Answer:
Given,
Let's assume the maximum safe height of wall = h
angle formed between ladder and ground = 70°
length of ladder = 16 ft
From the given data, it can be seen that ladder will form a right angle triangle structure with the wall
So,from the concept of trigonometry,
Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70
o
=
length of ladder
maximum safe height of wall
= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70
o
=
16 ft
h
= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70
o
=> h = 16 x 0.9396
=> h = 15.03 ft
So, the maximum safe height that can be reached by the ladder will be 15.03 ft.
Here is the Correct asnwer.
What is the value of x?
Enter your answer in the box.
x =[ ]
Answer:
(2x+2)=(3x-52)
2x+2=3x-52
2x-3x=-52-2
-x=-54
x=54
A student average 45 mph on a trip. What was the student’s speed in feet per second?
Answer:
66 foot per second
Step-by-step explanation:
-2(y - 3) = y + 24
please help
Answer:
y=-6
Step-by-step explanation:
1. -2y+6=y+24
2. -2y-y=24-6
3.-3y=18
4. y=-6
135 is 0.9% of what?
Answer: 15000
Step-by-step explanation: Step by step solution for calculating 135 is 0.9 percent of what number
We already have our first value of 135 and the second value of 0.9. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1135 = 0.9% × Y
STEP 2135 =
0.9
100
× Y
Multiplying both sides by 100 and dividing both sides of the equation by 0.9 we will arrive at:
STEP 3Y = 135 ×
100
0.9
STEP 4Y = 135 × 100 ÷ 0.9
STEP 5Y = 15000
Finally, we have found the value of Y which is 15000 and that is our answer.
You can easily calculate 135 is 0.9 percent of what number by using any regular calculator, simply enter 135 × 100 ÷ 0.9 and you will get your answer which is 15000
a bowl contains 75 balls. of these, 10 are white, 11 are red, 12 are blue, 13 are green, 14 are yellow and 15 are black. what is the smallest number of balls that can be selected from the bowl to be certain that at least one ball of every color is chosen?
We have to use pigeonhole principle to find balls from bowl. From 75 balls at least one out of 31 balls will be of black color, out of 23 balls will be red, out of 25 will be blue, out of 27 balls will be green, out of 29 will be yellow.
out of 75 balls for each ball to be chosen at least once then we have to compute each color of ball separately,
By using the pigeonhole principle's formula n(r - 1) + 1
For red ball,
N=11, k=1, [N/2]≥3
= 11(3-1)+1
= 23
Hence, out of 23 balls from 75 balls at least one will be of red color
For, blue ball
N=12, k=1, [N/2]≥3
= 12(3-1)+1
= 25
Hence, out of 25 balls from 75 balls at least one will be of blue color
For green color,
N=13, k=1, [N/2]≥3
= 13(3-1)+1
= 27
Hence, out of 27 balls from 75 balls at least one will be of green color
For yellow ball,
N=14, k=1, [N/2]≥3
= 14(3-1)+1
= 29
Hence, out of 29 balls from 75 balls at least one will be of yellow color
For black ball,
N=15, k=1, [N/2]≥3
= 15(3-1)+1
= 31
Hence, out of 31 balls from 75 balls at least one will be of black color
The pigeonhole principle states that if n items are put into m containers, where n > m, at least one container must contain more than one item. If there are k+1 or more pigeons dispersed throughout the k pigeonholes, at least one pigeonhole will have two or more pigeons. Proof. The statement's converse is that there can only be a maximum of k pigeons if each slot can only accommodate one bird.
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Select the correct answer
3/4x + 4 = 7
1. 4
2. 44/3
3. -3
4. 8
Answer:
A) x=4
Step-by-step explanation:
Answer:
1. 4
Step-by-step explanation:
3/4 x + 4 = 7 Multiply all the way through by 4 to clear the fraction
3x + 16 = 28 Subtract 16 from both sides
3x = 12 Divide both sides by 3
x = 4
height of the building is 50m. The angle from Nikko to the top of the building is 25 degrees. How far is Nikko from the Building? Draw a picture first
Answer:
107 meters
Step-by-step explanation:
You want Nikko's distance from a 50 m high building if the angle of elevation to the top is 25°.
TangentThe tangent relation tells you the acute angle in a right triangle is related to the sides by ...
Tan = Opposite/Adjacent
ApplicationIn this problem, the relation means ...
tan(25°) = building height / distance to building
Solving for the distance to the building, we get ...
distance to building = (building height)/tan(25°) = (50 m)/tan(25°)
distance to building ≈ 107.225 m
Nikko is about 107 meters from the building.
At 11:00 am, a body was found within a closed room of a mansion where the air temperature is a constant 70 degrees F. At the time of discovery, the core temperature was determined to be 85 degree F. One hour later, a second measurement showed the core temperature of the body was 80 degrees F. Assume the core temperature of the body at the time of death was 98.6 degrees F. Use Newton’s Law of Cooling to determine the time of death. Hint: Let t=0 represent 11:00 am and work backwards to 98.6 degrees F.
The time that has elapsed before the body was found is 1.5 hour
What is Newton's method of cooling ?Newton's law of cooling states that the rate of heat loss from a body is inversely related to the temperature difference between the body and its surroundings.
Given:
when time, t = 0, temperature = 98.6 ⁰F
when time, t = 1, temperature = 75⁰
when time, t = t, temperature = 80⁰
By Newton's method of cooling equation;
T(t) = [tex]T_s (T_0 - T_s)e^{kt[/tex]
T(t) = 70+ 28.6[tex]e^{kt[/tex]
Now, At the time of discovery
80 = 70+ 28.6[tex]e^{kt[/tex]
10= 28.6[tex]e^{kt[/tex]
Then, 1 hour later( t + 1) we have the second equation;
75= 70 + 28.6[tex]e^{kt[/tex]
28.6[tex]e^{kt[/tex] = 5
Now, divide equation 1 by equation 2;
2= [tex]e^{-k[/tex]
k = -0.693
The time when he dead body was discovered
10= 28.6[tex]e^{kt[/tex]
10= 28.6[tex]e^{-0.693[/tex]
-0.693t = ln (10 /28.6)
-0.693t = -1.05
t= 1.5 hour
Hence, the time that has elapsed before the body was found is 1.5 hour
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in a class of 45 student there are 12 girls what is the percentage of girls in the class?
The percentage of girls in a class are 26.67%.
What is percentage?
A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.
Given:
In a class of 45 student there are 12 girls.
We have to find the percentage of girls in the class.
Percentage of girls = (number of girls / Total number of students ) x 100
= (12 / 45) x 100
Percentage of girls = 26.6666
Percentage of girls ≈ 26.67
Hence, the percentage of girls in a class are 26.67%.
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can anyone please write this in word form.
Answer:
four x plus three divided by two
Step-by-step explanation:
circumference of a circle is 26.19. Find the diameter of the circle
0.4(20-10m) = 2.5 -2m -12.5
Answer: M=9
Step-by-step explanation:
Consider the expression (2.3x6)+(2.3x4)
Evaluate the expression. Show your work.
Answer: 23
Step-by-step explanation: To evaluate the expression (2.3x6)+(2.3x4), we can first use the order of operations to simplify the expression. Since the multiplication and division have the same precedence, we can evaluate them from left to right. Therefore, we have: (2.3x6)+(2.3x4) = (2.36)+(2.34)
Next, we can evaluate the multiplication to get: (2.36)+(2.34) = 13.8 + 9.2
Finally, we can evaluate the addition to get: 13.8 + 9.2 = 23
Therefore, the value of the expression (2.3x6)+(2.3x4) is 23.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
In the quadratic function f(x) = -x² – 5x + 12 the true statement is
The graph of the function is a parabola.The graph of the function opens downThe graph contains the point (0, 0)How to know the true statementsA quadratic equation when plotted traces a parabolic path hence the graph of the quadratic equation is said to be a parabola hence this is a true statement
When x² opens up when positive but down when negative. since the function is negative hence the curve opens down
from the attached graph the points in the graph is shown and the origin (0, 0) is inclusive
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several people form groups with eight people in each group. write an expression for the number of groups formed by p people. how many groups are formed if there are 96 people?
If 96 people divide into groups of eight, the following expression indicates that 12 groups are created.
Eight persons form groups made up of multiple people. a expression for how many groups made up of p people there are.
P = the number of groups.
12 groups out of 96
If there are 96 individuals, 12 groups are created.
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3. based on the results of this t-test, report the p value. explain what this means in context of a type 1 error.
based on the results of this t-test, report the p value. explain this means in context of a type 1 error is you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
What does p-value tell you about error?
The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis. If the p-value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
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the graph below shows the relationship between the number of hours cody works and the amount of money he earns at his job. Write a true statement about his relationship.
The true statement about his relationship is that the hours worked is directly proportional to the money earned.
What is the relationship shown in the graph?We know that a graph could be used to show the relationship between variables. This relationship can be shown by the use of the cartesian coordinates. The cartesian coordinates is directed in the x and the y plane as shown in the image in the question.
Now, we can see that the line of best fit that was drawn through the data points is point upwards. This would show us that as the number of hours worked is increasing, the money earned is also increasing.
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M inverly proportional to g^3
M=24 when g=2. 5
a) find a formula for M in term of g
b) work out the value of g when M=1/9
The answers to both the subparts using the inversely proportional property are shown:
(A) The formula will be: M = 375/g³
(B) The value of g is 15 when M = 1/9.
What do we mean by inversely proportional?When one variable decline, the others also decline in the same ratio.
When two variables move in opposite directions, one variable reduces as another increase, and the other increases as another variable lower, the variables are said to be inversely proportional.
Since M and g3 have an inverse relationship, we can say:
M = k/g^3
Assuming that g = 2.5 and that M = 24 then:
24 = k/(2.5)^3
24*(2.5)^3 = k = 375
(A) Formula for M in terms of G:
The formula will be M = 375/g³.
(B) Value of G when M = 1/9:
If M = 1/9, we get:
1/9 = 375/g^3
g^3 = 9*375
g = ∛(9*375) = 15
Therefore, the value of g is 15 when M = 1/9.
Therefore, the answers to both the subparts using the inverse proportional property are shown:
(A) The formula will be: M = 375/g³
(B) The value of g is 15 when M = 1/9.
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Hypatia has read 13 chapters of a 22-chapter book.
What percent of the chapters has she read?
Answer:
Step-by-step explanation:
13+22=35%
in the problem to the left if Tim mows 9 lawns this week, by how much will he have exceeded his goal
( Tim earns 120 plus 30 for each lawn he mows. )
PLEASE HELP
Answer:
Step-by-step explanation: 69
all the edges of a cube are expanding at a rate of 1/6 cm/sec. determine the rate of change of the volume of the cube when the edge length is 4 cm.
The volume of the cube will increase by 8 cubic centimeters per second.
Given,
The edge length of a cube is changing at a rate of 1/6 cm/sec.
We have to find the rate by which cube's volume changing when the edge length is 4 cm.
Here,
We have,
da/dt = 1/6 cm/sec
We know that, volume of cube is
V = a³
Differentiate with respect to t.
dV/dt = 3a² da/dt
Substituting da/dt = 1/6 and a = 4, we get;
dV/dt ₐ ₋ ₄ = 3 × 4² 1/6
dV/dt ₐ ₋ ₄ = 3 × 16 × 1/6
dV/dt ₐ ₋ ₄ = 16/2 = 8
Therefore,
The volume increased by 8 cubic centimeters per sec.
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The scatter plot shows the relationship between the average number of nightly customers and the number of months since a restaurant opened. The equation represents the linear model for this data. y = 5x + 120 What does the number 120 in the equation mean in this context? The restaurant has been open for 120 months. There were 120 customers per month after the restaurant was open 5 months. The number of customers per night increases by 120 each month. For every 5 months the restaurant has been open, there are 120 more customers per night. There were 120 customers per night when the restaurant opened. Number of Customers 300 270- 240- 210- L 180- ! 150- 120- Average nightly customers'
The number 120 in the equation of y = 5x + 120 mean is there were 120 customers per night when the restaurant opened.
How to read equation?For this case, the equation of y = 5x + 120 is for linear relationship.
Which is
y represent average number of nightly customer.
x represent number of months the restaurant opened.
For example for month 0 or for the first time restaurant open the nightly customer is,
y = 5(0) + 120
y = 0 + 120
y = 120
It mean the average number of nightly customer is 120 in the first time restaurant open. After month 0, in month 1 the nightly customer is increase by 5. So, total average nightly customer is 125, and so on.
Attached graph is for visualization and to make it easier to understand the equation mean.
Thus, number 120 in the equation is to represent there were 120 customers per night when restaurant opened.
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How can dilation scale factors help you identify points on a line passing through the origin given one additional point?
Answer options on the image.
The correct option for the dilation scale factor is-
The scale factor can be used by forming right triangle with the vertices at the origin, the additional Point P, and a leg along the x-axis.Explain the term dilation scale factor?The image's size will depend on the scale factor, which is used to dilate a mathematical entity (compared to the original object). An expansion happens when the scaling factor's absolute value exceeds one.Measure the distance from the dilation's center to a point just on preimage as well as the distance from the axis to a point on the final image.The following is a basic formula to determine a dilated figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.By creating a right triangle with vertices just at origin, Point P as an extra point, and a leg down the x-axis, the scaling factor can be applied.
