y = 2
y = 2 - x
In this equation, x is the input and y is the output. For different values of x, we will have different values of y.
Thus, this is the desired option.
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maths enlargements calculations of lines in shapes help pls
The length of the line segment BD is 3 centimeters.
How to find the missing length of triangle proportional to another triangle
Herein we find two triangles proportional to each other. According to Thales's theorem, two triangles are proportional when both have congruent angles. The geometric system is represented by the following expression:
AB / AD = BC / DE = AC / AE
By direct inspection we notice that the two triangles are proportional as they have congruent angles. If we know that DE = 10 cm, BC = 8 cm and AB = 12 cm, then the side AD has the following measure:
12 cm / AD = 8 cm / 10 cm
AD = (10 cm / 8 cm) × 12 cm
AD = 15 cm
And the length of the line segment BD is:
BD = AD - AB
BD = 15 cm - 12 cm
BD = 3 cm
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Can someone help me on this question? I think it’s the 2nd choice but I’m not sure
Answer:
5√3
Step-by-step explanation:
There are two triangles shown in the image.
First one is a 45°-45°-90° right triangle with side lengths represented with a-a-a√2 respectively to the angle measures.
The second triangle is 30°-60°-90° special right triangle with side lengths represented with b-b√3-2b respectively to the angle measures.
In first triangle hypotenuse (the side length represented with a√2) is given as 10√2 so a = 10.
This is also the measure of hypotenuse for the second triangle which is represented with 2b, so b = 5 in this case.
x is the side length that sees angle measure 60° which we said is represented with b√3, we said b = 5 so the value of x = 5√3 the answer is the first option.
a local hamburger shop sold a combined total of 483 hamburgers and cheeseburgers on Wednesday there were 67 fewer cheeseburgers sold in hamburgers how many hamburgers were sold on Wednesday
In linear equation, 275 hamburgers were sold on Wednesday .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.Let x = the number of hamburgers sold
Let x - 67 = the number of cheeseburgers sold
x + x - 67 = 483
2x = 483 + 67
2x = 550
x = 275
x = 275 hamburgers
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Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead?
Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.
Given statement;
Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.
→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.
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The length, L, of a rectangular garden is twice its width, W. The perimeter of the garden is 36 feet.
Answer:
L=12, W=6
Step-by-step explanation:
L=2W
(L+2L)=36
3L=36
2L=12
L=6
on their 560-mi trip, the bruins basketball team spent two more hours on the interstate highway than they did on local highways. they averaged 45 mph on local high-ways and 55 mph on the interstate highways. how many hours did they spend driving on local highways?
They spent 6.5 hours driving on local highways by travellin with diffrent average speeds.
Given that,
The bruins basketball team spent two more hours on the interstate than they did on local roadways during their 560-mile journey. They traveled at an average speed of 55 mph on interstates and 45 mph on local routes.
I=interstate
L=local
using d=rt the first rows gives you d=55t
the second row gives you 560-d=45(t-2)
Since the two distances add up to 560. Add the two distance expression and set their sum equal to the given total
560=55t+45(t-2) which equals
560=55t+45t-90
650=55t+45t
650=100t
6.5=t
Hence on local roadways, they traveled at various average speeds for 6.5 hours.
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a haunted house claims that 80% of customers are scared speechless. if this is true, what is the probability that 60% or less out of a group of 50 customers will be scared speechless?
Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.
Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.
Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.
Then, by binomial distribution,
P(x≤30) =r=030nCr*pr*q(n-r)
Now we can substitute given values and find the desired probability,
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r
The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.
P(x≤30) = 0.000932
Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.
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How much of a radioactive kind of promethium will be left after 265 hours if the half-life is 53
hours and you start with 15,488 grams?
grams
Impact Sports is having a sale this week. A portable basketball hoop has an original price of $159. It is on sale for 35% off the original price. What is the sale price of the basketball hoop?
Answer: 150*40/100=60
60+150=210.
Step-by-step explanation: