Answer:
24ft high
Step-by-step explanation:
Assuming the wall is perpendicular to the ground (so that it forms a right angle, and that when the ladder is placed on the ground and leaned up against the wall that it forms a right triangle), we can use the Pythagorean Theorem to describe the situation mathematically.
The Pythagorean TheoremFor any right triangle (a triangle that has a right angle) the Pythagorean Theorem applies. The Pythagorean Theorem describes the relationship between side lengths as [tex]a^2+b^2=c^2[/tex], where "c" is the length of the "hypotenuse" (the side across from the right angle), and "a" and "b" are the lengths of the "legs" (the other two sides that are touching the right angle). Since addition is commutative, it doesn't matter which leg you pick for side "a" or side "b", it only matters that the hypotenuse must be "c".
Given that the ladder is across from the right angle (the angle formed by the wall and the ground... the two "legs"), the ladder represents the hypotenuse in this situation.
Substituting known values, and solving the equation[tex]a^2+b^2=c^2[/tex]Substitute known values, and simplify...
[tex]a^2+(10)^2=(26)^2[/tex]
[tex]a^2+100=676[/tex]
Subtract 100 from both sides...
[tex](a^2+100)-100=(676)-100[/tex]
[tex]a^2=576[/tex]
Apply the square root property...
[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]
[tex]a=\pm 24[/tex]
[tex]a=24[/tex] or [tex]a=- 24[/tex]
Since the distance height the ladder will reach is not a negative number, we reject the negative solution. Hence, the ladder will reach 24ft high, if placed 10ft from the base of the wall.
14,246 is invested, part at 13% and the rest at 12%. If the interest earned from the amount invested at 13% exceeds the interest earned from the amount invested at 12% by $318.23, how much is invested at each rate? (Round to two decimal places if necessary
The amount of money invested at 13% was $8111, while $6135 was invested at 12%.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount invested at 13% and y represent the amount invested at 12%, hence:
x + y = 14246 (1)
Also:
0.13x = 0.12y + 318.23 (2)
Hence:
x = 8111, y = 6135
The amount of money invested at 13% was $8111, while $6135 was invested at 12%.
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Drag each equation to the correct location on the table. Determine which equations will result in extraneous solutions.
Answer:
extraneous: 2, 5, 7
not: 1, 3, 4, 6, 8
Step-by-step explanation:
ones that have root of an even number and equal a negative are extraneous
Need help regarding radioactive decay type of question
By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.
How to determine the initial mass of a radioactive isotope
Mass of radioactive isotopes (m (t)), in grams, decay exponentially in time according to the following model:
[tex]m(t) = m_{o}\cdot e^{-t/\tau}[/tex] (1)
Where:
[tex]m_{o}[/tex] - Initial mass, in gramst - Time, in yearsτ - Time constant, in yearsThe time constant can be found in terms of half-life:
τ = t'/㏑ 2
If we know that t' = 24100 yr, t = 1000 yr and m(t) = 5.4 g, then the initial mass of the radioactive isotope is:
τ = 24100 yr/㏑ 2
τ ≈ 34768.95 yr
[tex]5.4 = m_{o}\cdot e^{-1000/24100}[/tex]
[tex]m_{o} = 5.629\,g[/tex]
By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.
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can you please help me with this
Answer:
Point A
Step-by-step explanation:
Point A is closest to 9
every line counts as 0.1
If P= (-6,4) find Ry= -x (P)
The value of Ry= -x (P) is P' = (4, 6)
How to determine the transformation?The point is given as:
P = (-6, 4)
The transformation Ry= -x (P) means tha:
(x, y) = (y, -x)
So, we have:
P' = (4, 6)
Hence, the value of Ry= -x (P) is P' = (4, 6)
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One number is 5 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 331, find the numbers.
Answer:
33, 165, 133
Step-by-step explanation:
Check this file for the solution!
Answer:
33, 165, 133
Step-by-step explanation:
let the first number be n then
second number is 5n
third number is n + 100
sum the 3 numbers and equate to 331
n + 5n + n + 100 = 331 , that is
7n + 100 = 331 ( subtract 100 from both sides )
7n = 231 ( divide both sides by 7 )
n = 33
5n = 5 × 33 = 165
n + 100 = 33 + 100 = 133
the numbers are 33, 165, 133
Find the perimeter of the rectangle.
Answer:
10x² + 8x + 22
Step-by-step explanation:
The perimeter of a rectangle is the measurements of all four side lengths added together
(you can simply multiply both side lengths by 2, because they are the same on both sides--but I'll write them all out for clarity)
side A (top): 5x² + 3x + 7
side B (right): x + 4
side C (bottom): 5x² + 3x + 7
side D (left): x + 4
perimeter = side A + side B + side C + side D
5x² + 3x + 7 + x + 4 + 5x² + 3x + 7 + x + 4
now, as you might have noticed, this is a long equation
so, we must combine like terms:
(this is the problem reordered so like terms are next to each other:)
(5x² + 5x²) + (3x + x + 3x + x) + (7 + 4 + 7 + 4)
10x² + 8x + 22
So, the perimeter of this rectangle is 10x² + 8x + 22
hope this helps! have a lovely day :)
Which description best compares the graphs given by the equations: x-5y=-5 5x-25y=75
Considering the slopes of the given lines, they are parallel lines.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.The first line, in standard form, is given by:
5y = x + 5
y = 0.2x + 1.
The slope is of m = 0.2.
For the second line, we have that:
25y = 5x - 75
y = 0.2x - 3
The slope is of m = 0.2.
Same slope, hence the lines are parallel.
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The sets A and I are defined as follows: A={−2,−1,0,1,7} I= {−2,−1,1,2,8}. Find the intersection of A and I.
The intersection of A and I are {-2, -1, 1}
How to determine the intersection?The sets are given as;
A={−2,−1,0,1,7} I= {−2,−1,1,2,8}
The intersection of A and I are the common elements in both sets
The common elements in both sets -2, -1 and 1
This means that:
A n I = {-2, -1, 1}
Hence, the intersection of A and I are {-2, -1, 1}
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Round to the nearest whole number.
568.3
Answer:
568.3 into the nearest hundred
5.683
Answer:
568
Explanation:
A whole number is a number without any fractional part; in other words, it does not have any non-zero digits after the decimal point.
When you round a number to the nearest whole number, first look at the digit right after the decimal point;
• if the digit is less than 5, then the nearest whole number is the original number, but without any digit after the decimal point. [rounding down]
• if the digit is 5 or greater than 5, then the nearest whole number is the next whole number (i.e., add 1 to the original number and remove the digits after the decimal point). [rounding up]
I don’t know the answer and I need help asap
Answer:
The answer is
[tex]a \sin(theta) [/tex]
Step-by-step explanation:
The solution is in the image
Can you prove this statement using properties of logarithms? Assume all expressions exist
and are well-defined
3 log y z^9= log y z^27
Answer:
see below
Step-by-step explanation:
what 3 logy z^9 means you need to break it into two pieces, one log y z^9 means to find the exponent of y, and you can think z^9 as a number, and then if we multiple it with 3, which means three logs are summed,(the property of multiplication:3*2 means 2+2+2), thus log + log
has the property that the y is same z^9*z^9*z^9=z^(9+9+9)=z^27
Drag each tile to the correct box. The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below. A graph represents the water level to fill the tank on Y-axis per time on X-axis. Segments A, B, and C fill the tank from 10 to 60, 60 to 80, and 80 to 110 centimeters in the first 2, next 4, and last 3 minutes. Place the segments in the correct order from the least to the greatest rate of increase in the water level. B A C
The least to greatest slope, the segments are B, C, and A.
We have given that,
The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below.
A graph represents the water level to fill the tank on Y-axis per time on X-axis.
The rate of increase of water level is indicated by the slope of the segment. The slope is the ratio of rise to run, and is related to the angle the segment makes with the +x axis.
Segments that have more rise for the same run have greater slope. Segments that make a larger reference angle with the +x axis have a larger slope.
Here, segment B has the least slope, followed by C, then A, which has the largest slope.
In order, the least to greatest slope, the segments are B, C, and A.
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Answer: bca
Step-by-step explanation:
B C A
solve this question please?
Hence the value of the expression above are as listed below
f(6+4) = 25
f(6)+f(4) = 20
f(6-4) = 1
f(6)-f(4) = 6
f(6*4) = 67
f(6)*f(4) = 91
Functions and valuesGiven the expression below f(x) = 3x - 5
f(6+4) = f(10) =3(10) - 5
f(6+4) = 25
f(6) = 3(6) - 5
f(6) = 18 - 5 = 13
f(4) = 3(4) - 5
f(4) = 7
f(6)+f(4) = 13+7
f(6)+f(4) = 20
f(6-4) = f(2) =3(2) - 5
f(6-4) = 1
f(6) = 3(6) - 5
f(6) = 18 - 5 = 13
f(4) = 3(4) - 5
f(4) = 7
f(6)-f(4) = 13-7
f(6)-f(4) = 6
f(6*4) = f(24) =3(24) - 5
f(6*4) = 67
f(6) = 3(6) - 5
f(6) = 18 - 5 = 13
f(4) = 3(4) - 5
f(4) = 7
f(6)*f(4) = 13*7
f(6)*f(4) = 91
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Energy Drinks: Popular energy drinks contain green tea extract and caffeine. Do these energy drinks help you lose weight by increasing your metabolism? Researchers at a medical school designed an experiment to determine the chemical effects of green tea and caffeine on energy metabolism in healthy, lean, young adults. Researchers randomly assigned participants to 2 treatments. One group drank Formula A, a beverage with green tea and caffeine. The other group drank Formula B, a beverage with none of these ingredients but colored to look like Formula A. The beverages were blinded at the production site, so the experiment was double-blind. The researchers chilled the beverages to 6°C. Participants drank the beverages at the same time each day for three days. During the 3 days of the experiment, the researchers fed each participant the same diet. On the 3rd day participants spent 24 hours in a calorimeter chamber to measure their energy metabolism. The medical journal Obesity published the results in 2007. Which confounding variable is controlled by randomly assigning individuals to treatments? the effect of green tea and caffeine on energy metabolism the effect of green tea and caffeine on energy metabolism the physical fitness level of the participants the physical fitness level of the participants the time of day participants drank the beverages the time of day participants drank the beverages
The confounding variable which is controlled by randomly assigning individuals to treatments is: C. the time of day participants drank the beverages.
What is a confounding variable?A confounding variable is also referred to as a confounder and it can be defined as a type of variable that has the ability to influence both the independent and dependent variables.
Also, a confounding variable is usually not accounted for by the researcher and as such it can cause a spurious association between the independent and dependent variables.
In this context, we can infer and logically deduce that the time of day at which participants drank the beverages is a confounding variable which is controlled by randomly assigning individuals to treatments.
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solve for x: x = 0.7x + 24
Answer:
x=80
Step-by-step explanation:
x=0.7x+24
We move all terms to the left:
x-(0.7x+24)=0
We get rid of parentheses
x-0.7x-24=0
We add all the numbers together, and all the variables
0.3x-24=0
We move all terms containing x to the left, all other terms to the right
0.3x=24
x=24/0.3
x=80
Answer:
x = 80
Step-by-step explanation:
We are given the following equation.
x = 0.7x + 24
And we want to solve it for x.
For these kinds of equations, the way to solve for x is to isolate x on one side.
Because we have terms with x on both sides of the equation, we need to remove it from one side.
It's a good idea to remove x from the right side, as we also have our numbers on that side. If we move it to the left side, there aren't any numbers there, so we can more easily solve this equation.
Here is our equation again:
x = 0.7x + 24
Subtract 0.7x from both sides.
x = 0.7x + 24
-0.7x -0.7x
______________________
0.3x = 24
Now, we have variables on one side, and numbers on the other, but we aren't done yet.
Remember that we are solving for x, not 0.3x. (When x is written by itself, it is the same as 1x).
So, in order to find the value of 1x, we need to divide both sides by 0.3, as when a number is divided by itself, the value is 1. If there is a variable, the value will be 1*that variable (e.g. 1n, or n)
**Note that we don't divide by 0.3x, as if we did that, the left side would equal just 1, not 1x.
So, let's divide both sides by 0.3.
