[tex]\bold{Hey\ there!}[/tex]
[tex]\bold{What\ is\ the\ best\ approximation\ of\ the\ area\ of\ a\ circle\ with\ a\ diameter\ of\ 17\ meters.}[/tex] [tex]\bf{Use\ 3.14\ to \ approximate\ pi\}[/tex][tex]\bold{Firstly,\ highlight\ your\ key\ terms:} \\ \bold{\bullet \ \underline{Approximation\ of\ the\ area\ of\ a \ circle\ with\ a\ diameter\ of\ 17.}}}\\ \\ \bold{\bullet\ \underline{Use\ 3.14\ to\ approximate\ pi}}[/tex][tex]\bold{17\times3.14=53.38}[/tex][tex]\bold{If\ we're\ rounding\ upward\ then\ your\ answer\ would\ be\ A.53.4m^2}[/tex][tex]\boxed{\boxed{\bold{Answer:A).53.4m^2}}}}\checkmark[/tex][tex]\bold{Good\ luck\ on\ your\ assignment\ \& enjoy\ your\ day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Answer:
The answer is c 226.9 m2
Step-by-step explanation:
Hope this helps
A supervisor has asked her team to improve its average talk Time Performance the team's average talk time is 13 minutes per call in the average for the call center is 8 minutes per call the following week the supervisor reports the following results John's went from 15 minutes to 16.5 minutes George's went to from 15 minutes to 14 minutes Paul's went from 12 minutes to nine minutes and Ringoes went from 12 minutes to 2 minutes whose performance improve the most While most likely giving the best service to customers?
Answer:
john
Step-by-step explanation:
Let u=ln x and v= ln y. Write ln( √x · y^2) in terms of u and v.
Answer:
C
Step-by-step explanation:
We can use 2 properties of logarithms to write this:
1. ln(x*y) = lnx + ln y
2. ln(a^b) = b ln a
Using property 1, we can write as:
[tex]ln(\sqrt{x} *y^{2})\\=ln(\sqrt{x} )+ln(y^2)\\=ln(x^{\frac{1}{2}})+2lny\\=\frac{1}{2}lnx+2lny[/tex]
We know u = lnx and v = ln y, we simply substitute it now:
[tex]\frac{1}{2}lnx+2lny\\=\frac{1}{2}u+2v[/tex]
the correct answer is C
Answer:
c
Step-by-step explanation:
Do you think this graph looks more like a quadratic or exponential function? Why do you think so?
Answer:
Exponential Function
Step-by-step explanation:
The y-axis represents the number of Bacteria and x-axis represents the number of hours. If you observe closely you will see that the number of bacteria are doubling after each hour. For example, at time = 4 hours the number of Bacteria were about 50, at time = 5 hours the number of Bacteria were about 100 and at time = 6 hours the number of Bacteria increased to about 200.
This type of behavior is a property of exponential functions where we see a multiplicative rate of change in the values i.e. each value is a multiple of previous value. A rough model for this function would be:
[tex]f(x)=f(0)(2)^{x}[/tex]
Where, f(0) represents the number of bacteria at time = 0 hours i.e. number of Bacteria initially present and "x" represents the number of hours.
Find the rectangular coordinates of the point with the polar coordinates (8, 3 divided by 2 pi ). (1 point) (0, -8) (0, 8) (8, 0) (-8, 0)
Answer:
(x,y) = (0,-8)
Step-by-step explanation:
We know that a point in polar coordinates is represented by
(r, θ)
Where r is the distance from the origin and θ is the angle.
Rectangular coordinates can be found by
x = r*cos(θ)
y = r*sin (θ)
x = r*cos(θ) = 8* cos (3π/2)
y = r*sin (θ) = 8 sin(3π/2)
x = 8* cos (3π/2) = 8*0 = 0
y = 8* sin (3π/2) = 8*(-1) = -8
(x,y) = (0,-8)
Correct option is (A) (0,-8)
Now any point in polar coordinates is represented by
(r, θ)
where 'r' is the distance from the origin
and 'α' is the angle.
Rectangular coordinates can be found by using the formula:
[tex]x=r*cos(\alpha )\\y=r*sin(\alpha )[/tex]
Thus the x coordinate would be given as :
[tex]x=r*cos(\alpha )\\x=8*cos(\frac{3\pi }{2} )\\x=8*0\\x=0\\[/tex]
Similarly the y coordinate would be given as :
[tex]y=r*sin(\alpha )\\y=8*sin(\frac{3\pi }{2} )\\y=8*(-1)\\y=-8\\[/tex]
Thus (x, y) = (0,-8) is the required coordinates
Eight boys and seven girls showed up to one of the team's games. League rules limit each team to 10 players at a time (five girls and five boys) per game. Given this rule, how many combinations of 10 players are there among the 15 boys and girls who showed up at this particular game?
Answer:
1176 Combinations
Step-by-step explanation:
As mentioned in the question, there are total 8 boys and 7 girls.
Our objective is to create a team with 5 boys and girls each.
To select 5 boys out of 8, we will use combination.
=> 8C5 = [tex]\frac{8!}{5!(8-5!)}[/tex]
=> [tex]\frac{8.7.6.5!}{5!.3!}[/tex]
=> [tex]\frac{8.7.6}{6}[/tex]
=> 56
Similarly,
5 girls are selected using 7C5
=> 21
Therefore, the total combination of players are 56 * 21 = 1176
If x = 5, what additional information is necessary to show that triangle DAC is congruent to triangle BAC by SAS
Answer:
Lengths of AD and AB. They must be same for theorem SAS
Answer:
[tex]\overline{\rm AD} = \overline{\rm AB}[/tex]
Step-by-step explanation:
Two figures are congruent if they have the same shape and size, although their position or orientation are different. The congruence criteria correspond to the postulates and theorems that state what are the minimum conditions that two or more triangles must meet in order to be congruent. One of the congruence criteria is:
SAS (Side-Angle-Side): Two triangles are congruent if they have two sides and the angle determined by them respectively equal.
So, considering the previous information and the data provided by the problem. Then, the additional information necessary to show that triangle DAC is congruent to triangle BAC is:
[tex]\overline{\rm AD} = \overline{\rm AB}[/tex]
If the Laffite family deposits $8500 in savings account at 6.75% interest, compounded continuously, how much will be in the account after 25 years
Answer:
Option b
Step-by-step explanation:
We have a compound interest problem. With an annual interest rate of 0.675 and an initial payment of 8500, with t = 25 years
Then you must use the annual compound interest formula, which is represented by a growing exponential function:
[tex]y = e ^{ht}[/tex]
Where:
h is the interest rate of 0.675
y is the money in the savings account as a function of time
Then substitute the values in the formula and we have:
[tex]y = e ^{0.675(25)}[/tex]
[tex]y = 45,950.57[/tex]
Bo's gross annual income is $45,408. He is paid semimonthly and has 6% deducted from his paychecks for his 403(b). His employer matches his deduction, up to 3%. How much was deposited into Bo's 403(b) each payday?
113.52
157.18
170.28
227.04
170.28 is the answer
Answer:
170.28
Step-by-step explanation:
Got it right on the test.
A 65 inch wide screen television actually describes the length of the diagonal of a rectangular television with a length of 63 inches. What is the width of the television?
For this question we need to use the Pythagorean Theorem (a2+b2=c2) since the rectangle is being divided into two triangles.
we know the length of the triangle (63) and we know the hypotenuse (65) but not the width. To find the width, we can plug the values we know into our formula.
(63) squared + b squared = (65) squared
solve.
3969 + b squared = 4225
subtract 3969 from both sides.
b squared = 256
√b² = √256
b=16
A number is increased by 50% and then the result is decreased by 50%. What is the percent of decrease from the original number to the final number?
Final answer:
To find the percent of decrease, calculate the difference between the original and final numbers, divide by the original number, and multiply by 100. In this case, the percent of decrease is 25%.
Explanation:
To find the percent of decrease from the original number to the final number, we need to calculate the difference between the original number and the final number, then divide that difference by the original number and multiply by 100 to get the percentage.
Let's assume the original number is x. When the number is increased by 50%, it becomes 1.5x. When the result is decreased by 50%, it becomes 0.5 times 1.5x, which is 0.75x.
The decrease from the original number to the final number is x - 0.75x = 0.25x. To find the percent of decrease, we divide the decrease by the original number (0.25x / x) and multiply by 100 to get 25%. Therefore, the percent of decrease from the original number to the final number is 25%.
Final answer:
The overall percent change from the original number to the final number, after increasing by 50% and then decreasing by 50%, is a 25% decrease.
Explanation:
To find the percentage decrease from the original number to the final one after the series of increases and decreases described, we need to follow a couple of steps:
First, we increase the original number by 50%. If the original number is x, its increased value is x + 0.5x = 1.5x.
Next, we decrease this new number by 50%. The decreased value is 1.5x - (0.5 × 1.5x) = 1.5x - 0.75x = 0.75x.
To find the percentage change from the original value, we calculate (final value - initial value) / initial value × 100%. Using the value obtained from the second step, this becomes (0.75x - x) / x × 100% = -0.25x/x × 100% = -25%.
