How to find the measure of an exterior angle given the measure of the interior angle?
If you're going 80 miles per hour how long does it take to go 80 miles answer
A student has selected 8 books that she likes, but she has money only for 3 books. how many possible selections does she have?
If u lies on the same line as r and n, what terms describe the relationship the three points must have? (select all that apply.) noncollinear between the points collinear coplanar
Answer:
Collinear, coplanar, and between the points
Step-by-step explanation:
Collinear means that the points are in the same line.
Coplanar means that the points are in the same plane.
Between the points is used when three points are in the same line an you want tro express that one of them is between the others.
So those three relationships can apply for the three points.
noncollinear not apply because it means that the points don't lie in a line.
In the set of real numbers, the first number less than -3 is -4.
True
False
if x^2+14x-95=(x+a)(x+b), then the numerical value for ab is
A train fare costs £23.55
All train fares are increased by 2.8%
Work out the new fare.
[2 marks]
Answer.......
4 A savings account pays 3.6% per annum simple interest.
Heidi puts £400 into the account.
How much will she have in the account after 5 years?
[2 marks]
Answer .............
5 In one week the mass of a puppy increases from 1.8 kg to 2.25 kg
Work out the percentage increase of the mass.
[2 marks]
Answer............
To calculate an increase, multiply the original value by the percentage increase. For simple interest, use the formula Interest = Principal * Rate * Time. Percentage increase in mass can be found with the formula: [(Final mass - Initial mass) / Initial mass] * 100%. These methods result in a new train fare of £24.21, a bank balance after 5 years of £472, and a 25% increase in the puppy's mass.
Explanation:1. To work out the new fare, we first need to calculate how much the fare has increased by. 2.8% of £23.55 is found by multiplying 23.55 by 0.028, which comes out to £0.66 (rounded to the nearest penny). Adding this increase to the original fare gives us a new fare of £24.21.
2. The simple interest can be calculated using the formula Interest = Principal * Rate * Time. In this case, Heidi's investment of £400 (the principal) is earning 3.6% (the rate) in interest every year for 5 years (the time). So, the interest Heidi earns equals £400 * 3.6% * 5 = £72. Adding this to the original amount gives us £472.
3. The percentage increase in the puppy's mass is calculated as follows: [(2.25 kg - 1.8 kg) / 1.8 kg] * 100%. So, the mass has increased by 25%.
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Find the simple interest on a loan of $3,500 at 7.8% interest for 9 months
\sqrt{6} + 3 \sqrt{6}
Evaluate the expression when =m6 m2-18
Determine if the lines are parallel, perpendicular, or neither x-3y= 15 and y = -3+4
Answer:
Step-by-step explanation:
A swimming pool can be filled by either or both of two pipes of different diameters. it takes the smaller pipe twice the time that the larger pipe takes to fill the pool. if water flows through both pipes it take 213 hours to fill the pool. how long will it take the larger pipe to fill the pool? [hint: let x be the amount of the pool filled by the small pipe in one hour]
Step-by-step explanation:
Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe and V be the volume of swimming pool.
[tex]\texttt{Rate of small pipe},r_1=\frac{V}{t_1}\\\\\texttt{Rate of large pipe},r_2=\frac{V}{t_2}=\frac{V}{0.5t_1}=2r_1[/tex]
If both pipes are combined it takes 213 hours, that is
[tex]t=\frac{V}{r_1+r_2}\\\\213=\frac{V}{r_1+2r_1}\\\\V=639r_1[/tex]
Now we need to find how much time it takes to fill the pool by large pipe,
That is
[tex]t_2=\frac{V}{r_2}=\frac{639r_1}{2r_1}=319.5hours[/tex]
By large pipe only it will take 319.5 hours to fill the pool.
Angles A and B are complementary. If m/ A= 3x - 8 and m/ B = 5x + 10, whqt is the measure of each angle ? Show your work and explain the steps
1. The measure of angle A is [tex]\(22^\circ\).[/tex]
2. The measure of angle B is[tex]\(68^\circ\).[/tex]
Explanation:To find the measures of angles A and B, we can use the fact that they are complementary, meaning their measures add up to[tex]\(90^\circ\).[/tex]Let's set up an equation using the given information:
[m_A + m_B = 90]
Given that[tex]\(m_A = 3x - 8\)[/tex]and (m_B = 5x + 10), substitute these expressions into the equation:
3x - 8 + 5x + 10 = 9
Combine like terms:
8x + 2 = 90
Subtract 2 from both sides:
8x = 88
Divide by 8:
x = 11
Now that we know the value of (x), we can find the measures of angles A and B:
[tex]\[m_A = 3x - 8 = 3(11) - 8 = 33 - 8 = 25\][/tex]
[tex]\[m_B = 5x + 10 = 5(11) + 10 = 55 + 10 = 65\][/tex]
Therefore, the measure of angle A is \(25^\circ\) and the measure of angle B is [tex]\(65^\circ\).[/tex] To check, we can verify that these angles are indeed complementary:
25 + 65 = 90
So, angles A and B satisfy the condition of being complementary.
Kristin is 20 miles behind a truck that is driving 50 miles per hour. How long will it take her to catch up to the truck? How far will she go in that time
It will take Kristin 24 minutes to catch up to the truck. She will travel a distance of 20 miles in that time.
Explanation:To calculate how long it will take for Kristin to catch up to the truck, we can use the equation: time = distance / speed. Since Kristin is 20 miles behind the truck, she will need to cover a distance of 20 miles to catch up to the truck. Assuming she drives at a constant speed, we can use her speed as the truck's speed since she needs to match it to catch up.
Time to catch up = 20 miles / 50 miles per hour = 0.4 hours = 24 minutes.
In that time, Kristin will travel the same distance as the truck. So, she will go 20 miles in 24 minutes.
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If one candy bar weighs 3 ounces what is the weight of 11 candy bars
Final answer:
The weight of 11 candy bars is calculated by multiplying the weight of one candy bar, which is 3 ounces, by 11. The total weight for 11 candies is equal to 33 ounces.
Explanation:
If one candy bar weighs 3 ounces, the weight of 11 candy bars can be found by multiplying the weight of one candy bar by the number of candy bars. The calculation would be as follows:
Multiply the weight of one candy bar by the number of candy bars: 3 ounces × 11 = 33 ounces.
Therefore, the weight of 11 candy bars is equal to 33 ounces.
To convert 3.4 hours into seconds which two ratios could you multiply by
Katherine owns the trendy boutique where Clara works as a shop assistant. Deanne loves the clothes in Katherine's boutique and shops there often. Which of these three people is a consumer?
Answer:
Deanne
Step-by-step explanation:
Deanne is a consumer
Susan can run 2 city blocks per minute. she wants to run 60 blocks. how long will it take get to finish if she has already run 18 blocks?
HELP ME PLEASE
Olga deposited $1500 in a savings account that pays 7.5% interest compounded quarterly. What is the balance in her account at the beginning of the third quarter?
A. $1,590
B. $1,560
C. $1,585.97
D. $1,591.81
ok let me make one thing clear: i have put up questions like this before but i am NOT TRYING TO JUST GET ANSWERS. I legit want to learn this. It is just hard for me i guess.. so sorry if this answer seems simple to you but its not to me so if you could please explain your answer CLEARLY, in particular with "compound quarterly." please explain so i can use the principles later on. Thank you!
If Tara spends $219 a month for her car payment and she makes $3200 a month what percent of her monthly income is spent on her car payment
A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number of miles the car travels on one gallon of fuel
round miles up to 84
round gallons down to 2
and divide
84 /2 = 42 miles per gallon ( estimate)
How many ways are there to distribute six different toys to three different children such that each child gets at least one toy?
PLEASE HELP!!!
1. The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1).
Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not.
2.The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).
Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram
I need help finding v
Write the following linear equation in standard for: 2y = -8x - 18 ??
A.y = -4x - 9
B.8x + 2y = -18
C.2y + 18 = -8x
D.18 + 8x = -2y
The local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16Bikes in the bike rack’s. What expression shows the total number of empty spaces in the bike racks
"The correct expression to show the total number of empty spaces in the bike racks is [tex]\( 4 \times 15 - 16 \).[/tex]
To arrive at this expression, we start by calculating the total capacity of all the bike racks combined. Since there are 4 bike racks and each can hold 15 bikes, the total capacity is [tex]\( 4 \times 15 \).[/tex] This gives us the maximum number of bikes that can be parked in all the racks.
Next, we subtract the number of bikes that are currently parked in the racks from the total capacity. There are 16 bikes parked. Therefore, the expression to find the number of empty spaces is:
[tex]\[ \text{Total capacity} - \text{Number of bikes parked} \][/tex]
Substituting the given numbers into the expression, we get:
[tex]\[ 4 \times 15 - 16 \][/tex]
This expression represents the total number of empty spaces in the bike racks. When evaluated, it will give us the number of spaces available for additional bikes to be parked."
A 14.5-gallon gasoline tank is 3 — 4 full. how many gallons will it take to fi ll the tank?
It would take 3.625 gallons of gasoline to fill a 14.5-gallon tank that is already 3/4 full.
Explanation:The question asks how many gallons of gasoline are needed to fill a 14.5-gallon tank that is already 3/4 full. To find the amount needed to fill the tank, we first determine how much gasoline is currently in the tank by multiplying 14.5 gallons by 3/4:
14.5 gallons × 3/4 = 10.875 gallons
This means that there are 10.875 gallons of gasoline in the tank at the moment. To find out how much more gasoline is needed to fill the tank, we subtract this amount from the tank's total capacity:
14.5 gallons - 10.875 gallons = 3.625 gallons
Therefore, it would take 3.625 gallons of gasoline to fill the tank.
Find h(-1), h(0), and h(4) for the given function h(x)=-2x^2-4
what is 2.6 repeating as a fraction
A music competition on television had five elimination rounds. After each elimination, only half of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition:
x
1
2
3
4
5
f(x)
64
32
16
8
4
Compute the average rate of change of f(x) from x = 3 to x = 5 and describe what it represents
A. −6 contestants per round, and it represents the number of contestants who will reach the final round
B. −28 contestants per round, and it represents the number of contestants who will reach the final round
C. −6 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round
D. −28 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round
Answer:
The correct option is C.
Step-by-step explanation:
The given table represent the number of contestants in each round of the competition.
The average rate of change of f(x) from x = 3 to x = 5.
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
[tex]m=\frac{f(5)-f(3)}{5-3}[/tex]
[tex]m=\frac{4-16}{2}[/tex]
[tex]m=\frac{-12}{2}[/tex]
[tex]m=-6[/tex]
The average rate of change of f(x) from x = 3 to x = 5 is -6, it represents the average rate at which the number of contestants decreased from the third round to the fifth round.
Therefore option C is correct.