Answer:
Step-by-step explanation:
We have the equation
[tex] 2(3^t) = 1458[/tex]
Dividing by 2 on both sides we get
[tex] 3^t = 729[/tex]
Taking the natural logarithm on both sides we get
[tex] t \ln(3) = \ln(729)[/tex]
So t = \frac{\ln(729)}{\ln(3)} = 6.
So at 6 weeks we get 1458 infected people.
The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of the object.
Answer:
v=√E/m or v=√E /√m
Step-by-step explanation:
Complete question below:
The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of
the object.
E = mv^2
Solve the formula for v.
Solution
E=mv^2
Where,
E=kinetic energy
m=mass
v=speed of the object
E=mv^2
Divide both sides by m
E/m=mv^2/m
E/m=v^2
It can be rewritten as
v^2=E/m
Square root both sides
√(v^2)=√E/m
v=√E/m
Or
v=√E/√m
This is to say speed (v)=square root of kinetic energy (E) Over masa(m)
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 61 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 61 and 94?
Answer:
P(61≤ X≤94) = 49.85%
Step-by-step explanation:
From the given information:
The mean of the bell shaped fluorescent light bulb μ = 61
The standard deviation σ = 11
The objective of this question is to determine the approximate percentage of light bulb replacement requests numbering between 61 and 94 i.e P(61≤ X≤94)
Using the empirical (68-95-99.7)rule ;
At 68% , the data lies between μ - σ and μ + σ
i.e
61 - 11 and 61 + 11
50 and 72
At 95%, the data lies between μ - 2σ and μ + 2σ
i.e
61 - 2(11) and 61 + 2(11)
61 - 22 and 61 +22
39 and 83
At 99.7%, the data lies between μ - 3σ and μ + 3σ
i.e
61 - 3(11) and 61 + 3(11)
61 - 33 and 61 + 33
28 and 94
the probability equivalent to 94 is when P(28≤ X≤94) =99.7%
This implies that ,
P(28≤ X≤94) + P(61≤ X≤94) = 99.7%
P(28≤ X≤94) = P(61≤ X≤94) = 99.7 %
This is so because the distribution is symmetric about the mean
P(61≤ X≤94) = 99.7 %/2
P(61≤ X≤94) = 49.85%
Use Descartes' Rule of Signs to find the number of possible positive real roots and the number of possible negative real roots for the function f(x) = x^4+ 2x^3-3x^2- 8x - 4.
a positive 1; negative 3 or 1
b. positive 1; negative 3 or 5
C. positive 3; negative 3 or 1
d. positive 3; negative 3 or 5
Answer:
a positive 1; negative 3 or 1
Step-by-step explanation:
To determine the number of positive roots, we have to determine the number of sign changes for f(x) = x⁴ + 2x³ - 3x² - 8x - 4.
The coefficients in f(x) are +1, +2, -3, -8, -4.
Since there is only one sign change from +2 to -3, we have 1 positive root.
To determine the number of negative roots, we have to determine the number of sign changes for f(-x) = (-x)⁴ + 2(-x)³ - 3(-x)² - 8(-x) - 4 = x⁴ - 2x³ - 3x² + 8x - 4
The coefficients in f(-x) are +1, -2, -3, +8, -4.
Since there is three sign change from +1 to -2, from -3 to +8, and from +8 to -4. So,we have 3 or 1 negative root, since the number of negative roots is equal to the number of sign changes or an even number less than the number of sign changes. So, 3 -2 = 1
So, the number roots are of positive 1; negative 3 or 1
Answer:
a.positive 1; negative 3 or 1
Step-by-step explanation:
EDGE 2020
Which equation describes the line graphed above? A. -4x-5 B. -1/5x-4 C. -5x-4 C. -4x-1/5
The equation is -1/5x-4 represented by the graph. The correct option is B.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Let us check the equation -1/5x-4. The line goes down one and turns right 5. The Slope is -1/5x and the y-intercept is at -4. The graph of the equation is attached with the answer below.
Hence, option B is correct.
To know more about equations follow
https://brainly.com/question/2972832
#SPJ5
P = e f e = 4.8 correct to 2 significant figures. f = 0.26 correct to 2 significant figures. Work out the lower bound for the value of P . Give your answer correct to 3 significant figures. (2 marks)
Answer:
Step-by-step explanation:
P = efe =4.8
f =0.26
substitute the value of P and f into the equation to obtain the value of e
4.8 = e*0.26*e
4.8 = 0.26*e^2
make e^2 the subject of the formula
e^2 =4.8/0.26 =18.62
find the square root of e
e =[tex]\sqrt{x} 18.46\\[/tex]
e = 4.3
Lower bound of P = 4.8 - 4.79 = 0.01
Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees. What is the measure of angle O in parallelogram LMNO? 35° 75° 105° 155
Answer:
C, 105 Degrees
Step-by-step explanation:
So the two opposite sides of a parallelogram is equal to each other and the two adjacent angles are supplementary. So if (x+40)+3x=180, this means that 4x+40=180. This gives us 4x=140, so x=35. If we plug it back into the equation it ascertains as such: 3(35)= 105. The answer for this question and angle O is 105 degrees, or C.
The measure of angle O in this parallelogram is 105°.
The properties of a parallelogramThe opposite angles of a parallelogram are equal.The Opposite sides of the parallelogram are equal and parallel.The diagonals of the parallelogram bisect each other.The Sum of the angles = 360°
Solution
Because the properties says that opposite angles are equal.
Angle L = (x + 40)
angle O = (3 x)
Applying the first property
x+40+x+40+3x+3x = 360
collect the like termsx+x+3x+3x+40+40 = 360
8x+80 = 360
8x = 360-80
8x = 280
Divide through the equation by 8
x = 280/8
x = 35
The question wants us to find the value of angle O
O = 3x
O = 3*35
= 105
The value of angle O is equal to 105°
Read more on parallelograms here:
https://brainly.com/question/970600
Job A3B was ordered by a customer on September 25. During the month of September, Jaycee Corporation requisitioned $3,200 of direct materials and used $4,700 of direct labor. The job was not finished by the end of September, but needed an additional $3,700 of direct materials and additional direct labor of $7,900 to finish the job in October. The company applies overhead at the end of each month at a rate of 150% of the direct labor cost incurred. What is the balance in the Work in Process account at the end of September relative to Job A3B?
Answer: $14,950
Step-by-step explanation:
Given: Cost of Direct Materials = $3,200
Cost of direct labor = $4,700
Overhead rate = 150%
So, Overhead cost = 150% x (Total direct labor cost)
= $(150% x 4,700) =$ ( 1.5 x 4,700) [150% = 1.5]
= $7,050
Work in Progress = Direct Materials + Direct labor + Overhead
= $(3,200+4,700+7,050)
=$14,950
Hence, the balance in the Work in Process account at the end of September relative to Job A3B = $14,950
Please help me with this question ASAP!
Answer:
The fourthStep-by-step explanation:
[tex]x^2+y^2-14x+10y+25=0\\\\x^2-14x\ +\ y^2+10y+25=0\\\\\underline{x^2-14x+49} -49+\underline{y^2+10y+25}=0\\\\\underline{x^2-2\cdot x\cdot7+7^2}-49+\underline{y^2+2\cdot y\cdot5+5^2}=0 \\\\\underline{(x-7)^2}-49+\underline{(y+5)^2}=0\\\\\underline{\underline{(x-7)^2+(y+5)^2=49}}[/tex]
URGENT
What else would need to be congruent to show that AABC= ADEF by the
AAS theorem?
Answer:
AC = EF
Step-by-step explanation:
ABC = DEF
You would need to know that AC = EF
In the first place, using deduction we know that we dont need another angle. We also know that BC does not equal DF by looking at the angles on the triangles.
The solution is : ∠C ≅ ∠F is congruent to show that ΔABC ≅ ΔDEF, else would need to be congruent to show that AABC= ADEF by the AAS theorem.
What is AAS theorem?The angle-angle-side theorem, or AAS, tells us that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.
here, we have,
to find congruency in a triangle:
ΔABC ≅ ΔDEF
Therefore,
AAS congruence rule or theorem states that if two angles of a triangle with a non-included side are equal to the corresponding angles and non-included side of the other triangle, they are considered to be congruent.
Therefore,
∠C ≅ ∠F
Hence, The solution is : ∠C ≅ ∠F is congruent to show that ΔABC ≅ ΔDEF, else would need to be congruent to show that AABC= ADEF by the AAS theorem.
learn more on AAS here:
brainly.com/question/2699309
#SPJ7
Is (0, 3) a solution to the following system?
Y=-x+3
Y=2x-3
A No, because it does not check in either equation.
B. No, because it does not check in the first equation.
C. No, because it does not check in the second equation.
D. Yes, because it checks in both equations.
Solve each equation with (0, 3)
y = -x + 3
3 = -0 + 3
y = 3 (correct since y = 3 in (0, 3))
y = 2x - 3
3 = 2(0) - 3
3 = 0 - 3
3 = -3 (incorrect since it isn't equal)
So... No, because it does not check in the second equation.
Best of Luck!
Find the y-intercept and the axis of symmetry of f(x)=ax2+2ax+3.
Answer:
[tex] y= cx^2 +dx +e[/tex]
We see that:
[tex] c = a, d= 2a , e= 3[/tex]
The axis of symmetry is defined by this formula:
[tex] X= - \frac{d}{2c}[/tex]
And replacing we got:
[tex] X= -\frac{2a}{2a}= -1[/tex]
Thn the axis of symmetry would be X=-1
Step-by-step explanation:
For this case we have the following function:
[tex] y = ax^2 +2ax +3[/tex]
If we compare this function with the general expression of a quadratic formula given by:
[tex] y= cx^2 +dx +e[/tex]
We see that:
[tex] c = a, d= 2a , e= 3[/tex]
The axis of symmetry is defined by this formula:
[tex] X= - \frac{d}{2c}[/tex]
And replacing we got:
[tex] X= -\frac{2a}{2a}= -1[/tex]
Thn the axis of symmetry would be X=-1
Look at triangle ABC
A (4.5)
5
4
3
2
1
B (2.2)
C (4.2)
1
5 -4 -3 -2 -1 0
1
23
4
5
-1
N
-3
-4
5
What is the length of side AB of the triangle?
A) 3
B) 5
C) square root of 6
D) square root of 13
Answer:
[tex] \sqrt{13} [/tex]Option D is the correct option.
Step-by-step explanation:
Given,
A ( 4, 5 ) , B ( 2 , 2 ) , C ( 4 , 2 )
Let,
A ( 4 , 5 ) → ( x1 , y1 )
B ( 2 , 2 ) → ( x2 , y2 )
Now, finding the length of AB
Use the distance formula to find the length of AB
[tex] = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
plug the values
[tex] = \sqrt{ {(2 - 4)}^{2} + {(2 - 5)}^{2} } [/tex]
Calculate the difference
[tex] = \sqrt{ {( - 2)}^{2} + {( - 3)}^{2} } [/tex]
Evaluate the power
[tex] = \sqrt{4 + 9} [/tex]
Add the numbers
[tex] = \sqrt{13} [/tex]
Hope this helps..
Best regards!!
What is the value of 3x squared when x = 2?
Answer:
Step-by-step explanation:
[tex](3x)^{2}[/tex]=[tex](3(2))^{2}[/tex] =36
(OR)
3([tex]x^{2}[/tex])=3(4)=12
Its depend on your sentence structure, what u r asking!!
The value of 3x squared when x = 2 is 36.
Given expression [tex](3x)^2[/tex].
We have to calculate the value of this at [tex]x=2[/tex].
Now putting the value of x in the expression we get,
[tex](3\times2)^{2}[/tex]
Or,[tex]6^{2}[/tex]
[tex]36[/tex]
Hence the value of [tex](3x)^2[/tex] at [tex]x=2[/tex] will be 36.
For more details follow the link:
https://brainly.com/question/14170328
Bella is going back to school shopping and her favorite store is having a sale. She sees there are 4 packages of 15 tops for $18 and 5 packages of 10 tops for $16 which is the better deal? How do you know
Answer:
The 4 packages of 15 tops for $18 is a better deal
Step-by-step explanation:
We can see which set of tops have the lowest unit price.
4 packages of 15 tops for $18:
4*15=60
There is a total of 60 tops for $18, which means each top costs 18/60 dollars, or $0.30.
5 packages of 10 tops for $16
5*10=50
There is a total of 50 tops for $16, which means that each top costs 16/50 dollars, or $0.32.
0.32>0.3
The 4 packages of 15 tops for $18 is a better deal :)
Have a great day
513 to the nearest 100
Answer:
500
Step-by-step explanation:
Answer:
500
Step-by-step explanation:
2
What is the solution of the equation 6x - 3 = -51?
A. -9
B. -8
c. 8.
D. 9
Answer:
x = -8
Step-by-step explanation:
6x - 3 = -51
Add 3 to each side
6x - 3+3 = -51+3
6x = -48
Divide each side by 6
6x/6 = -48/6
x = -8
A shoe salesperson earns a 5% bonus on weekly sales over $3,000. Consider these functions to answer the following questions. f(x) = x – 3,000 g(x) = 0.05x Part A In your own words, explain what each of the functions represents.
Answer:
g(x)= 0.05x represents the amount of bonus, f(x)=x-3,000 represents weekly sales over $3,000.
Step-by-step explanation:
The function f(x) represents how much money earned by sales person weekly over $3000.
And function g(x) represents the amount of bonus earned by salesperson.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called function.
According to the given question.
The percent of bonus earned by salesperson weekly on sales over $3,000 is 5%.
Also, we have two functions.
[tex]f(x) = x - 3000[/tex]
and [tex]g(x) = 0.05x[/tex]
For the function, f(x) if x is the amount of money earned salesperson in a week, then f(x) will represents how much money salesperson earned apart form $3000.
And the function g(x) represents the amount of bonus earned by the salesperson.
Hence, the function f(x) represents how much money earned by sales person weekly over $3000. And function g(x) represents the amount of bonus earned by salesperson.
Find out more information about function here:
https://brainly.com/question/12431044
#SPJ2
Please answer this now in two minutes
Answer:
x = 6.6
Step-by-step explanation:
Data obtained from the question include the following:
Angle X = 15°
Angle Y° = 23°
Side y = 10
Side x =..?
The value of side x can be obtained by using the sine rule as shown below:
x/Sine X = y/Sine Y
x/Sine 15 = 10/Sine 23
Cross multiply
x × Sine 23 = 10 × Sine 15
Divide both side by Sine 23
x = (10 × Sine 15) / Sine 23
x = 6.6
Therefore, the value of x is 6.6.
please help :) Which expression is equivalent to 7 × 7 × 7? A.) 3 times 7 B.) 3 to the 7 power C.) 7 times 7 times 7 times 3 D.) 7 to the 3 power
Answer: D) 7 to the 3 power.
Step-by-step explanation:
Answer:
D. 7 to the 3 power
Step-by-step explanation:
I know I'm very late but dont judge :V
This is also seven t the power of three
Find the local and global extrema for the polynomial function f whose complete graph is provided.
Answer:
your mark is correct
Step-by-step explanation:
The marked answer choice is correct.
(2, -18) is not a global minimum, because there are function values that are lower.
(0, -6) is not a global maximum, because there are function values that are higher.
A global maximum is also a local maximum.*
_____
* More correctly, a global maximum is either a local maximum or the end point of an interval. No intervals are involved in this question.
What is the value of x in the triangle? a 30-60-90 triangle with short leg length x and hypotenuse length 8 A. B. C. D.
In a 30-60-90 triangle with short leg length x and hypotenuse length 8. the value of x in the triangle is 8 [tex]\sqrt{3}[/tex] / 3.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the longest side and is referred to as the hypotenuse.
In a 30-60-90 triangle the ratio of the side lengths is 1 : 2 : [tex]\sqrt{3}[/tex]
To find the length of the short leg, x, you can create this proportion:
x / 8 = 1 / [tex]\sqrt{3}[/tex]
x = 8 × 1 / [tex]\sqrt{3}[/tex]
x = 8 / [tex]\sqrt{3}[/tex]
By rationalizing the denominator by multiplying the numerator and denominator by [tex]\sqrt{3}[/tex].
x = 8 [tex]\sqrt{3}[/tex] / 3
Learn more about the right triangle;
https://brainly.com/question/6322314
Angle bcd is a circumscribed angle of circle a. What is the length of line segment ac?
Step-by-step explanation:
Answer:
The length of segment AC is 10 units ⇒ 1st answer
Step-by-step explanation:
Look to the attached figure
In circle A
∵ AB is a radius
∵ BC is a tangent to circle A at B
- The radius and the tangent are perpendicular to each other
at the point of contact
∴ AB ⊥ BC at point B
∴ m∠ABC = 90°
In ΔABC
∵ m∠B = 90°
∵ AB = 8 units
∵ BC = 6 units
- By using Pythagoras Theorem (Square the hypotenuse is
equal to the sum of the squares of the other two sides of
the triangle)
∵ (AC)² = (AB)² + (BC)²
∴ (AC)² = (8)² +(6)²
∴ (AC)² = 64 + 36
∴ (AC)² = 100
- Take √ for both sides
∴ AC = 10 units
The length of segment AC is 10 units
follow me plzzz
Answer:A
On edge.
Step-by-step explanation:
A box contains 5 blue, 4 red, and 3 yellow marbles. Two marbles are randomly drawn and not replaced. What is the probability of drawing a blue then a red marble?
Answer:
5/33
Step-by-step explanation:
5/12 * 4/11 = 20/132 = 10/66 = 5/33
what does 9! mean in math?
Answer:
9! means 9 factorial
Step-by-step explanation:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Find the equation of the line.
Answer:
y = 2x + 4
Step-by-step explanation:
y = mx + b
b = y-intercept = 4
m = slope = rise/run = 4/2 = 2
y = 2x + 4
Which of the following best describes the relationship between (x-3) and the
polynomial x2 + 4x2 + 2?
A. It is impossible to tell whether (x-3) is a factor.
B. (x-3) is a factor
C. (x-3) is not a factor.
Answer:
C
Step-by-step explanation:
If (x - 3) is a factor of the polynomial then evaluating the polynomial for x = 3 should give a result of zero, that is
3² + 4(3)² + 2 = 9 + 36 + 2 = 47 ≠ 0
Thus (x - 3) is not a factor → C
Forty-nine is subtracted from a number. The difference is divided by 11. The quotient is 3. What is the number?
Answer:
N = 82
Step-by-step explanation:
(N - 49)/11 = 3
N - 49 = 33
N = 82
The marked price of a watch is 30% above the cost price. When it is sold allowing
20% discount on it, there is a gain of Rs 150. Find the marked price of watch.
Answer:
The marked price = Rs 4,475.
Step-by-step explanation:
Let the marked price of the watch = x
Let the cost price of the watch = y
The given information are;
The marked price of the watch = 30% above the cost price
The discount when it was sold = 20%
The gain when it was sold = Rs 150
Therefore, we have marked price = y + 30/100×y = y + 0.3·y = 1.3·y
The selling price with 20% discount is therefore, 1.3·y - 0.2×1.3·y
The selling price = 1.04·y
The gain = Selling price - cost price = 1.04·y - y = 0.04·y
Rs 150= 0.04·y
y = Rs 150/0.04 = Rs 3,750
Therefore, the marked price = 1.3×y = 1.3×3,750 = Rs 4,875
The marked price = Rs 4,475.
Real solution in this system of equations
BRAINLIEST WILL BE GIVEN
Answer:
A
Step-by-step explanation:
Firstly we find the x value. x-7=0; x=7
Secondly we introduce x value in 1st ecuation. So
(7-3)^2 +(y+1)^2=16, 16+y^2+2y+1=16,
Consider this ecuation: y^2+2y+1=0
y1=( -b+Δ)/ 2a, y2= (-b-√Δ)/2a, Δ=√b^2-4ac=√4-4=0
y1,2= -2/2= -1
1 Real solution x=7 and y= -1.
Find the sum of two consecutive odd numbers is 56 find the numbers
Answer:
[tex]\boxed{\sf 27 \ and \ 29}[/tex]
Step-by-step explanation:
Let the first consecutive odd integer be [tex]\sf x[/tex].
Let the second consecutive odd integer be [tex]\sf x+2[/tex].
The sum of the two numbers is 56.
[tex]\sf x+x+2=56[/tex]
[tex]\sf 2x+2=56[/tex]
[tex]\sf 2x=54[/tex]
[tex]\sf x=27[/tex]
Put x as 27 for the second consecutive odd integer.
[tex]\sf 27+2=29[/tex]
The two numbers are 27 and 29.