The m∠POS would be - 65° by the angle addition postulate and substitution postulate.
Given, m∠POQ = 19° , m∠QOR = 31° and m∠ROS = 15°
Angle Addition Postulate is the measure of the larger angle is the sum of the measures of the two smaller angles.
Substitution postulate states that a quantity may be substituted for its equality in any expression.
Then substitute the angle measurements into the resulting equation to find, m∠POS:
m∠POQ + m∠QOR = m∠POR (by angle addition)
m∠POR + m∠ROS = m∠POS (by substitution)
m∠POS = m∠POQ + m∠QOR + m∠ROS
= 19° + 31° + 15°
= 65°
Thus, the m∠POS would be - 65° by the angle addition postulate and substitution postulate.
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If 80% of a number is 288 and 95% of the same number is 342, find 15% of that
number.
Answer:54
Step-by-step explanation:
There are quicker ways to solve this but a simple and easy way to do this would be by dividing your number by the percent so 288/80 and with this, you would get your number for 1 percent or 3.6. Now you can multiply that number by the percent your need to find so 15. And 15 x 3.6 is = 54.
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
last choice
Step-by-step explanation:
trust me
Answer:
Go for the fourth option.
In a class, two out of every 10 students fails. If there are 50 students in the class, how many pass the test
Step-by-step explanation:
\(thank \: you\)
Answer:
10 students
Step-by-step explanation:
10 students=2 fail
50 students=10 fail
Hope this helps! Thanks.
19. What is the total amount to be repaid on a 1-year term
loan of $800 with an interest rate of 14%?
A. $892
B. $902
C. $912
D. $922
Answer: the answer is C $912.
Step-by-step explanation: The interest on the loan is calculated as follows:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the length of the loan in years. Substituting the given values, we get:
Interest = $800 x 0.14 x 1
Interest = $112
Therefore, the total amount to be repaid is the sum of the principal and the interest, which is:
Total amount = Principal + Interest
Total amount = $800 + $112
Total amount = $912
To find the partial Sun of this series Ev100 n=1
There two formulaes for getting the sum of a series.
If the common ratio, r < 1, we use
\(S_n=\text{ }\frac{a(1-r^n)}{1-r}\)This is to ensure that we don't get a negative term in the bracket.
As r = 1/2 in less than 1 as in our case, we apply this formula.
If otherwise, we use:
\(S_n=\text{ }\frac{a(r^n-1)}{r-1}\)Thus our answer is TRUE
Which function has the same range as \(f(x)= - 2\sqrt{x} =-3 + 8\\\)
Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].
To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).
The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.
In other words, the range of f(x) is (-∞, 5].
So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.
Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.
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What is the reciprocal of 5/4
Answer:4/5
Step-by-step explanation:
U know it's baby #####
Use the exponential regression equation that best fits the data (10,4). (12,20), (13,35), and (16,300) to estimate y when x = 15.
A 53.1
В. 97.2
C. 146.7
D. 254.8
Answer:
c 146.7
Step-by-step explanation:
cuz
Determine whether the equation is a linear equation in two variables. 5y = x - 5
Answer:
Yes
Step-by-step explanation:
start with 5y=x-5
divide both sides by 5 to get:
y= x/5 - 1
since a linear equation is represented by y=mx+b, and this can be represented in that form, this is a linear equation.
SUSTAINIBILTY COUNTS! ENERGY CHALLENGE WHAT TO DO: COMPARITIVE STUDY OF CONSECUTIVE ELECTRIC BILLS o of post summer break with all calculations.
SUSTAINIBILTY COUNTS! ENERGY CHALLENGE
WHAT TO DO: COMPARITIVE STUDY OF CONSECUTIVE ELECTRIC BILLS HOW TO DO: 1) Examine your electricity bills of pre summer break.
2) List the various electrical appliances used in your home.
3) Find out the power consumption, duration for the device in use.
Do estimate calculation of your bills as per power consumption.
4) Make an energy reduction plan and determine how far you could implement it.
5) Re – examine your electricity bill of post summer break with all calculations.
6) WRITE your reduction plan & change in the bill.
Given statement solution is :-
1) Gather your electricity bills from the period before the summer break.
2) Create a comprehensive list of all the electrical appliances used in your home.
Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.
3) Research or locate the power consumption information for each appliance.
4) Identify areas where energy consumption can be reduced, such as:
Turning off lights when not in use.
Setting air conditioner temperatures at an optimal level.
Using energy-efficient appliances.
5) After the summer break, collect your electricity bill for the corresponding period.
6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.
Provide recommendations for further improvements or adjustments to achieve even greater sustainability.
To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:
Examine your electricity bills of pre-summer break:
Gather your electricity bills from the period before the summer break.
Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.
List the various electrical appliances used in your home:
Create a comprehensive list of all the electrical appliances used in your home.
Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.
Find out the power consumption and duration for each device in use:
Research or locate the power consumption information for each appliance.
