Both the gongs will strike together at 3 pm.
Given,
Two gongs strike at intervals 90 and 60 minutes respectively.
Use LCM to find at what time they will strike together
Using prime factorization:
LCM of (60,90)=[tex]2^2*3^2*5=4*9*5=180[/tex]
They will strike together after 180 minutes i.e. 3 hours
Hence, if they start simultaneously at 12 noon then they will strike together again at 3 pm
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Triangle - Interior Angles Find the measure of the indicated angle in each triangle. 3 27 311>P 26 A ma m2Q= 1 s 스 minta mothed
Answer: We are goinf to sovle triangle Number-03:
[tex]m\angle Q=?[/tex]We know that the sum of angles in a triangle is 180 degrees, therefore we can do the following:
[tex]\begin{gathered} m\angle Q+30+31=180^{\circ} \\ \therefore\rightarrow \\ m\angle Q=180^{\circ}-61=119^{\circ} \\ \therefore\rightarrow \\ m\angle Q=119^{\circ} \end{gathered}[/tex]This is the unknown angle that we were interested in.!
Sylvia has 9 nickles. She wants to split the money equally between herself and two friends. How much will each person receive?
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
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
1 Evaluate 0.1m + 8 – 12n when m = 30 and n = 1/4.
Answer:
8
Step-by-step explanation:
0.1(30)+8-12(0.25)
3+8-3
=8
6.f(x) = 2x + 3x +1g(x)=7X - 2x+7XFind h(x) = f(x) - gix)A.h(x) = -7% -5€ -5x-1B.h --- 5 -- |318
rearrange the terms and simplify
[tex]\begin{gathered} h(x)=-7x^3-7x^2+2x^2+3x+2x+1 \\ =-7x^3-5x^2+5x+1 \end{gathered}[/tex]The right option is A
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.
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]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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the table below shows the length of time a plumber takes on a job and price he charges. what does the y-intercept represent?
The data that represents the y-intercept in a table is always the output/result. In the given table, it shows the cost that the plumber charges after the given hours of work.
Thus, the y-intercept in the data is the total cost of repairs.
The answer is letter B.
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
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! :)
You will complete the following question on your own paper. Make sure to show ALL work including a picture you draw. He 2 A point on the ground is 50 feet from my house. The angle of elevation to the top of the house is 48º. Find the height of the house to the nearest tenth. Finis the following template: "Last Name First Name Assignment
ANSWER
The height of the house is 55.5 feet
EXPLANATION
Since this forms a right triangle, we can use the tangent of the elevation angle to the top of the house to find its height - because we know the lenght of the adjacent side and we want to know the lenght of the opposite side:
[tex]\begin{gathered} \tan 48º=\frac{h}{50} \\ h=50\tan 48º \\ h=55.53062574\approx55.5\text{ feet} \end{gathered}[/tex]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
You have $500,000 saved for retirement. Your account earns 8% interest. How much will you be able to pullout each month, if you want to be able to take withdrawals for 15 years?$
The rule of the payout annuity is
[tex]P=\frac{d(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}}[/tex]P is the initial amount
d is regular withdrawals
r is the annual rate in decimal
n is the number of periods in a year
t is the time
Since you have $500 000 saved, then
P = 500000
Since the interest is 8%, then
r = 8/100 = 0.08
Since the time is 15 years, then
t = 15
Since you want the monthly amount, then
n = 12
Substitute them in the rule to find d
[tex]\begin{gathered} 500000=\frac{d(1-(1+\frac{0.08}{12})^{-12(15)})}{\frac{0.08}{12}} \\ 500000(\frac{0.08}{12})=d(1-(\frac{151}{150})^{-180}) \\ \frac{10000}{3}=d(1-(\frac{151}{150})^{-180}) \\ \frac{\frac{10000}{3}}{(1-(\frac{151}{150})^{-180})}=d \\ 4778.260422=d \end{gathered}[/tex]Then you will be able to pull $4778.260422 each month
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]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
1. Find Each Right triangles missing length. If necessary, round to thenearest tenth,5 pointsleg =8 cm, leg= 21 cm
We have a right triangle, for which we know the two legs.
We can calculate the hypotenuse H by applying the Pythagorean theorem:
[tex]\begin{gathered} H^2=L^2_1+L^2_2=8^2+21^2=64+441=505 \\ H=\sqrt[]{505}\approx22.5 \end{gathered}[/tex]The missing length (the hypotenuse) is approximately 22.5 cm.
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
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Quadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side HI. Round your answer to the nearest tenth if necessary
we have:
[tex]\frac{HI}{DE}=\frac{IF}{EB}[/tex]so
[tex]\begin{gathered} \frac{HI}{23}=\frac{59}{14} \\ 14HI=59\cdot23 \\ 14\cdot HI=1357 \\ HI=\frac{1357}{14} \\ HI=96.9 \end{gathered}[/tex]answer: HI = 96.9
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.
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]DEF~△VXW.244FED122WXVWhat is the similarity ratio of △DEF to △VXW?Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
We are given two triangles. We notice that each corresponding angle is equal, therefore, by Angle Angle Angle (AAA) theorem the triangles are similar. This means that each corresponding side is at the same ratio. That ratio is called the similarity ratio and it is obtained by finding the quotient between any two corresponding sides, like this:
[tex]r=\frac{DF}{VW}=\frac{DE}{VX}=\frac{FE}{WX}[/tex]Where "r" is the similarity ratio. Now, we substitute the sides:
[tex]r=\frac{4}{2}=\frac{4}{2}=\frac{2}{1}=2[/tex]Therefore, the similarity ratio is 2.
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]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
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
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
Multiply4V3 * 10V12 * V6*V2Enter your answer, in simplest radical form, in the box.
Given:
[tex]4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2}[/tex]Simplify the expression.
[tex]\begin{gathered} 4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10\sqrt[]{4\times3}\cdot\sqrt[]{3\times2}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10(\sqrt[]{2^2})\sqrt[]{3}\cdot\sqrt[]{2}\cdot\sqrt[]{3}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10(2)\sqrt[]{3}\cdot2\sqrt[]{3} \\ =(4\times20\times2)(\sqrt[]{3})^2\cdot\sqrt[]{3} \\ =480\sqrt[]{3} \end{gathered}[/tex]Answer:
[tex]4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2}=480\sqrt[]{3}[/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
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: