Given
[tex]\frac{x-1}{x}=20[/tex]Solution
[tex]\begin{gathered} \frac{x-1}{x}=\frac{20}{1} \\ \text{cross multiply} \\ 1(x-1)=20(x)_{} \\ we\text{ have} \\ x-1=20x \\ \text{collect the like terms} \\ -1=20x-x \\ -1=19x \\ \text{rewrite} \\ 19x=-1 \\ \text{Divide both sides by 19} \\ \frac{19x}{19}=-\frac{1}{19} \\ \\ x=-\frac{1}{19} \end{gathered}[/tex]The final answer
[tex]x=-\frac{1}{19}[/tex]Ratio of boys to girls is 6 to 5. If there are 60 girls how many boys are there?
Given that
There are 60 girls and the ratio of boys to girls is 6:5.
Explanation -
Let the boys be b.
Then the ratio can be represented in fraction form as
[tex]\begin{gathered} \frac{b}{g}=\frac{6}{5} \\ \frac{b}{60}=\frac{6}{5} \\ b=\frac{6}{5}\times60=6\times12=72 \\ So\text{ there are 72 boys.} \end{gathered}[/tex]Hence, the final answer is 72.which of the following would be an equivalent ratio to 2:90?
Male teachers = 2
Male students = 180/2 = 90
The ratio of male teachers to male students
2:90
2/90, simplify by 2 = 1/45
3.5 feet3 feet3 feet2 feet4.5 feet
The shape in the image is a trapezium. The area of a trapezium is given by:
[tex]A_{trapezium}=\text{ }\frac{1}{2}\text{ (a + b)h}[/tex]From the image, a= 3.5 feet, b= 4.5 feet and h = 2 feet.
Thus, we have:
[tex]\begin{gathered} A_{trapezium}=\text{ }\frac{1}{2}\text{ ( 3.5 + 4.5) 2} \\ A_{trapezium}=8ft^2 \end{gathered}[/tex]Hence, the area of the figure is 8 square feet
Sylvia has 9 nickles. She wants to split the money equally between herself and two friends. How much will each person receive?
Jimmy is working at a factory where they make cars and trucks in the ratio five to four if the factory makes 100 trucks how many cars will it produce
From the basic knowledge of ratio:
cars : trucks
[tex]\begin{gathered} \frac{5}{4}\text{ = }\frac{x}{100} \\ \text{cross}-\text{ multiply,} \\ 4\text{ }\times\text{ x = 5 x 100} \\ 4x\text{ = 500} \\ \text{Divide both sides, we have:} \\ x\text{ =500/4} \\ x\text{ = 125} \end{gathered}[/tex]what is 2/13×2/4?what is 2 * 3 what is 5 * 3 hey what is the answer
if ABC is an equilateral triangle and BD = 54 inches. find the value of x round to the nearest tenth
Solution
Step 1
Draw half of the given triangle
Step 2
State a known fact of an equilateral triangle to help with the question
Since the triangle is an equilateral triangle, each angle in triangle ADC = 60 degrees
Because the sum of angles in a triagle = 180 degrees and an equilateral triangle has all sides and angles equal
Therefore each angle = 180/3 = 60 degrees
so in the triangle ABD,
Step 3
Find the value of x using a trigonometric ratio
To find the length of x, we will use the trig ratio SOH(sine, opposite, hypothenuse)
[tex]\begin{gathered} \text{Sine 60 = }\frac{opposite}{\text{hypothenuse}} \\ \text{opposite}=\text{ 54inches} \\ \text{hypothenuse = x inches} \end{gathered}[/tex]
After substitution we will have that
[tex]\begin{gathered} \sin e\text{ 60 = }\frac{54}{x} \\ \text{but sine 60 = }\frac{\sqrt[]{3}}{2} \\ \frac{\sqrt[]{3}}{2}=\frac{54}{x} \\ \sqrt[]{3}x=108 \\ x\text{ =}\frac{108}{\sqrt[]{3}} \\ x\text{ =36}\sqrt[]{3} \\ x\text{ }\approx\text{62.4 inches to the nearest tenth} \end{gathered}[/tex]Therefore, x = 62.4 inches to the nearest tenth
Solve the following inequality. Give the solution set in both interval and graph forms -8 less than or equal to 2x+4 less than or equal to 14
The given inequality is -8 less than or equal to 2x+4 less than or equal to 14. In written form, we have
- 8 ≤ 2x + 4 ≤ 14
The first step is to subtract 4 from the left and right hand sides. We have
- 8 - 4 ≤ 2x + 4 - 4 ≤ 14 - 4
- 12 ≤ 2x ≤ 10
Dividing through by 2, we have
- 6 ≤ x ≤ 5
can you help me with this assignment
The two lines are said to be parallel if thier slopes are equal
where, the slope of a line is express as:
[tex]\begin{gathered} y\text{ =m(x-a)+b} \\ \text{ m is the slope} \end{gathered}[/tex]The given expression of line : y= -2x - 1
On comparing with the general equation of line, slope is
m = (-2)
A) x + 2y =-10
Simplify the general equation of line
x+2y =-10
2y=-10-x
y= -x/2 -5
Here slope is (-1/2)
So, the lines are not parallel
B) 2x-y=4
Simplify in the general equation of line
2x-y=4
y=2x-4
Here slope is 2
So, the lines are not parallel.
C)2y-x=-6
Simplify in the general equation of line
2y - x = -6
2y = x - 6
y = x/2 - 3
Here slope is 1/2
So, the lines are not parallel.
D) 2x + y =-6
Simplify in the general equation of line
2x + y =-6
y = -6 -2x
y = -2x -6
Here slope = (-2)
So, the lines are parallel.
The equation 2x + y =-6 & y= -2x - 1 have slope = (-2)
So, the lines are parallel
Answer : D) 2x + y =-6
Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If the ellipse is placed on a large coordinate grid with its center at (0, 0), the equation x^2/2500 + y^2/8100 = 1 models the path of the track. The units are given in yards. How long is the major axis of the track? Explain how you found the distance.show the steps
Step 1
Given:
center (0,0)
the equation given should have been:
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]We need to identify the larger denominator. If it is under x, the ellipse is horizontal. If it is under y, the ellipse is vertical. 8100 is the larger denominator and is under y, therefore, the ellipse is vertical
Step 2
The general equation of an ellipse is given as;
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]h and k are the center values which are both 0.
a = length of the semi-major axis
b = length of the semi-minor axis
The given equation is;
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]which is equivalent to;
[tex]\frac{x^2}{50^2}+\frac{y^2}{90^2}=1[/tex][tex]\begin{gathered} a^2=90^2 \\ \sqrt[]{a^2}=\sqrt[]{90^2} \\ a=90\text{ yard},\text{ the semi-major ax}is \end{gathered}[/tex]The length of the major axis will thus be; 90x2=180 yards
Answer; 180 yards
SLV is a 45°-45°-90° triangle with leg SV. If SV = m, determine the length ofthe other leg and the hypotenuse.
Since angles S and L are congruent, the triangle SLV is isosceles with base SL, that means SV = LV.
Since SV = m, we have LV = m
Now, to calculate the hypotenuse, we can use Pythagorean theorem:
[tex]\begin{gathered} SL^2=SV^2+LV^2 \\ SL^2=m^2+m^2 \\ SL^2=2m^2 \\ SL=m\cdot\sqrt[]{2} \end{gathered}[/tex]When multiplying or dividingpolynomials using the Tabular Method, write the number of terms for the polynomial ax^2+bx+c
Explanation
Answer
The number of terms for the polynomial is 3
Point O is the center of this circle. What is m
If the point o is the center of the circle, then the measure of ∠CAB = 48 degrees
The point o is the center of the circle
∠COB = 96 degrees
Here we have to apply the circle theorem
The circle theorem is defined as the measure of angles joined to any point on the circumference of the circle from the same arc is equal to the one by two of the angle subtended at the center by the same arc.
Then the equation will be
∠COB = 2 × ∠CAB
Substitute the values in the equation
2 × ∠CAB = 96
∠CAB = 96 / 2
Divide the terms
∠CAB = 48 degrees
Hence, If the point o is the center of the circle, then the measure of ∠CAB = 48 degrees
Learn more about circle theorem here
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Write a linear cost function for the following situation. Identify all variables used.A ski resort charges a snowboard rental fee of $20 plus $5.50 per hour.GLEEDIdentify all variables used. Choose the correct answer below.A. C(t) represents the number of hours the snowboard was used after renting a snowboard for t dollars.B. C(t) represents the number of snowboards that can be rented for t dollars.C. C(t) represents the cost for renting t snowboards.D. C(t) represents the cost of renting a snowboard for t hours.A linear cost function for the situation is C(t) =___(Use integers or decimals for any numbers in the expression.)
GIVEN:
We are told that a ski resort charges a snowboard rental fee of $20 plus $5.50 per hour.
Required;
Select the correct option to represent the meaning of C(t).
Also, write a linear function for the situation;
Step-by-step solution;
For the rental per hour, a fee of $5.50 is charged, which means for t number of hours, the rental would be 5.50 times t or, 5.50t. Note also that a fixed rental fee of $20 is already included regardless of how many hours rental is paid. This now means the rental would be $20 plus $5.50t.
Note that the variable t represents how many hours the snowboard was rented for. Therefore, we have;
ANSWER:
Option D:
C(t) represents the cost of renting a snowboard for t hours
A linear cost function for the situation is;
[tex]C(t)=20+5.50t[/tex]A rectangular paperboard measuring 32 in long and 24 in wide has a semicircle cut out of it, as shown below.Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
We need to subtract the area of the semicircle that was cut out of the paperboard from its original area.
The original area of the paperboard was the area of a rectangle 32in long and 24 in wide:
[tex]32in\cdot24in=768in^{2}[/tex]And the area of the semicircle, noticing that its radius r is 24in/2, is given by:
[tex]\frac{\pi r^2}{2}=\frac{3.14\cdot(12in)^{2}}{2}=\frac{3.14\cdot144in^2}{2}=226.08in^2[/tex]Thus, the area of the paperboard that remains is:
[tex]768in^2-226.08in^2=(768-226.08)in^{2}=541.92in^{2}[/tex]Therefore, the answer is 541.92 in².
I solved part A of the problem I just need help solving part B
Given:
The function given is,
[tex]g(x)=0.009x-17.66[/tex]x represents the years.
Required:
The predicted increase in the temperature in the year 2011.
Explanation:
The predicted increase in the temperature in the year 2011 is given by,
[tex]\begin{gathered} g(2011)=0.009\times(2011)-17.66 \\ \Rightarrow g(2011)=0.439 \\ \Rightarrow g(2011)=0.4\degree \end{gathered}[/tex]Final Answer:
[tex]0.4\degree C[/tex]I need help to solve this I don't quite understand how to do these
Recall the definition of the sine of an angle in a right triangle:
[tex]\sin (A)=\frac{\text{Side opposite to A}}{\text{ Hypotenuse}}[/tex]In the given diagram, the length of the side opposite to the angle of 53° has a length of 10, while the length of the hypotenuse is x. Then:
[tex]\sin (53)=\frac{10}{x}[/tex]Isolate x from the equation:
[tex]x=\frac{10}{\sin (53)}[/tex]Use a calculator to find the value of the expression for x:
[tex]\begin{gathered} x=12.52135658\ldots \\ \Rightarrow x\approx12.5 \end{gathered}[/tex]write 33_88 in simplest form
Answer
33 : 88 = 3 : 8
(33/88) = (3/8)
Explanation
33 : 88
THe best way is to do this is to divide both numbers by 11
(33/11) : (88/11)
= 3 : 8
Hope this Helps!!!
Miguel and 3 of his friends went to the movies. They originally had a total of $40.00. Each boy had the same amount of money and spent $7.50 on a ticket. How much money did each boy have left after buying his ticket. Write and solve and equation.
Solution
Miguel and 3 of his friends went to the movies.
They originally had a total of $40.00.
