Answer: 5.8 ft
Step-by-step explanation:
We can use the Pithagorean Theorem in this problem, in order to find the length of the rope:
[tex]h^{2}=a^{2}+b^{2}[/tex]
Where:
[tex]h[/tex] is the length of the rope (the hypotenuse of the right triangle formed by the height of the tent, the rope and the ground)
[tex]a=5 ft[/tex] is the height of the tent (one of the legs of the right triangle)
[tex]b=3 ft[/tex] is the other leg of the right triangle
Solving the equation with the given data:
[tex]h^{2}=5^{2}+3^{2}[/tex]
Finding [tex]h[/tex]:
[tex]h=\sqrt{(5 ft)^{2}+(3 ft)^{2}}[/tex]
[tex]h=\sqrt{25 ft+9 ft}[/tex]
[tex]h=5.83 ft \approx 5.8 ft[/tex] This is the total length of nylon rope
Two numbers have a sum of 1 and a product of -12. Use the quadratic equation n^2+n-12=0 to determine the 2 numbers
Answer:
4 and -3
Step-by-step explanation:
4-3=1
4(-3)=-12
The two numbers that have a sum of 1 and a product of -12 is -4 & 3
Solving quadratic equationsFrom the question, we are determine the two unknown numbers by solving the quadratic equation
The given quadratic equation is
n² + n -12 = 0
The quadratic equation can be solved as follows
n² + n -12 = 0
By factorizing
n² +4n -3n -12 = 0
n(n+4) -3(n+4) = 0
(n+4)(n-3) = 0
Then,
n+4 = 0 OR n -3 = 0
∴ n = -4 OR n = 3
Hence, the two numbers that have a sum of 1 and a product of -12 are -4 & 3
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P( 4) =
13 and Q( 4) = 8, evaluate P( 4) Q(4).
Which equation could be used to find the length of the hypotenuse?
5 ft
o 2²+5² = c²
0 2² +0²= 5²
O c²-2² = 5²
O 5²-2² = c²
Answer:
(base)² + (altitude)² = (hypotenuse) ²Therefore,
2²+5² = c² will be matched.
The equation that could be used to find the length of the hypotenuse is 2²+5² = c².
What is Pythagoras theorem?Pythagorean theorem is a fundamental relation in between the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
Given is right triangle we need to find an equation to determine the length of the hypotenuse,
To find the length of the hypotenuse of a right triangle you can use the Pythagorean theorem, that can be written as:
(base)² + (altitude)² = (hypotenuse)²
In this case, a=2, b=5 and c=c, so according to the Pythagorean theorem:
2²+5²=c²
Hence the equation that could be used to find the length of the hypotenuse is 2²+5² = c².
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Ming has two job offers, in different states. The first job (a marketing manager) earns a salary of $51,000 and there is no state income tax. The second job (a graphic designer) earns a salary of $54,000 and the state income tax rate is 6%. The government also takes out 6.2% for Social Security, 1.45% for Medicare, 15% for federal income tax. The health benefits are the same for both jobs. Which job should he take?
a. The marketing manager because it pays about $70 more each month.
b. The marketing job because it pays about $300 more each month.
d. The graphic design job because it pays about $250 more each month
10 points
Answer:
A. 1
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The other dude did have the right answer, but for an explanation, you:
1. Take the 51,000 and multiply it by 22.65% (The sum of taxes for this job). You get 39448.5. You take 39448.5 and divide it by 12 (for monthly net income) and you get 3287.375 a month.
Then you:
2. Take 54,000 and multiply it by 28.65 (the sum of taxes for this job (remember that this job has an extra tax of 6%)). You get 38529. You take 38529 and divide it by 12 (for monthly net income) and you get 3210.75 a month.
Finally:
3. You just compare the monthly net incomes and see that marketing manager job pays around 70 more dollars a month. Hope that helped!
Which product is grater than 63. it's I ready work
Answer:
Step-by-step explanation:
bruh
Answer:
I need more information
Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 litre and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.
Answer:
The diameter of the smaller can is ≅ 9.14 cm
Correct statement and question:
Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 liter and a diameter of 12 cm and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
Let's recall that:
A. The formula of the volume of a cylinder is π*r²*h, where:
r is the radius of the cylinder (half of the length of the diameter) and h, represents the height of the cylinder.