This information is typically provided on the appliance itself or in the user manual.
Note down the power rating of each device in watts (W) or kilowatts (kW).
Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).
Calculate the estimated electricity consumption and cost:
Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).
Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.
Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.
Sum up the estimated costs for all appliances to get the total estimated electricity bill.
Make an energy reduction plan and determine implementation:
Identify areas where energy consumption can be reduced, such as:
Turning off lights when not in use.
Setting air conditioner temperatures at an optimal level.
Using energy-efficient appliances.
Unplugging devices when not in use.
Determine the feasibility of implementing these energy reduction measures in your home.
Re-examine your electricity bill of post-summer break:
After the summer break, collect your electricity bill for the corresponding period.
Calculate the actual energy consumption and cost using the same method as in step 4.
Compare the actual post-summer break bill with the estimated pre-summer break bill.
Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.
Document your reduction plan and changes in the bill:
Write a report summarizing your findings and observations.
Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.
Provide recommendations for further improvements or adjustments to achieve even greater sustainability.
By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.
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If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) (a) Find the average speed over the given time intervals.
Answer:
A. (I) v = 46.42 m/s; (ii) v = 47.35 m/s; (III) v = 48.09 m/s; (iv) v = 48.26 m/s; (v) v = 58.28 m/s
B. v = 48.28 m/s
Note: the question is missing some values. The full Question is provided below:
If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.)
(a) Find the average speed over the given time intervals. (i) [1, 2] m/s (ii) [1, 1.5] m/s (iii) [1, 1.1] m/s (iv) [1, 1.01] m/s (v) [1, 1.001] m/s
(b) Estimate the speed when t = 1. m/s
Step-by-step explanation:
Height, y = 52t - 1.86t²
Velocity = ∆y/∆t = 52 - 1.86 * 2t = 52- 3.72t
A. Average velocity = (v1 + v2)/2
(i) At t = 1, 2
Average velocity = (52 - 3.72*1 + 52 -3.72*2)/2 = 46.42 m/s
(ii) At t = 1,1.5
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.5)/2 = 47.35 m/s
(iii) At t = 1,1.1
Average velocity = (52 - 3.72*1 + 52 -3.72*1.1)/2 = 48.09m/s
(iv) At to = 1, 1.01
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.01)/2 = 48.26 m/s
(iv) At t = (1, 1.001)s
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.001)/2 = 48.28 m/s
B. Speed at t = 1s
Velocity = 52 - 3.72 * 1 = 48.28 m/s
An experiment consists of rolling a special 22-sided die. All of the numbers, 1 through 22, are equally likely. Find the probability of each event. a. A 5 rolling a number greater than 10 and even. b. B 5 rolling a prime number or a number divisible by 5. c. C 5 rolling at most an 11. d. D 5 rolling a number divisible by 2 and 3.
Answer:
Below.
Step-by-step explanation:
A. There are 12 numbers greater than 10 and the even ones are 12, 14, 16, 18, 20 and 22.
So Probability = 6/22
= 3/11.
B. Prime numbers on the die are 2,3,5,7,11,13,17,19 (8) and numbers divisible by 5 are 5, 10, 15 and 20 Total 8+4 = 12.
So Probability = 12/22
= 6/11.
C. First 11 numbers:
So Probability = 11/22
= 1/2.
D. Numbers divisible by 2 and 3 are 6, 12, 18.
So Probability = 3/22.
A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and
7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:
Answer:
Cost for each pound of jelly beans: $2.75
Cost for each pound of almonds: $3.75
Step-by-step explanation:
Let J be the cost of one pound of jelly beans.
Let A be the cost of one pound of almonds.
Using the given information, we can create a system of equations.
Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:
\(\implies 3J + 5A = 27\)
Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:
\(\implies 9J + 7A = 51\)
Therefore, the system of equations is:
\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)
To solve the system of equations, multiply the first equation by 3 to create a third equation:
\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)
\(9J+15A=81\)
Subtract the second equation from the third equation to eliminate the J term.
\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)
Solve the equation for A by dividing both sides by 8:
\(\dfrac{8A}{8}=\dfrac{30}{8}\)
\(A=3.75\)
Therefore, the cost of one pound of almonds is $3.75.
Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.
Using the first equation:
\(3J+5(3.75)=27\)
\(3J+18.75=27\)
\(3J+18.75-18/75=27-18.75\)
\(3J=8.25\)
\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)
\(J=2.75\)
Therefore, the cost of one pound of jelly beans is $2.75.
Please help! I’ll also give brainliest! Thank you!
Answer: Union of two sets.
Explanation: "An element is in the union of two sets if it is in the first set, the second set, or both. The symbol we use for the union is ∪ . The word that you will often see that indicates a union is "or".
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In the figure below, C lies on AD, the measure of BAC is 65 degrees the measure of BCD is 100 degrees, and the measure of ABC is x degrees
Answer:C. 35
Step-by-step explanation:
Solve and check please i need help
Which of the following describes the best method of solving two-step equations? A. Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable. B. Apply the addition property of equality first, and then apply the multiplication property of equality to isolate the variable. C. Apply only the multiplication property of equality to isolate the variable. D. Apply only the addition property of equality to isolate the variable.
The best method of solving two-step equation is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable"
How to solve two step equationFor instance:
40 = 5(x) - 5
40 = 5x - 5
Add 5 to both sides40 + 5 = 5x
45 = 5x
x = 45/5
x = 9
Therefore, the correct answer is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable".
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1.Use the Pythagorean Theorem to find AD and DC. Then find AC using addition. Show your calculations.
Answer:
c=a2+b2=102+172≈19.72308
Step-by-step explanation:
a calculator bro its easy
A cylindrical steel pipe with a liquid is 21 cm long with radius 0, 4 cm and its hollow part is of radius 0, 1 cm. What is the volume of liquid, in litres, in the pipe? A. 9000 litres B. 9400 litres C. 9900 litres D. 10100 litres
Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.
To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.
Given:
Length of the cylindrical steel pipe (hollow part) = 21 cm
Radius of the solid cylinder = 0.4 cm
Radius of the hollow cylinder = 0.1 cm
First, let's calculate the volume of the solid cylinder (hollow part):
V1 = π × \(r1^2\) × h
V1 = π × \((0.4 cm)^2\) × 21 cm
Next, let's calculate the volume of the hollow cylinder:
V2 = π × \(r2^2\) × h
V2 = π × \((0.1 cm)^2\) × 21 cm
Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:
Volume of liquid = V1 - V2
Let's calculate these values:
V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³
V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³
Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³
To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:
Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L
Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.
Therefore, none of the options A, B, C, or D provided is the correct answer.
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Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C
How to calculate the debt using the stack methodFrom the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.
The amount of 150 dollars would then be added to the debt that has the second highest rate.
Hence the amount of debt that would be paid off first would be the first debt based on the stack method.
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Pic includes all informatin
Answer: 8squares
Step-by-step explanation:
What is 6.5555555555556 in a fraction
Answer:
59/9
explanation: just divide 59 divided by 9
Use the applet to give the square a side length of 1.3 cm. At this moment, what is the measure of the perimeter of the square (in cm) in units of the side length of the square (in cm)
Answer:
Perimeter, P = 5.2 cm
Step-by-step explanation:
Perimeter is the sum of all the sides.
All sides of a square is equal. Here, the side of a square is 1.3 cm.
The perimeter of a square is given by :
P = 4 × side
It means,
P = 4 (1.3 cm)
P = 5.2 cm
Hence, the perimeter of the square is 5.2 cm.
Work out the balance for £240 invested for 20 years at 7% per annum
Step-by-step explanation:
It depends in the type on interest
Simple Interest
PxRxT
£240 x 0.07x 3 = £50.4
£240 + £50.4 = £290.4
Compound Interest
Px(1+R)^T
£290.4 x (1 + 0.07)³ = £355.7524872= €355.76
An isosceles trapezoid has a perimeter of 108 metres. Its shorter base measures 11.5 metres and its longer base measures 28.1 metres. The two remaining sides have the same length; what is that length?
The length of one of the remaining sides is 34.20 meters.
What is the length?A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Perimeter of an isosceles trapezoid = sum of lengths of sides of a trapezoid
length of shorter base + length of longer base + (2 x legs)
108 = 11.5 + 28.1 + (2 x legs)
108 = 39.60 + (2 x legs)
108 - 39.60 = (2 x legs)
68.40 = (2 x legs)
leg = 68.40 / 2
= 34.20 meters
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Help asap please with this questions
I need this now please look into it and let me know
Adam and his dad share the cost of a meal in the ratio of 2:3.
Adam's dad pays £52.20.
What is the total cost of the meal?
RT = ___
RS = RU...Reason?
RT = ___ and Reason?
RST = RUT...Reason?
Answer:
okay i will answer but i dont see the question
Step-by-step explanation:
Solve the inequality below.
2x < 12
To solve the inequality 2x < 12, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides by 2:
2x < 12
x < 6
Therefore, the solution to the inequality is x < 6. This means that all values of x that are less than 6 satisfy the inequality. We can represent this graphically on a number line:
<=======()------6-------------->
The open circle () indicates that x cannot be equal to 6, but can be any value less than 6. The arrow indicates that the inequality is true for all values of x to the left of the open circle.
In summary, the solution to the inequality 2x < 12 is x < 6.
I'm 15 BTW
Question
New Orleans has 283 hotels with a population of 391, 006. If Atlanta was proportional to New Orleans in hotels to
population and Atlanta has a population of 498, 000, how many hotels will Atlanta have? Round to the nearest whole
number.
Is my answer correct or incorrect? True or false
Answer:
Youre correct
Step-by-step explanation:
Answer:
it is true
Step-by-step explanation: