Final answer:
Toby will have £4867.20 in his savings account.
Explanation:
To determine how much Toby will have in his savings account after 2 years with a 4% per annum compound interest rate, we can use the formula for compound interest:
A = P(1 + r)ⁿ
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of years the money is invested.Given:
Toby's initial investment (P) is £4500.The annual interest rate (r) is 4%, or 0.04 when expressed as a decimal.The money is invested for n = 2 years.Using these values in the formula:
A = £4500(1 + 0.04)²
A = £4500(1.04)²
A = £4500(1.0816)
A = £4867.20
Therefore, Toby will have £4867.20 in his savings account after 2 years.
For this question please tell me if I'm right or wrong. If I'm wrong please correct me.
Please use the following image below in order to answer the question correctly:
Tell whether PK is best described as a radius, chord, diameter, secant, or tangent of ⊙P.
What can PK be best described as?
Please show all the work on how you got your answer.(Note: I am not asking for an explanation if you're unable to give me one. All that I am asking for is for the work to be shown so I can see how you got your answer)
Answer:
PK represents a radius. Radius only goes half way of the circle.
Answer:
B) chord
Step-by-step explanation:
N and M are two points on the circumference and the segment MN doesn't pass through the centre, so it's a chord
What is the surface area of a cylinder with base radius 4 and height 7?Either enter an exact answer in terms of \pi or use 3.14 for \piπpi and enter your answer as a decimal
Answer:
The surface area is 88*pi square units.
Step-by-step explanation:
The surface area of a cylinder is given by two times the area of the base plus the area of the sides. This is given bellow:
surface area = 2*(base area) + (side area)
base area = pi*r²
base area = pi*(4)²
base area = pi*16 = 16*pi
side area = 2*pi*r*h
side area = 2*pi*4*7
side area = 8*7*pi
side area = 56*pi
surface area = 2*(16*pi) + 56*pi
surface area = 32*pi + 56*pi
surface area = 88*pi
The surface area is 88*pi square units.
Answer:
112π cubic units
Step-by-step explanation:
The volume of a cylinder is the area of the base × height.
The area of a circle is πr to the 2nd power
So the area of the base is π × 4 to the second power = 16π
The height of the cylinder is 7, so the volume is 16π × 7 = 112π cubic units
What's the circumference
of a bicycle wheel with
a 27-inch diameter?
| Solution:
Given:
The diameter of the bicycle wheel is 27 inches.
We need to determine the circumference of the bicycle wheel.
Circumference of the bicycle wheel:
The circumference of the bicycle wheel can be determined using the formula,
[tex]C=\pi d[/tex]
where d is the diameter of the bicycle wheel.
Substituting d = 27 and π = 3.14, we have;
[tex]C=(3.14)(27)[/tex]
Multiplying, we get;
[tex]C=84.78 \ in[/tex]
Thus, the circumference of the bicycle wheel is 84.78 inches.
to display The number of female members in band class over the past five years use a
Answer:
For the 1st row its Line Graph and Changes over time.
For the 2nd Row its Bar Graph and Categorical.
Step-by-step explanation:
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
Step-by-step explanation:
x3 - 9x2 + 5x - 45
x2 (x - 9) + 5(x - 9)
(x - 9) and (x2 + 5) are the factors
Answer:
C
Step-by-step explanation:
EDGE 20-21
A certain triangle has a 30° angle in a 60° angle. Which must be a true statement about the triangle
Answer:
It is a right triangle.
Step-by-step explanation:
A right triangle is a triangle with at least one angle with 90 degrees.
We know that every triangle has 180 degrees. The other unknown angle is 180 - (30+60) = 180 - 90 = 90. That means that the other angle is 90 degrees. Therefore, it is a right triangle
We also know that in this triangle, that the square of one side plus the square of another is side is equal to the square of the hypotenuse of the triangle. (According to Pythagorean theorem)
Answer:
The second-longest side is the square root of 3 times as long as the shortest side.
Khan academy plz help me
Answer:
B is filling the tank most quickly
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
A, (7,2), the time goes slow, so it cannot be correct.
C, you can see is more lower than the other two. That means it is the slowest.
B, is going at a average rate, but faster than A and C. If you find a coordinate on B, for an example (2,2). 2 gallons in 2 minutes.
A cube has side length of 1 meter. Determine the volume of the cube. Include all of your calculations in your final answer.
Answer:
1
Step-by-step explanation:
Volume of Cube = a³
a is the length of one side of cube
Volume = a³ = 1³ =1x1x1 = 1
Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1.5 m/s, how fast is the area of the spill increasing when the radius is 30 m?
Answer:
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
Step-by-step explanation:
Derivative Rule:
[tex]\frac{d}{dx}x^n=nx^{n-1}[/tex] [tex]\frac{d}{dx}(y^n)=ny^{n-1}\frac{dy}{dx}[/tex]Given that
The radius of the oil spill increases at a rate 1.5 m/s.
i.e [tex]\frac{dr}{dt}= 1.5\ m/s[/tex]
We need to find the rate of area increase i.e [tex]\frac{dA}{dt}[/tex] .
We know,
The area of the oil spills A = [tex]\pi r^2[/tex] ( since it spreads in circular pattern)
[tex]\therefore A=\pi r^2[/tex]
Differentiating with respect to t
[tex]\frac{dA}{dt}=\pi. 2r\frac{dr}{dt}[/tex]
Plug the value of [tex]\frac{dr}{dt} =1.5 \ m/s[/tex]
[tex]\frac{dA}{dt}=\pi. 2r(3\ m/s)[/tex]
[tex]\Rightarrow \frac{dA}{dt}=6\pi r \ m/s[/tex]
Plug r= 30 m
[tex]\Rightarrow \frac{dA}{dt}=6\pi (30\ m) \ m/s[/tex]
=180 π m²/s
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
If Bill has 5 apples and eats 3 of them, how much is left.
Answer:
2 apples Follow me if u have any more request next time
Step-by-step explanation:
5-3=2
What is the difference between the measure of an arc and the arc length? Explain.
The measure of an arc is the degree/radian measure. You measure the central angle to find the measure of an arc.
The arc length is the actual length (like 2pi inches or 7 cm, etc.). You find the length of the curved part (the arc), not the straight distance between the 2 points given.
What is the range of possible sizes for side x? it is a triangle with one side having 4.0, and the other having 5.6. picture attached below, thanks in advance :)
Given:
Given that the two sides of the triangle are x, 4.0 and 5.6
We need to determine the range of possible sizes for the side x.
Range of x:
The range of x can be determined using the triangle inequality theorem.
The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".
Thus, applying the theorem, we have;
[tex]x=4.0+5.6[/tex]
[tex]x=9.6[/tex]
Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".
Thus, we have;
[tex]x=5.6-4.0[/tex]
[tex]x=1.6[/tex]
Thus, the range of possible values for x are [tex]1.6<x<9.6[/tex]
In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.
Explanation:In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.
Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.
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What is an expression to represent the equation
Answer:
8 + [tex]\frac{x}{4}[/tex]
Step-by-step explanation:
I'm assuming you want an answer to the top section of the question.
We can start with 8.
8
When a problem asks for the sum, it's looking for addition, so we use the + sign.
8 +
The problem says "a number," so let's represent that with x. Basically, x just means a number we don't know.
8 + x
The "number" is divided by 4, so we'll just put x/4 as our second term.
8 + [tex]\frac{x}{4}[/tex]
The number of hours of daylight y for day x (x = 1 to 365) in Anchorage, Alaska, can be modeled by y=7.0sin(2π365x−1.4)+12.4. What is the minimum number of hours of daylight in Anchorage?
Answer:
5.4 hours
Step-by-step explanation:
As the number of hours of daylight y is modeled as a function of sin, and sin has the minimum value of -1. Therefore
[tex]sin(2\pi 365x-1.4) \geq -1[/tex]
[tex]7sin(2\pi 365x-1.4) \geq -7[/tex]
[tex]7.0sin(2\pi 365x-1.4)+12.4 \geq 5.4[/tex]
[tex]y \geq 5.4[/tex]
So the minimum number of hours of daylight in Anchorage is 5.4 hours
Final answer:
The minimum number of hours of daylight in Anchorage, Alaska, can be found using the equation provided. By considering the minimum value of the sine function, we determine that Anchorage experiences a minimum of 5.4 hours of daylight.
Explanation:
The minimum number of hours of daylight in Anchorage, Alaska, can be determined by examining the mathematical model y=7.0sin(2ω⁄365x−1.4)+12.4.
The amplitude of the sine function in this equation is 7.0, which determines the maximum variation above or below the average value.
Since the sine function oscillates between -1 and 1, the minimum value of the sine part of the equation will be -1.
Therefore, the minimum number of hours of daylight, y, occurs when the sine function is at its minimum value. By substituting -1 into the equation, we get y=7.0×(-1)+12.4, which simplifies to y=5.4.
This means that the minimum number of hours of daylight in Anchorage is 5.4 hours.
find perimeter and area pleasee
Answer:
Perimeter: 36 m
Area: 60 m squared
Step-by-step explanation:
The perimeter is the sum of the exterior side lengths of the shape. Here, we see that there are two side lengths given, but we need to find the third one.
Notice that the triangle is split up into two right triangles, which means that we can use the Pythagorean Theorem to solve for half of the remaining side. The right triangles have hypotenuses of 13 and one leg of 12. That means the second leg will be [tex]\sqrt{13^2-12^2} =\sqrt{169-144} =\sqrt{25} =5[/tex].
So, the third side is made up of the two legs with length 5. This makes the length of the remaining side: 5 + 5 = 10.
Now, we can calculate the perimeter: P = 10 + 13 + 13 = 36 meters.
The area is calculated by the formula: [tex]A=\frac{1}{2} bh[/tex] , where b is the base and h is the height. Here, the base is what we found above, 10, and the height is the length that makes a perpendicular with the base, which is 12. So, the area is: [tex]A=(1/2)*10*12=(1/2)*120=60[/tex]. So, the area is 60 square meters.
Hope this helps!
Answer:
36m
60m²
Step-by-step explanation:
Base of 1 right angle triangle:
sqrt(13² - 12²)
5
Base of the bigger triangle:
5 + 5 = 10
Perimeter = 13 + 13 + 10
36 m
Area = ½ × 10 × 12
60 m²
The combined volume of all the things and aquarium is 1.25×10 to the six power gallons the aquarium plants to install a new dolphin take with a volume of 250,000 gallons what was the total volume of all the tanks at the aquarium after the new dolphin tank is installed
Answer:
1,500,000 gallons
Step-by-step explanation:
In this question, we are to calculate the total volume of the aquarium after installing a new dolphin tank.
Mathematically, to calculate this, we simply need to add the the volume of the new dolphin tank to the volume of the things in the aquarium before bringing the dolphin tank.
The volume of all the things in the aquarium before installing the dolphin tank is 1.25 * 10^6 = 1,250,000 gallons
now let’s add the volume of the dolphin tank which is 250,000 gallons
that would be 1,250,000 + 250,000 = 1,500,000 gallons or 1.5 * 10^6 gallons
can absolute value equations be equal to zero? my textbook says no but there are multiple equations equaling 0 or a negative numbers once I simplify.
Absolute value equations can equal zero but cannot equal a negative number. This is because the absolute value of a number is its distance from zero on the number line, which is always zero or positive.
Explanation:In the field of mathematics, absolute value equations can indeed be equal to zero. The absolute value of a number is its distance from zero on the number line, irrespective of direction. Therefore, the only number whose absolute value (distance from zero) is zero, is zero itself.
One can encounter such a situation in an equation like |x|=0, where the solution is x=0, simply because 0 is the only number that is at zero distance from zero. However, for an absolute value equation to be equal to a negative number, this is impossible, because absolute value is a measurement of distance and cannot be negative. So, if your simplified equations are resulting in negative values, you might want to double-check your work.
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What is the value of 4/15 divided 2/3
Answer:
⅖
Step-by-step explanation:
4/15 ÷ 2/3
4/15 × 3/2
2/5
Answer: 2/5 or 0.4
Step-by-step explanation: When dividing a fraction by another fraction you will always find the reciprocal of the second fraction and then multiply to get your answer.
4/15 divided by 2/3
4/15 multiplied by 3/2
0.4 or 4/10 or 2/5 is the value of 4/15 divided by 2/3
Total amount of rain each county received for five days. Palm Beach 2.3., Broward 3.5,and Dade 3.0. On average,how many inches of rain did each county received each day.
Answer: On average, each country receives 2.93 inches of rain each day.
Step-by-step explanation:
Since we have given that
Palm Beach = 2.3
Broward = 3.5
Dade = 3.0
So,the average inches of rain each country would receive each day would be :
[tex]\dfrac{2.3+3.5+3.0}{3}=\dfrac{8.8}{3}=2.93\ inches[/tex]
Hence, on average, each country receives 2.93 inches of rain each day.
It would take 150 minutes to fill a swimming pool using 5 taps.
a) How many minutes will it take to fill the pool if only 3 of the taps are used?
Complete the following.
b) An assumption being made in my working is that all the taps are flowing at the same time.
Answer:
250 minutes
Step-by-step explanation:
a) Assuming all taps flow at the same rate, the time is inversely proportional to the number of taps. Using 3/5 of the total taps will take 5/3 of the time required when all taps are used.
For 3 taps, the time is ...
(5/3)(150 minutes) = 250 minutes
__
b) An assumption being made in my working is that all the taps are flowing at the same rate.
a) It will take 250 minutes to fill the pool using 3 taps. B) The assumption being made here is that all the taps are flowing at the same rate r and that they are all turned on at the same time, working in parallel to fill the pool.
Let's denote the rate at which each tap fills the pool as r liters per minute.
With 5 taps working together, it takes 150 minutes to fill the pool. Therefore, the combined rate of 5 taps is [tex]\( \frac{1}{150} \)[/tex] of the pool per minute. We can express this as:
[tex]\[ 5r = \frac{1}{150} \][/tex]
Now, we want to find out how long it will take to fill the pool using only 3 taps.
The combined rate of 3 taps will be 3r.
To find the time t it takes for 3 taps to fill the pool, we set up the equation:
[tex]\[ 3r = \frac{1}{t} \][/tex]
We can solve for r using the first equation:
[tex]\[ r = \frac{1}{5 \times 150} \][/tex]
Substituting this value into the second equation gives us:
[tex]\[ 3 \times \frac{1}{5 \times 150} = \frac{1}{t} \][/tex]
Solving for t
[tex]\[ t = \frac{1}{3 \times \frac{1}{5 \times 150}} \][/tex]
t = 250
So, it will take 250 minutes to fill the pool using 3 taps.
b) The assumption being made here is that all the taps are flowing at the same rate r and that they are all turned on at the same time, working in parallel to fill the pool.
This implies that the flow rate of each tap does not change regardless of how many taps are being used simultaneously, and that there are no other factors (like water pressure changes) affecting the flow rate when fewer taps are used.
Alec can buy bottles of water in packages of 6 for $12.12 or in packages of 4 for $9.72. How much money does he save by buying 48 bottles of water at the better price?
48/6 = 8
He needs to buy 8 of the six pack size for a total of :
8 x 12.12 = $96.96
Or
48/ 4 = 12 Of the 4 packs for a total of
12 x 9.72 = $116.64
He would save
116.64 - 96.96 = $19.68 by buying 8 of the six packs.
Answer:
—————————————-
He saves $19.68
—————————————-
Hope this helps!!!!
—————————————-
Step-by-step explanation:
—————————————-
6 bottles for $12.12
Find the unit rate:
12.12/6
=2.02
This tells us that using this price, each bottle costs $2.02
—————————————-
4 bottles for $9.72
Find the unit rate:
9.72/4
=2.43
This tells us that using this price, each bottle costs $2.43
—————————————-
The first deal is better because you are paying less for each bottle.
—————————————-
So now you know which “deal to use,”
—the first one— (6 bottles for $12.12)
Since each bottle costs $2.02 here, you can multiply:
48 x $2.02 = $96.96
—————————————-
In the second deal, where 4 bottles cost 9.72 bucks,
Each bottle is for $2.43
48 x $2.43 = $116.64
—————————————-
How much does he save by going with the first deal?
$116.64 - $96.96 = $19.68
what is the measure of JKL?
Answer:
97
Step-by-step explanation:
83 and JKL form a straight line so they add to 180 degrees
83+ JKL = 180
Subtract 180 from each side
83-83+ JKL = 180-83
JKL = 97
Answer:
97°
Step-by-step explanation:
Interior + exterior angle = 180
Interior angle (JKL) = 180 - 83
97
3(x+2)^2=48
Show steps
National League Hockey play-off games go into overtime if the score is tied at the end of a game. Overtime lasts until one of the teams scores a goal. From years of experience we know that the distribution of the lengths of the overtime periods is right skewed with a mean of 9.8 minutes and a standard deviation of 12 minutes. What is the (approximate) probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes? Give your answer to 3 decimal places, e.g, 0.123.
Answer:
0.07215 = 0.072 to 3 d.p.
Step-by-step explanation:
Central limit theorem explains that the sampling distribution obtained from this distribution will be approximately a normal distribution with
Mean = population mean
μₓ = μ = 9.8 minutes
Standard deviation of the distribution of sample means = σₓ = (σ/√n)
σ = 12 minutes
n = sample size = 30
σₓ = (12/√30) = 2.191
Probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes
Required probability = P(x > 13)
Since we've established that this distribution of sample means approximates a normal distribution
We first standardize 13 minutes.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (13 - 9.8)/2.191 = 1.46
Required probability
P(x > 13) = P(z > 1.46)
We'll use data from the normal probability table for these probabilities
P(x > 13) = P(z > 1.46) = 1 - P(z ≤ 1.46)
= 1 - 0.92785 = 0.07215
Hope this Helps!!!
Solve for x
-14 - 5 = -10x - 45
Answer:
x = -13/5 OR -2.6
Step-by-step explanation:
Take steps to isolate x:
-14 - 5 = -10x - 45
-19 = -10x -45
26 = -10x
x = 26/-10
x = -13/5 OR -2.6
Answer:X=-13/5 is the simplified answer
Step-by-step explanation:
-14-5=-10x-45
-19=-10x-45
-19+45=-10x-45(+45)
26=-10x
26/-10=x
x=-13/5
Need help I’m stuck on this one. I should ask my teacher but I get help from here faster. Need the answer ASAP. Thank you guys so much
Answer:
(0, 15/6) (15/7,0)
Step-by-step explanation:
Just set the other value to 0 and you can very quickly solve these.
) Jennifer and Krystal have to stuff and mail 1000 envelopes for a new marketing campaign. Jennifer can do the job alone in 6 hours. If Krystal helps, they can get the job done in 4 hours. How long would it take Krystal to do the job by herself?
Answer:
12 hours
Step-by-step explanation:
Let's call the Jennifer's speed J, and the Krystal's speed K.
If Jennifer works alone, she can do the job in 6 hours, so:
J*6 = 1000
J = 1000/6 = 500/3
If Jennifer and Krystal work together, they can do the job in 4 hours, so:
(J+K)*4 = 1000
J+K = 250
Using the value of J, we can find K:
500/3 + K = 250
K = 250 - 500/3 = 250/3
Now, to find the time that Krystal would take if she works alone:
K * time = 1000
250/3 * time = 1000
time = 1000/ (250/3) = 1000*3/250 = 12 hours
Answer:
12 hours
Step-by-step explanation:
please check the attached files for explanation
Which is the solution to the inequality? y minus 27 greater-than-or-equal-to negative 13
Answer:
y is greater than or equal to 14
Step-by-step explanation:
Answer:
y ≥ 14
Step-by-step explanation:
y - 27 ≥ -13
you manipulate this inequality like it is an equation. Only take care that the inequality swaps if you multiply by a negative. In this case, that is not needed.
y - 27 +27 ≥ -13+27
y ≥ 14
c=1 when a randomly chosen card out of a standard deck of 52 playing cards is a heart and c=2 otherwise. draw a histogram showing probibility distribution for the random variable
Answer:
The possible values of c are 1 or 2. There are 13 hearts in a deck of cards and 52-13 = 39 cards that are not. There are a total of 52 cards to choose from, so the possibilities for each value of c are found by dividing the number of results for that value by 52. (Image 1)
Histogram is attached for your reference.
Leah is measuring the weight of adult rhinos at the zoo. Which unit of measurement should she use to eliminate the need to write the values in scientific notation
Answer:
TONS!!!!!!!!!!!!Step-by-step explanation:
The tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.
It is given that Leah is measuring the weight of adult rhinos at the zoo.
It is required to find the unit of measurement she should use to eliminate the need to write the values in scientific notation.
Given options:
1) grams
2) feet
3) gallons
4) tons
What is measurement?It is defined as the numerical quantity that gives an idea about an object's weight, length, width, and many more. It can be used to compare two objects.
We know the feet are the unit of measuring the length and gallons are the unit of measuring the volume.
The grams and tons are the units of measuring the weight.
Grams would use to measure a small amount of weight whereas we would use the tons to measure a large amount of weight. Ton is a metric unit that equals 1000 kilograms.
Thus, the tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.
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