A ladder 8 m long is leaning against a building. How high on the building will the ladder reach when the bottom of the ladder is x = 1m from the building?
Answers
Answer:
7.9
Step-by-step explanation:
this would just be sqrt (8^2 - 1^2) or sqrt 63 or about 7.9
The ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given that:
A ladder 8 m long is leaning against a building.
From the data given, a right angle triangle is formed:
Applying the Pythagoras theorem:
Building high² = 8² - 1²
Building high² = 63
Building high = 7.9 meters
Thus, the ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
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Related Questions
HELP PLEASE
2. You are making necklaces for your friends. You have 72 blue beads and 42 red beads. Each friend will receive an identical necklace, and all beads must be used.
(A) What is the greatest number of friends who can receive a necklace? Explain your reasoning.
(B) How many of each color bead will each friend receive on the necklace? Explain your reasoning.
Answers
A. The greatest number of friends who can receive a necklace made from a combination of 72 blue and 42 red beads is 6.
B. Each friend will receive a necklace with 12 blue beads and 7 red beads.
How is this determined?The solution to this problem can be determined by considering the highest common factors of 72 and 42.
The common factors of 72 and 42 are 2 and 3.
The factors of 72 are 2, 3, and 12.
The factors of 42 are 2, 3, and 7.
2 x 3 = 6
When 6 divides 72 = 12
When 6 divides 42 = 7
Data and Calculations:Number of blue beads = 72
Number of red beads = 42
The highest number that can divide 72 and 42 without a remainder is 6.
Thus, each friend's necklace will contain 19 beads (12 blue beads and 7 red beads).
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You have $2000 to invest in an account and need to have $2500 in five years. What annual interest rate would you need to have in order to have this if the amount is compounded monthly?
a 3.77%
b4.47%
c2%
d5.5%
please answer
Answers
The annual interest rate needed to reach the given amount in five years is 4.47%.
Hence, option B) is the correct answer.
What is the annual interest rate needed?Compound interest is expressed as;
A = P( 1 + r/n )^(nt)
Making rate r the subject of the formula;
r = n[ (A/P)^(1/nt) - 1 ]
Given that;
Principal P $2000Final Amount A = $2500Number of times interest applied per time period n = monthly = 12Time t = 5We substitute into our formular above
r = n[ (A/P)^(1/nt) - 1 ]
r = 12[ (2500/2000)^(1/(12×5)) - 1 ]
r = 12[ (1.25^(1/60) ) - 1 ]
r = 12[ 1.0037598 - 1 ]
r = 12[ 0.0037598 ]
r = 0.447
Next we convert to percentage
r = 0.447 × 100%
r = 4.47%
The annual interest rate needed to reach the given amount in five years is 4.47%.
Hence, option B) is the correct answer.
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Add these fraction
1) 2/3 + 6/3
2) 4/6+9/6
3) 6/6+6/6
Answers
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
What is the value of the addition operation?Given that;
1) 2/3 + 6/3
We combine the numerators over the common denominators
= ( 2 + 6 ) / 3
= 8/3
2) 4/6 + 9/6
We combine the numerators over the common denominators
= ( 4 + 9 ) / 6
= 13/6
3) 6/6 + 6/6
We combine the numerators over the common denominators
= ( 6 + 6 ) / 6
= 12/6
= 2
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
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Calculate the price elasticity of supply for Bobbie's Bakery's banana bread. When the price changes by 29% the quantity supplied changes by 55%. Round your answer to two decimal places.
Answers
The price elasticity of demand is 1.90.
What is the price elasticity of demand?Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good. It is expected that quantity supplied would be positively related to the price of the good.
Price elasticity of supply = percentage change in quantity supplied / percentage change in price
55% / 29% = 1.90
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Petsmart's marketing team finds in their most recent report that they sell 45 guinea pigs a
year. Their sales team wanted to increase their sales and grabbed a sample of 8 types of
rodents to put on a flash sale. They sold an average of 34 rodents with a standard
deviation of 21 rodents.
Answers
Answer:
p(x)=x3-3x2+4x+50 and g(x)=x-3
Determine the area under the standard normal curve that lies to the left of (a) Z=081. (b) Z=0.43. (c) Z= -0.33. and (d) Z= 1.04.
Answers
Using the normal distribution, the areas to the left are given as follows:
a) 0.7910.
b) 0.6664.
c) 0.3707.
d) 0.8508.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X, and is also the area to the left of Z.Hence:
The area to the left of Z = 0.81 is of 0.7910.The area to the left of Z = 0.43 is of 0.6664.The area to the left of Z = -0.33 is of 0.3707.The area to the left of Z = 1.04 is of 0.8508.More can be learned about the normal distribution at https://brainly.com/question/4079902
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Use the diagram to determine which statement is true
Answers
The answer is d.
Finding area of ABCD :
Find side lengthside = √3² + 4²side = 52. Apply formula to find area
area = 5²area = 25Finding area of GHIA :
area = 4²area - 16Finding area of DEFG :
area = 3²area = 9Now, let's see whether is true.
Area (ABCD) - Area (GHIA) = Area (DEFG)25 - 16 = 99 = 9∴ Hence, it is proved √
Match each number on the left with the correct description of the number on the right.
Answers
The Apollo space program lasted from 1967 until 1972 and included 13 missions.The missions lasted from as little as Z hours to as long as 30ours.The duration of each flight is listed below. 9 195 241 295 142% 142% 147 a.Expain why the flight times b.Find Mean and the Median of flight times c.Find range and the standard deviation of flight times
Answers
The mean and the median based on the information given will be 166.08 and 195.
How to calculate the value?It should be noted that the mean is also the average. It's gotten by adding all the numbers and dividing by 13. This will be 166.08.
The median is simply the middle number. This will be 195.
The range will be:
= 301 - 7
= 294
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A cube has it's one edge 5 cm and a cuboid measures 4m multiple 3m multiple 2m which has a greate surface area and how much ?
Answers
Answer:
Gievn that l=3m,b=5m,h=4m
L.S.A=2(l+b)h
=2×(3.5)×4
=2×8×4
=64sq.m
Step-by-step explanation:
Jada is solving the equation shown below.
Negative one-half (x + 4) = 6
Which is a possible first step to begin to simplify the equation? Select two options.
Divide both sides of the equation by –2.
Subtract 4 from both sides of the equation.
Multiply both sides of the equation by –2.
Distribute –2 over (x + 4).
Distribute Negative one-half over (x + 4).
Answers
Answer:
Distribute -1/2 over (x+4)
Step-by-step explanation:
-0.5(x+4) = 6
-0.5x - 2 = 6
-0.5x = 8
x = -16
Answer:
Multiple both sides by -2 or Distribute negative one-half over (x+4)
Step-by-step explanation:
-1/2(x+4) = 6
If I multiple both sides by -2, I am clearing the fraction:
(-2)(-1/2)(x+4) = 6(-2)
x+4 = -12
x = -16
OR
-1/2(x + 4) = 6
-1/2x -2 = 6 Remember, a negative times a positive is a negative.
-x - 4 = 12 multiply both sides by 2
-x = 16
x = -16
18. Find the value of 3x² x 2(x-3y) divide by 6 when x is 6 and y is 1
Answers
Answer:
11664
Step by Step:
Evaluate for x=6,y=1
3(6^2)(6^2)(6−(3)(1))
3(6^2)(6^2)(6−(3)(1))
=11664
Please please Help!
Need Answer to Multiple Choice! Brainliest!
The scores on the ACT exam are normally distributed with a mean of 21 and a standard
deviation of 5. If we selected a random sample of 37 test takers, what is the probability that the
sample mean of those test takers who would be less than a 19.8?
a) .0721
b) .5000
c) .0808
d) .0582
Answers
Answer:
a) 0.0721
Step-by-step explanation:
Let the random variable X be the score on the ACT exam.
Given:
mean (μ) = 21standard deviation (σ) = 5Therefore, the random variable X is normally distributed:
[tex]X \sim\textsf{N}(21,5^2)[/tex]
Z-score for a sample mean
[tex]\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)[/tex]
[tex]\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}[/tex]
Given:
[tex]\overline{x}[/tex] = 19.8μ = 21σ = 5n = 37Therefore, the test statistic is:
[tex]\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)[/tex]
Using the Z-tables to find the probability:
[tex]\implies \text{P}(Z \leq -1.46)=0.0721[/tex]
A clothing business finds there is a linear relationship between the number of shirts, n , it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $14 . Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
Because this answer involves an expression that is more complex than a whole number times n , remember to type in multiplication symbols *. For example, if you wanted to enter 12n , type this in as (1/2)*n.
Answers
The value P price they charges for shirts is (-0.008n) + 38
According to the statement
we have given that the 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $14 .
And we have to find the linear equation.So,
Let p = price
n = number of shirts
m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)
b = y intercept
And they gives us the two points like here (1000, $30) and (3000, $14) which have to be on our line.
To find the slope m, you use m = (p₁-p₂)/(n₁-n₂)
Filling in from our points m = (30-14)/(1000-3000)
m = 16/-2000
m = -0.008
Now that we have the slope and a point, we can find our equation
p-p₁=m(n-n₁)
p-30=(-.008)(n-1000)
p-30= (-.008n) + 8
p=(-.008n) + 38
So, The value P price they charges for shirts is (-0.008n) + 38
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While traveling in Europe, you notice that the price of gas is $1.12 per liter. What is the price per gallon?
Answers
. Trevor mows 5 times as
many lawns in the
summer as he does in
the fall. If he mows 20
lawns in the summer,
how many does he mow
in the fall?
Answers
Answer:
4 lawns
Step-by-step explanation:
20/5
20/5=4
Hope this helps
help me with this pls and ty
Answers
Answer:
It is the second answer.
Step-by-step explanation:
When numbers with the same base are multiplied, you add the bases.
1/2 + 3/4 is the same as
2/4 + 3/4 = 5/4
So now we have 2 ^5/4^2. When we have a power raised to a power. We multiply the powers.
5/4(2)
(5/4(2/1) = 10/4 = 5/2. The second answer is the same way to describe
2^(5/2)
Solve for x. Find all solutions from 0 to 2 π . Show all work as you solve each problem - you may need more space to show your work for each. Remember there may be more than 1 solution for x.
Questions are attached below
Answers
Answer:
x=189
Step-by-step explanation:
please mark me as brainiest
Create a problem with a quadratic equation that you would solve graphically and solve it.
Answers
The solutions to the quadratic problem are x = -1 and x= 4
Solving Quadratic equations graphicallyFrom the question, we are to create a problem with a quadratic equation and solve graphically
Consider the quadratic equation
x² -3x -4 = 0
The graph of the quadratic equation is shown below
We can observe that the graph cuts the x-axis at the point x = -1 and x = 4
Hence, the solutions to the quadratic problem are x = -1 and x= 4
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Question about a rational expression
The equation is -9=6/v
In the explanation, it tells me to multiply v on both sides. My question is why do you multiply v on both sides and not 6?
When I did the problem I multiplied 6 on both sides and got -54=v, but apparently the answer is -2/3 so I’m confused as to why you multiply v on both sides and not 6.
Answers
You have to multiply v both sides because
6/v x v = 6 and helps you get rid of the v on the right side.
If you multiply by 6, 6/v x 6 = 36/v, that’s why it don’t work.
Answer:
-9=6/v
-9v=6
v=-6/9
v=-2/3
If the side length of of rectangle is 3x-3 and the top length is 6, how do I write a linear equation the represents the area and a linear equation that represents the perimeter, all measurements are in cm if that is useful.
Answers
Perimeter of the rectangle is: 6x + 6 cm
Area of the rectangle is: 18x - 18 cm²
What is the Area and Perimeter of a Rectangle?Area = (length)(width)
Perimeter = 2(length + width).
Given the following:
Length of rectangle = 3x - 3
Width = 6
Area = (3x - 3)(6)
Area = 18x - 18 cm²
Perimeter = 2(3x - 3 + 6) = 2(3x + 3)
Perimeter = 6x + 6 cm
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How many proportional relationships are shown in the coordinate plane below/
Answers
Answer:
I wish I could I didnt do good with this in math
Convert 45 32’ 55” into decimal degrees to the nearest two decimal places
Answers
The decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
Converting degrees into decimalThe given degree is:
45⁰ 32' 55''
This can be converted to decimal as shown below
[tex]45+\frac{32}{60} +\frac{55}{3600}[/tex]
This can be simplified further as:
[tex]45^o32'55'' = 45+0.53+0.0153\\\\45^o32'55'' = 45.55^0[/tex]
Therefore, the decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
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13)
Medical officials want to determine if birth weights are lower than usual in Southeast Asia. They randomly weigh 100 babies, and they determine that the average birth weight is 6 pounds 8 ounces.
State the variable.
What are the units for the variable?
State the population.
State the sample.
POINTS Out OF
7
What is the individual.
What is the Parameter.
What is the statistic.
Answers
See below for the response to each question
The variableThis is the item that is being surveyed.
The surveyed item is birth weights
Hence, the variable is birth weights
The units of the variableFrom the question, we have:
Average birth weight is 6 pounds 8 ounces.
Hence, the units of the variable are pounds and ounces
The populationThis is the total number of babies in Southeast Asia
Hence, the population of interest is the babies in Southeast Asia
The individualThis is the people in the survey
Hence, the individual in the study is the 100 babies that were randomly surveyed
The parameter of interestThis is the value that gives the required information.
Hence, the parameter of interest is the average birth weight
What is the statistic involvedThe statistic is the average
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In Hawaii”s Kona iron man competition, Gretchen swims the first 7/8 of a mile in 70 minutes. At this pace, how many minutes will it take for Gretchen to swim the entire 2 2/5 mile course
Answers
It would Gretchen 192 minutes to swim the entire 2 2/5 mile course.
What is speed?
Speed is distance divided by the time taken to cover the distance.
In this case, we can determine distance covered in a minute by dividing the speed by the distance, which is distance of 7/8 mile(i.e. 0.825 mile) over the time take to cover the distance.
speed per minute=0.825/70
speed per minute=0.0125 mile/minute
With this, we can determine the time in minutes it would take to cover 2.4 miles(2/5=0.4)
0.0125=2.4/time
0.0125*time=2.4
time=2.4/0.0125
time=192 minutes
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Savings account at a bank pays 5% simple interest in account at Bank B pays 2% compounded interest the table shows the balance in each account after an initial deposit of $1000 which describes the balance after a long period of time
Answers
Answer:
The balance in Bank B will be greater.
Step-by-step explanation:
Because simple interest is just interest on the principle only which is 50 every year doesn't change but with compound interest you will get 2% Interest every year. principle+interest
How do i find the slope of these points? (−4, 3) and (2, 9)
Answers
Answer:
Divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Step-by-step explanation:
Answer:
The value of the slope b/n these two pts. will be 1.
Step-by-step explanation:
Greetings !
For finding slope from two points of a line (x₁, y₁) and (x₂, y₂), we use the formula (y₂ - y₁) / (x₂ - x₁).
Thus, m=(y₂ - y₁) / (x₂ - x₁)
m=(9-3)/(2-(-4))m=6/6m=1.The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, yˆ=b0+b1x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Table
6 steps
Answers
The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607
How to determine the regression equation?The table of values is given as:
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Next, we enter the above values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 305Sum of Y = 15.5Mean X = 61Mean Y = 3.1Sum of squares (SSX) = 34Sum of products (SP) = -14.5r = -0.9607Regression Equation = ŷ = bX + a
b = SP/SSX = -14.5/34 = -0.42647
a = MY - bMX = 3.1 - (-0.43*61) = 29.11471
So, the regression equation is
y = -0.42647x + 29.11471
And the correlation coefficient is -0.9607
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explain me the formula for a point that forms a partiton of a ratio on a segment in the 2nd grade real numbers.
Let’s say the ratio a:b, our formula those becomes
{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}
From the question, we can identify that
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
Answers
The partition point is (-7/2, 23/4)
How to determine the partition point?The given parameters are:
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
The partition point is calculated as:
(x, y) = ((bx1 + ax2)/(a + b) ,( by1+ay2)/a+b)
So, we have:
(x, y) = ((3 * -6 + 1 * 4)/(1 + 3) ,(3 * 8 + 1 * -1)/1+3)
Evaluate
(x, y) = (-14/4, 23/4)
Simplify
(x, y) = (-7/2, 23/4)
Hence, the partition point is (-7/2, 23/4)
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Express the confidence interval (0.065,0.143) in the form of p - E
Answers
The confidence interval expressed in the form p - E is:
(0.104 - 0.039, 0.104 + 0.039).
What are the mean and the margin of error of a confidence interval?The mean is the mean of the bounds, hence:
p = (0.065 + 0.143)/2 = 0.104.
The margin of error is the difference between the bounds and the mean, hence:
E = 0.104 - 0.065 = 0.143 - 0.104 = 0.039.
Hence the interval in the desired format is:
(0.104 - 0.039, 0.104 + 0.039).
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