Therefore, the overall percent change is a 25% decrease from the original number.
Complete the statement: A prime number is a whole number greater than 1 whose only factors are ______ and _______.
first blank- zero (0)
second balnk- the prime number
Answer:A prime number is a whole number greater than one whose only factors are 1 and itself
How long would it take for a ball dropped from the top of a 256-foot building to hit the ground
For the following question, find the length of the missing side leave. Your answer in simplest radical form.
Please help I’m so confused on this lesson!
The length of the missing side is √445 meters.
For a right triangle, the Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (the legs).
In this case, we are given the lengths of the two legs, which are 11 meters and 18 meters. We need to find the length of the hypotenuse, which is the missing side.
Steps to solve:
Step 1: Substitute the given values into the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where:
a = 11 meters (shorter leg)
b = 18 meters (longer leg)
c = the missing side (hypotenuse)
Step 2: Evaluate the equation:
[tex]11^2 + 18^2[/tex]= [tex]c^2[/tex]
121 + 324 = [tex]c^2[/tex]
445 = [tex]c^2[/tex]
Step 3: Take the square root of both sides to solve for c:
c = √445
The length of the missing side is √445 meters
Caleb's puppy weighs 2,250 grams. If the puppy weighed 600 grams at his last visit to the veterinarian's office, what is the percent increase in the puppy's weight rounded to the nearest whole number?
Answer: 275%
Step-by-step explanation:
Given : The current weight of the puppy : 2,250 grams
The weight of the puppy at the last visit = 600 grams
Increase in weight :-
[tex]2250\text{ grams}-600\text{ grams}=1650\text{ grams}[/tex]
Now, the formula to calculate the percentage increase is given by :-
[tex]\dfrac{\text{Increase in quantity}}{\text{Previous quantity}}\times100[/tex]
The percentage increase in weight is given by :-
[tex]\dfrac{1650}{600}\times100=275\%[/tex]
Hence, the percent increase in the puppy's weight = 275 %.
Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel?
Answer:
it took a total of 260 minutes or 4 hours and 20 minutes from Collin's house to his hotel.
Step-by-step explanation:
As each of the activities described is an independent activity that does not overlap, we can easily sum up the durations of each to find the total time Collin took from his house to the hotel.
We add it as follows :
he drove to the airport for 45 minutes + he waited at the airport for the flight to depart for 90 minutes + his fight duration was 70 minutes + upon landing, he gathered his luggage for 20 minutes + he drove to the hotel for 35 minutes.
So, 45+90+70+20+35 = 260 minutes
Answer:
The numbers can be added in any order.
Step-by-step explanation:
Just got this quiz question right.
Hope this helps :)
Please help me out!!!!!!!!
the correct answer would be 46°
It would be 46° but since there is an x = ? The "?" would be replaced with 46°
I hope this helps! ^^ You can just put 46° For your answer.
Expand
6
∑ 3n
n=2
a.2+3+4+5+6
b.3+6+9+12+15
c.6+9+12+15+18
d.3+6+9+12+15+18
Answer:
Step-by-step explanation:
d.3+6+9+12+15+18 sum 6 terms multiple of 3
what is equivalent to (5x-6) (2x+3) ?
a. (5x-6) (2x) + (5x -6) (3)
b. (5x-6) (2x) - (5x-6) (3)
c. (5x) (2x) + (6) (3)
d. (5x-6) (2x) + (-6)(3)
The expression is equivalent to (5x-6) (2x) + (5x-6) (3).
Option (A) is correct.
It is to find equivalent of (5x-6) (2x+3).
What is polynomial?An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable.
when we multiply to (5x-6) to (2x+3).
Each term of (5x-6) is multiply to (2x+3).
so (5x-6) is multiply to 2x and (5x-6) is multiply to 3 separately.
so, the expression is equivalent to (5x-6) (2x) + (5x-6) (3).
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Describe how to translate the graph of g(x) = ln x into the graph of f(x)= ln (-5)+5
Answer:
B
Step-by-step explanation:
We know:
1. Replacing -x into x of an equations reflects the graph on the y-axis
2. If f(x) is a function, then f(x)+a is a vertically translated graph of the original graph, a units up
Looking at the original function of ln x and the transformed graph of ln(-x) +5, we see that we have replaced x with -x, which means it is a reflection across the y-axis.
Also, we have added a five after the function, so that means it is a vertical translation of 5 units up.
Looking at the answer choices, we see that B is the correct answer.
Use factoring and the zero-product property to solve the following problems.
Answer:
see explanation
Step-by-step explanation:
Divide through by 2
2a² - 5a + 3 = 0
To factor the quadratic
Consider the factors of the product of the coefficient of the a² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 3 = 6 and sum = - 5
The factors are - 2 and - 3
Use the factors to split the a- term
2a² - 2a - 3a + 3 = 0 ( factor the first/second and third/fourth terms )
2a(a - 1) - 3(a - 1) = 0 ← factor out (a - 1)
(a - 1)(2a - 3) = 0
Equate each factor to zero and solve for a
a - 1 = 0 ⇒ a = 1
2a - 3 = 0 ⇒ 2a = 3 ⇒ a = [tex]\frac{3}{2}[/tex]
Answer:
a = 3/2 or 1
Step-by-step explanation:
4a²-10a+6=0
(Divide by 2)
2a²-5a+3=0
(Now factorise)
(2a-3)(a-1)
a = 3/2 or 1
How many terms are in the following sequence? 131072, ..., 8, 4, 2
Answer:
17 terms
Step-by-step explanation:
131072 = 2^17
8 = 2^3
4 = 2^2
2 = 2^1
Apparently, the sequence is powers of 2 from 17 down to 1, so there are 17 terms in the sequence.
Please help if you can i keep getting stuck
Ice cream in the shape of a sphere sits atop a cone as shown in the diagram below. Assume there is no ice cream inside the cone until after the ice cream melts. The diameter of the sphere and the diameter of the cone are both 4cm, and the height of the cone is 7.5 cm.
Part A: Determine whether the cone could contain all of the ice cream if it melted.
Part B: What would be the smallest cone in height in whole centimeters that would allow the cone to contain all of the melted ice cream if the diameter of the cone remains unchanged.
Part C: If the container of the ice cream changed to a cylinder as shown in the diagram below, what would be the smallest height of the cylinder needed to the nearest whole centimeter to contain the melted ice cream. Assume there is no ice cream n the cylinder before the ice cream melts. Please provide explanations so i can see where i messed up?
Answer:
Part A) The cone couldn't contain all the ice cream if it melted.
Part B) The height of the cone would be [tex]8\ cm[/tex]
Part C) The height of the cylinder would be [tex]3\ cm[/tex]
Step-by-step explanation:
Part A) Determine whether the cone could contain all of the ice cream if it melted
step 1
Find the volume of the ice cream (sphere)
The volume is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (2)^{3}=\frac{32}{3}\pi\ cm^{3}[/tex]
step 2
Find the volume of the cone
The volume is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
[tex]h=7.5\ cm[/tex]
substitute
[tex]V=\frac{1}{3}\pi (2)^{2}(7.5)=\frac{30}{3}\pi\ cm^{3}[/tex]
step 3
Compare the volume of the sphere and the volume of the cone
[tex]\frac{30}{3}\pi\ cm^{3} < \frac{32}{3}\pi\ cm^{3}[/tex]
The volume of the cone is less than the volume of the sphere
therefore
The cone couldn't contain all the ice cream if it melted.
Part B) What would be the smallest cone in height in whole centimeters that would allow the cone to contain all of the melted ice cream if the diameter of the cone remains unchanged
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]V=\frac{32}{3}\pi\ cm^{3}[/tex]
[tex]r=2\ cm[/tex]
substitute in the formula and solve for h
[tex]\frac{32}{3}\pi=\frac{1}{3}\pi (2)^{2}h[/tex]
simplify
[tex]32=(2)^{2}h[/tex]
[tex]32=4h[/tex]
[tex]h=32/4=8\ cm[/tex]
Part C) If the container of the ice cream changed to a cylinder as shown in the diagram below, what would be the smallest height of the cylinder needed to the nearest whole centimeter to contain the melted ice cream
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]V=\frac{32}{3}\pi\ cm^{3}[/tex]
[tex]r=2\ cm[/tex]
substitute in the formula and solve for h
[tex]\frac{32}{3}\pi=\pi (2)^{2}h[/tex]
simplify
[tex]\frac{32}{3}=(2)^{2}h[/tex]
[tex]\frac{32}{3}=4h[/tex]
[tex]h=\frac{32}{12}=2.67\ cm[/tex]
Round to the nearest whole centimeter
[tex]2.67=3\ cm[/tex]
Let u= ln x and v=ln y. Write ln(x^3y^2) in terms of u and v.
a. 3u + 2v
Step-by-step explanation:To solve this problem, we need to apply some properties of logarithms. Properties are useful to simplify complicated expressions. Here we need to use a very useful property of logarithms called the logarithm of a product is the sum of the logarithms, that is:
[tex]log_{b}(MN)=log_{b}(M)+log_{b}(N)[/tex]
From the function, it is then true that:
[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2})[/tex]
The other property we must use is Logarithm of a Power:
[tex]log_{b}M^{n}=nlog_{b}M[/tex]
Then:
[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2}) \\ \\ ln(x^{3}y^{2})=3ln(x)+2ln(y)[/tex]
Since:
[tex]u=ln(x) \\ v=ln(y)[/tex]
Then:
[tex]ln(x^{3}y^{2})=3u+2v[/tex]
Finally, the correct option is:
a. 3u + 2v
Answer:
A edge
Step-by-step explanation:
I found a place that will give me 20% discount if i spend over $50.My nill $75.How much money will i save?
Are the polygons similar? If they are, choose the correct similarity statement and scale factor.
The similarity is ΔRST ~ Δ UVW and Scale Factor is 5/6.
What is Similarity?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given:
From the Two Triangles we can see that
<VUW = <SRT = 32
and, SR / VU = TR / WU
10/ 12 = 15/ 16
5/6 = 5/6
So, By SAS similarity Criteria both Triangles are Similar.
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The perimeter of a playing field for a certain sport is 320 ft. The field is a? rectangle, and the length is 48 ft longer than the width. Find the dimensions.
Answer:
length: 104 ftwidth: 56 ftStep-by-step explanation:
Let L and W represent the length and width of the field. Then the perimeter is given by ...
P = 2(L +W)
Filling in the given information, we have ...
320 = 2(L +W)
L = W +48 . . . . . . the length is 48 ft longer than the width
Using the second equation in the first, we get
320 = 2((W +48) +W)
320 = 4W +96 . . . . . . simplify
224 = 4W . . . . . . . . . . subtract 96
56 = W . . . . . . . . . . . . .divide by 4
L = 56 +48 = 104 . . . . find L using the above relation
The width of the field is 56 ft; the length is 104 ft.
The width of the playing field is 56 ft and the length is 104 ft.
Explanation:To solve this problem, let's set up an equation using the information given. Let's say the width of the field is x ft. Since the length is 48 ft longer than the width, the length can be represented as x + 48 ft. The formula for the perimeter of a rectangle is P = 2(l + w), so we can set up the equation: 320 = 2(x + 48 + x). Now, we can solve for x by simplifying and solving the equation.
320 = 2(2x + 48)
320 = 4x + 96
4x = 320 - 96
4x = 224
x = 224/4
x = 56
So, the width of the field is 56 ft and the length is 56 + 48 = 104 ft.
To solve this problem, we must use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
According to the question, the length is 48 ft longer than the width, therefore we could express the length as L = W + 48. The perimeter provided is 320 ft. Now we can plug these values into the perimeter formula.
320 = 2(W + 48) + 2W
After simplification, this formula becomes 320 = 4W + 96.
To isolate W, you subtract 96 from both sides to get: 320 - 96 = 4W + 96 - 96, which simplifies to 224 = 4W. Dividing both sides by 4 gives W = 56 ft. This is the width of the field. The length, then, is 56 ft + 48 ft = 104 ft (since the length is 48 ft longer than the width).
So, the dimensions of the field are 104 feet by 56 feet
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I NEED HELP PLEASE!!
if Q=2.1R+5 find Q when R=5
Answer:
If Q=2.1(R)+5, then it would be 2.1(5)+5=15.5 ?
Step-by-step explanation:
Find the lowest common denominator for these fractions and then add and simplify. 2/3 and 1/6
Answer:
Step-by-step explanation:
12 is the common denominator
The answer will be 6!!
I'm taking a chance on a spinner with 20 outcomes how likely is to land on an even number
Answer:
50% chance
Step-by-step explanation:
You would have a 50% chance of landing on a even number
If the relation is a function, list the domain and range. If the relation is not a function, choose "not a function". C = {(9, 1) (8, -3) (7, 5) (-5, 3)} Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3} Domain: {1, -3, 5, 3} Range: {9, 8, 7, -5} not a function
Answer:
Domain: {9, 8, 7, -5}Range: {1, -3, 5, 3}Step-by-step explanation:
The function is a special relationship where each input has a single output.
We have C = {(9, 1); (8, -3); (7, 5); (-5, 3)}.
It's a function:
each values of x: 9, 8, 7, -5 has one value of y: 1, -3, 5, 3.
The doimain is set os x: {9, 8, 7, -5}.
The range is set of y: { 1, -3, 5, 3}.
F = {(x, y ) | x + y = 10}.
Domain: {10} Range: {10}