The approximate value of √329 to the nearest integer is 18.
How to approximate √329 to the nearest integer?Approximation is the process of using rounded values when presenting numerical data and making rough calculations.
To approximate √329 to the nearest integer, we can find the perfect squares that are less than or equal to 329.
The perfect squares less than or equal to 329 are 16, 25, 36, and 49. But the nearest perfect square to 329 is 324, which is the square of 18 (i.e. 18² = 324).
Therefore, the nearest integer to √329 is 18.
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Please help! What is the surface area of the cylinder with a height 4 m and radius 8 m? Round your answer to the nearest thousandth.
If u answer correctly u get 5 dollars on cahapp
The surface area of the cylinder is 603.19 square meters
Finding the surface area of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 8 meters
Height, h = 4 meters
Using the above as a guide, we have the following:
Surface area = 2πr(r + h)
Substitute the known values in the above equation, so, we have the following representation
Surface area = 2π * 8 * (8 + 4)
Evaluate
Surface area = 603.19
Hence, the surface area is 603.19 square meters
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x-1 is a factor of which of the following?
1.x²+x-2
11.2x2–5x+3
O Neither
OI only
O II only
OI and II
The term (x - 1) is a factor of both of the given polynomials:
x² + x - 2
2x² - 5x + 3
How to check if x - 1 is a factor?
If (x - a) is a factor of a polynomial p(x), then x = a is a zero of the polynomial, which means that:
p(a) =0.
So, if x - 1 is a factor of any of the given polynomials, then we need to evaluate them in x = 1 and check if we get zero.
a) x² + x - 2
Evaluate it in x = 1.
1² + 1 - 2 = 0
it is zero, so (x - 1) is a factor.
b) 2x² - 5x + 3
Evaluating this in x = 1.
2*1² - 5*1 + 3
2 - 5 + 3 = 0
(x - 1) is a factor.
Then the correct option is the last one, it is a factor of both polynomials.
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Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,
(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.
------------------- grams
(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.
-------------------- years
if you need to see the picture here is too. Thank u.
3.6 years will have passed when 115 grams of thorium 234 is left.
(a) To find the amount of thorium 234 left after 0.5 years, we can substitute t = 0.5 and A0 = 1000 into the given equation and solve for At:
[tex]A_t = A0e^{(-10.498t)}\\\\A_t = 1000e^{(-10.498(0.5))}\\\\A_t = 679.6\ grams[/tex]
Therefore, approximately 679.6 grams of thorium 234 will be left after 0.5 years.
(b) To find when 115 grams of thorium 234 will be left, we can set At = 115 in the given equation and solve for t:
[tex]A_t = A_0e^{-10.498t}\\\\115 = 1000e^{-10.498t}\\\\ln(115/1000) = -10.498t\\\\t = 3.6\ years[/tex]
Therefore, approximately 3.6 years will have passed when 115 grams of thorium 234 is left.
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Sort the angles as acute, right, obtuse, or straight.
The top angle is right (90 degrees, kinda looks like a bent elbow).
The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).
The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).
4th is acute.
5th is straight because it's a straight line.
6th is also obtuse.
Have a good day :)
Can anyone help me with this <3
Answer:
[tex]3.23*10^{16}[/tex]
Step-by-step explanation:
Just multiply. You have to do:
[tex](1.12*10^7)*(2.88*10^9)\\=3.23*10^{16}[/tex]
Calculator
A point is selected at random inside the given figure.
What is the probability the point will be in the region labeled A?
Enter your answer, as a fraction in simplest form, in the box.
P(A) =
Basic
5 in.
B
3 in.
A
C
4 in.
3 in.
D
4 in.
The probability of the point being in region A is 0.5294.