0.3x = 24
÷0.3 ÷0.3
__________
x = 80
Topic: solving linear equations
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5. It is reported that 20% of Canadian are on CERB (Canada Emergency Response Benefit). In order to further investigate this topic, a researcher selects a random sample of 10 Canadian across the country. Assuming that this is a proper Binomial experiment, what is the probability that at least 3 Canadian are on CERB in the sample? [3 Marks]. 5. It is reported that 20 % of Canadian are on CERB ( Canada Emergency Response Benefit ) . In order to further investigate this topic , a researcher selects a random sample of 10 Canadian across the country . Assuming that this is a proper Binomial experiment , what is the probability that at least 3 Canadian are on CERB in the sample ? [ 3 Marks ] .
Using the binomial distribution, it is found that there is a 0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are:
n = 10, p = 0.2.
The probability that at least 3 Canadian are on CERB in the sample is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]
[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778.
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222[/tex]
0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.
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What is the solution to this equation?
-1/5(x+1 1/4)=-2 1/2
Answer:
О x = 10 3/4
[tex]x = 10\frac{3}{4}[/tex]
Step-by-step explanation:
-1/5 ( x + 1 3/4) = -2 1/2
Particularly:
1 3/4 = 1 + 3/4 = 4/4 + 3/4 = 7/4
-2 1/2 = -2 - 1/2 = -4/2 - 1/2 = -5/2
Then:
-1/5 (x + 7/4) = -5/2
(x*-1/5 + 7/4*-1/5) = -5/2
(-x/5 + ((7*-1) / (4*5))) = -5/2
-x/5 + (-7/20) = -5/2
-x/5 - 7/20 = -5/2
-4x/20 - 7/20 = -50/20
-4x - 7 = -50
-4x = -50 + 7
-4x = -43
x = -43/-4
x = 43/4
43/4 = 40/4 + 3/4 = 10 + 3/4 = 10 3/4
A _______________ can be used to display an interval of values from a data set.
A. dot plot
B. any of these
C. bar graph
D. histogram
Answer:
The histogram
The histogram is a popular graphing tool. It is used to summarize discrete or continuous data that are measured on an interval scale. It is often used to illustrate the major features of the distribution of the data in a convenient form.
Hope it helps :)
Answer:
D. Histograph can be used to display an interval of values from a data set
HELP ASAP
will mark brainliest
m=1/4
(or m=0.25)
M= rise/run
= 1/4
Hope this helps!
Interpreting a Line of Best Fit
Use the graph and equation to answer the question.
A graph with number of visitors on the x-axis and amount of money on the y-axis. A trend line has equation y = 7.48 x + 2,245.21.
The graph includes ordered pairs displaying the relationship between the number of visitors at a museum during regular hours in a day (x) and the amount of money the museum collects during the given day (y).
The slope indicates that the museum
for every additional
, and the y-intercept could represent the daily average
.
Answer: A, C, C.
100%
Step-by-step explanation:
suppose a radioactive substance decays according to the equation y=200e^-0.75t, where y represent the mass in gram after t hours. calculate the mass of the substance after 3.5 hours have elapsed
Answer:
i am not sure
Step-by-step explanation:
On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform B and zip to the other platform. What is the coordinate when you reach half way?
he midpoint between the Platform B and C is ( )
, ( )
The coordinates of the mid-point between points B and C is given by:
(-5, -10).
What is the mid-point concept?The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.
The points in this problem are given as follows:
B(-40, -30), C(30, 10)
Hence the coordinates of the mid-point are:
x = (-40 + 30)/2 = -5.y = (-30 + 10)/2 = -10.More can be learned about the mid-point at https://brainly.com/question/10956693
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The transportation department has to put a railing along the outer curve of this road. The road is 20 feet wide. What is the length of the outer curve to the nearest foot? Use the value
Using the arc length formula, the length of the outer curve is approximately 85 feet.
How to Find the Length of an Arc?Arc length = ∅/360 × 2πr.
Apply the arc length formula to find the length of the outer curve, given the following:
∅ = 70°π = 3.14r = 50 + 20 = 70 feetPlug in the values
Arc length = 70/360 × 2(3.14)(70)
Arc length = 70/360 × 2(3.14)(70) ≈ 85 feet.