Since each boy have the same amount, let the amount each boy have left after the ticket be m
The amount each boy have left is
[tex]4\times m=4m[/tex]Each boy spent $7.50 on a ticket, i.e
[tex]4\times7.5[/tex]The amount of money that each boy have left can be expressed as
[tex]\begin{gathered} 4m+4(7.5)=40 \\ 4(m+7.5)=40 \end{gathered}[/tex]Solving for m
[tex]\begin{gathered} 4(m+7.5)=40 \\ \text{Divide both sides by 4} \\ \frac{4(m+7.5)}{4}=\frac{40}{4} \\ m+7.5=10 \\ \text{Collect like terms} \\ m=10-7.5 \\ m=\text{ \$2.5} \end{gathered}[/tex]Hence, each boy have $2.5 left after buying his ticket.
Answer: $2.50 would be your answer!
Step-by-step explanation: $7.50 x 4 = 30
40$ - 30 = 10
10 ÷ 4 = 2.50
hope this helps! :)
y=20-4x. the volume of the box is V cm ^3 find in terms of x
b. The volume of a box is computed as follows:
[tex]V=\text{length}\cdot\text{width}\cdot\text{height}[/tex]Substituting with length = 3x, width = x, and heigth = y = 20 - 4x, we get:
[tex]\begin{gathered} V=3x\cdot x\cdot(20-4x) \\ V=3x^2(20-4x) \\ V=3x^2\cdot20-3x^2\cdot4x \\ V=60x^2-12x^3 \end{gathered}[/tex]c.
[tex]\frac{d}{dx}(x^n)=n\cdot x^{n-1}[/tex]Applying this rule to V, we get:
[tex]\begin{gathered} \frac{dV}{dx}=60\cdot2\cdot x-12\cdot3\cdot x^2 \\ \frac{dV}{dx}=120x-36x^2 \end{gathered}[/tex]complete the table of order pairsfor the given linear equationx+4y = 16x | y0 0 1
Given the equation:
[tex]x+4y=16[/tex]to find the first value, we have to make x = 0 and solve for y, then, we have the following:
[tex]\begin{gathered} x=0 \\ \Rightarrow0+4y=16 \\ \Rightarrow4y=16 \\ y=\frac{16}{4}=4 \\ y=4 \end{gathered}[/tex]then, on the first row, the value of y is 4.
For the next two, notice that we now have values for y, this means that we have y = 0 and y = 1. Solving each case for x, we get:
[tex]\begin{gathered} y=0 \\ \Rightarrow x+4(0)=16 \\ x=16 \end{gathered}[/tex]and
[tex]\begin{gathered} y=1 \\ \Rightarrow x+4(1)=16 \\ \Rightarrow x=16-4=12 \\ x=12 \end{gathered}[/tex]therefore, the table should look like this:
22) A game is played using one die. If the die is rolled and shows a 2, the player wins $8. If the die
shows any number other than 2, the player wins nothing. If there is a charge of $1 to play the
game, what is the game's expected value?
A) $0.33
B) $7.00
C)-$0.33
D) -$1
The game's expected value is (A) $0.33
How to determine the expected amount the player wins or lose?From the question, we have the following parameters that can be used in our computation:
Outcome of 2 = Win $8
Other outcomes = Win $0
A die has the following sample space
S = {1, 2, 3, 4, 5, 6}
Using the above sample space, the individual probabilities are:
P(Outcome of 2) = 1/6
P(Others) = 5/6
The expected value is calculated as
Expected value = Sum of the products of the probability and the amount win/lose
So, we have
Expected = 1/6 * 8 + 5/6 * 0
Evaluate the products
Expected = 1.33
The charge is $1
So, we have
Expected = 1.33 - 1
Evaluate
Expected = 0.33
Hence, the expected amount is $0.33
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write 2.25% as fraction to the simplest form
2.25% can also be written as 0.0225 if we divide 2.25% by 100% and we eliminate the percentages:
To make the decimal 0.0225 a fraction, we have to multiply by a number in which the decimal will be an integer:
[tex]\frac{0.0225}{1}\times\frac{10000}{10000}=\frac{225}{10000}[/tex]Simplifying the fraction obtained:
[tex]\frac{225}{10000}=\frac{9}{400}[/tex]Answer:
[tex]\frac{9}{400}[/tex]Write an equation that can be used to find what ticket prices to set in order to raise $3800.If 200 adults attended and 250 children, find the cost of an adult ticket
Variables
x: cost of an adult ticket, in dollars
y: cost of a child ticket, in dollars
If 1 adult ticket is sold, then x dollars are raised. In consequence, if 200 adult tickets are sold, then 200x dollars are raised.
Similarly, if 250 child tickets are sold, then 250y dollars are raised.
Combining these amounts and raising $3800, we get:
200x + 250y = 3800
During your morning workout you run for 20 seconds for every 3 seconds you sprint. Write a proportion that shows the relationship between the number of seconds you run, the number of seconds you sprint, and the constant of proportionality
During your morning workout you run for 20 seconds for every 3 seconds you sprint. Write a proportion that shows the relationship between the number of seconds you run, the number of seconds you sprint, and the constant of proportionality
In the part 1 we calculate the constant of proportionality
k=20/3
Remember that
y -----> the number of seconds you run
x -----> the number of seconds you sprint
so
The linear equation that represent the relationship between x and y is
y=(20/3)x
the proprtion is
y/x=20/3k=20/3Part 3
Rewrite the proportion as an equation to represent the number of seconds you run in terms of the number of seconds you sprint
the proportion is
y/x=20/3
frewrite as equation
y=(20/3)xArtemis starts his hike at an elevation of 350 feet. He descends 60 feet, ascends 135 feet, ascends 250 feet, and finally descends 128 feet. Which equation describes his final elevation in feet? 350 + 60 + 135 + 250 + 128 = 923 B 350 + (-60) + 135 + 250 + 128 803 C 350 + (-60) + 135 + 250 + (-128) = 547 D 350 + (-60) + 135 + (-250) + 128 = 303
Total 350feet
Note descend you subtract and ascend you add
350-60+135+250-128=547
The correct option is C
I need help with finding the area as 8.7 as the height and I also need to know how to check the height is 8.7
The given figure is a trapezium as two sides are parallel and two are non parallel.
The parallel sides of the trapezium are a=3 mi and b=11 mi.
The height of the trapezium is h=8.7 mi.
The expression for the area of the trapezium is,
[tex]\text{Area}=\frac{1}{2}(a+b)\times h[/tex]Substituting the known values in the above expression,
[tex]\begin{gathered} \text{Area}=\frac{1}{2}(3\text{ mi+11 mil)}\times8.7\text{ mi} \\ =\frac{14\text{ mi}}{2}\times8.7\text{ mi} \\ =7\text{ mi}\times8.7\text{ mi} \\ =60.9mi^2 \end{gathered}[/tex]Thus, the required area is 60.9 square miles.
Allied Health - A wound was measured to be 0.8 cm in length. Whaat is the greatest possible error of this measurement?
The answer is 0.05cm
Explanation
Precision = 0.1
∴ Greatest Possible Error (GPE) = 0.1/2
GPE = 0.05cm
Hence the greatest possible error of the measurement is 0.05cm
Kevala sells sodas and sundaes at his food stand. One week the number of sodas he made was 4 fewer than 5 times the number of sundaes. If he made 96 sodas, how many sundaes did he make?
hello
let sundaes be represented by x and soda by y
on this particular week, we made sodas 4 fewer than 5 times the numbers of sundaes
let's write an equation for this
[tex]y=5x-4[/tex]with this equation, we can know the numbers of sundaes he made
remember that y is representing soda and x is representing sundaes
[tex]\begin{gathered} 96=5x-4 \\ \text{solve for x} \\ \text{collect like terms} \\ 96+4=5x \\ 100=5x \\ \text{divide both sides by the coefficient of x} \\ \frac{100}{5}=\frac{5x}{5} \\ x=20 \end{gathered}[/tex]from the calculations above, Kevala made 20 sundaes and 96 soda
Convert:47.0 grams Cu = ? moles
In 1 grams of Cu there are 0.015736631731344 moles
So, for 47.0 gram Cu : Multiply 47.0 by 0.015736631731344 :
47.0 gram Cu = 47.0 x 0.015736631731344
47.0 gram Cu = 0.73962 mol
Answer : 0.73962 mol