Let us assume that the top of the femur is circular. We would calculate the cross sectional area by applying the formula,
Area = πr^2
where
π = 3.14
r = radius
Given that diameter = 2.34,
radius = diameter/2 = 2.34/2
radius = 1.17
Cross sectional area = 3.14 x 1.17^2 = 4.298 cm^2
Given that the length = 48cm,
volume = 48 x 4.298 = 206.304 cm^3
206.304 cm^3 can support 30 times the weight of the adult. Thus,
ratio of volume to weight = 30
206.305/weight = 30
206.305 = 30 x weight
weight = 206.305/30 = 6.88
If the giant is 5 times larger than the average adult, it means that
radius of the giant's bone = 5 x 1.17 = 5.85
Area = 3.14 x 5.85 = 18.369
length of femur = 48 x 5 = 240
Volume of the giant's femur = 240 x 18.369 = 4408.56
This means that 4408.56 cm^3 should support 30 times the giants weight
Thus,
Weight of the giant = 5 times the weight of the adult
Weight of the giant = 5 x 6.88 = 34.4
Dividing the volume by the weight, we have
4408.56/34.4 = 128.15
This is more than 30
Now, the ratio of the giant's weight to the normal adult's weight should be 5. We have
146.952/6.88 = 128
This means that the femur can support up to 128 tims the weight of the giant. Since it is more than 30, then, the femur could support the giant's weight.
Emaan charges a fixed amount for a bracelet, with an additional charge for each charm a customer adds to the bracelet. Write a linear function / thatEmaan can use to find the price of a bracelet.Charms 5 10 20 30Cost ($) 110 180 320 460A f(x)=2x + 100B. f(x) = 14x + 40C. f(x) = 6x + 80OD. fx)=12x + 60
ANSWER :
B. f(x) = 14x + 40
EXPLANATION :
We can let x = number of charms and y = cost as points (x, y)
Using two-point formula :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]with two points from the given, (5, 110) and (20, 320)
[tex]\begin{gathered} y-110=\frac{320-110}{20-5}(x-5) \\ y-110=14(x-5) \\ y-110=14x-70 \\ y=14x-70+110 \\ y=14x+40 \\ \text{ Change y into f\lparen x\rparen} \\ f(x)=14x+40 \end{gathered}[/tex]Jose catches the ball and throws it to first base (2, 0), choose the equation that is perpendicular to the path shown on the graph.
Perpendicular lines have opposite and inverse slopes, then if the first line has a slope "m1" the slope of the second line "m2" can be calculated by means of the following formula:
[tex]m2=-\frac{1}{m1}[/tex]In order to find the slope of the first line (the path of the ball after being hitten by Pedro), we need to find two points (x1, y1) and (x2, y2)where it goes through, so we can use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]As you can see in the graph, this line passes through the points (0, 0) and (2, 8). By replacing (0,0) and (2, 8) into the above formula, we get:
[tex]m1=\frac{8-0}{2-0}=\frac{8}{2}=4[/tex]Then, the slope of the second line would be:
[tex]m2=-\frac{1}{m1}=-\frac{1}{4}[/tex]Now that we know the slope of second the line we can formulate its slope-intercept equation, the slope-intercept equation is given like this:
y = mx + b
Where m is the slope and b is the y-intercept.
By replacing -1/4 for m, we get:
[tex]y=-\frac{1}{4}x+b[/tex]And we know that the line passes through the first base, located at (2, 0), by replacing 2 for x and 0 for y into the above equation we can solve for b to get:
[tex]\begin{gathered} y=-\frac{1}{4}x+b \\ 0=-\frac{1}{4}\times2+b \\ 0=-\frac{1}{2}+b \\ \frac{1}{2}=b \\ b=\frac{1}{2} \\ b=0.5 \end{gathered}[/tex]By replacing 0.5 into the equation of the line we get:
[tex]y=-\frac{1}{4}x+0.5[/tex]Then, option E is the correct answer
Hours Worked D. Write an equation that could be used to find y, the number of dollars Mr. David earns for working x hours.
The equation that could be used to find the amount of dollars is y = 30x
Explanation:To get he equation that could be used to find the number of dollars for working x hours, we will use the equation of line formula:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]slope formula is given as:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]To get the slope, we will pick any two points on the line:
[tex]\begin{gathered} u\sin g\text{ points (0, 0) and (3, 90)} \\ x_1=0,y_1=0,x_2=3,y_2\text{ = }90 \\ m\text{ = }\frac{90\text{ - 0}}{3-0} \\ m\text{ = 90/3 = 30} \end{gathered}[/tex]The y intercept is the value of y when x crosses the y axis.
The line starts from the origin as a result y = 0
Substitute the values:
[tex]\begin{gathered} y\text{ = 30x + 0} \\ \\ y\text{ = 30x} \end{gathered}[/tex]The equation that could be used to find the amount of dollars is y = 30x
John has twice as many arrowheads as Kathy does Terri has two fewer than Kathy altogether they have 38 arrowheads how many arrowheads does Kathy have
Given data:
The expression for the number of arrowheads John have J=2K.
The expression for the number of arrow Terri have T=K-2.
The expressionn for the total number of arrowheads is,
[tex]J+K+T=38[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 2K+K+(K-2)=38 \\ 4K=40 \\ K=10 \end{gathered}[/tex]Thus, Kathy have 10 numbers of arrowheads.
Hideki earns $23,992 annually. Find his bi-weekly gross salary.
we know that a year has aproximately 52 weeks, so it has 26 periods of two weeks.
then the bi-weekly gross salary of Hideki will be:
[tex]\frac{23,992}{26}=\frac{11,996}{13}\approx923\text{ dollars}[/tex]Joeseph Cheyenne is earning an annual salary of 24,895.He has been offered the job in the ad .How much more would he earn per month if he is paid:a.The Minimum?b.The Maximum?
Amount earned annually = 24,895
since 12 months are in 1 year'
Amount earned per month = annualy amount earned/12
Amount earned per month = 24,895/12
Amount earned per month = 2074.58
Hence the amount he will earned per month if he is paid a minimum is 2074.58
What is the value of w?
W =
PLS HELP
If f is an exponential function and f(x)=ab^x and f contains (2,3) and (4,5), the. B =
Step 1
[tex]f(x)=ab^x[/tex]when x = 2, f(2) = 3
[tex]\begin{gathered} f(2)=ab^2 \\ ab^2\text{ = 3 ------------------------------ (1)} \end{gathered}[/tex]when x = 4, f(4) = 5
[tex]\begin{gathered} f(4)=ab^4 \\ ab^4\text{ = 5 ------------------------- (2)} \end{gathered}[/tex]Step 2: Solve equations 1 and 2 simultaneously to find the value of a and b.
[tex]\begin{gathered} \text{From equation 1, make b}^2\text{ subject of relation and substitute} \\ in\text{equation 2} \end{gathered}[/tex]Therefore
[tex]\begin{gathered} \text{From ab}^2\text{ = 3} \\ b^2\text{ = }\frac{3}{a} \end{gathered}[/tex][tex]\begin{gathered} \text{From equation 2} \\ ab^4\text{ = 5} \\ a\text{ x (}\frac{3}{a})^2\text{ = 5} \\ a\text{ x }\frac{9}{a^2}\text{ = 5} \\ \frac{9}{a}\text{ = 5} \\ \text{Cross multiply} \\ 5a\text{ = 9} \\ a\text{ = }\frac{9}{5} \end{gathered}[/tex]Step 3: Substitute a in equation 1 to find the value of b.
[tex]\begin{gathered} b^2\text{ = }\frac{3}{a} \\ b^2\text{ = 3 }\frac{.}{.}\text{ a} \\ b^2\text{ = 3 }\frac{.}{.}\text{ }\frac{9}{5} \\ b^2\text{ = 3 x }\frac{5}{9} \\ b^2\text{ = }\frac{5}{3} \\ \text{b = }\sqrt[]{\frac{5}{3}} \end{gathered}[/tex]Final answer
[tex]b\text{ = }\sqrt[]{\frac{5}{3}}[/tex]Find the distance between I and J on the number line below.
The position of I on the number line is -11.
The position of J on the number line is -3.
The distance between I and J can be determined as,
[tex]\begin{gathered} IJ=-3-(-11) \\ =-3+11 \\ =8 \end{gathered}[/tex]Thus, the required distance is 8.
Point P is the center of the circle. How many points of tangency are shown?1232
The tangency point, is the only intersection of the line with the circumference. We say a line is tangent to a circle when they "touch" only at a precise spot.
In this figure, Q, R and S are the points where the line that contains them just "touches" the circle. Those are the tangency points, therefore we have 3 tangency points.
