Answer: The smallest possible area of the tabletop=[tex]113\text{ square inches}[/tex]
The largest possible area of the tabletop =[tex]1662\text{ square inches}[/tex]
Step-by-step explanation:
Given: The minimum radius of the tabletop = 6 inches
The maximum radius of the tabletop = 23 inches
We know that the area of circle is given by :-
[tex]A=\pi r^2[/tex], where r is the radius of the circle.
Now, the smallest possible area of the tabletop that will fit on Timothy’s table is given by :-
[tex]A_s=(3.14159265359) (6)^2=113.097335529\approx113\text{ square inches}[/tex]
The largest possible area of the tabletop that will fit on Timothy’s table is given by :-
[tex]A_s=(3.14159265359) (23)^2=1661.90251375\approx1662\text{ square inches}[/tex]
Answer:
113 square inches
1,662 square inches
Step-by-step explanation: Have a good day :)
What is the five-number summary for the data set?
76, 100, 88, 83, 97, 94, 90, 99, 82, 86, 95, 81, 79, 95
Enter your answers in the boxes.
Minimum:
First quartile:
Median:
Third quartile:
Maximum:
Answer:
Min: 76
Q1: 82
Med: 89
Q2: 95
Max: 100
Step-by-step explanation:
First arrange the data set 76, 100, 88, 83, 97, 94, 90, 99, 82, 86, 95, 81, 79, 95 in ascending order:
76, 79, 81, 82, 83, 86, 88, 90, 94, 95, 95, 97, 99, 100
The minimum number is 76 and the maximum number is 100. There are 14 numbers, the median is the average of two middle terms:
[tex]Med=\dfrac{88+90}{2}=89[/tex]
The middle term of first 7 numbers is 82 and the middle term of the second seven numbers is 95, so the five-number summary is
Min: 76
Q1: 82
Med: 89
Q2: 95
Max: 100
Solve the equation of e^x-2=(1/e^6)^x+3.
Answer:
x = -16/7
Step-by-step explanation:
The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...
x ≈ 1.60945071137
_____
Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...
e^(x-2) = (1/e^6)^(x+3)
x -2 = -6(x +3) . . . . . . . . take the natural log of both sides
x -2 = -6x -18 . . . . . . . . . eliminate parentheses
7x -2 = -18 . . . . . . . . . . . add 6x
7x = -16 . . . . . . . . . . . . . add 2
x = -16/7
16.4
19.6
10.6
21.2
question 45
Answer: FIRST OPTION
Step-by-step explanation:
You need the formula for calculate the arc lenght:
[tex]arc\ length=2\pi r(\frac{C}{360})[/tex]
Where "r" is the radius and and "C" is the central angle in degrees.
You know that the radius is:
[tex]r=7.5[/tex]
And the central angle ∠CAT is:
[tex]C=\angle CAT=125\°[/tex]
Then, you need to substitute these values into the formula [tex]arc\ length=2\pi r(\frac{C}{360})[/tex] to calculate the length of CT.
Then, this is:
[tex]arc\ length=CT=2\pi (7.5)(\frac{125\°}{360})[/tex]
[tex]arc\ length=CT=16.4[/tex]
Edward wants to have $50,000 in 10 years for college. What single deposit would he need to make now into
an account that pays 4.3% interest, compounded daily, to meet his goal?
Answer:
[tex]\$32,526.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ A=\$50,000\\ r=0.043\\n=365[/tex]
substitute in the formula above
[tex]\$50,000=P(1+\frac{0.043}{365})^{365*10}[/tex]
[tex]P=\$50,000/[(1+\frac{0.043}{365})^{3,650}]=\$32,526.28[/tex]
What are the domain and range of the piecewise function below? HELP ASAP
The domain is the set of all point where you can evaluate the function.
As you can see, the first piece is defined from -infinity to 2 (included).
The second piece is defined from 2 to 6 (excluded).
The third piece is defined from 6 (excluded) to +infinity.
So, the domain of the function is composed by all the real numbers which are not 6:
[tex](-\infty,6)\cup(6,\infty) = \mathbb{R}\setminus\{6\} = \{x \in \mathbb{R}\ :\ x\neq 6\}[/tex]
As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.
The second piece is constantly equal to 2, so it adds nothing.
