Evaluate the logarithmic expression. log1/2​ a) 4 b) −3 c) 3 d) −2

We will have the following:

e)

From this we will find the x & y-intercepts as follows:

*x-intercepts: We replace y = 0 to find them, that is:

So, the x-intercepts are located at (4, 0) & (-4, 0)

*y-intercepts: We replace x = 0 to find them, that is:

So, the y-intercepts are located at (0, 8) & (0, -8).

*The domain is [-4, 4] and the range is [-8, 8].

*We graph it as follows:

Answer:

Well first we find out how many hours 1 man takes

So we say

Unknown. ×given

Known

20 divided

8. × 1

=2,5 hr/1 man

Then we multiple the wanted man by the single hour man

5 ×2,5

=12,5 hrs

Hope this answer helps

Answer:

Six apples.

Step-by-step explanation:

18 apples divided by 3 minutes equals 6 apples.

The addition of 11/3 and (-5/6) is about 2.8 which is shown on a number line.

A number line is a representation of real numbers in the form of a graded straight line.

The addition of 11/3 and (-5/6) is:

11/3 + (-5/6)

= 11/3 - 5/6

= (22-5)/6

= 17/6

= 2.8

Hence, the addition of 11/3 and (-5/6) is about 2.8 which is shown on a  number line.

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To calculate the value of X that Ellen should deposit in the bank, we need to determine the present value of the future payments that will accumulate to $50,000 in six years.

Using the formula for compound interest, the present value can be calculated as follows:

PV = X/(1 + r)^1 + X/(1 + r)^2 + X/(1 + r)^3,

where r is the annual interest rate (5%) expressed as a decimal.

To find the value of X, we set the present value equal to $50,000 and solve for X:

50,000 = X/(1 + 0.05)^1 + X/(1 + 0.05)^2 + X/(1 + 0.05)^3.

Once we determine the value of X, we can proceed to the next step.

For the second part of the question, after four years, the bank raises the interest rate to 6%.

From year four to year six, Ellen's money will continue to accumulate interest.

To find the amount donated, we calculate the future value of the remaining amount after deducting the down payment of $50,000:

Remaining amount = X/(1 + 0.06)^2 + X/(1 + 0.06)^3 + X/(1 + 0.06)^4.

The donated amount is then the difference between the remaining amount and the total accumulated after six years.

By evaluating these expressions, we can determine the value of X and the amount donated by Ellen.

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The Above ratio can be stated as :

There is 4 boys for every 5 girls in the class, Therfore the Correct choice is :

Step-by-step explanation:

5z, 5x and 5y are all unlike terms.

If there was something like 5z + 5x - 3z + 5y, then both 5z and -3z have something in common and so therefore are said to be like terms.

Hope my description helps.

Good night.

Answer:

764-118=s

Step-by-step explanation:

The school has 764 students. Taking away the third graders will let you know how many are left in the other grades. Please marl brainliest.

Oh, and assuming you want the total number in each grade, 1-6? its          (764-118)%5=s

Answer:

118+s=764 is the correct answer.

The cost of each lily is $3.50, and the cost of each rose is $2.25.

Let's use the variables L and R to represent the cost of each lily and each rose, respectively.

From the problem, we can write a system of two equations based on the information about the two arrangements:

5L + R = 19.75 (equation 1)

6L + 3R = 27.75 (equation 2)

To solve for L and R, we can use elimination. First, we can multiply equation 1 by 3:

15L + 3R = 59.25 (equation 3)

Then, we can subtract equation 2 from equation 3:

9L = 31.5

Solving for L, we get:

L = 3.50

Now we can substitute this value back into either equation 1 or equation 2 to solve for R. Let's use equation 1:

5L + R = 19.75

5(3.50) + R = 19.75

17.50 + R = 19.75

R = 2.25

Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.

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Answer:

m=-1/2

hope this helps

Answer:

-1/2

Step-by-step explanation:

9+3=12 and -1-5=-6

-6/12=-1/2

Answer:

Step-by-step explanation:

We can use the ratios of similar triangles to solve this problem. Let's call the height of the tree "h". Then, we have two similar right triangles:

Kaylee's triangle: the height is 1.45 meters, the length of the shadow is 34.2 meters, and the angle between the height and the shadow is theta.

Tree's triangle: the height is h meters, the length of the shadow is 39.55 meters, and the angle between the height and the shadow is also theta.

Using these two triangles, we can set up the following proportion:

h / 39.55 = 1.45 / 34.2

Cross-multiplying, we get:

h * 34.2 = 39.55 * 1.45

Simplifying:

h = (39.55 * 1.45) / 34.2

h = 1.68176

So the height of the tree is approximately 1.68 meters (to the nearest hundredth of a meter).

Using the Riemann sum, we divide the interval [2, 4] into n equal subintervals, where Δx = (4 - 2) / n.

To find the expression for the area under the graph of the function f(x) = x^2 √(1/2x) as a limit, we can use the definition of a Riemann sum and take the limit as n approaches infinity of the sum from i = 1 to n.

The Riemann sum is a method to approximate the area under a curve by dividing it into smaller rectangular regions. In this case, we need to express the area under the graph of f(x) as a limit of a Riemann sum.

The expression for the area under the graph of f(x) as a limit is given by:

lim n → ∞ Σ i=1^n [f(xi) Δx]

In this formula, xi represents the ith subinterval, Δx represents the width of each subinterval, and f(xi) represents the value of the function at a point within the ith subinterval.

To calculate the Riemann sum, we divide the interval [2, 4] into n equal subintervals, where Δx = (4 - 2) / n. Then, for each subinterval, we evaluate f(xi) and multiply it by Δx. Finally, we sum up all these values as n approaches infinity.

However, without evaluating the limit or specifying the specific method of partitioning the interval, it is not possible to provide a more precise expression for the area. The given information is insufficient to calculate the exact value.

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Answer:

A. 3/10

B.1/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

5/33

......................................................

the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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The distance between the cars changes by 60.42mph.

Distance is a measurement of how far apart two objects or locations are. Distance in physics or common language can refer to a physical length or an assumption based on other factors. |AB| is a symbol that can be used to represent the distance between two points. "Distance from A to B" and "Distance from B to A" are frequently used interchangeably. A distance function or metric is a technique to describe what it means for elements of some space to be "close to" or "far away" from each other in mathematics. It is a generalization of the idea of physical distance. Through dimensions like time, space, and isolation, an object may be psychologically distanced from itself.

Calculations:

\(d=\sqrt{80^{2}+50^{2} } \\\)

d=94.34

1st car -- 40mph/hr

2nd car-- 50 mph/hr

The positions of cars at 4pm

Distance travelled by 1st car = 80m

Distance travelled by 2nd car = 50m

\(d^{2}=a^{2} +b^{2}\)

2d.dd/dt=2a(da/dt) +2b(db/dt) =d(dd/dt) =a(da/dt)+b(db/dt)=94.34(dd/dt)=50*50+80*40

dd/dt=(2500+3200)(94.34)  =60.419

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ANSWER :

EXPLANATION :

Answer:

1. 54ft squared  2. 48 cm squared

Step-by-step explanation:

Answer: angle 1 and 3 measure 29 degrees.

angle 2 and 4 measure 151 degrees.

Step-by-step explanation:

=============================================================

Explanation:

The first and second equations have 5x and 15x. Note how -3*5x = -15x which helps us get rid of the x terms when we add.

We can multiply both sides of the first equation by -3 to get -15x+6y = -48

An equivalent system of equations is

\(\begin{cases}-15x+6y = -48\\15x-7y = 51\end{cases}\)

Add the equations straight down. The x terms add to -15x+15x = 0x = 0, so the x terms go away.

The y terms add to 6y+(-7y) = -1y = -y

The terms on the right hand side add to -48+51 = 3

So we end up with -y = 3 meaning y = -3  

This leads to....

5x-2y = 16

5x-2(-3) = 16

5x+6 = 16

5x = 16-6

5x = 10

x = 10/5

x = 2

Or you could use the other equation

15x-7y = 51

15x-7(-3) = 51

15x+21 = 51

15x = 51-21

15x = 30

x = 30/15

x = 2

Either way, we have x = 2 and y = -3 pairing up.

Answer:

C. −7.8v −1.7

Step-by-step explanation:

add like terms

-5.2v  + (-2.6v) = −7.8v

(-2.8) + 1.1 = -1.7

Answer:

C )  −8v−1.7

Step-by-step explanation:

1 ) − 5.2v − 2.8 + 1.1 −2.6v

2) = − 5.2v + −2.8 + 1.1 + − 2.6v

Combine Like Terms:

3 ) = − 5.2v + − 2.8 + 1.1 + − 2.6v

4 ) = ( − 5.2v + − 2.6v ) + ( −2.8 + 1.1 )

5 ) = − 7.8v + − 1.7

Hope this helps! :)

Answer: 147.32 cm

Step-by-step explanation:

1 inch= 2.54 cm

So, 58 inch= (58x2.54) cm

                  = 147.32 cm

Conversion of measurement units is the conversion between different units of the measurement. The number of centimetre in the 58 inches are 147.32 centimetre. thus the option 4 is the correct option.

What is the conversion of measurement units?

Conversion of measurement units is the conversion between different units of the measurement.

Given information

There is total inches given in the problem is 58 inches.

Inches to centimetre-

When we convert the unit inches to the unit centimetre, we need to multiply the unit of inches by 2.54.

There is total 58 inches, we have. To convert this into the centimetre multiply it  by 2.54.

Thus the number of centimetre in the 58 inches are,

\(=58\times2.54\\=147.32\)

Hence the number of centimetre in the 58 inches are 147.32 centimetre. thus the option 4 is the correct option.

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Answer:

2 hours; $130

Step-by-step explanation:

We can do this by setting up an equality since we are finding when they are the same. Say x is the number of horus:

65 * x = 60 + 35* x

30 * x = 60

x = 2 hours

The cost will be the same at two hours, and plugging it in, we can get 65*2=130.

Answer:

she made a profit of $35

Step-by-step explanation:

351-316=35

Answer: profits by $35, gained 11%

Step-by-step explanation:

The given system of differential equations is:

Jx' = Ax + By

y' = Cx + Dy

To find the solution to the given system of differential equations, let's first rewrite the system in matrix form:

Jx' = A*x + B*y

y' = C*x + D*y

where

J = [-67 -210]

A = [21 66]

B = [0]

C = [0]

D = [1]

Now, let's solve the system using the initial conditions. We'll differentiate both sides of the second equation with respect to t:

y' = C*x + D*y

y'' = C*x' + D*y'

Substituting the values of C, x', and y' from the first equation, we have:

y'' = 0*x + 1*y' = y'

Now, we have a second-order ordinary differential equation for y(t):

y'' - y' = 0

This is a homogeneous linear differential equation with constant coefficients. The characteristic equation is:

r^2 - r = 0

Factoring the equation, we have:

r(r - 1) = 0

So, the solutions for r are r = 0 and r = 1.

Therefore, the general solution for y(t) is:

y(t) = c1*e^0 + c2*e^t

y(t) = c1 + c2*e^t

Now, let's solve for c1 and c2 using the initial conditions:

At t = 0, y(0) = -5:

-5 = c1 + c2*e^0

-5 = c1 + c2

At t = 0, y'(0) = 17:

17 = c2*e^0

17 = c2

From the second equation, we find that c2 = 17. Substituting this into the first equation, we get:

-5 = c1 + 17

c1 = -22

So, the particular solution for y(t) is:

y(t) = -22 + 17*e^t

Now, let's solve for x(t) using the first equation:

Jx' = A*x + B*y

Substituting the values of J, A, B, and y(t), we have:

[-67 -210] * x' = [21 66] * x + [0] * (-22 + 17*e^t)

[-67 -210] * x' = [21 66] * x - [0]

[-67 -210] * x' = [21 66] * x

Now, let's solve this system of linear equations for x(t). However, we can see that the second equation is a multiple of the first equation, so it doesn't provide any new information. Therefore, we can ignore the second equation.

Simplifying the first equation, we have:

-67 * x' - 210 * x' = 21 * x

Combining like terms:

-277 * x' = 21 * x

Dividing both sides by -277:

x' = -21/277 * x

Integrating both sides with respect to t:

∫(1/x) dx = ∫(-21/277) dt

ln|x| = (-21/277) * t + C

Taking the exponential of both sides:

|x| = e^((-21/277) * t + C)

Since x can be positive or negative, we have two cases:

Case 1: x > 0

x = e^((-21/277) * t + C)

Case 2: x < 0

x = -e^((-21/277) * t + C)

Therefore, the solution to the

given system of differential equations is:

x(t) = C1 * e^((-21/277) * t) for x > 0

x(t) = -C2 * e^((-21/277) * t) for x < 0

y(t) = -22 + 17 * e^t

where C1 and C2 are constants determined by additional initial conditions or boundary conditions.

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