The length of the outer curve is approximately 85 feet.
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5m-8=2m+2
what does m equal
Answer:
m = 10/3
(as a decimal: m = 3.333...)
Step-by-step explanation:
5m - 8 = 2m + 2
5m - 8 = 2m + 2
- 2m - 2m (make all "m" on one side to isolate variable)
3m - 8 = 2
+ 8 + 8 (get m entirely on 1 side)
3m = 10
÷3 ÷3 (divide by 3 to get 1m)
m = 10/3
(as a decimal: m = 3.333...)
hope this helps!! have a lovely day :)
Can anyone help me solve this question?
Answer: 110
Step-by-step explanation:
<ABC = <DEF
180 - <DEF = 180 - 70
<BED = 110
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 8. Event B: The sum is not divisible by 4 and not divisible by 5.
(3,6) (4,6) (5,6) (6,6) (4,5) (5,5)
Each of these pairs is equiprobable and which i will be using throughout the exercise:
[tex]p(pair) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} [/tex]
[tex]p(a) = (\frac{1}{36} \times 2) \times 4 + \frac{1}{36} \times 2 = \frac{5}{18} [/tex]
The 2 (2!) is to account for permutations like ( 3 , 6 ) and ( 6 , 3 ) and the 4 are the different combinations that are composed of different numbers.
The 2 (2!) is to account for permutations like ( 3 , 6 ) and ( 6 , 3 ) and the 4 are the different combinations that are composed of different numbers.Whereas combinations like ( 5 , 5 ) cannot be switched in order, so we do not multiply by 2!
Event BPairs that yield a sum divisible by 4 or 5: 0,4,5,8,10,12,(1,3) (2,2) (2,6) (4,4) (5,3) (6,6) (1,4) (2,3) (5,5) (4,6)
[tex]p(not \: b) = ( \frac{1}{36} \times 2) \times 6 + \frac{1}{36} \times 4 = \frac{4}{9} [/tex]
[tex]p(b) = 1 - p(not \: b) = 1 - \frac{4}{9} = \frac{5}{9} [/tex]
WILL MARK BRAINLIEST
Answer: constant of proportionality = 0.75
How to find constant of proportionality?
Constant of proportionality is the same as the slope of a straight line.
Slope formula is given by:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here take two points: (0, 0), (4, 3)
[tex]So, \sf \ slope : \dfrac{3-0}{4-0} = \dfrac{3}{4} \quad or \quad 0.75[/tex]
Hence, the constant of proportionality is 0.75
Answer:
Constant of proportionality = 0.75
Step-by-step explanation:
To find the constant of proportionality of a graph that goes through the origin:
• First select a point on the graph whose coordinates you can easily read; in this case such a point is already marked (4, 3).
• Next, simply divide the y-value by the x-value of the coordinates to find the constant of proportionality:
Constant of proportionality = y ÷ x
⇒ 3 ÷ 4
⇒ 0.75
Which of the following is a non-proportional relationship?
There are 24 students per teacher.
There are 50 apple trees in 1 square mile.
A swimming pool costs $9 per day of use plus a registration fee $12.
There are 10 fish in each fish tank.
You design a new app for cell phones. Your revenue for x downloads is given by f(x) = 3x Your profit
is $20 less than 90% of the revenue for x downloads. Create a function p to model the profit. Find
the profit for 90 downloads.
Answer:
p = 2.7x - 20
p(90) = $223
Step-by-step explanation:
revenue → f(x) = 3x ,where x is the number of downloads.
the statement “Your profit p is $20 less than 90% of the revenue for x downloads”
means
[tex]p=90\% f\left( x\right) -20[/tex]
means
[tex]p=\frac{90}{100} \times f\left( x\right) -20[/tex]
means
[tex]p=\frac{9}{10} \times (3x) -20[/tex]
means
[tex]p=\frac{9}{10} \times (3x) -20[/tex]
means
[tex]p=2.7x -20[/tex]
………………………………
the profit for 90 downloads :
= p(90)
= 2.7×(90) - 20
= $223