The third piece spans the y axis from -2 to -infinity, so the range is
[tex](-\infty,-2)\cup[0,\infty) = \mathbb{R}\setminus [2,0) = \{x \in \mathbb{R}\ :\ x\geq 0\ \lor\ x<-2\}[/tex]
The domain is the set of all point where you can evaluate the function.
As you can see, the first piece is defined from -infinity to 2 (included).
The second piece is defined from 2 to 6 (excluded).
The third piece is defined from 6 (excluded) to +infinity.
So, the domain of the function is composed by all the real numbers which are not 6:
As for the range, it is the set of all values taken by the function. We can see that the first piece spans the y axis from 0 to infinity.
The second piece is constantly equal to 2, so it adds nothing.
The third piece spans the y axis from -2 to -infinity, so the range is
jason answered 12 questions correctly on a test worth 150 points. each question was worth 10 points. what percent did jason earn on the test?
Answer:
He earned 120% out of 150%.
Step-by-step explanation:
The test is work 150 points, while each question being 10 points each, so we can divide this and we will get 15 questions. Then we can just multiple, 10 by 12 and get 120, this means he got 12 out of 15 questions right, or 120%out of 150%.
If the volume of a rectangular prism is 1440cm, width is 5cm length is 2cm what is the height
Answer:144
Step-by-step explanation: 144 since width times length times height equals volume. so 5 times 2 times ? equals 1440. So 10 times ? equals 1440. So next 1440 divided by 10 equals 144. So the answer is 144.
Answer:
Step-by-step explanation:
144 cm.
HELPPPPPPP Consider the equation 3/4 y = 2.4x. Solve the equation for y. What is the constant of proportionality?
1.8y is the answer because first you do 3/4y into a decimals number and then it’s 0.75 then I times it by 2.4 which is 1.8y
To solve the equation 3/4 y = 2.4x for y, we multiply both sides of the equation by 4/3 to eliminate the fraction. Simplifying the equation gives us y = 3.2x. The constant of proportionality in this equation is 3.2.
Explanation:To solve the equation 3/4 y = 2.4x for y, we need to isolate y on one side of the equation. First, we can multiply both sides of the equation by 4/3 to eliminate the fraction:
3/4 * y = 2.4x
y = (2.4x)/(3/4)
Next, we can simplify the equation by multiplying the numerator and denominator of the fraction by the reciprocal of 3/4, which is 4/3:
y = (2.4x) * (4/3)
y = (9.6x)/3
y = 3.2x
Therefore, the equation 3/4 y = 2.4x can be solved for y to give the expression y = 3.2x. The constant of proportionality in this equation is 3.2, which indicates that y is directly proportional to x with a scale factor of 3.2.
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A city in the country determines public servants different than usual. The city asks citizens to rank candidates and the person with the highest point total wins. First place votes get 4 points, second place votes get 2 points and third place votes get 1 point. If John Tyler received 867 first place votes, 301 second place votes and 432 third place votes, how many total points did he obtain?
A) 1600
B) 2467
C) 3370
D) 4502
First Place Vote: 4x867= 3468
Second Place Vote: 2x301= 602
Third Place Vote: 1x432= 432
3468+602+432= 4502.
Your answer is therefore D.
I hope this helps! :)
Answer:
D) 4502
Step-by-step explanation:
It is given that,
Points for first place = 4 points
Second place = 2 points
Third place = 1 point
Thus, First Place Vote : 4 × 867 = 3468
Second Place Vote: 2 × 301= 602
Third Place Vote: 1 × 432= 432
Thus, Total Points = 3468 + 602 + 432 = 4502.
Hence, last option is correct.
Harold moves no more than 43 of his sheep and goats into another field. Fewer than 22 of his animals are goats.
Let s represent the number of sheep and g represent the number of goats identify two inequalities that represent this situation.
A. g<22
B. s>22
C. s+<43 with the line under
D. s-g<45 with the line under
Answer:Options 'A' and 'C' are correct.
Step-by-step explanation:
Let the number of sheep be 's'.
Let the number of goats be 'g'.
According to question, we have given that
the number of sheep and goats are not more than 43.
The number of goats are fewer than 22.
So, the inequalities would be
[tex]g<22\\\\and\\\\s+g<43[/tex]
Hence, Options 'A' and 'C' are correct.
The two inequalities for Harold's sheep and goats situation are A. g < 22 and C. s + g ≤ 43.
To represent the situation described about Harold's sheep and goats, we need to set up two inequalities based on the given information:
A. g < 22: This inequality indicates that the number of goats (g) is fewer than 22.C. s + g ≤ 43: This inequality means that the total number of sheep and goats combined (s + g) is at most 43.Using these inequalities, we can help Harold determine how to distribute his sheep and goats in the new field.
HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELP!
Answer:
Five more than the square of a number= 5 + x²
Five more than twice a number = 5 + 2x
Five less than the product of 3 and a number = 3x - 5
Five less the product of 3 and a number = 5 -3x
Twice the sum of a number and 5 = 2(x + 5)
The sum of twice a number and 5 = 2x + 5
The product of a cube of a number and 5= 5x³
The cube of the product of 5 and a number= (5x)³
Olá
Answer:
(5x)³=
(5x) ao cubo
5.5.5=125X³
2(x+5)= 2x+10
2x=10
x=10/2
X=5
2x+5= 2x - 5 = 0
2x = 0 + 5
2x = 5
x = 5/2
3x-5= 3x= +5
X= 5/3 or X= 1,6
5+2x= 2x=-5
X= -5/2
5+x²= x²+5 a=1 b= 5 c=0
5²-4.1.0 (corta,pois -4.1.0=0)
=25
x= -b +/- raíz de bhaskara/ 2.a
x=-5 +/- 5/2
x'= 0/2=0
x"= -10/2= -5
5-3x= 3x=-5
X= -5/3
5x³ = 0 a=5 b= 0 c=0
0²-4.5.0
= 0 (duas raízes reais e iguais)
x'= 0
x"= 0
Espero ajudar♥
Jada,Elena,and lin walked a total of 37 miles last week. Jada walked 4 more miles than Elena, and Lin walked two more miles than jada.
What is your question??
The sum of two numbers is equal to 63 and their difference is equal to 12. Find the numbers.
Answer:
a + b = 63
a - b = 12
So, a - b = 12 which can also be written as a = b + 12
Then use substitution and plug in (b + 12) for a in the first equation
(b+12) + b =63
-12 -12
---------------------
2b = 51 so b=25.5
Now, you know b which can be used to find a
63- 25.5= 37.5
So, a = 37.5 and b = 25.5
Answer:
25.5 and 37.5
Step-by-step explanation:
37.5-12=25.5
25.5+37.5=63
(0, -3), (2, -2), (4, -1), (6, 0),...
These ordered pairs follow a pattern. If (10, y) is in this pattern, what is the value of y?
f 4 g 1 h 3 j 2
the answer is J) 2
because the x values are going up in twos and the yard values are adding one each time.
so
(8,1)
and
(10, 2)
hope this helps
Please Answer this question.
Answer:
The correct answer option is A. [tex]\frac{x^{12}}{64}[/tex].
Step-by-step explanation:
We are given the following expression and we are to simplify it:
[tex] ( 4 x ^ { - 4 } ) ^ { - 3 } [/tex]
Distributing the power among the terms to get:
[tex] 4 ^ { - 3 } . 4 ^ { - 4 * - 3 } [/tex]
[tex]4^{-3}.x^{12}[/tex]
[tex]\frac{x^{12}}{4^3}[/tex]
[tex] \frac { x ^ { 1 2 } } { 6 4 } [/tex]
Help Me PLZZZZZZZ
Raoul's taxable income is $38,438. He is filling as head of household, and he has already paid $4428 in federal taxas.
What will he receive or pay after he figueres his taxas for the year?
Options:
A. He will receive a refund of $908
B. He will pay $908
C.He Will receive a Refund of $916
D.He will pay $916
Answer:
He will pay 916
Step-by-step explanation:
The following image is a graph of f(t)= a sin(bt+c)+d. Use the graph to determine the amplitude, period, phase shift, and vertical shift of the function.
Answer:
Step-by-step explanation:
b.)
amplitude: 4
period; 4pi
phase shift; pi/2
vertical shift: -3
Analyzing the graph shows that the parameters are in
b. amplitude: 4
period; 4π
phase shift; π/2
vertical shift: -3
What is amplitude?Amplitude: The amplitude of a periodic function is the measure of its maximum displacement from its average or equilibrium position.
Period: The period of a periodic function is the distance along the x-axis between one cycle of the function and the next identical cycle.
Vertical Shift: The vertical shift (or translation) of a function is a vertical displacement of the entire graph either upward or downward.
Phase Shift: The phase shift is a horizontal displacement or translation of a function.
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Amir pitches a baseball at an initial height of 6 feet, with a velocity of 73 feet per second. If the batter misses, about how long does it take the ball hit the ground?
Hint: Use H(t) = −16t2 + vt + s.
4.64 seconds
2.94 seconds
2.28 seconds
0.08 second
Answer:4.64
Step-by-step explanation: I took the test on this and it was correct
Answer:
4.64
Step-by-step explanation:
bcuz sir ghost said so
Find the Area of the circle
Answer: 530 cm^2
Step-by-step explanation:
A = 3.14 * r^2
A = 3.14 * 13 * 13
A = 3.14 * 169
A = 530 cm ^2
Which of the following is equal to sqrt. (50(a^6) (b^7))
Answer:
5 · a³ · b³ · √5b
Step-by-step explanation:
Start with √(50a^6b^7). Rewrite 50 as the product of the largest possible perfect square and a multiplier: 50 = 25 · 2. Then √50 = 5√2.
a^6 is already a perfect square, so find its square root: √a^6 = a^3.
b^7 = b · b^6, so √b^7 = b^3√b
Now rewrite (50(a^6) (b^7)) as √(50a^6b^7).
Then rewrite √(50a^6b^7) as 5√2 · a³ · b³ · √b.
This latter result can be simplified to 5 · a³ · b³ · √5b
This matches possible answer #1.
A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
The wide would be 7.2 cm
Step-by-step explanation:
Let
x------> the wide of the proportional wall map
we know that
Using proportion
45/27=12/x
x=27*12/45
x=7.2 cm
A football team lost a total of 56 yards in their first game. Which expression results in an integer that represents the team's average per quarter? IF YOU DON"T KNOW THE ANSWER PLEASE DON'T ANSWER! AND PROVIDE AN EXPLANATION IF YOU CAN!
F. \frac{-56}{4}
G. -56 Divided by 25
H -56 divided by (-4)
J. \frac{56}{-25}
Answer:
F
Step-by-step explanation:
You have to divide the the total number of yards lost (so 56) by 4 quarters. We know that lost yards are negative so therefore -56 divided by 4 is the answer
Which expression represents the volume of the cone that is times the volume of the pyramid that it fits inside? (2r2h) (4r2h)
Answer:
D! found it out for the brainly gang:)
Step-by-step explanation:
The expression represents the volume of the cone that is times the volume of the pyramid that it fits inside is Pi/4(4r²/3).
We have given that the expression represents the volume of the cone
that is times the volume of the pyramid that it fits inside
(2r^2h) (4r^2h)
What is the formula for the volume of the cone?
The formula for the volume of a cone is ⅓ r^2h cubic units.
where r is the radius of the circular base and h is the height of the cone.
Therefore from the given we get the volume of a pyramid is Pi/4(4r²/3).
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20. what is the missing value to the nearest hundredth
tan _ = 15
• 0.97°
• 0.27°
• 88.09°
• 86.19°
Answer:
86.19°
Step-by-step explanation:
Let x represent the missing value.
The given trigonometric equation becomes:
[tex]\tan x=15[/tex]
We take the inverse tangent of both sides to obtain:
[tex]\tan^{-1}(\tan x)=\tan^{-1}(15)[/tex]
This implies that;
[tex]x=\tan^{-1}(15)[/tex]
We use at least a scientific calculator to evaluate this and obtain:
[tex]x=86.18592517\degree[/tex]
To the nearest hundredth, the missing value is [tex]x=86.19\degree[/tex]
The price of an item yesterday was $160 . Today, the price fell to 104 . Find the percentage decrease.
Jesse wants to go skydiving. Each skydive is 14,000 feet high. Jesse wants to do 2 jumps which will cost him $400. In addition, Jesse must pay a $100 training fee. What is the price per foot of skydive if the training fee is added to the final price?
Answer:
Price per foot of skydive is 31.11 repeated, or 31 1/9
Step-by-step explanation:
Jesse is going on 2 jumps, which is 14000*2=28000.
Each Skydive is $400, and two jumps would be $800. Plus a $100 training fee, it would cost $900 for 2 jumps.
28000/900=31.1111 repeated.
A trebuchet launches a projectile from a hilltop 30 feet above ground level on a parabolic arc at a velocity of 40 feet per second. The equation h = ?16t2 + 40t + 30 models the projectile's h height at t seconds. How long will it take for the projectile to hit its target on the ground? (to the nearest tenth of a second)
Answer:
t = 3.1 seconds
Step-by-step explanation:
Set the equation h = -16t^2 + 40t + 30 equal to 0 (0 represents ground level).
Then h = -16t^2 + 40t + 30 = 0
Applying the quadratic formula with a = -16, b = 40 and c = 30,
-40 ± √( 1600 - 4[-16][30] )
t = -----------------------------------------
2(-16)
-40 ± √ 3520
t = -------------------------
-32
-40 - 59.33
Only the positive t value makes sense. It is t = ------------------
-32
t = 3.1 seconds
The volume of a rectangular prism is 3 25/36 cubic units, and the base area of the prism is 3 1/6 square units. The height of the rectangular prism is a. 1 1/6units b. 1 1/2 units c. 3 1/6 units d. 3 1/3 units. The number of cubic blocks, each with a volume of 1/36 cubic units, needed to fill the rectangular prism is a. 7 b. 19 c. 133 d. 152. ?
Answer:
The height of the prism is [tex]1\frac{1}{6}[/tex] units ⇒ answer a
The number of blocks needed is 133 ⇒ answer c
Step-by-step explanation:
* Lets explain how to solve the problem
- The volume of a rectangular prism is
→ V = Area of the base × its height
- The volume of the rectangular prism is [tex]3\frac{25}{36}[/tex] units³
- The area of its base is [tex]3\frac{1}{6}[/tex] units²
- Substitute the values of the volume and area of the base in the rule
∴ [tex]3\frac{25}{36}=3\frac{1}{6}*h[/tex]
- Divide the two sides by [tex]3\frac{1}{6}[/tex]
∴ [tex]h=\frac{7}{6}=1\frac{1}{6}[/tex] units
* The height of the prism is [tex]1\frac{1}{6}[/tex] units
- The volume of each cubic block is [tex]\frac{1}{36}[/tex] units³
- The number of blocks = volume of the prism ÷ volume of the block
∵ The volume of the prism is [tex]3\frac{25}{36}[/tex] units³
∵ The volume of each block is [tex]\frac{1}{36}[/tex] units³
∴ The number of blocks = [tex]3\frac{25}{36}[/tex] ÷ [tex]\frac{1}{36}=133[/tex]
∴ The number of blocks = 133
* The number of blocks needed is 133
Answer:
1st one is 1 1/6
2nd one is 133
I did the test on Plato and this was right :)
ΔABC is similar to ΔMNO. The scale factor of ΔABC to ΔMNO is 3⁄2. What's the length of NO?
A. 4 units
B. 1 unit
C. 3⁄2 units
D. 6 units
Answer:
a
Step-by-step explanation:
When two triangles are similar, their corresponding sides are in proportion. The length of NO cannot be determined from the given information.
Explanation:When two triangles are similar, their corresponding sides are in proportion. In this case, the scale factor is 3/2, meaning that the corresponding sides of triangle ABC and triangle MNO are in the ratio of 3:2.
To find the length of side NO, we can set up the proportion:
AB/MN = BC/NO = AC/OO
Since we know that AB = 3 and MN = 2, we can solve for NO:
3/2 = BC/NO
3NO = 2BC
NO = (2/3)BC
Therefore, the length of NO is (2/3) times the length of BC.
Since we don't know the length of BC, we cannot determine the exact length of NO. The answer choices provided do not match the information given, so none of the given options can be correct.
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Mahmoud spent 1/6 of the day working in the flower bed Mahmoud spent 2/3 of that time adding mulch to the flower bed what fraction of the day did Mahmoud spend adding mulch?
Answer: 5/6
Step-by-step explanation:
Add both of the fractions.
1/6+ 2/3
Need to make the denominator the same for both fractions.
Denominator would be 6. Multiply by 2 up and down for 2/3
1/6+4/6
5/6