A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
Answers
The distance up the building that the ladder would reach, given the ladder height and the base of the building, is 13.4 ft.
How to find the height ?To find out how far up the building the ladder reaches, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
Assuming the height that the ladder reaches is x, the formula would be:
x ² + 4 ² = 14 ²
x ² = 14 ² - 4 ²
x ² = 196 - 16
x = √ 180
x = 13. 4 ft
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Related Questions
Which problem could be solved with the expression 5 x ( 2 + 4 ) ÷ 6 ?
1. Hayden made 222 bracelets before school and 444 after school each day for 555 days. Then he split the bracelets into 666 equal groups. How many bracelets did Hayden have in each group?
2. Khai, the dog, ate 222 bones on Monday, 444 bones on Tuesday and 666 bones on Wednesday. On Thursday, she ate 555 times more bones than the other days combined. How many bones did Khai eat on Thursday?
3. Shadi is building a new back deck. He puts 222 nails and 444 screws in each board. He did this to 555 boards. How many total screws and nails did he use?
PLEASE ANSWER AS SOON AS POSSIBLE!
I know its a lot to read but I would REALLY appreciate if you could answer this with the problem numbers 1, 2, and 3. THANK YOU!
Answers
Answer:
1
Step-by-step explanation:
This is the only problem that could be answered with this equation, because you would add the bracelets he made (2+4) then times that number by the days he made them, 5, then divide by the number of groups, 6. Which equals 5 x ( 2 + 4 ) divided by 6.
I hope this helps!
What is the measure of b 35 right angle
Answers
Answer:
acute angle and angle between zero and 90 degrees right angle and 90 degree angle obtuse angle and angle between 90 and 180
Answer:
what kind of people are the best division
Paul flips a fair coin five times. In how many ways can he flip at least three tails?
Answers
Answer:
16
Step-by-step explanation:
We can use the binomial distribution formula to find the probability of flipping three coins tails, four coins tails, and five coins tails. This is because the probability of P(x=3) is going to give the same result if we had defined the entire set, counted how many had 3, and then divided that by the entire set. So we can use this to find how much % of the data set is going to have at least 3.
So the binomial distribution formula is defined as: [tex]P_x=(^n_x)p^x(1-p)^{n-x}[/tex], where n=number of trials, x=how many successes (in this case it will be 3, 4, and 5) and p=probability of success.
The binomial coefficient is defined as: [tex](^n_x)=\frac{n!}{k!(n-x)!}[/tex].
So let's define the variables.
x = 3, 4, 5 since we want to find the probability of getting at least 3. This means we want the probability of getting 3, 4, or 5 tails, and then we simply add up these probabilities.
n = 5, since Paul is flipping the coin 5 times
p = 0.5 since the probability of flipping tails is 0.50
So let's plug the information in!
[tex]P_{x\ge3} = P_3 + P_4 + P_5[/tex]
[tex]P_3=\frac{5!}{3!2!}*0.5^30.5^2 = 0.3125[/tex]
[tex]P_4=\frac{5!}{4!1!}*0.5^4*0.5^1=0.15625[/tex]
[tex]P_5 = \frac{5!}{5!0!}0.5^50.5^0 = 0.03125[/tex]
Now let's add up all these probabilities to get:
[tex]0.3125 + 0.15625 + 0.03125 = 0.5[/tex]
This means 50% of the time Paul will flip three or more tails.
To translate this to the number of ways, we need to find how many combinations there are which can generally be defined as: [tex]options^{length}[/tex] and in this case options = tails and heads so 2, and the length is 5. So we get: [tex]2^5 = 32[/tex]
Now multiply the 32 by the 0.5 and you get 16, which is the amount of ways he can flip at least three tails
Answer:
16
Step-by-step explanation:
Which expresses the correct factorization
of….? look at pic
Answers
Answer:
Option 1
Step-by-step explanation:
Find 2 numbers that multiply to give 16 and sum to give +8 :
These numbers are 4 and 4
Now split +8x into +4x and +4x and factor each part :
x²+4x+4x+16 = 0
x(x+4)+4(x+4) = 0
Keep 1 bracket and the terms outside the brackets make their own :
(x+4)(x+4) = 0
(x+4)² = 0
Therefore answer will be Option 1
Hope this helped and have a good day
(a+b)^2 = a^2 + 2ab + b^2
(x+4)^2 = x^2 + 8x + 4
need help don’t know what to do
Answers
Solve for the product of four and two thirds multiplied by seven eighths.
A. three and nineteen twenty fourths
B. four and two twenty fourths
C. four and sixteen twenty fourths
D. five and two twenty fourths
Answers
The outcome of the product is 4 + 2/24, so the correct option is B.
How to solve the product?
Here we want to solve:
(4 + 2/3)*(7/8)
Using the distributive property of the product we get:
4*(7/8) + (2/3)*(7/8)
28/8 + 14/24
Now we can multiply the first fraction by (3/3) (it does not change the fraction).
(3/3)*28/8 + 14/24
84/24 + 14/24 = 98/24
Now we can rewrite it as:
98/24 = (96/24) + (2/24) =4 + 2/24
Then the correct option is B.
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Find the domain and range of the exponential function h(x) = 125 x .
Explain your findings.
As x decreases, does h increase or decrease? Explain.
As x increases, does h increase or decrease? Explain.
Answers
The domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.
What is the domain and range of the exponential function?As with other exponential functions, it follows that the domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.
Additionally, by observation, the function has a positive variable correlation, hence;
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explian GOLDEN RATION singinficane
Answers
[tex]\large\bold\blue{ANSWER:-}[/tex]
Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
A sample of 337 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according to major ("biology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below.
Answers
Using it's concept, the relative frequency of business majors in the sample is of 0.16 = 16%.
What is a relative frequency?
A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 337 students, of which 30 + 24 = 54 students are business majors, hence the relative frequency is:
r = 54/337 = 0.16 = 16%.
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Allen is 5 feet 9 inches tall, terrel is 6 feet 2 inches tall. what is the average height
Answers
The average height is [tex]5feet[/tex] and [tex]11.5[/tex] inches if Allen is [tex]5 feet 9 inches[/tex] tall and Terrel is [tex]6 feet 2 inches[/tex] tall.
How to find the average height ?
Allen height is [tex]5feet ,9inches[/tex]
Terrel height is [tex]6feet,2inches[/tex]
And we know that [tex]1feet=12inches[/tex]
So Allen height is
[tex]=5*12+9\\=60+9\\=69 inches[/tex]
And Terrel height is
[tex]=6*12+2\\=72+2\\=74inches[/tex]
Average of the Allen and Terrel height is
[tex]\frac{69+74}{2\\} \\=143/2\\=71.5inches[/tex]
And average height in feet is [tex]5feet,11.5inches[/tex]
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Each side of a square is increasing at a rate of 5 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 9 cm2
Answers
The area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another
Let the side of a square be x.
So,
Area of square = [tex]x^{2}[/tex]
A =[tex]x^{2}[/tex]
Differentiating with respect to time we get,
dA/dt = 2x dx/dt
When area = 9 [tex]cm^{2}[/tex] the side becomes 3 cm
At x = 3cm and dx/dt = 5 cm/s (Given)
dA/dt = 2.3.5 = 30 [tex]\frac{cm^{2} }{sec}[/tex]
Thus the area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
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how much greater is 9 hundredths than 8 thousandths
Answers
9 hundredths is greater than 8 thousandths by 82 thousandths
Place valueFrom the question, we are to determine how much greater 9 hundredths is than 8 thousandths
9 hundredths = 9/100 = 0.09
8 thousandths = 8/1000 = 0.008
Then,
0.09 - 0.008 = 0.082
= 82/1000
≡ 82 thousandths
Hence, 9 hundredths is greater than 8 thousandths by 82 thousandths
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A circle with a diameter of 10 cm and a central angle of 30° is drawn below.
what is the area, to the nearest tenth of a square centimeter, of the sector formed by the 30° angle?
(A) 5.2 (B) 6.5 (C) 13.1 (D) 26.2
Answers
Answer:
B 6.5
Step-by-step explanation:
The area of a whole circle is
a = [tex]\pi[/tex][tex]r^{2}[/tex] A whole circle is 360 degrees. We only have part of a circle. We were also given the diameter and we need the radius. The radius is half of the diameter.
a = [tex]\frac{30}{360} \pi 5^{2}[/tex]
a= 6.5 rounded.
A whole circle exists 360 degrees. The radius exists half of the diameter.
[tex]$$a = (30/360) $\pi 5^2[/tex]
a = 6.5 rounded.
The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.
How to calculate the area of a circle with diameter?The diameter of the circle exists double the radius of the circle. Therefore the area of the circle formula utilizing the diameter exists equivalent to π/4 times the square of the diameter of the circle. The formula for the area of the circle, utilizing the diameter of the circle
π/4 × [tex]$$diameter^2[/tex].
Given: diameter of the circle = 10 cm
then the radius of the circle is half of the diameter
Radius of the circle = 10/2 = 5 cm
Area of circle = [tex]$$\pi $r^2[/tex]
Where r be the radius of the circle
A whole circle exists 360 degrees. The radius exists half of the diameter.
[tex]$$a = (30/360) $\pi 5^2[/tex]
simplifying the above equation we get
[tex]$$a = 25$\pi$ /$12[/tex]
a = 6.5 rounded.
The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.
Therefore, the correct answer is option (B) 6.5
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13.222.. - 1.3222.. = ??
Answers
Answer:
Answer
Answer in decimal
11.8998
The design of a building that has a square pyramid roof as a roof is shown. The cost of material for the outside of the building and for the roof
ranges from $25 per square foot to $50 per square foot. The budget for this material is $500,000. The rectangular front of the building has a
length twice as long as its height. The slant height of the roof is the same as the height of the rectangular front of the building.
What is the maximum possible length of the rectangular front of the building to the nearest foot?
feet
The maximum possible length of the rectangular front of the building is
A. 164
B. 41
C. 82
D. 29
Answers
The maximum possible length of the rectangular front of the building is 23 feet
How to determine the maximum possible length?The complete question is attached
Let the length of the rectangular front be x and the height be y.
So, we have:
x = 2y
The building has 4 congruent sides.
So, the area of the 4 sides is
A = 4 * (x * y)
This gives
A = 4 * (x * 2x)
Evaluate
A = 8x²
For the triangular roof, we have:
Slant height, l = y
Base, b = x
So, the area of the 4 triangular faces is
A = 0.5 * 4 * xy
This gives
A = 2xy
Recall that:
x = 2y
Make y the subject
y = 1/2x
So, we have:
A = 2x * 1/2x
A = x²
The cost of designing the buildings is
C = 25 * 8x² + 50 * x²
C = 200x² + 50x²
C = 250x²
This gives
250x² = 500000
Divide both sides by 250
x² = 2000
Square both sides
x = 45
Recall that:
y = 1/2x
This gives
y = 1/2 * 45
y = 23
Hence, the maximum possible length of the rectangular front of the building is 23 feet
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Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
Answers
The surface area of the composite figure is 444m²
Given a composite figure which is shown in the question.
The area of a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces. Area is the sum of the areas of the faces.
Firstly, we will find the area of front and end triangles by using the formula
Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.
Here, h=6 and b=16 and substitute these values in the formula, we get
A₁=2×(1/2)×16×6
A₁=2×8×6
A₁=96m²
Now, we will find the area of the left and right side rectangles which joined both the triangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=10 and b=5 and substitute these values in the formula, we get
A₂=2×10×5
A₂=100m²
Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=16 and b=4 and substitute these values in the formula, we get
A₃=2×16×4
A₃=128m²
Furthermore, we will find the area of the left and right side rectangles which joined by the front and end rectangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=4 and b=5 and substitute these values in the formula, we get
A₄=2×4×5
A₄=40m²
Now, we will find the area of the base of the composite figure which is rectangle.
We will find the area by using the formula Area=l×b.
here, l=16 and b=5 and substitute these values in the formula, we get
A₅=16×5
A₅=80m²
So, the surface area of the given composite figure will be
Surface area=A₁+A₂+A₃+A₄+A₅
Surface area=96m²+100m²+128m²+40m²+80m²
Surface area=444m²
Hence, the surface area of the given composite figure is 444m².
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Write an equation in the form y = m x + b for the following table:
x y
-6 -42
-4 -26
-2 -10
0 6
2 22
4 38
6 54
8 70
y= ?
Answers
Answer: y=8x+6
Step-by-step explanation:
The slope is
[tex]\frac{70-54}{8-6}=\frac{16}{2}=8[/tex]
So, the slope is 8.
Since the y-intercept is 6, the equation is y=8x+6.
Jesse ran 250 kilometers last week. How many meters did Jesse run?
Answers
Answer:
250,000 Meters
Step-by-step explanation:
1 Km = 1000 meters
250x1000= 250,000 meters
An advertising company charges $60 per half-page advertisement and $100 per full-page advertisement. michael has a budget of $1340 to purchase 15 advertisements. define a variable for each unknown. write a system of equations to represent the situation. how many half-page advertisements does michael purchase? show your work. how many full-page advertisements does michael purchase? show your work.4
Answers
The number of half page advertisements that Michael purchased is 4 while the full page advertisements is 11.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.
Let the number of half page ads be represented by h
Let the number of full page ads be represented by f.
Total number of advertisements = 15
h + f = 15 ....... (i)
h = 15 - f
Therefore, the system of equations to represent the situation will be:
60h + 100f = 1340 ........ (ii)
Put the value of h into equation (ii)
60(15 - f) + 100f = 1340
[tex]\Rightarrow[/tex] 900 - 60f + 100f = 1340
Collect like terms
100f-60f = 1340-900
[tex]\Rightarrow[/tex] 40f = 440
[tex]\Rightarrow[/tex] f = 11
The number of full-page advertisements that Michael purchased is 11.
Since h + f = 15
[tex]\Rightarrow[/tex] h + 11 = 15
[tex]\Rightarrow[/tex] h = 15 - 11
[tex]\Rightarrow[/tex] h = 4
The number of half page advertisements that Michael purchased is 5.
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Which expression does this graph illustrate?
Answers
Answer:
D
Step-by-step explanation:
The red line starts with a filled in circle that mean that the number -12 is included. The graph is saying that x can be -12 or any number above -12. The line under the > is telling you that 12 is included.
There are 120 students in class 7. it is known that 2 3 out of them like maths, out of which 35 are girls. also, out of total students, 3 5 are boys. (3) (a) what is the number of girls in the class? (b) how many students like maths? (c) how many boys like maths?
Answers
maths questions can be solved using unitary method.
Answer:
(a) The total number of girls in the class are 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths are 45
Solution:
According to the question, [tex]\frac{3}{5}[/tex] of total students are boys
number of boys = [tex]\frac{3}{5}[/tex] × 120 = 72
Also, According to the question, [tex]\frac{2}{3}[/tex] of total students like maths
number of students = [tex]\frac{2}{3}[/tex] × 120 =80
(a) The total number of girls in the class = total number of students - total number of boys
total number of girls in the class = 120 - 72 = 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths = total number of students that like maths - total number of girls that like maths
total number of boys like maths = 80 - 35 = 45
What is unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
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Zhang is constructing a loading ramp (BA) that is 4-feet high (AC). The back of the base (BC) must be 12.8 ft. How long must the entire base (BD) be?
Proportion : __________________
Front of base: __________
Total base: __________
Answers
Answer:
Step-by-step explanation:
This is a geometric means problem where the height (length AC of 4) is the geometric mean between the base BC and the base DC. The proportion is
[tex]\frac{12.8}{4} =\frac{4}{CD}[/tex] . Cross multiply to get
12.8CD = 16 and divide both sides by 12.8 to get that
CD = 1.25
That means that the length of the whole thing, BD, is
12.8 + 1.25 = 14.05
Which of the following is equal to the fraction below?
(5/9)^8
A. 8(5/9)
B. 5^8/9
C. 5/9^8
D. 5^8/9^8
Answers
Answer:
D. [tex]\displaystyle{\dfrac{5^8}{9^8}}[/tex]
Step-by-step explanation:
The law of exponent defines that:
[tex]\displaystyle{\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}}[/tex]
In word, you simplify the expression by expanding an exponent to both numerator and denominator.
So from the expression [tex]\displaystyle{\left(\dfrac{5}{9}\right)^8}[/tex], you expand the exponent 8 in both numerator and denominator then you'll end up with D choice!
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On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
Answers
The graphed function, F(x), has a value greater than 0 over the intervals (-0.7, 0.76) and (0.76, ∞) . F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞) is the correct statement [Fourth choice].
About a Graphed Function
The function graph of an object F stands for the set of all points in the plane that are (x, f(x)). The graph of f is also known as the graph of y = f. (x). The graph of an equation is thus a specific example of the graph of a function. A graphed function is a function that has been drawn out on a graph.
It is evident from the attached graph that the supplied function exceeds 0 for the following range:
-0.7 < F(x) < 0.76
And, 0.76 < F(x) < ∞
As a result, the intervals for which the given graphed function, F(x) is greater than 0 are as follows,
(-0.7, 0.76) and (0.76, ∞)
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search for research that has utilized analytical tools mentioned in the readings (i.e., single-sample ztest, t tests) and identify why that analysis was appropriate for the data.
Answers
The given analytical tools:
a. The single sample z-test analysis is appropriate for the data where the sample size is large and all data points are independent. Where the standard deviation is given(known).
b. The single sample t-test analysis is appropriate for the data where the sample size is small and the population variation or standard deviation is unknown.
What is single sample z-test analysis?This is a type of hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are given(known).
z = (X - μ)/(σ/√n)
Where X - sample mean, μ - population mean, σ - population standard deviation, and n - sample size.
Here the sample size is large and all data points are independent.
What is single sample t-test analysis?This is a type of parametric hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are not given(unknown).
t = (X - μ)/(s/√n)
Where X - sample mean, μ - population mean, s - sample standard deviation, and n - sample size.
Here the sample size is small.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y>2x + 122x + y ≤ -5
Answers
The solution to the system of inequalities is (-3.375, 1.75)
How to graph the inequalities?The system of inequalities is given as:
3y > 2x+12
2x+y ≤ -5
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(-3.375, 1.75)
Hence, the solution to the system of inequalities is (-3.375, 1.75)
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what is the slope of -3x
Answers
Answer:
The slope is -3, in a y=mx+b equation the x coefficient is the slope
Therefore -3 is the slope of -3x.
Complete the system that models the heights of the ball and the receiver’s hands over time. h = -16t² 14t h = -16t² t
Answers
Answer: The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
A quarterback throws a football toward a receiver from a height of 6 ft. The initial vertical velocity of the ball is 14 ft/s. At the same time that the ball is thrown, the receiver raises his hands to a height of 8 ft and jumps up with an initial vertical velocity of 10 ft/s.
The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8
Answer:
6
10
8
Step-by-step explanation:
A pot contains 3/4 gallon of soup.A serving is 1/16 gallon.How many servings does the pot contain?
Answers
by taking the quotient between the volume in the pot and the volume of each serving, we conclude that there are 12 servings.
How many servings does the pot contain?
The number of servings is given by the quotient between the volume in the pot and the volume of each serving, so we have:
Volume in the pot = 3/4 gallon.Volume of each serving = 1/16 gallon.N = (3/4)*/(1/16) = 12
So there are 12 servings in the pot.
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A prism with volume 244 cm³ is dilated with a factor of 4
What is the volume of the image?
Enter your exact answer, as a decimal, in the box.
cm³
Answers
Step-by-step explanation:
the volume of a 3D object is always calculated in some way by multiplying the 3 dimensions with each other.
so, if every dimension is then changed by a factor f (4 in our case), then the volume changes by f×f×f = f³, as the factor has to be included in the calculation for each dimension. and as they are multiplied with each other, so are the scaling factors in each case.
in our case the prism is dilated by the factor 4.
that means that every side length, every height, ..., each dimension is increased by the factor 4.
and therefore, the volume increases by the factor 4³ = 64.
so, the volume of the new image is
244 × 64 = 15,616 cm³
Volume changes by f × f × f = f³
Volume increases by the factor of 4³ = 64
The volume of the new image exists 244 × 64 = 15616 cm³.
What is the volume of the prism?The volume of a 3D object exists always computed in some form by multiplying the 3 dimensions by each other.
The volume changes by f × f × f = f³, as the factor, contains to be included in the calculation for each dimension and as they exist multiplied with each other, so exist the scaling factors in each case.
Here, the prism exists dilated by factor 4 which indicates that every side length, every height and each dimension exists increased by factor 4.
Volume increases by the factor of 4³ = 64
The volume of the new image exists 244 × 64 = 15,616 cm³.
To learn more about the volume of the prism refer to:
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