B. 1 liter = 1,000 milliliters = 1,000 cubic centimeters
Therefore, we can find the height of the larger can, this way:
V = π*r²*h
Replacing with the value we know:
d = 12 ⇒ r = 6
1,000 = 3.1416 * 6² * h
1,000 = 113.0976h
h = 1,000/113.0976
h = 8.84 cm (rounding to the next hundredth)
Now we can find the ratio of the radius to the height of the larger can to find the measures of the smaller can, this way because the cylinders are mathematically similar:
Ratio = Radius/Height
Ratio = 6/8.84
Ratio = 0.6787
It means the radius of the smaller can is 0.6787 multiplied by the value of the height of the smaller can. Let x represent the height h of the smaller can, we can write this equation to solve for x:
V = π*r²*h
Replacing with the values we know:
height = x
radius = 0.6787x
440 = π * (0.6787x)² * x
440 = 3.1416 * 0.4606x² * x
440 = 1.4471x³
x³ = 440/1.4471
x³ = 304.06
∛x = ∛304.06
x = 6.73 ⇒ height of the smaller can = 6.73 cm and radius of the smaller can = 6.73 * 0.6787 = 4.57
If radius = 4.57 cm ⇒ diameter = 2 * 4.57 = 9.14 cm
The diameter of the smaller can is ≅ 9.14 cm
The diameter of the 440 ml can is approximately 9.12 cm.
To determine the diameter of the smaller can, we use the fact that the two cans are mathematically similar. This means that their dimensions have a constant ratio, known as the scale factor.
The capacity of the larger can is 1 liter (1000 ml), and the capacity of the smaller can is 440 ml.
The scale factor for volumes is given by:
Scale Factor (Volume) = (Volume of smaller can) / (Volume of larger can) = 440 ml / 1000 ml = 0.44
Since the cans are similar, the scale factor for the linear dimensions (such as diameter) is the cube root of the volume scale factor:
Scale Factor (Diameter) = ∛(Scale Factor (Volume)) = ∛(0.44)
Using a calculator, we find:
∛(0.44) ≈ 0.76
Now, we multiply the diameter of the larger can by this scale factor to find the diameter of the smaller can:
Diameter of the smaller can = Diameter of the larger can × Scale Factor (Diameter) = 12 cm × 0.76 ≈ 9.12 cm
Therefore, the diameter of the 440 ml can is approximately 9.12 cm.
Complete question:
Two cylindrical cans are mathematically similar.
The larger can have a capacity of 1 liter and the smaller can have a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can if the diameter of the larger can is 12 cm.
The quadratic equation x^{2}-6x=12 is rewritten in the form (x+p)^2=q, where q is a constant. What is the value of p ?
Answer:
p = - 3
Step-by-step explanation:
Given
x² - 6x = 12
To obtain the required form use the method of completing the square
add ( half the coefficient of the x- term )² to both sides, thus
x² + 2(- 3)x + 9 = 12 + 9
(x - 3)² = 21
Thus p = - 3
Given the quadratic functions expressed as;
x² - 6x = 12
The value of p given the quadratic expression is -3
Complete the square at the left hand side of the equation.
Add the square of the half of coefficient of x to both sides.
coefficient of x = -6
Half of coefficient of x = -6/2 = -3
Square of the result = (-3)² = 9
Add 9 to both sides of the equation
x² - 6x + 9 = 12 + 9
Factoring the left hand side
(x-3)² = 21
Comparing the result with (x+p)² = q
The value of p wil be -3
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PLEASE HELP.
What is the value of X in the photo below? (please show work)
Value of x is 5. I remember doing this last year..
35a+45b=80
then we would do 99-80, and that gives us the value of c, 19
What must be the length of ZY in order for ZY to be tangent to circle X at point Y?
14 units
15 units
16 units
17 units
Answer:
15 unitsStep-by-step explanation:
In the image attached you can notice that line ZY is tangent at point Y.
Remember that the radius is always perpendicular to tangents, by definition, that means [tex]XY \perp ZY[/tex].
That means [tex]\triangle XYZ[/tex] is a right triangle where [tex]\angle Y = 90\°[/tex].
All these facts are deducted form having ZY as a tangent.
We know by given that
[tex]XZ=8+9=17[/tex]
[tex]XY=8[/tex], becaus it's the radius.
Using Pythagorean Theorem
[tex]17^{2} =8^{2}+ZY^{2}[/tex]
Solving for [tex]ZY[/tex]
[tex]ZY=\sqrt{17^{2} -8^{2} } \\ZY=\sqrt{289-64}\\ ZY=\sqrt{225}\\ ZY=15[/tex]
Therefore, the length of ZY must be 15 units to be tangent to circle X.
Answer:
15 units
Step-by-step explanation:
The guy above me has got it right! :D
Given: x + 2y = -6. Solve for x.
Answer:
x= −6−2y
Step-by-step explanation:
Subtract 2y from both sides of the equation x= −6−2y
Answer:-6-2y
Step-by-step explanation:
X+2y=-6
subtract 2y from both sides
X+2y-2y=-6-2y
X=-6-2y
What is the measure of Arc XY in the diagram below ?
is it 71 ?
Answer:
maybe just 41?
Step-by-step explanation:
It's asking for the small arc XY, so that would just be 41. Correct me if i'm wrong
Typically seven out of every 100 babies bom in the River Creek hospital have a birth defect, most of
them minor defects
A. What typical percentage of the babies have birth defects?
b. What typical percentage of the babies do not have birth defects?
c. About how many babies with birth defects would you expect to find in a group of 500 babies
Answer: I believe that the answer is either C or A
Step-by-step explanation:
Typically, 7% of babies born in the River Creek hospital have birth defects, which means 93% of babies do not. In a group of 500 babies, about 35 are expected to have birth defects.
Explanation:A. The typical percentage of babies having birth defects is 7%, because 7 out of every 100 is the equivalent of 7% when expressed as a percentage.
B. To find the percentage of babies that do not have birth defects is therefore 100%-7% = 93%, because the percentage of babies that have defects and those that do not should add up to 100%.
C. If you were to expect about 7% of babies to have a birth defect in a group of 500 babies, you would calculate it as: 500 x 0.07 = 35 babies. So, you would typically expect to find about 35 babies with birth defects in a group of 500 babies.
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Nerissa paid a total of $8 for 4 packs of pencils she purchased from the convenience store. Let p represent the cost of one pack of pencils.
Which equation shows an equality between two different ways of expressing the cost for all the pencils?
WILL MARK BRAINLIEST
Answer: 4*p=8
Step-by-step explanation:
You can use inverse operation to answer this equation.
write out you problem: 4 x p =8The inverse of multiplication is divisionyou do 4/4 which gives you one but the 4 will cancel itself outDo 8/4 which gives you 2under the equation write p = 2And be sure to line the p up with the p, the equal sign with the equal sign, and the 2 stays where it is ( which should be already lined up with the 8)Answer:
4*p=8
Step-by-step explanation: I took the test
Use percent to find the new amount. You may round to the
nearest whole number when necessary.
56 increased by 25%
Good morning
Answer:
70Step-by-step explanation:
56 increased by 25% = 56+25%
= 56 + 56×(25÷100)
=70
________________________________
:)
A light bulb consumes 960 watt hours per day. How many watt hours does it consume in 3 days and 18 hours
Answer:
3600
Step-by-step explanation:
960*3=2880
To find how many per hour: 960/24= 40
40*18=720
720+2880=3600
Answer:
3600 watts
Step-by-step explanation:
960 multiplied by 3 , then divide 18 by 24. Multiply 0.75 by 960, and then add 2880 and 720.
A pack of 100 recordable DVDs contains 5 defective disks. You select four disks . What is the probability of selecting at least three non-defective disks
Answer: 3% (3/100), 4% (1/25), and 5% (1/20)
Step-by-step explanation:
So, there are 100 recordable DVDs, and 5 are defective. The way you find the answer is by dividing 100 by 100, which equals one. That means you have a one percent chance to select one random DVD. But, since you need to find the probability of selecting at least three non-defective DVDs, you would need to multiply 1 by 3, 4 or 5 to get the percentages for you probability.
Final answer:
The probability of selecting at least three non-defective disks from a pack with 5 defective ones among a total of 100 is found by summing the probabilities of selecting exactly three non-defective disks plus the probability of selecting all four non-defective disks.
Explanation:
The question asks for the probability of selecting at least three non-defective disks from a pack that contains 100 recordable DVDs, with 5 being defective. To solve this, we consider the scenarios where 3 or 4 non-defective disks are chosen out of the 4 disks we pick. We will calculate these probabilities using the hypergeometric distribution, which is apt for scenarios where we have a finite population without replacement.
Calculating the Probability:
Let X represent the number of non-defective disks selected.
There are two outcomes where at least three disks are non-defective: when exactly 3 are non-defective (one is defective) or when all 4 are non-defective.
Probability of selecting 3 non-defective disks and 1 defective disk (X = 3):
P(X = 3) = [number of ways to choose 3 non-defective from 95]
imes [number of ways to choose 1 defective from 5] / [number of ways to choose 4 from 100].
Probability of selecting 4 non-defective disks (X = 4):
P(X = 4) = [number of ways to choose 4 non-defective from 95] / [number of ways to choose 4 from 100].
The total probability of selecting at least three non-defective disks is the sum of these two probabilities: P(X = 3) + P(X = 4).
6/8 bigger or less then 1/2
Answer: /2 is not greater than 6/8 and the answer to the question "Is 1/2 greater than 6/8?" is no. Note: When comparing fractions such as 1/2 and 6/8, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.
Answer:
6/8 is greater than 1/2
Step-by-step explanation:
What is the probability that 13 people have different birthdays
please help me again
Answer:
60
Step-by-step explanation:
Step 1: Solve for x
x + 3x + 2x = 180
6x / 6 = 180 / 6
x = 30
Step 2: Find the measure of angle C
Angle C = 2x
Angle C = 2(30)
Angle C = 60 degrees
Answer: 60
FGHI is a parallelogram. Find the measure of angle I.
*show your work please*
Answer:
I = 130
Step-by-step explanation:
The sum of all four angles in a four-sided closed shape will ALWAYS be equivalent to 360 degrees. Also, the opposite angles of a parallelogram will ALWAYS be equivalent. This means F = H.
To begin, the measure of F, y + 7, and the measure of H, 3y - 79, are equal. This equation looks like: y + 7 = 3y - 79
Now subtract y from both sides: 7 = 2y - 79
Add 79 to both sides: 86 = 2y
And divide both sides by 2: 43 = y
Now that you have the value of y, plug 43 into y and solve for both equations:
43 + 7 = 3(43) - 79
50 = 129 - 79
50 = 50
So now we know that the measure of angles F and H are 50. 50 + 50 is 100.
Since we know that the sum of all four sides must be equivalent to 360. subtract 100 from 360 to get the sum of the measures of angles I and G:
360 - 100 = 260
So now 260 must equal I + G. Since I and G must be equivalent, just divide 260 by 2 and you have your answer: 260/2 = 130
is this true or false
Answer:
This is false
Step-by-step explanation:
xy is one term, x+y would be two terms
Answer:
False
Step-by-step explanation:
In an algebraic expression with terms, the terms are added together. Here all you have is x multiplied by y. xy is a single term. Since no term is being added to the term xy, all you have is one term, not two.
James has 4 test scores of 82, 77, 75 and 84. What score does James need on the next test to
have an average of 80? State what x represents, state the equation, and then state the answer.
Answer:
average = sum of observations/number
80=400/5
Therefore, the sum of the scores has to equal 400.
Step-by-step explanation:
400-(82+77+75+84)=x
400-(318)=x
x=82
That is the minimum score needed.
Y2222222222222222222222222
Answer:
This is a statement not a question
You have a large beach ball that has a radius of 15 inches. What is the volume of the ball? Use 3.14 for pi.
Answer:
Therefore,
[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]
Step-by-step explanation:
Given:
Spherical Shape Ball
[tex]Radius =15\ inches[/tex]
pi = 3.14
To Find:
Volume of Ball= ?
Solution:
Formula for Volume of Sphere is given by
[tex]\textrm{Volume of Sphere}=\dfrac{4}{3}\pi (Radius)^{3}[/tex]
Substituting the given values we get
[tex]\textrm{Volume of Ball}=\dfrac{4}{3}\times 3.14\times 15^{3}=14130\ inches^{3}[/tex]
Therefore,
[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]
3. Which linear equation corresponds to the line graph?
Ay=3x
B.
y=x-2
c. y = 1/²
P. y = 2x
Answer:
Y=1/3x
Step-by-step explanation:
1) there is no y intercept as x=0 when y=0 so that rules out y=x-2
2) next, we will use the formula for slope to find the value of m
Y2-Y1/X2-X1
Where y2=-1
Y1=0
X2=-3
X1=0
So
-1-0/-3-0=-1/-3
Aka 1/3
So y=1/3x
Hope this helps!
What are the expressions?
Here we need to solve some expressions. Remember the following rules:
[tex](+)(+)=+ \\ \\ (-)(-)=+ \\ \\ (+)(-)=- \\ \\ (-)(+)=-[/tex]
Then, from the left side:
[tex]5-2\cdot 7=5-14=\boxed{-9} \\ \\ 5-2\cdot 4=5-8=\boxed{-3} \\ \\ 5-2\cdot 0=5-0=\boxed{5} \\ \\ 5-2\cdot -3=5+6=\boxed{11} \\ \\ 5-2\cdot 10=5-20=\boxed{-15} \\ \\ 5-2\cdot -8=5+16=\boxed{21} \\ \\[/tex]
from the right side:
[tex]-(-4)+3=4+3=\boxed{7} \\ \\ -(6)+3=-6+3=\boxed{-3} \\ \\ -(-8)+3=8+3=\boxed{11} \\ \\ -(-5)+3=5+3=\boxed{8} \\ \\ -(2)+3=-2+3=\boxed{1} \\ \\ -(15)+3=-15+3=\boxed{-12} \\ \\ -(-6)+3=6+3=\boxed{9}[/tex]
The following data points represent the number of
alligators in each body of water near Tom's house.
8,5, 12, 15
Find the mean absolute deviation (MAD) of the data
set.
alligators
Answer:
3.5 alligators
Step-by-step explanation:
i did khan academy
Answer:
3.5
Step-by-step explanation:
I just answered it :) it was correct btw
Which of the following lines is perpendicular
to the equation given below?
y=-2x+8
The equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.
A line is perpendicular to another line if their slopes are negative reciprocals of each other. The slope of the line y = -2x + 8 is -2, so the slope of a line perpendicular to it would be 1/2.
Of the above choices, only line (C) has a slope of 1/2. Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + b, where b is the y-intercept.
To find the value of b, we can substitute a point on the line y = -2x + 8 into the equation y = 1/2x + b. For example, the point (0, 8) lies on the line y = -2x + 8. Substituting this point into the equation y = 1/2x + b, we get:
8 = 1/2 * 0 + b
b = 8
Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.
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Find the area of the circle. 26m. Round to the nearest tenth.
Answer:
Step-by-step explanation:
A=[tex]\pi r^{2}[/tex]
A=3.14*26*26
A=2122.64
A=2122.6[tex]m^{2}[/tex]
The calculated area is 530.66 [tex]m^2[/tex], which rounds to 530.7 [tex]m^2[/tex].
To find the area of a circle with a given diameter, you first need to find the radius, which is half of the diameter. Since the diameter provided in the question is 26 meters, the radius would be 13 meters. The formula to calculate the area (A) is A = π[tex]r^2[/tex], where (pi) is approximately 3.14 and r is the radius of the circle.
Using the aforementioned radius of 13 meters, the area can be calculated as follows:
A = 3.14 x [tex](13 m)^2[/tex]= 3.14 x 169 = 530.66 [tex]m^2[/tex]
When rounded to the nearest tenth, the area of the circle is 530.7 [tex]m^2[/tex].
what is the equation of this line of best fit in slope intercept form
Option B:
Equation of the line of best fit in slope-intercept form is [tex]y=\frac{1}{2}x+1[/tex].
Solution:
Take two points on the line (0, 1) and (4, 3).
So, [tex]x_1=0, y_1=1, x_2=4, y_2=3[/tex].
Slope of the line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{3-1}{4-0}[/tex]
[tex]$m=\frac{2}{4}[/tex]
[tex]$m=\frac{1}{2}[/tex]
y-intercept means the point which crosses at y-axis.
Here the point on the y-axis is (0, 1).
y-intercept (b) = 1
Slope-intercept form:
y = mx + b
[tex]$y=\frac{1}{2}x+1[/tex]
Equation of the line of best fit in slope-intercept form is [tex]y=\frac{1}{2}x+1[/tex].
Option B is the correct answer.