Yvette wants to have $650,000 when she retires in a year. If she currently has$600,000 to put in a 1-year CD, which APR and compounding period will allowher to reach her goal?A. An APR of 8.02%, compounded monthlyB. An APR of 8.01%, compounded dailyO C. An APR of 8.03%, compounded quarterlyO D. An APR of 8.04%, compounded semiannually
The formula for the compound interest is given as
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]To check the value for the compounding at 8.01% daily
[tex]\begin{gathered} A=600,000(1+\frac{8.01}{365000})^{365} \\ A=600000(1+0.00021945)^{365} \\ A=600000(1.00021945)^{365} \\ A=600000(1.083385881) \\ A=650,031 \end{gathered}[/tex]By compounding the value at 8.02% monthly
[tex]undefined[/tex]What is the approximate volume of the cylinder?Use 3.14 for301.44 cm150.72 cm38 cm904.32 cm226.08 cm6 cm
The formula to find the volume of a cylinder is:
[tex]\begin{gathered} V=\pi r^2h \\ \text{ Where V is the volume,} \\ \text{r is the radius and} \\ \text{h is the height of the cylinder} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} r=6\operatorname{cm} \\ h=8\operatorname{cm} \\ V=\pi r^2h \\ V=(3.14)(6\operatorname{cm})^2(8\operatorname{cm}) \\ V=(3.14)(36\operatorname{cm}^2)(8\operatorname{cm}) \\ V=904.32\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the approximate volume of the cylinder is 904.32 cubic centimeters.
Pep Boys Automotive paid $208.50 for a pickup truck bedliner. The original selling price was $291.90, but this was marked down 35%. If operating expenses are 28% of the cost, find the operating loss
The cost price is C.P.=$208.50
The original selling price is $291.90
Operating expenses are 28% of the cost.
Thus,
28% of cost=28% of 208.50=$58.38
Thus the break event point is
Break event point=208.50+58.38=$266.88
The original selling price is marked 35% down.
Thus the reduced price is
Reduced price=(100%-35%)x291.90=65%x291.90=$189.735
Thus the operating loss is given by
Operating loss=Break event point-Reduced price=266.88-189.735=$77.15
Thus the operating loss is $77.15
Your kite is stuck in a tree that is 35 feet tall. The angle your string makes with the groundis 66°. Rather than worrying about the kite, you decide to calculate how much string youhave let out. Assuming the string is held tight and makes a straight line to the ground, howmuch string have you let out?
The situation described is shown below:
The length of the string is the hypotenuse of the right triangle. Then we have that:
[tex]\begin{gathered} \sin 66=\frac{35}{s} \\ s=\frac{35}{\sin 66} \\ s=38.31 \end{gathered}[/tex]Therefore the length of the string is 38.31 ft
find initial value of the car and after 13 years
According to the given expression, the initial value is $19,900 because
[tex]V(0)=19,900(0.95)^0=19,900(1)=19,900[/tex]Then, after 13 years means t = 13.
[tex]V(13)=19,900(0.95)^{13}=10,215.51[/tex]After 13 years, the value of the car is $10,215.51.
Devin went for a bicycle ride . the graph below shows his trip. Note : distance distance is the number of kilometers from home
Given the graph in the attached image;
a.
We want to find the speed during the first four AB and the second hour BC.
Let us write out the coordinates of A,B and C on the graph;
[tex]\begin{gathered} A=(0,0) \\ B=(1,10) \\ C=(2,15) \end{gathered}[/tex]The speed for each hour is the slope of the line within that time.
So, the slope of line AB is;
[tex]\begin{gathered} m_{AB}=\frac{\Delta y}{\Delta x}=\frac{10-0}{1-0} \\ m_{AB}=10\text{ km/h} \end{gathered}[/tex]the slope of line BC is;
[tex]\begin{gathered} m_{BC}=\frac{15-10}{2-1}=\frac{5}{1} \\ m_{BC}=5\text{ km/h} \end{gathered}[/tex]Therefore, the speed at the first hour AB is;
[tex]10\text{ km/h}[/tex]The speed at the second hour BC is;
[tex]5\text{ km/h}[/tex]b.
Comparing the speed in the first hour AB to the speed in the second hour BC as calculated in question a above.
We can see that the speed in the first hour is more than the speed in the second hour.
The speed between A and B is double the speed between B and C.
Since the speed between A and B is 10 km/h and the speed between B and C is 5 km/h, so the speed between A and B is double the speed between B and C.
I am not sure how to do this can I get some help please
A car depreciates at 2.5%. If we subtract this value from 100%, we have
[tex]100-2.5=97.5[/tex]This means that every year, the car value will be 97.5% the value of the previous year. To find 97.5% of a quantity we multiply our quantity by 97.5 and divide by 100, or, written in decimals, this is the same as multiplying by 0.975. Then, every year the car depreciates, we're multiplying again by 0.975.
The starting value of the car is 50,000. After 6 years of depreciation at 2.5%, we multiplied this value by 0.975 six times, or, 0.975 to the sixth power.
[tex]50,000\times(0.975)^6=42,953.4150513\ldots\approx42,953.42[/tex]In 6 years, the value of the car will be 42,953.42.
a triangle has side lengths of 6cm,8cm and 9cmwhat would it be classified as: acute, obtuse and right
Lets draw a picture of our triangle:
A right triangle has one angle thats 90 and a corner that look like an L. Pythagorean theorem applies to this triangle.
On the other hand, obtuse triangles have one angle that's greater than 90 degrees and in acute triangles all angles are less than 90 degrees.
Its not a right triangle because If we apply Pythagorean theorem, we get
[tex]\begin{gathered} 6^2+8^2=9^2 \\ 36+64=81 \\ 100=81\text{ Its wrong!!} \end{gathered}[/tex]Therefore, we have an obtuse triangle because the angle between sides with lenght 6cm and 8cm is greater than 90 degrees.
Please help need by October 31
The triangles are similar triangles and the value of x is 5
How to determine if the triangles are similar?From the question, we have the following parameters that can be used in our computation:
Triangle 1 and triangle 2
From the figure, we can see that both triangles have the same corresponding angle measurements
This means that the triangles are similar triangles if and only if the corresponding side lengths are in proportion
For the corresponding side lengths to be in proportion, the following must be true
12 : 20 = 3 : x
Express as fracton
20/12 = x/3
Multiply both sides by 3
x = 3 * 20/12
Evaluate
x = 5
Hence, the value of x is 5
Read more about similar triangles at
https://brainly.com/question/11920446
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How to find the number of cans to fill the playground.
Given
base = 10.6 yd
height = 6.4 yd - 1.4 yd = 5 yd
Solve for the area of the parallelogram first
[tex]\begin{gathered} A=bh \\ A=(10.6\text{ yd})(5\text{ yd}) \\ A=53\text{ yd}^2 \end{gathered}[/tex]Now that we have solved for the area, divide by 4 square yards, to determine the number of cans of sealant needed.
[tex]53\div4=13.25[/tex]The result is 13.25 cans, therefore the city will be needing 14 cans in total for the treatment.
A set of equations is given below:Equation C: y = 5x + 10 Equation D: y = 5x + 2Which of the following best describes the solution to the given set of equations? (5 points)One solutionNo solutionTwo solutionsInfinitely many solutions
The system of equations:
y = 5x + 10
y = 5x + 2
Has no solutions. There are several ways to explain why. We'll give the following:
Each equation corresponds to a line of slope m = 5 (the coefficient of x) but they are not the same line because the y-intercept of the lines is different. This means we have two parallel lines and they will never meet. So there is no solution for the system.
If we equate y on both equations, we have:
5x + 10 = 5x + 2
Simplifying by 5x:
10 = 2
We obtain a false condition, the equation is false and we cannot find any solutions. If the equation were true, we would have infinitely many solutions
Answer: No solution
A fuel pump filled a semitruck with 99 gallons of fuel in 11 minutes.How many gallons of fuel were pumped per minute?
Gallons of fuel pumped
We want to know the number of gallons per minute
We just need to divide 99 gallons in 11
99 ÷ 11 = 9
Answer: They were pumped 9 gallons per minuterefer to the diagram. what is an opposite side , what is an adjacent side. what is the hypotenuse
Answer:
The hypotenuse of a right triangle is the largest side of the triangle. In triangle ABC, the hypotenuse is AB because it has the greatest length.
The adjacent side of an angle is the side that is closer to the angle, it forms the angle with the hypotenuse. For example, the adjacent side of angle A is AC because it is closer to angle A.
The opposite side is the side that is across to the angle, in this canse, the opposite side of angle A is BC.
What is the value of x in the equation shown below? 0.25x + 13 = 4(x-8)
Explanation:
To solve this first we have to eliminate the parenthesis using the distributive property in the subtraction on the right side. Also, I'll write the decimal coefficient 0.25 as a fraction 1/4:
[tex]\frac{1}{4}x+13=4x-32[/tex]Now we have to put all the x's on the same side of the equation and the numbers on the other side:
[tex]\begin{gathered} 13+32=4x-\frac{1}{4}x \\ 45=\frac{15}{4}x \end{gathered}[/tex]Now we divide both sides by 15 and multiply both sides by 4:
[tex]\begin{gathered} \frac{45}{15}\cdot4=\frac{15}{4}\cdot\frac{4}{15}\cdot x \\ 3\cdot4=x \\ 12=x \end{gathered}[/tex]Answer:
x = 12
Mrs. Fowler is wrapping up this aquarium light kit for her husband for Christmas,How much wrapping paper will she need to cover the entire surface area of thebox?The length is 7.5 inches, the width is 2 inches and the height is 3 inches.
The acquarium light kit has the shape of a rectangular prism.
Here, we are to find the area of the acquarium light kit.
To find the area, use the formula for the Area of a rectangular prism below:
[tex]A=2(wl+hl+hw)[/tex]Where
Length, l = 7.5 inches
Width, w = 2 inches
Height, h = 3 inches
Now, substitute values into the formula above.
We have:
[tex]\begin{gathered} A=2(2\ast7.5\text{ + 3}\ast7.5\text{ + 3}\ast2) \\ \\ A=2(15+22.5+6) \\ \\ A=2(43.5) \\ \\ A=87in^2 \end{gathered}[/tex]Therefore, she will need 87 inches of wrapping paper to cover the entire surface area of the box.
ANSWER:
[tex]87in^2[/tex]hi hope your doing great. God bless you for helping students making a difference. will you pls explain in detail the result. +/x 24+55--------
Ok, here we have a multiplication and unit conversion, so first we carry out the multiplication and then we convert:
If you run 14 kilometers each week, in five weeks you will have run a total of:
14
x 5
------
70 Kilometers
But if we look at it, no option says 70 kilometers, then it is necessary to pass it to meters:
1 kilometer is equal to 1000m
So 70 kilometers are equal to how many meters?
70
x1000
----------
70000 meters
So, finally we get that the correct option is option D
You have prizes to reveal! GoWhich sign makes the statement true?2/3 ? 0.66666...><=
0.6666... can be expressed as
[tex]0.\bar{6}[/tex]which means that the 6 repeats indefinitely. So, the answer is =
A circle has a radius of 2 feet. What is the area of a sector when the central angle is 15 degrees?
Hello!
First, let's calculate the area of the whole circle, using the formula:
[tex]\begin{gathered} A_{\circ}=\pi\cdot r^2 \\ A_{\circ}=3.14\cdot2^2 \\ A_{\operatorname{\circ}}=3.14\times4 \\ A_{\operatorname{\circ}}=12.56 \end{gathered}[/tex]Now, remember: the central angle is 15º, and we calculated considering 360º (whole circle). So, let's divide it, look:
[tex]\frac{360\degree}{15\degree}=24[/tex]In 360º, there are 24 sectors with 15º each. So, let's divide the obtained area by 24 to obtain the area of one sector:
[tex]\frac{12.56}{24}\cong0.52\text{ feet}^2[/tex]I need help to find the missing probability. A and B are independent.P(B)=11/20 P(A and B)= 33/80P(A)=?
Independent event
P(A and B) = P(A) x P(B)
33/80 = P(A) x11/20
p(A) = (33/80) / (11/20 )
p(A) = (33x20)/(88x11)
= 660/968 = 165/242
=0.6818
4x^2+6x=18 quadratic formula roots
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
4x² + 6x = 18
Step 02:
quadratic formula:
4x² + 6x = 18
4x² + 6x - 18 = 0
a = 4
b = 6
c = - 18
[tex]x\text{ =}\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex][tex]x\text{ =}\frac{-6\pm\sqrt{(6)^2-4(4)(-18)}}{2(4)}=\frac{-6\pm\sqrt{36+288}}{8}=\frac{-6\pm\sqrt{324}}{8}[/tex][tex]\begin{gathered} x1\text{ = }\frac{-6+18}{8}=\frac{12}{8}=\frac{3}{2} \\ \\ x2=\frac{-6-18}{8}=\frac{-24}{8}=-3 \end{gathered}[/tex]The answer is:
x1 = 3 / 2
x2 = - 3