Which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
Answers
In general, a function f(x) means that the input is x and the output is f(x) (or simply f).
Therefore, in our case, the input is the length of the race and the outcome is the time.
The better option is Time(length), option A.Related Questions
q divided by 4 + 8q, for q=8
Answers
We have to calculate the value of the expression:
[tex]\frac{q}{4+8q}[/tex]when q = 8.
To calculate this, we replace q with its value and solve as:
[tex]\frac{q}{4+8q}=\frac{8}{4+8\cdot8}=\frac{8}{4+64}=\frac{8}{68}=\frac{2}{17}[/tex]Answer: 2/17
14. A waterway contains 10.3 milligrams of an impurity per gallon of water. How many micrograms of impurity arepresent per liter of water?
Answers
1) Gathering the data
10.3 mg of impurity per gallon of water
? μg of impurity per liter?
2) Since this is a matter of units conversion, then let's work remembering
the Metrical and Customary equivalences:
1 μg = 0.001 mg
1 gallon = 3.78 liters
3) As we have a ratio, let's write it as a ratio:
[tex]undefined[/tex]H is the circumcenter of triangle BCD, BC=18, and HD=14. Find CH.
Answers
Given that H is the circumcenter of the triangle.
It means, the length between each vertex point of the triangle and the point H is the radius of the circle.
Thus, the line DH=CH=BH are the radius of the circle.
It is given that DH=14.
Therefore CH=14.
Hence the value of CH is 14.
Find the area of the figure below. Type below. 9) 8 in 21 in 28 in B
Answers
Explanation
Step 1
to find the total area , we need to divide the figure in a rectangle plus harf circle
so, the area for a rectangle is given by:
[tex]\text{Area}_{rec\tan gle}=length\cdot width[/tex]and the area for a circle is
[tex]\text{Area}_{circle}=\pi\cdot radius^2[/tex]but, we need the area of a half circle ,so
[tex]\text{Area}_{half\text{ circle}}=\frac{Area_{circle}}{2}=\pi\cdot radius^2[/tex]so, the toal area of th figure is
[tex]Area_{figure}=Area_{rec\tan gle}+Area_{half\text{ circle}}\text{ }[/tex][tex]\begin{gathered} Area_{figure}=length\cdot width+\pi\cdot radius^2 \\ \end{gathered}[/tex]Step 2
Let
length= 28 in
width=21 in
radius = 8 in
replace and calculate
[tex]\begin{gathered} Area_{figure}=length\cdot width+\pi\cdot radius^2 \\ Area_{figure}=(28\cdot21)+\pi\cdot8^2 \\ Area_{figure}=588+64\pi \\ Area_{figure}=789.06in^2 \\ \text{rounded} \\ Area_{figure}=789\text{ square inches} \end{gathered}[/tex]I hope this helps you
The endpoints CD are given. Find the coordinates of the midpoint m. 24. C (-4, 7) and D(0,-3)
Answers
To find the coordinates of the midpoint
We will use the formula;
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2})[/tex]x₁ = -4 y₁=7 x₂ = 0 y₂=-3
substituting into the formula
Xm = x₁+x₂ /2
=-4+0 /2
=-2
Ym= y₁+ y₂ /2
=7-3 /2
=4/2
=2
The coordinates of the midpoint m are (-2, 2)
I need to find out how much money my school loans for donating 2200 pounds of clothing
Answers
Firs we need to find the equation of the line
x= clothing donations (pounds)
y= Amount earned (dollars)
We have the next points
(0,0)
(100,400)
We will calculate the slope
[tex]m=\frac{400-0}{100-0}=4[/tex]Therefore the equation is
y=4x
then if x=2200
y=4(2200)
y=8800
Teresa has a bookcase with 8 shelves. There are n books on each shelf. Using n, write an expression for the total number of books.
Answers
Answer:
8*n
Step-by-step explanation:
You solve this question by multiplying the number of shelves by the number of books to find the total number of books on the shelves.
If the carrier transmits 12 kW, what is the modulated power if modulation index is (1/√2) ?
Answers
The modulated power is 15 kW.
The modulated power is given by the formula P_T= P_C (1+ (m_a^2)/2) and is connected to the total power of the carrier signal and the modulation index.
To obtain the modulated power, substitute the values in the given equation and simplify.
Given,
Power of carrier signal (P_C) = 12 kW
= 12000 W
Modulation index ( m_a) = 1/√2
Consequently, when we change the variables in the equation, we get
P_T= P_C (1+ (m_a^2)/2)
=12000 (1+ (1/√2)^2/2)
= 12000 (1+ 1/4)
= 12000 * 5/4
= 3000*5
= 15000 W
= 15 kW
Hence, modulated power is 15 kW.
To learn more about modulated power here
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A car wheel has a radius of 35 cm.(a) What is the circumference of the wheel? Give your answer correct to 2 decimal places.(b) If the wheel rotates 100 000 times, how far does the car travel?
Answers
Explanation
(a) The formula for the circumference of a circle is as follows:
[tex]C=2\pi r[/tex]Where r is the radius of the circle. So, we have:
[tex]X=2\pi r=2\cdot3.1415\ldots\cdot35=219.9114\ldots\approx219.91[/tex]So, the circumference is approximately 219.91 cm.
(b) Assuming the wheel is always in contact and every rotation make sthe exact same length of travel, every rotation will make the car travel approximately 219.91 cm.
If the wheel rotates 100,000 times, the car will travel 100,000 times as many, so it will travel:
[tex]100,000\cdot219.91=21,991,000[/tex]So, the car will travel approximately 21,991,000 cm which is equivalente to 219.91 km.
Answer
(a) the circumference is approximately 219.91 cm
(b) the car will travel approximately 21,991,000 cm or 219,91 km.
we know,
circumference of the wheel= 2 pi r
=2*22/7*35
= 220cm (it covers 220 cm in one rotation)
Now if the wheel rotates 100000 times,
it will travel = 220* 1000000
= 220000000 cm
= 220000000/100m
=2200000m
8 Madison has two plants. She waters the spider plant every 4 days and the cactus every 6 daysShe water bo November 30. What is the next day that she will water both plants?
Answers
Two plants
Spider plant 4 days
Cactus plant 6 days
Then find when
4X = 6Y
find m.c.m (minimum common multiple) of 4 and 6
m.c.m (4,6) = 12
SO therefore, if both plants were watered November 30, then
add 12 days to Nov 30
12 days after Nov 30 = December 12
In the diagram below, FG is parallel to CD. If the length of CD is the same as the length of FE, CE = 26, and FG = 11, find the length of FE. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Answers
Answer:
The length of FE is √286 units.
Explanation:
Let the length of FE = x
Since FG is parallel to CD, then triangles EFG and ECD are similar triangles.
The ratio of the corresponding sides are:
[tex]\frac{FE}{CE}=\frac{FG}{CD}[/tex]Substitute the given values from the diagram above:
[tex]\frac{x}{26}=\frac{11}{x}[/tex]We then solve the equation for x.
[tex]\begin{gathered} \text{ Cross multiply} \\ x^2=26\times11 \\ \text{ Take the square root of both sides} \\ x=\sqrt{26\times11} \\ x=\sqrt{286} \\ \implies FE=\sqrt{286}\text{ units} \end{gathered}[/tex]The length of FE is √286 units (in simplest radical form).
Could I assistance receive some on this question it’s very confusing
Answers
We need to translate the vertex F of triangle BDF. When we translate it 2 units to the left and 4 units down, we obtain the point F'.
We know that triangle BDF has vertices B(4,3), D(6,3), and F(6,1).
The first coordinate of each point represents its x-coordinate (the distance from the y-axis). And the second coordinate of each point represents its y-coordinate (the distance from the x-axis).
So, this triangle is shown below:
Now, we need to translate the point F 2 units to the left, to obtain the redpoint below. And then translate it 4 units down, to obtain F' (the yellow point):
Therefore, the F' has coordinates:
F'(4,-3)
I’m the relationship shown by the data linear, if so, model with an equation . A. The relationship is linear;
Answers
The relation is data if the difference between every 2 x is equal and the difference between every 2 y is equal
Since:
-5 - (-7) = -5 + 7 = 2
-3 - (-5) = -3 + 5 = 2
-1 - (-3) = -1 + 3 = 2
Since:
9 - 5 = 4
13 - 9 = 4
17 - 13 = 4
Then
The difference between every 2 x is constant and the difference between every 2 y constant
Then the relation is linear
Since the form of the linear equation is
[tex]y-y_1=m(x-x_{1)}[/tex]m is the rate of change of y with respect to x (the slope of the line)
(x1, y1) is a point on the line
Let us find m
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ \Delta y=4 \\ \Delta x=2 \\ m=\frac{4}{2} \\ m=2 \end{gathered}[/tex]Since x1 = -7 and y1 = 5, then
[tex]\begin{gathered} y-5=2(x--7) \\ y-5=2(x+7) \end{gathered}[/tex]you decide to work part time at a local supermarket. The job pays $14.50 per hour and you work 24 hours per week. Your employer withhold 10% of your gross pay for federal taxes, 7.65% for FICA taxes and 3% for state taxes. Complete parts a through F
Answers
The gross pay that the employee will get is $276.14.
How to calculate the amount?The job regarding the question pays $14.50 and the person works 24 hours per week. The weekly pay will be:
= 24 × $14.50
= $348
Also, the employer withhold 10% of your gross pay for federal taxes, 7.65% for FICA taxes and 3% for state taxes. Therefore, the gross pay will be:
= Weekly pay - Federal tax - Fica tax - state tax
= $348 - (10% × $348) - (7.65% × $348) - (3% × $348)
= $348 - $34.80 - $26.62 - $10.44
= $276.14
The pay is $276.14.
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What is the probability that a student does not play on a sports team?
Answers
Answer:
P = 0.5
Explanation:
The probability can be calculated as the division of the number of students that does not play on sports team by the total number of students.
Taking into account the table, there is a total of 20 students and from those 10 does not play on a sports team. Therefore, the probability is:
P = 10/20 = 0.5
May I please get help finding the length to this. I tried many times.m but I couldn’t find answer for it
Answers
Both triangles are similar, so:
[tex]\frac{x}{3}=\frac{6}{4.5}[/tex]Solving for x:
4.5x = 3(6)
4.5x = 18
x = 4
classify given equation as rational or irrational:2 root 3 + 3 root 2 - 4 root 3 + 7 root 2
Answers
Irrational
Explanation
[tex]2\sqrt{3}+3\sqrt{2}-4\sqrt{3}+7\sqrt{2}[/tex]
Step 1
simplify
[tex]\begin{gathered} 2\sqrt{3}+3\sqrt{2}-4\sqrt{3}+7\sqrt{2} \\ \lparen2-4)\sqrt{3}+\left(3+7\right)\sqrt{2} \\ -2\sqrt{3}+4\sqrt{2} \\ \end{gathered}[/tex]Step 2
the square root of 2 is an irrational number,because there is not number such that
[tex]\sqrt{2}=\frac{a}{b}[/tex]and
The square root of 3 is an irrational number √3 cannot be expressed in the form of p/q
hence
the sum of 2 irrational numbers gives a irrational result,Sum of two irrational numbers is always irrational.
so, the answer is
Irrational
I hope this helps you
Hello. I would like help with problem. Quick answer is OK.Thank you
Answers
not continuous, 2 holes. Option A is correct
Explanations;For a function to be continuous, the left hand limit of a function must be equal to the right hand limit at the point x = a
From the graph shown you can see that the limit of the function from the left is not equal to the limit of the function from the right at x = 0. Therefore, we can conclude that there are discontinuities at x = 0.
You can also see that the function has 2 holes at (0, 0) and (0, -1).
what is the least common denominator for the two fractions 2 / 5 3 / 2
Answers
The multiples of the denominator of 2/5 is,
5,10,15,20,25....
The multiples of the denominator of 3/2 is,
2,4,6,8,10.....
Thus, the required least common denominator is 10.
use the listing method to represent the following set. picture attached
Answers
The correct option is A
{3, 4, 5, 6, ...}
Explanation:The condition given states that x is greater or equal to 3.
The only option that corresponds to this condition is:
{3, 4, 5, 6, ...}
The distance around a water fountian is 150 inches what is the distance from the edge of the fountian to the center
Answers
Answer:
The distance from the edge of the fountain to the centre is approximately 23.87 inches.
The water fountain forms a circle. The distance around the water fountain is the circumference of the circle formed.
Therefore,
circumference = 2πr
150 = 2πr
The distance from the edge of the fountain to the centre is the radius of the circle formed. Therefore,
75 = πr
r = 75 / 3.14159
r = 23.8732616287
r = 23.87 inches
The distance from the edge of the fountain to the centre is approximately 23.87 inches.
See attached pic for problem. Only need help with #2
Answers
SOLUTION
Part 1
The independent variable are the predicting varaible for which other variable are depends on. The are the x- values
Hence
The indepedent varibles is school year
The dependent variable are the responses variables. They are the y-values for which depends on othere values,
Hence
The dependent variable for the data given is
The Tution
Part 2
To find the function, we need to set up the data as given in the table below.
The years has an interval of 1 and each fees difer by 4, the to obtain the x-values we use the mid-point
[tex]x=\frac{\text{lower}+\text{higher}}{2}\text{ for each }[/tex]Hence
The data plot will be
The linear is given by the form
[tex]\begin{gathered} y=ax+b \\ \text{Where }^{} \\ a=561.043,\text{ b=-0.0000}010994 \\ \text{Hence } \\ y=561.043x-0.0000010994 \end{gathered}[/tex]THerefore
The linear regression is y = 561. 043x -0.0000010994
Then for exponenetial we have
[tex]\begin{gathered} y=e^{ax+b} \\ \text{Where } \\ a=0.0286229,b=-47.2727 \\ \text{Hence } \\ y=e^{0.029x-47.27} \end{gathered}[/tex]Hence
The exponential regression is y = e^(0.029x-47.27)
For the power represion we have
[tex]\begin{gathered} y=ab^x \\ \text{Where } \\ a=2.9495\times10^{-21,}b=1.02904 \\ \text{Hence } \\ y=2.9495\times10^{-21,}(1.02904)^x \end{gathered}[/tex]Hence
The power regression is
y= 2.9495 x 10^-21 (1.02904)ˣ
Part 3
The graoh lot for linear function is given below
The graph for the exponential plot is
The graph for the power regression plot is given below as
The circumference of a circle is 278.71m. What is the approximate area of the circle? Use 3.14 for pi. Explain how the area of a circle changes when the circumference of a circle changes ( round the final answer to the nearest whole number as needed , round all the intermediate values to the nearest thousandth as needed )
Answers
The circumference of a circle can be found through the formula:
[tex]C=2\cdot\pi\cdot r[/tex]clear the equation for the radius
[tex]r=\frac{C}{2\pi}[/tex]find the radius of the circumference
[tex]\begin{gathered} r=\frac{278.71}{2\pi} \\ r\approx44.358 \end{gathered}[/tex]find the area of the circle using the formula
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot(44.358)^2 \\ A\approx6181 \end{gathered}[/tex]In the picture, the first answer circled is the original answer of the problem. My math teacher simplified this to get the second circled answer. Could you explain how he simplified it?
Answers
We have an algebraic problem where we have to solve for "w"
[tex]3x+2k=\frac{15y}{9w-18v}[/tex]Solving for "w"
[tex]\begin{gathered} 9w-18v=\frac{15y}{3x+2k} \\ w=\frac{\frac{15y}{3x+2k}}{9}+\frac{18v}{9} \\ w=\frac{15y}{27x+18k}+2v \end{gathered}[/tex]The previous result is the solution to the problem without simplifying, the error is that you have in the image, in the denominator the factor "23x" in reality this is "27x"
Now we can simplify this by taking out the third part of the whole fractional term
For him we divide everything by 3, being the third part of 15, 27, and 18 respectively 5, 9, and 6.
[tex]w=\frac{5y}{9x+6k}+2v[/tex]Find the values of sin 0, cos 0, and tan e for the given right triangle. Give the exact values.sin 0=cos 0=tan 0=87
Answers
We can use the definition:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]Looking at the figure we can see the values:
But we don't have the hypotenuse value, we must use the Pythagorean theorem to find it
[tex]\begin{gathered} \text{hypotenuse = }\sqrt[]{7^2+8^2} \\ \\ \text{hypotenuse = }\sqrt[]{113} \end{gathered}[/tex]Now we have the hypotenuse we can find all values
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}}=\frac{8}{\sqrt[]{113}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}}=\frac{7}{\sqrt[]{113}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{8}{7} \end{gathered}[/tex]the product of a number and 3, increased by 5, is 7 less than twice the number. write an equation
Answers
Answer:
[tex]3x + 5 = 2x - 7[/tex]
The current population of a threatened animal species is 1.3 million, but it is declining with a half-life of 25 years. How many animals will be left in 35 years? in 80 years?Question content area bottom(Round to the nearest whole number as needed.)
Answers
Given:
it is given that the current population of a threatened animal species is 1.3 million, but it is declining with a half-life of 25 years.
Find:
we have to find that how many animals will be left in 35 years and in 80 years.
Explanation:
we know 1.3million = 1300000
The decay law is
[tex]P(t)=1300000\times(\frac{1}{2})^{\frac{t}{25}}[/tex]
where t is in years and p(t) is the population at time t.
Now, the number of animals left in 35 years is
[tex]\begin{gathered} P(35)=1300000\times(\frac{1}{2})^{\frac{35}{25}} \\ P(35)=1300000\times(\frac{1}{2})^{1.4} \\ P(35)=492608(by\text{ rounded to nearest whole number\rparen} \end{gathered}[/tex]Therefore, 492608 animals will be left in 30 years.
Now, the number of elements left in 80 years is
[tex]\begin{gathered} P(80)=1300000\times(\frac{1}{2})^{\frac{80}{25}} \\ P(80)=1300000\times(\frac{1}{2})^{3.2} \\ P(80)=141464(by\text{ rounded to nearest whole number\rparen} \end{gathered}[/tex]A stock is worth $28,775 and drops 33% in one day. What percent does the stock have to grow the next day to get back to $28,775
Answers
ANSWER:
49.254%
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value after it has drops by 33%, like this:
[tex]\begin{gathered} 28775-28775\cdot33\% \\ \\ 28775-28775\cdot0.33 \\ \\ 28775-9495.75=19279.25 \end{gathered}[/tex]Now, we calculate what should grow by the following equation:
[tex]\begin{gathered} 19279.25+19279.25\cdot \:x=28775\: \\ \\ x=\frac{28775\:-19279.25}{19279.25} \\ \\ x=\frac{9495.75}{19279.25} \\ \\ x=0.49254\cong49.254\% \end{gathered}[/tex]The percent that should grow is 49.254%
HELP ME PLEASE!!! Question 1Jim is planning his spring garden. He will construct a rectangular gardensurrounded by a chain link fence. The length of Jim's garden will be 8 feet morethan 3 times its width (w).(Drawing and labeling a diagram may be helpful)Part A: Write an expression in terms of w to represent the amount of chain linkfencing (the perimeter) Teeded to enclose Jim's garden.
Answers
We have a rectangular garden.
The length L is 8 feet more than 3 times its width.
3 times the width is 3w, so we will add 8 to it and equal it to the length L:
[tex]L=8+3w[/tex]The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:
[tex]\begin{gathered} P=2L+2w \\ P=2(8+3w)+2w \\ P=16+6w+2w \\ P=16+8w \end{gathered}[/tex]The perimeter has a value of P=16+8w.
We can draw the diagram as:
Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?
We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.
[tex]\begin{gathered} P=16+8w \\ 88=16+8w \\ 88-16=8w \\ 72=8w \\ w=\frac{72}{8} \\ w=9.75 \end{gathered}[/tex]The width is 9.75 feet.
If b is a positive real number and m and n are positive integers, then.A.TrueB.False
Answers
we have that
[tex](\sqrt[n]{b})^m=(b^{\frac{1}{n}})^m=b^{\frac{m}{n}}[/tex]therefore
If b is a positive real number
then
The answer is true