Thus, this triangle will plot a new point, the image of P, on the line with any dilation given to it.
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Write an expression to show how to find Milan's age when Raul is 14
The expression to show how to find Milan's age when Raul is 14 is x + 6 = 14.
What is an expression to calculate the age?An expression is simply used to show the relationship between the variables in the data.. Addition, subtraction, multiplication, and division are possible mathematical operations.
Let Milan's age be x
Rauls age = x + 6
Therefore, when Raul is 14, Milan will be:
x + 6 = 14
Collect like terms
x = 14 - 6
x = 8
Milan is 8 years.
The expression is x + 6 = 14
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Complete question
Milan is 6 years younger than Raul. Write an expression to show how to find Milan's age when Raul is 14
6. A solution containing 80% chicken broth is to be mixed with water to
make 200L containing 60% chicken broth. How much of each should be
mixed?
x = amount of the 80% broth
y = amount of water with 0% broth
keeping in mind that water has no broth in it, so 0% of broth, let's plug in those percentages in decimal format to see how much each one has.
what's 80% of "x"? well (8/100) * x = 0.80x.
what's 0% of "y"? well hell is just 0.
what's 60% of 200? well anyhow is just 120.
[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{broth only}}&\stackrel{\textit{liters of}}{\textit{broth only}}\\ \cline{2-4}&\\ \textit{80\% Sol'n}&x&0.80&0.80x\\ water&y&0.00&0\\ \cline{2-4}&\\ mixture&200&0.60&120 \end{array}~\hfill \begin{cases} x + y = 200\\\\ 0.80x+0=120 \end{cases} \\\\[-0.35em] ~\dotfill\\\\[/tex]
[tex]\stackrel{\textit{using the 2nd equation}}{0.8x=120}\implies x=\cfrac{120}{0.8}\implies \boxed{x=150~liters} \\\\\\ \stackrel{\textit{using the 1st equation}}{150 + y = 200}\implies y=200-150\implies \boxed{y=50~liters}[/tex]
y=-7x-1
thank you for your time in advans
What is it you are trying to solve with the given equation? Are you graphing it? Determining the slope and y-intercept? Finding slope? Elaborate a bit more, if you could, on what you seek and I'll see what I can do to help. Tysm!
Enter the equation of the line in slope-intercept form that has a slope of -4 and passes through (0, 21).
Answer:
y = -4x + 0 or y = -4x
Step-by-step explanation:
y = mx + b
y = -4x + b
21 = -4(0) + b
21 = 0 + b
b = 0
y = -4x + 0 or y = -4x (the 0 is unnecessary to write but you could write it both ways)
Could you please give me brainliest? Thank you!
consider the following binomial experiment: a study in a certain community showed that 6% of the people suffer from insomnia. if there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia?
Using the binomial probability concept, the standard deviation of the number of people who suffer from insomnia is =24.21
What is binomial probability?
When an experiment or survey is repeated numerous times, the likelihood that the results will be SUCCESS or FAILURE is known as the binomial distribution. The prefix "bi" implies "two" or "twice," therefore the term "binomial" refers to a distribution type with two probable outcomes. A coin flip, for instance, can only result in one of two outcomes: heads or tails, and completing a test can result in either passing or failing.
standard deviation =[tex]\sqrt{n*p(1-p)}[/tex]
p = probability of success = 6% = 0.06
1 - p = 1 - 0.06 = 0.94
Sample size, n = 10400
Substituting the values into the equation :
[tex]\sqrt{10400*0.06(1-0.04)}[/tex]
[tex]\sqrt{10400*0.06(0.94)}[/tex]
[tex]\sqrt{10400*0.0564}[/tex]
[tex]\sqrt{586.56}[/tex]
= 24.21
Hence, the standard deviation is 24.21.
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Erica has some stickers in her sticker album. Each week she plans to add 9 stickers. Erica had 50 stickers after 4 weeks. Assume the relationship is linear. Find the rate of change and initial value.
Rate of change: 9
Initial value: 14
explanation:
9 x 4 = 36 (she adds 9 stickers every week, it's 4 weeks)
50 - 36 = 14 (subtract what she added to find initial value)
if the slope of a line is k, and the line passes through the points (0, k 3) and (-3 , 0), what is the value of k
Answer:
1
Step-by-step explanation:
assuming your points are (0,3) and (-3,0) you would "rise" 3 and "run" 3 to get from one point to the next on a graph, making your rise over run (aka slope) 3/3 which is equal to 1.