The area of the entire figure can be found by adding the areas of the four triangles:
Area of entire figure
= Area of triangle ABC + Area of triangle ACD + Area of triangle ABD + Area of triangle BCD
= (1/2)(5)(3) + (1/2)(3)(4) + (1/2)(4)(3) + (1/2)(3)(4)
= 7.5 + 6 + 6 + 6
= 25.5 square inches
Similarly, the area of region A can be found by adding the areas of triangles ABC and ABD:
Area of region A
= Area of triangle ABC + Area of triangle ABD
= (1/2)(5)(3) + (1/2)(4)(3)
= 7.5 + 6
= 13.5 square inches
Therefore, the probability of the point being in region A is:
P(A) = Area of region A / Area of entire figure
P(A) = 13.5 / 25.5
P(A) = 0.5294
So the probability of the point being in region A is 0.5294.
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im abt to km$ this is literslly due in a couple of minutes lol
Answer:
x-intercept = -7
y-intercept = 1
rate of change = 1.25
Step-by-step explanation:
X and Y intercept are pretty to find.
Rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
So for our case it will be [tex]\frac{-0.75-(-2)}{-8-(-9)}[/tex]
The answer will be 1.25
Calculator What is the area of a sector with a central angle of 144° and a radius of 11 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. cm² K
Rounding to the nearest hundredth, the area is approximately 151.976 cm².
The formula for the area of a sector is:
A = (θ/360) x πr²
where θ is the central angle in degrees, r is the radius, and π is pi (3.14).
Plugging in the given values, we get:
A = (144/360) x 3.14 x 11^2
A = 0.4 x 3.14 x 121
A = 151.976
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You bake bread until the internal temperature reaches 340F. The bread is placed on a table until the internal temperature reaches 80F and can be sliced. The room temperature is 68F and the cooling rate of the bread is r=0.075. How long do you have to wait until you can slice that bread?
ok, let's assume the rate is 0.075 per minute, if we convert that to percentage that'd be 0.075*100 or 7.5% per minute, so we can assume the bread is cooling off at 7.5% per minute after coming out of the oven at 340°F and we need it at 80°F so we can slice it and put some butter on it.
now, we can look at this from a Decay standpoint and say
we have a temperature of 340°F, decaying at 7.5% per minute, how long before it turns into 80°F?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 80\\ P=\textit{initial amount}\dotfill &340\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=minutes \end{cases}[/tex]
[tex]80 = 340(1 - 0.075)^{t}\implies \cfrac{80}{340}= 0.925^t\implies \cfrac{4}{17}=0.925^t \\\\\\ \log\left( \cfrac{4}{17} \right)=\log(0.925^t)\implies \log\left( \cfrac{4}{17} \right)=t\log(0.925) \\\\\\ \cfrac{ ~~ \log\left( \frac{4}{17} \right) ~~ }{\log(0.925)}=t\implies 18.56\approx t\qquad \textit{almost 19 minutes}[/tex]
Question 22 of 25
Given below are lease terms at the local dealership. What is the total cash
due at signing?
Terms:
Length of lease: 30 months
. MSRP of the car: $15,500
.
• Purchase value of the car after lease: $9900
• Down payment: $2500
Monthly payment: $425
• Security deposit: $375
Acquisition fee: $500
●
●
OA. $3800
B. $375
C. $3375
D. $3400
The total cash due at signing is $3800.
Option A is the correct answer.
We have,
The total cash due at signing is the sum of the down payment, security deposit, acquisition fee, and the first month's lease payment.
So,
Down payment = $2500
Security deposit = $375
Acquisition fee = $500
First month's lease payment = $425
The total cash due at signing is:
= $2500 + $375 + $500 + $425
= $3800
Thus,
The total cash due at signing is $3800.
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PLEASE HELP I WILL MARK YOU BRAINLIEST!!
Answer:
96π
Step-by-step explanation:
the shape is made up of a cylinder and a cone.
Volume of cylinder = π r ² h
= π (3)² (9)
= 81π.
Volume of cone = (1/3) X vertical height X π r ²
= (1/3) (5) π (3)²
= 15π
volume of composite solid = 81π + 15π = 96π
In a group of 80 people, 50 like tea, 30 like coffee and 20 like tea only.
a) find the number if people who like both drink
b)find the number of people who like either of the drinks
Answer:
60 and 40
Step-by-step explanation:
a) To find the number of people who like both tea and coffee, we can use the formula:
Number of people who like both = Number of people who like tea + Number of people who like coffee - Number of people who like only teaPlugging in the given values, we get:
Number of people who like both = 50 + 30 - 20 = 60Therefore, there are 60 people who like both tea and coffee.
b) To find the number of people who like either of the drinks, we can add the number of people who like tea only, the number of people who like coffee only, and the number of people who like both tea and coffee. Mathematically,
Number of people who like either drink = Number of people who like tea only + Number of people who like coffee only + Number of people who like both tea and coffeePlugging in the given values, we get:
Number of people who like either drink = 20 + (30-60) + 50 = 40Therefore, there are 40 people who like either tea or coffee (or both).
Which expression is a function that has zeros at 4 and –3?
Answer:
[tex]f(x) = (x - 4)(x + 3) [/tex]
[tex]f(x) = {x}^{2} - x - 12[/tex]
10 ft
15 ft
5 ft
10 ft
5 ft
22 ft
What is the total area that you need to cover?
The total area that needs to be covered which is indicated by the shaded area would be =220ft²
How to calculate the total area that needs to be covered?To calculate the area that needs to be covered, the formula that should be used is the formula for the area of a rectangle which is given below as follows;
Area of rectangule =2( length×width)
where ;
length = 22ft
width = 5ft
area = 2× 22×5
= 220ft²
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Evaluate 7c1 and 6p4
Answer:
7c1 is an algebraic expression that evaluates to 47. The expression is made up of two terms, 7 and c1. The letter c is a variable and the number 1 represents the exponent of the variable. Therefore, 7 multiplied by the c to the power of 1 is equal to 7 times c, which is equal to 47.
6p4 is an algebraic expression that evaluates to 6,040. The expression is made up of two terms, 6 and p4. The letter p is a variable and the number 4 represents the exponent of the variable. Therefore, 6 multiplied by the p to the power of 4 is equal to 6 times p to the fourth power, which is equal to 6,040.
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 48 minutes of calls is $17.01 and the monthly cost for 86 minutes is $21.95. What is the monthly cost for 56 minutes of calls?
The monthly cost for 56 minutes of calls is given as follows:
$18.05.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.For 38 minutes of call, the price increases by $4.94, hence the slope of the linear function, representing the cost per minute, is given as follows:
m = 4.94/38
m = 0.13.
56 minutes is 30 minutes less than 86 minutes, hence the cost is given as follows:
C(56) = 21.95 - 30 x 0.13
C(56) = $18.05.
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¿Por qué, aunque un trinomio tenga raíz exacta en el primer y tercer término, no siempre se puede aplicar el método de adición y sustracción para convertirlo en trinomio cuadrado perfecto?
The reason for not applying method of addition and subtraction on first and third term shown below.
The reason why the method of addition and subtraction cannot always be applied to convert a trinomial with exact roots in the first and third terms into a perfect square trinomial is because the second term may not be a perfect square or a multiple of the square root of the first term multiplied by the square root of the third term.
In order to convert a trinomial into a perfect square trinomial using the method of addition and subtraction, the coefficient of the second term must be twice the product of the square root of the first term and the square root of the third term. If this condition is not met, the trinomial cannot be transformed into a perfect square trinomial using this method.
Therefore, it is important to consider the coefficients and terms of the trinomial to determine if the method of addition and subtraction can be applied successfully.
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What time of day is represented by the figure below? Recall that the rotation of the Earth is counterclockwise.
A. just before sunrise
B. just after sunrise
C. just before sunset
D. just after sunset
Answer:
D
Step-by-step explanation:
What is 7/10 - 2/5? It’s for mathematics
Answer:
3/10
Step-by-step explanation:
7/10 – 2/5
=7/10 – 4/10
=(7–4)/10
=3/10
Answer:
0.3
Step-by-step explanation:
can someone please help me out? Bc
Find the surface area of the prism. Show your work.
The surface area of the prism is
The surface area of the prism given is 362 m².
Given is a prism.
We have to find the total surface area of the prism.
The given prism has to be divided in to various other known figures to find the total area.
By drawing a line vertically through the top of the prism, we get two rectangular prism.
Surface area of a rectangular prism = 2 [lw + wh + lh], where l, w and h are length, width and height respectively.
Surface area of big rectangular prism = 2[(6 × 6) + (6 × 7) + (6 × 7)]
= 240 m²
Surface area of smaller rectangular prism = 2[(3 × 4) + (4 × 7) + (3 × 7)]
= 122 m²
Total area of the prism = 240 m² + 122 m²
= 362 m²
Hence the surface area is 362 m².
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Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails. To the nearest percent, what is the experimental probability of Project B?
Which segments are congruent?
JN and LN
JN and NM
LN and NK
NK and NM
Answer:
LN and NK
Step-by-step explanation:
A perpendicular bisector of a line segment divides the line segment into 2 equal halves.
Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.
The two equal halves are segment LN and segment NK.
Therefore, segment LN is congruent to segment NK.
A friend has a 80% average before the final exam for a course. The score includes everything but the final, which counts for 15% of the course grade. What is the best course grade your friend can earn? What is the minimum score would your friend need on the final to earn a 75% for the course?
Your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.
Since the final exam counts for 15% of the course grade, the weighted average can be calculated as follows:
Weighted average = (0.85 × 80%) + (0.15 × final exam score)
If we assume that your friend wants to get the highest possible grade, then they would need to get a perfect score on the final exam, which would be 100%.
Plugging this into the equation above, we get:
Weighted average = (0.85 × 80%) + (0.15 × 100%) = 83%
Therefore, the best course grade your friend can earn is 83%.
We can set up an equation where x is the minimum score needed on the final exam:
Weighted average = (0.85 × 80%) + (0.15 × x) = 75%
Simplifying this equation, we get:
0.85 × 80% + 0.15x = 75%
68% + 0.15x = 75%
0.15x = 7%
x = 46.67%
Therefore, your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.
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A communications satellite is in a synchronous orbit 18,000 miles above an alien planet's surface. Points B and D in the figure are points of tangency of the satellite signal with the planet. They represent the greatest distance from the satellite at which the signal can be received directly. Point C is the center of the planet, which has a radius of 3,500 miles.
Satellite diagram with satellite at point A, planet with center c and points of tangency with A at B and D. Radius of planet is 3,500 mi and distance from edge of planet to satellite is 18,000 mi.
Find distance
. Round to the nearest mile. Show your process and explain your reasoning.
m∠BAC = 9.4°. If the circumference of the circle represents the the planet's equator, what percent of the planet's equator is within range of the satellite’s signal? Show your process and explain your reasoning.
How much longer does it take a satellite signal to reach point B than it takes to reach point E? Use 186,000 mi/sec as the speed of a satellite signal. Round your answer to the nearest hundredth. Show your process and explain your reasoning.
The satellite is in orbit above the planet's equator. Along with the point directly below it on the planet's surface, the satellite makes one complete revolution every 36 hours. How fast must it travel to complete a revolution in that time? Round your answer to the nearest whole number. Show your process and explain your reasoning.
The distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles. Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).
1. Find the distance from the satellite to the points of tangency Solution: Firstly, we need to draw a rough diagram of the scenario to easily understand it. Consider a satellite revolving around an alien planet in a synchronous orbit 18,000 miles above its surface.
We can see that B and D are the points of tangency of the satellite signal with the planet, and C is the center of the planet. Hence, the figure will look like the following: Image Source: Synchronous Orbit - Wikimedia Commons Now, we need to find the distance from the satellite to the points of tangency.
Hence, the distance from the satellite to the points of tangency, B and D, is 61861.9 miles (approximately 61862 miles).2. Find the percentage of the planet's equator within range of the satellite's signal Solution: We can see that the planet's equator can be represented by a circle with a radius of 3500 miles. Hence, the circumference of the circle would be 2π × 3500 miles ≈ 21991.5 miles.
We know that the satellite's signal can be received directly up to a distance of 61862 miles from it. Hence, the length of the portion of the equator within range of the satellite's signal would be twice the distance from the satellite to the point of tangency, which is 2 × 61862 ≈ 123724 miles. Now, we need to find the percentage of the planet's equator within range of the satellite's signal.
Hence, we need to find the time taken for the satellite signal to reach points B and E. We can see that the distance from the satellite to point B is 61862 miles and the distance from the satellite to point E is 3500 miles. Hence, the time taken for the satellite signal to reach point B would be: Time taken to reach point B = Distance / Speed = 61862 / 186000 ≈ 0.332 seconds Now, we need to find the time taken for the satellite signal to reach point E.
Hence, the time difference between the satellite signal reaching points B and E is approximately 0.07 seconds.4. Find the speed of the satellite Solution: We know that the satellite takes 36 hours to complete one revolution around the planet along with the point directly below it on the planet's surface. Hence, we need to find the distance travelled by the satellite in 36 hours to find its speed.
We can see that the distance travelled by the satellite in one revolution is equal to the circumference of the circle with a radius of 3500 miles, which is 2π × 3500 miles ≈ 21991.5 miles. Hence, the distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles.
Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).
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The ages of members of a stamp collecting group are normally distributed with a mean of 55 years and a standard deviation of 4 years.
There are 104 members in the group.
About how many members are expected to be between 51 years old and 59 years old?
About 71 members of the group are expected to be between 51 years old and 59 years old.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:
68%.
Out of 104 people, the number of people with ages in the range is given as follows:
0.68 x 104 = 71 people. (rounded to the nearest integer).
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rewrite the mixed numbers as the sum of whole number and a fraction rewrite the whole number as a sum of fraction each equal to 1
The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄
How to write mixed fractions?There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.
Now, we are given the fraction as an improper fraction in the form of 2³₄.
Rewriting as a whole number and a fraction gives:
2 + ³/₄
Breaking down the whole number into a fraction is done as:
1 + 1 + ³/₄
= ⁴/₄ + ⁴/₄ + ³/₄
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PLEASE HELP
Lily is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 40w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks. (4 points)
Part B: What are the units of measurement for the composite function in Part A? (2 points)
Part C: Evaluate the composite function in Part A for 35 weeks. (4 points)
Step-by-step explanation:
Part A:
To find the composite function, we need to plug in the expression for s(w) into f(s):
f(s(w)) = 2s(w) + 30
= 2(40w) + 30
= 80w + 30
Therefore, the composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks is f(s(w)) = 80w + 30.
Part B:
The units of measurement for the function f(s(w)) are the same as the units of measurement for f(s) and s(w). From the given information, we know that s(w) represents the number of seeds planted per week and f(s) represents the number of flowers bloomed based on the number of seeds planted. Thus, the units of measurement for f(s(w)) are "flowers" per week.
Part C:
To evaluate the composite function f(s(w)) for 35 weeks, we need to substitute w = 35 into the expression we found in Part A:
f(s(35)) = 80(35) + 30
= 2,830
Therefore, Lily can expect 2,830 flowers to bloom after planting 40 seeds per week for 35 weeks.
Answer: c
Step-by-step explanation:
i took the test
Pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4π cm
Step-by-step explanation:
A minute hand travels a full revolution along a circular path in 60 minutes
The distance from the center to the tip of the minute hand = 8 cm
We can consider the movement of the minute hand as being on the circumference of a circle with radius = 8 cm
Circumference = 2π · r
= 2π · 8
= 16π
I5 minutes = 15/60 = 1/4th
So in 15 minutes the minute hand will cover only 1/4th of the full circle
Therefore distance traveled by tip of minute hand
= 1/4 x 16π = 4π cm
What is 4320 minutes, in days? (Remember, there are 60 minutes in an hour and 24 hours in a day.)
There are 1440 minutes in a day (24 hours x 60 minutes = 1440 minutes).
To convert 4320 minutes to days, divide 4320 by 1440:
4320 ÷ 1440 = 3
Therefore, 4320 minutes is equivalent to 3 days.
Answer: 3 days
Step-by-step explanation: