(Solve the problem down below & simplify the answer. Round to the nearest hundredth as needed.)
Answers
From the given information, we know that the decreasing function values is
[tex]V(t)=3600(3^{-0.15t})[/tex]and we need to find the time t when V(t) is equal to $1200. Then by substituting this values into the function, we have
[tex]1200=3600(3^{-0.15t})[/tex]By dividing both sides by 3600, we get
[tex]3^{-0.15t}=\frac{1200}{3600}=\frac{1}{3}[/tex]So we have the equations
[tex]3^{-0.15t}=\frac{1}{3}[/tex]From the exponents properties, we know that
[tex]3^{-0.15t}=\frac{1}{3^{0.15t}}[/tex]so we have
[tex]\frac{1}{3^{0.15t}}=\frac{1}{3}[/tex]or equivalently,
[tex]3^{0.15t}=3[/tex]This means that
[tex]0.15t=1[/tex]Then, by dividing both sides by 0.15, we obtain
[tex]t=\frac{1}{0.15}=6.6666[/tex]So, by rounding to the nearest hundreadth, the answer is 6.67 years
Related Questions
Hi, can you help me answer this question please, thank you!
Answers
SOLUTION
3To calculate the test statistics, we use the following steps:
Step 1: We write out the parameters
[tex]\begin{gathered} sample\text{ mean (}\bar{\text{x}}\text{)}=0.9 \\ \text{standard deviation(s)=}0.58 \\ \operatorname{mean}(\mu)=0.8 \\ n=32 \end{gathered}[/tex]Step 2: Write out the formula for the test statistics (t)
[tex]t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt[]{n}}}[/tex]step 3: Find t
[tex]\begin{gathered} t=\frac{0.9-0.8}{\frac{0.58}{\sqrt[]{32}}} \\ t=\frac{0.1}{0.1025} \\ t=0.97532 \\ t\approx0.98 \end{gathered}[/tex]Hence, the test statistic is approximately 0.98 to two decimal places.
Cuantas veses cabe el 13 en 47
Answers
Hay 3 veces 13 en 47.
La respuesta la divides 47 por 13 lo que te daría 3.6153846153846.
graph the image of the figure given in the translation
Answers
You have a figure (black lines) with the following points:
C(-4,0)
G(-5,-2)
Q(-2,-5)
I(-1,0)
After a translation, the figure becomes the red one, with the following points:
C'(1,2)
G'(0,-1)
Q'(3,-4)
I'(4,1)
You can notice that each x' coordinate of the new figure is respecto the previous figure:
x' = x + 5
Furthermore, for y':
y' = y +1
That is, the transformation applied to the figure (black lines), is:
T<5,1>
In fact, for each point you have:
T<5,1>C(-4,0) => C'(-4+5 , 0 + 1) = C'(1 , 1)
T<5,1>G(-5,-2) => G'(-5 + 5 , -2 + 1) = G'(0 , -1)
T<5,1>Q(-2,-5) => Q'(-2 +5 , -5 + 1) = Q'(3 , -4)
T<5,1>I(-1,0) => I'(-1 + 5 , 0 + 1) = I'(4 , 1)
Pre calculus 6a. Consider the equation x^5 - 3x^4 + mx^3 + nx^2+ ox + q = 0, where m, n, P, q € R.The equation has three distinct real roots which can be written as log2a, log2b and log2C.The equation also has two imaginary roots, one of which is di where dE R.Show that abc = 8.6b. The values a, b, and C are consecutive terms in a geometric sequence. Show that one of the real roots is equal to 1.6c. Given that q = 8d^2, find the other two real roots.
Answers
We have a fifth degree polynomial:
[tex]x^5-3x^4+mx^3+nx^2+px+q=0[/tex]This polinomial has 3 real roots, that can be expressed as: log2(a), log2(b) and log2(c).
Also, it has two imaginary roots, one of which is di (they have to be conjugate, so the other imginary root is -di).
We have to show that abc = 8.
If we consider the information given, we have some information about all the roots.
We can rewrite the polynomial in factorized form as:
[tex]\begin{gathered} (x-\log _2a)(x-\log _2b)(x-\log _2c)(x-di)(x+di)=0 \\ (x-\log _2a)(x-\log _2b)(x-\log _2c)(x^2+d^2)=0 \end{gathered}[/tex]As the polynomial is defined for real numbers, we can write a polynomial with only the real roots as:
[tex](x-\log _2a)(x-\log _2b)(x-\log _2c)=0[/tex]Then, we can relate the roots as:
[tex]\begin{gathered} 2^{(x-\log _2a)(x-\log _2b)(x-\log _2c)}=2^0 \\ 2^{(x-\log _2a)}\cdot2^{(x-\log _2b)}\cdot2^{(x-\log _2c)}=1 \\ \frac{2^x}{2^{\log_2a}}\cdot\frac{2^x}{2^{\log_2a}}\cdot\frac{2^x}{2^{\log_2a}}=1 \\ \frac{2^{3x}}{a\cdot b\cdot c}^{}=1 \\ abc=2^{3x} \\ abc=2^3\cdot2^x \\ abc=8\cdot2^x \end{gathered}[/tex]Can anyone answer this
Answers
Answer:
(d) The triangles are similar, because each has angles that measure 36°, 62°, and 82°.
Step-by-step explanation:
Given triangle A has angles 36° and 82°, and a figure showing angles related to triangle B, you want to know if the triangles are similar.
SimilarityThe triangles will be similar if the angles of one are congruent to the angles of the other. Between the two triangles, we are given 3 different angle values, so we need to find at least two additional angle values in order to determine if the triangles are similar.
Angle sum theoremThe sum of angles in a triangle is 180°, so the third angle of triangle A will be ...
angle = 180° -36° -82° = 62°
Exterior angleThe exterior angle of triangle B, given as 144°, is the sum of the remote interior angles:
144° = 62° +angle
82° = angle
ComparisonNow, we have the angles of triangle A as 36°, 62°, and 82°. Two of the angles of triangle B are known to be 62° and 82°, matching those of triangle A.
The triangles are similar, because each has angles that measure 36°, 62°, and 82°.
An influencer is planning a lunch banquet. The equation C 410 + 22g models the relation between the
cost in dollars, C, of the lunch banquet and the number of
guests, g.
Find the cost if the number of guests is 50.
The cost is blank
dollars
Answers
The cost, if the number of guests is 50, will be $22500.
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation.So, the relationship between the dollar cost of the dinner, C, and the number of guests, g, is represented by the equation C = 410 + 22g.
We can see that the equation we have been given is in the form of a slope-intercept equation, y = MX + b, where m denotes the slope of the line and b denotes the y-intercept or beginning value.We can observe that the slope and C-intercept of the following equation are 22 and 410, respectively.The C-intercept tells us that when there are 0 guests in the banquet, the cost would be $450.When we have 50 guests at the banquet the cost would be:
50 x 450= $22500Hence, the cost, if the number of guests is 50, will be $22500.
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Please help step by step
Answers
The set of values for y={-3, 0, 5} for given values of x={0, 3, 8} and the equation is 3x-3y=9 and the domain D={0≤x≤8}.
What is Domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
The given equation,
3x-3y=9
When x=0, 3*0-3y=9
-3y=9
y=-3
When x=3, 3*3-3y=9
-3y=0
y=0
When x=8, 3*8-3y=9
3y=15
y=5
The set of values for the equation 3x-3y=9 and the domain D=0≤x≤8 is given as x={0, 3, 8} and y={-3, 0, 5}.
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Please help with 7-9 they are related to the same circle
Answers
40º
7) In this problem, we can see that both tangent lines to that circle come from the same point O.
So, we can write out the following considering that there is one secant line DO and one tangent line to the circle AO
[tex]\begin{gathered} m\angle1=\frac{1}{2}(160-80) \\ m\angle1=\frac{1}{2}(80) \\ m\angle1=40^{\circ} \end{gathered}[/tex]
PLEASE HELP ME I'M OFFERING ALL OF MY POINTS AND I WILL GIVE BRAINLIEST
Answers
Answer:
m∠1 = 80°
m∠2 = 80°
m∠3 = 100°
Step-by-step explanation:
Same-side Exterior Angles Theorem
When two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).
Therefore:
⇒ m∠1 + 100° = 180°
⇒ m∠1 + 100° - 100° = 180° - 100°
⇒ m∠1 = 80°
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Therefore:
⇒ m∠2 = m∠1 = 80°
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore:
⇒ m∠3 = 100°
Given the information marked on the figures below, classify each quadrilateral as a "Parallelogram" or "Not necessarily a parallelogram."
Note that each figure is drawn like a parallelogram, but you should not rely on how the figure is drawn in determining your answers.
If necessary, you may learn what the markings on a figure indicate.
Answers
Noted that the Diagonals of a parallelogram bisect each other. Here in PQSR, it does bisect PT =ST and QT = TR). Hence, PQSR is a parallelogram.
Note that IGHJ is a parallelogram. This is because the opposite sides of a parallelogram are congruent. Here, H = I and G = J. Hence, IGHJ is a parallelogram.
It is correct to state that CABD is a parallelogram because of the alternative interior angles ACB = CBD and ABC = BCD.
VWYX is NOT a parallelogram. The rule states that if opposites sides are congruent then the quadrilateral is a parallelogram. In this case, clearly, line VW ≠ XY and VX ≠ WY.
What is a parallelogram?A parallelogram (which could be a rhombus, rectangle, or square) is a quadrilateral with congruent and parallel opposing sides.
There are six critical parallelogram characteristics to note. They are:
The opposite sides are equal (AB = DC).Angles that are perpendicular to one other are congruent (D = B).(A + D = 180°) Consecutive angles are additive.All angles are proper if one is correct.The diagonals of a parallelogram intersect.The diagonals of a parallelogram divide it into two congruent triangles.Learn more about parallelograms:
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help 1,3,7,13,21_ _ next please I don't know the answer
Answers
1+2=3
3+4=7
7+6=13
13+8=21
21+10= 31
So next term is clearly 31
how do i find the final areahint: i have to square my units
Answers
Given:
A figure is given.
Required:
To find the area of the given figure.
Explanation:
The given figure is made up of three figures. So we will find the area of the three figures.
Area of square
[tex]\begin{gathered} A_1=(side)^2 \\ A_1=(3)^2 \\ A_1=9 \end{gathered}[/tex]Area of the triangle
[tex]undefined[/tex]Draw triangle QRS with altitude RT. If m/RSQ = 43°, then find the m/TRS.
Do not include a degrees symbol on your answer.
Answers
The measure of angle TRS would be of 37º.
What is the measure of angle TRS?The vertices of the triangle can be attributed freely, hence we attribute as is in the drawing.
The altitude RT bisects the triangle forming a right angle, with R and T, hence the internal angles of the triangle TRS are as follows:
43º -> as given in the problem.90º -> due to the bisection.x. -> Angle TSR, which is the missing measure that we need to find to solve this problem.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle TSR can be found as follows:
43 + 90 + x = 180
133 + x = 180
x = 180 - 133
x = 47º -> m<TSR = 47º.
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Which linear inequality is represented by the graph?
Answers
The linear inequality that is represented by the graph is y ≤ x/3 - 4. The correct option is the second option y ≤ x/3 - 4
Graph of Linear inequalitiesFrom the question, we are to determine the linear inequality that is represented by the graph
First, we will determine two points on the line
The line in the graph passes through (0, -4) and (3, -3)
Using the equation,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
(y - -4)/(x - 0) = (-3 - (-4))/(3 - 0)
(y + 4)/x = (-3 + 4)/3
(y + 4)/x = 1/3
y + 4 = 1/3x
y = 1/3x - 4
y = x/3 - 4
This is the equation of the line
In the given graph, the line is a solid line and the solution of the inequality is below the line
Thus,
The inequality becomes y ≤ x/3 - 4
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pls help??
A.24
B.50
C.84
D.75
Answers
A
I got it right on the test and i got the answer on another app
4+3(x+23)=5x-2 write the answer without varible
Answers
Answer:
4+3(×+23)=5×-2
Step-by-step explanation:
4+3×+69=3×from here you will group like terms 4+69=3×-3×
=73=×
this implies that ×=73
find the measure of the missing angles
Answers
The most appropriate choice for Vertically opposite angle will be given by-
b = 126°, c = 54°
What is Vertically opposite angle?
At first we need to understood what is angle
Angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Vertically opposite angle
The angle formed by two intersecting straight lines and are opposite to one another at a specific vertex is called vertically opposite angle.
Vertically opposite angles are equal.
Here,
∠b = 126° [Vertically Opposite Angle]
∠c = 180° - 126° [Angle on a straight line]
= 54°
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f(x) = 4x and g (x) = 4x -3. find the product of ( f . g ) (x)
Answers
Here, I hope it's helpful.
Answer:
16x² - 12x
Step-by-step explanation:
(f • g )(x)
= f(x) × g(x)
= 4x(4x - 3) ← multiply each term in the parenthesis by 4x
= 16x² - 12x
117 divided by 18. Show the answer as a fraction in lowest terms
Answers
Answer:
Im unsure what your asking but the answer is 6 1/2 in fraction form and 6.5 in decimal form :/
Step-by-step explanation:
math
When 117 is divided by 18 we get 117/18 in fraction form.
To divide 117 by 18, we perform long division.
We start with the first digit of the dividend (1) and divide it by the divisor (18).
Since 18 is larger than 1, the quotient for this step is 0.
We then bring down the next digit (1) and place it next to the previous result.
Again, since 18 is larger than 11, the quotient for this step is 0.
Therefore, the result of dividing 117 by 18 is 0 with a remainder of 117.
In fraction form, this can be expressed as 117/18.
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find the endpoint S given R(5,1) and midpoint M(1,4)
Answers
Given:
Point R: (5, 1)
Midpoint M: (1, 4)
Since it's been mentioned that point M is a midpoint. Finding S, the graph should look like this:
Let's determine the translation from point M to R, because the opposite of it will be the translation to get point S.
From Point M to R:
[tex]\text{ }\Delta x\text{ = 5 - 1 = 4 (4 units to the right)}[/tex][tex]\Delta y\text{ = 1 - 4 = -3 (3 units downward)}[/tex]Therefore, getting to the endpoint S, it will have 4 units to the left and 3 units upward.
We get,
[tex]x_S\text{ = 1 - 4 = -3}[/tex][tex]y_S\text{ = 4 + 3 = 7}[/tex]Therefore, the missing endpoint is: -3, 7
21 -6 - NO a) D : {all real numbers}, R: {all real numbers Ob) D: {all real numbers), R; {y >0} O c) D: all real numbers), R: {y < 0} O d) D: {x>0}, R: {all real numbers
Answers
The domain is
[tex]D\colon\mleft\lbrace x\ge0\mright\rbrace[/tex]and the range
[tex]R=\text{all real numbers}[/tex]Then, the answer is d)
4592 round to the nearest ten
Answers
Answer:
4590
Step-by-step explanation:
less the 5 round down
Answer:
4590
Step-by-step explanation:
When rounding to the nearest ten we use these following rules.
We round the number up to the nearest ten if the last digit in the number is 5,6,7,8 or 9.
We round the number down to the nearest ten if the last digit in the number is 1,2,3, or 4.
If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.
A bag contains 4 black and 3 pink balls. A ball is picked from the bag and is not replaced. A second ball is then picked from the bag.
The tree diagram below can be used to calculate various probabilities.
What is the probability of picking one
ball of each colour?
A
4/49
B
24/42
C
1/2
D
12/42
Answers
Answer:
1/2
Step-by-step explanation:
There are 4 possibilities:
First ball Second ball
1. Black Pink
2. Black Black
3. Pink Pink
4. Pink Black
The first and the forth options are the the probabilities that there is picked one ball for each color. (2 possibilities )
The second and the third options are the probabilities that there ate picked 2 balls of same colour.
(2 possibilities)
There are 4 possibilities in total. So the probability is 2/4=1/2
Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.y = −2x +1x-intercept: ( ?,0)y-intercept: (0,?)
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function
[tex]y=-2x+1[/tex]STEP 2: Determine the x-intercept for the given function.
To determine the x intercept, we set y equals zero and solve for x. Therefore, we have:
[tex]\begin{gathered} y=-2x+1 \\ y=0 \\ \therefore\Rightarrow0=-2x+1 \\ Collect\text{ like terms,} \\ 0-1=-2x \\ -1=-2x \\ Divide\text{ both sides by -2} \\ -\frac{1}{-2}=\frac{-2x}{-2} \\ \frac{1}{2}=x \\ x=0.5 \\ \\ \therefore x-intercepts\Rightarrow(0.5,0) \end{gathered}[/tex]STEP 3: Get the y-intercept
We can get the y-intercept by setting x towards zero and solve for y
[tex]\begin{gathered} y=-2x+1 \\ x=0 \\ y=-2(0)+1 \\ y=0+1 \\ y=1 \\ \\ \therefore y-intercept\Rightarrow(0,1) \end{gathered}[/tex]STEP 4: Plot the graph of the given function
after how many hours will the two trucks be 558 miles apart?
Answers
Given:
a.) A truck travels due west at an average speed of 48 miles per hour.
b.) The other truck travels due east at an average speed of 45 miles per hour.
Let's determine how many hours will the two trucks be 558 miles apart.
We will be using the following equation:
Let the two trucks be named Truck A and Truck B.
Let x = the time the two trucks will be 558 miles apart
[tex]\text{ (Speed of Truck A)(x) + (Speed of Truck B)(x) = 558 miles}[/tex]We get,
[tex]\text{ 48x + 45x = 558}[/tex]Let's find x,
[tex]\text{ 48x + 45x = 558}[/tex][tex]\text{ 93x = 558}[/tex][tex]\text{ }\frac{\text{93x}}{93}\text{ = }\frac{\text{558}}{93}[/tex][tex]\text{ x = }6[/tex]Therefore, the two trucks will be 558 miles apart after 6 hours.
What’s the correct answer answer asap for brainlist
Answers
Joseph Hayden is known for his larger structures out of very short, simple musical motifs, often derived from standard accompanying figures.
Evaluate. 5[83–(8-1)²]
Answers
5 [ 83- (8-1)²]
we will first work on the inner parenthesis
5 [ 83 - (7)²]
5[ 83 - 49]
5[34]
=170
Find B – C, if B={2, 4, 6, 8} and C={3, 4, 5, 6}
Answers
Answer:
Solution
verified
Verified by Toppr
Given, A={1,2,3,4}, B={2,4,6,8} and C={3,4,5,7}.
Now, B∩C={4}.
The A−(B∩C)={1,2,3}.
Answer:
B-C=(2,4,6,8)-(3,4,5,6)
=(2,8)
because we have to remove only maching number from B or any other.
Six friends went out for dinner. The total cost of their dinner was $92,82. If they divide the bill equally, how much should
each friend pay?
Provide your answer below:
Answers
Answer:$15.47 per person
Step-by-step explanation:
The total cost of the bill, divided into 6 groups:
92.82/6=15.47
26 is 50% of what number?