math work pls help!!

Answer:

\(\theta=0.99^{\circ}\)

Step-by-step explanation:

Given that,

The height of a cell tower, P = 70 m

The tower casts a shadow of 45 meters on the ground.

We need to find the angle of elevation of the shadow to the top of the cell tower. We can use trigonometry to find it.

\(\tan\theta=\dfrac{P}{B}\)

Put all the values,

\(\tan\theta=\dfrac{70}{45}\\\\\theta=\tan^{-1}\left(\frac{70}{45}\right)\\\\\theta=0.99^{\circ}\)

Hence, the angle of elevation is equal to \(0.99^{\circ}\).

It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

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Step-by-step explanation:

-4(2x+3) = 2x+6-(8x+2)

-8x-12 = 2x + 6 -8x -2

cut off -8x two sides of the equation

-12 = 2x + 6 -2

-12 -4 = 2x

-16 = 2x

2x = -16

x = -8

The solution to the equation is \(x = -5\)

The equation of the function is given as:

\(-4(2x + 3) = 2x + 6 - (8x + 2)\)

Open the brackets

\(-8x - 6 = 2x + 6 - 8x - 2\)

Evaluate the like terms

\(- 6 = 2x + 6 - 2\)

Collect like terms

\(2x = -6 - 6 + 2\)

Evaluate the like terms

\(2x = -10\)

Divide through by 2

\(x = -5\)

Hence, the solution to the equation is \(x = -5\)

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Answer: 6 (z+13)

Step-by-step explanation:

Answer:

Step-by-step explanation:

10-z=6

We move all terms to the left:

10-z-(6)=0

We add all the numbers together, and all the variables

-1z+4=0

We move all terms containing z to the left, all other terms to the right

-z=-4

z=-4/-1

z=+4

Answer:15

Step-by-step explanation:

In a square each side is the same length so you simply take 60 and divide it by 4 and you get 15.

The linear system Ax = b is called homogeneous if b = 0; otherwise, it is called inhomogeneous. When all of the constant terms in a system of linear equations are zero, the system is said to be homogeneous. The related homogeneous system of a nonhomogeneous system is obtained by setting the constant term in each equation equal to zero.

There is always one solution, the zero vector, to a homogeneous system. A homogeneous system that has undergone a row operation maintains its homogeneity. It is significant to notice that we frequently exclude the final column of constant terms when representing a homogeneous system as a matrix since row operations would not change that column. So, rather than using an augmented matrix, we employ a standard matrix. There could be no specific solution and an empty solution set in the nonhomogeneous system. In a nonhomogeneous linear system of n equations in n variables, the origin is not always present at the intersection of the solution sets. Although an infinite intersection is still theoretically possible, a single point is still the most likely scenario for the intersection. But, there is also the chance of an empty intersection, which has no solution, as might occur, for instance, when intersecting two parallel lines.

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This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

Amount is a numerical value that refers to the total sum of money or other type of payment due. It is used to quantify the size of a transaction, the cost of goods or services, or any other type of financial transaction. Amounts can be expressed in a variety of different currencies, and they can be negative (owing) or positive (owed).

To calculate the amount of work required to pump all the water from the rectangular swimming pool into a drain at the top edge, we must first calculate the volume of the water in the pool. Volume is calculated by multiplying the length, width, and depth of the pool, which in this case is 20 ft x 20 ft x 8 ft = 3,200 cubic ft. Since the pool is filled to 1 ft below the top, the volume of water is 3,200 ft3 - 20 ft3 = 3,180 ft3.

Next, we must calculate the weight of the water, which is the volume multiplied by the weight density of water (62.4 lb/ft3). The weight of the water in the pool is 3,180 ft3 x 62.4 lb/ft3 = 197,952 lbs.

Finally, to calculate the amount of work required to pump the water from the pool into a drain at the top edge, we must multiply the weight of the water (197,952 lbs) by the height of the drain (8 ft). This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

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Answer:

with?

Step-by-step explanation:

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

The alternative hypothesis is two-sided if it states that a parameter is different from the null hypothesis value (i.e., it can be larger or smaller). In other words, a two-sided alternative hypothesis allows for the possibility of the parameter being either larger or smaller than the null value.

On the other hand, the alternative hypothesis is one-sided if it specifically states that the parameter is either larger than the null hypothesis value or smaller than the null value. A one-sided alternative hypothesis focuses on only one direction of the parameter's deviation from the null value.

To summarize:

- Two-sided alternative hypothesis: Allows for the parameter to be larger or smaller than the null value.

- One-sided alternative hypothesis: Focuses on either the parameter being larger or smaller than the null value.

If you would like to represent this explanation using LaTeX code, you can use the following snippet:

The alternative hypothesis is \(\textbf{two-sided}\) if it states that a parameter is \(\textbf{different}\) from the null hypothesis value. It is \(\textbf{one-sided}\) if it specifically states that the parameter is \(\textbf{larger}\) or \(\textbf{smaller}\) than the null value.

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Answer:

r^2/3 s^1/2/ rs=r^2/3-1×s^½-1=r^-1/3s^-1/2 =

\( \frac{1}{ {r}^{ \frac{1}{3} }s {}^{ \frac{1}{2} } }\)

so option E is a required answer.

Answer: E

I got it right

Step-by-step explanation:

The value of the constant k in the equation m(t) = m(0) * 10^(-kt) can be determined by using the given information that 400 grams of the material decays to 40 grams in 10 years.

We are given the equation m(t) = m(0) * 10^(-kt) to describe the decay of the radioactive sample, where m(t) is the mass at time t, m(0) is the initial mass, and k is the constant we need to find.

Using the given information, we can substitute the values into the equation:

m(t) = 400 grams

m(0) = initial mass (unknown)

t = 10 years

m(t) = m(0) * 10^(-kt)

Substituting the values, we have:

400 = m(0) * 10^(-k * 10)

To find the value of k, we can rearrange the equation and solve for k:

10^(-k * 10) = 400 / m(0)

Taking the logarithm of both sides, we have:

-10k = log(400 / m(0))

Simplifying further:

k = -log(400 / m(0)) / 10

Now we can use the fact that the material decays to 40 grams in 10 years:

40 = m(0) * 10^(-k * 10)

Substituting the value of k we found, we have:

40 = m(0) * 10^(log(400 / m(0)) / 10 * 10)

Simplifying further:

40 = m(0) * 10^(log(400 / m(0)))

Now we need to solve this equation to find the value of m(0). We can use trial and error or numerical methods to find the value that satisfies the equation.

Once we find the value of m(0), we can substitute it back into the equation for k:

k = -log(400 / m(0)) / 10

Therefore, the value of k can be determined by solving the equation using the given information.

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Answer:

(-6,9)

Step-by-step explanation:

x + y = 3

0 + y = 9

We can subtract the two equations.

(x-0) + (y-y) = (3-9)

x=-6

y=9

(-6,9)

Answer:

The intrest rate is 8% and after 7 years she will have made 149.90 in total intrest.

Answer:

y = 4(5)^x

Step-by-step explanation:

We can use the form y = ab^x to write the exponential function that passes through the given points.

First, we need to find the values of a and b. We can use the two points to create a system of equations:

0.8 = ab^(-1)

100 = ab^(2)

We can solve for a by multiplying the first equation by b and substituting it into the second equation:

100 = ab^(2)

100 = (0.8b)b^2

125 = b^3

b = 5

Now we can solve for a using either of the original equations:

0.8 = ab^(-1)

0.8 = a/5

a = 4

Therefore, the exponential function that passes through the given points is:

y = 4(5)^x

Step-by-step explanation:

1.5x + 6-3= 4.5x- 2

1.5x+3=4.5x-2

we transposed

4.5x-1.5x= 3+2

3x= 5

we divide both sides by 3

3x/3= 5/3

x= 5/3

Answer:

3/2

Step-by-step explanation:

Using two points we can find the slope of a line

(0,1) and  (2,4)

The slope is given by

m= (y2-y1)/( x2-x1)

   = (4-1)/(2-0)

   = 3/2

The solution is: the following defines slope, the answer will be A,D and F.

The formula to calculate the slope is

m = y2-y1/x2-x1

A is right.

then, we have,

also, the slope can be calculated with rise and run

i.e. rise over run

m = rise/run

the correct formula is B.

and also apply F

ratio of change in y values (rise) for a segment of the graph to the corresponding change in x values (run)

F is correct.

the answer will be A,D and F.

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Answer:

16 in wide

Step-by-step explanation:

set up a proportion

20. ?

---- = ----

5. 4

20 •4 = 80

80 ÷ 5 = 16 in

Work Shown:

804/d = 6/4

804*4 = 6d

3216 = 6d

6d = 3216

d = 3216/6

d = 536

Answer:

A. 26.7

Step-by-step explanation:

According to the given measurement, the circumference of this circle is closest to 26.7 inches. Hence option A is correct.

Use the concept of a circle defined as:

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

Additionally, every angle possesses rotational symmetry around the center.

The circumference of a circle = 2πr

Given that,

Diameter of the circle = 8.5 inches

Since the radius of the circle is = diameter/2

Therefore,

The radius of this circle = 8.5/2 inches

The radius of this circle = 4.25 inches

Now, from the above formula of circumference,

Circumference of this circle = 2π(4.25)

Since π ≈ 3.14

So,

Circumference of this circle = 9x3.14

Circumference of this circle = 28.26 inches.

Hence,

The circumference is closest to 26.7 which is option A.

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To find the component form of the velocity of the airplane, we need to break down the velocity vector into its horizontal (x) and vertical (y) components.

Given that the airplane is flying 25 degrees west of north at 800 km/h, we can determine the horizontal and vertical components using trigonometry.

The vertical component (Vy) represents the velocity in the north direction, and the horizontal component (Vx) represents the velocity in the east direction.

To calculate Vy, we use the sine function:

Vy = V * sin(θ)

Vy = 800 * sin(25°)

To calculate Vx, we use the cosine function:

Vx = V * cos(θ)

Vx = 800 * cos(25°)

Therefore, the component form of the velocity vector is:

Velocity = (Vx, Vy) = (800 * cos(25°), 800 * sin(25°))

Calculating the values:

Vx ≈ 722.6 km/h

Vy ≈ 342.0 km/h

Hence, the component form of the velocity vector is approximately (722.6 km/h, 342.0 km/h).

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Answer:

5/6

Explanation

Probabaility is the likelihood or chance that an event will occur. Mathematically;

Probabiblity = Expected outcome/Total outcome

Since a pair of dice is rolled;

Total outcome for n dice = 6^n

For a pair of dice, total outcome is 6^2 = 36

For the expected outcome

If we got different numbers on both dice, the outcomes wil be 30 since the only periods we will have the same value are [(1, 1), (2,2), (3,3), (4,4), (5,5), (6,6)] which is 6 outcomes

getting different numbers on both dice = 36 - 6 = 30

Probability of getting different numbers on both dice = 30/36

Probability of getting different numbers on both dice = 5/6

The pattern in the table suggests that the value of "a" follows a specific sequence: -64, -12, 1/16, 1/64.

The given sequence shows a pattern of alternating signs and decreasing magnitudes. In the first term, "a" is negative 64, indicating a negative value. In the second term, "a" is negative 12, which is a smaller negative value than the previous term. Then, in the third term, "a" is 1/16, which is a positive fraction with a smaller magnitude than the previous term. Finally, in the fourth term, "a" is 1/64, a positive fraction with an even smaller magnitude.

This pattern suggests that the values of "a" are gradually decreasing in magnitude and alternating in sign. The progression from negative values to positive fractions indicates a transition from negative to positive values with decreasing magnitudes. This pattern could be represented by a geometric sequence with a common ratio of 1/4.

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(a) A 600-gallon tank starts off containing 300 gallons of water and 40 lbs of salt. Thus, the volume V(t) of water in the tank at any time t is given by V(t) = 2 - 2(1/3) e^(-2t) or V(t) = 2/3 + (4/3)e^(-2t)

Water with a salt concentration of 2lb/gal is added to the tank at a rate of 4gal/min. At the same time, water is removed from the well-mixed tank at a rate of 2gal/min. Consider V(t) as the volume of water in the tank at any time t.The rate of change of volume of water is given by dV/dt = Rate of Inflow - Rate of Outflow . The rate of inflow is the volume of water added per minute, which is given by 4 gallons/min. The rate of outflow is the volume of water removed per minute, which is given by 2 gallons/min.

∴  dV/dt = 4 - 2V(t) is the differential equation for volume of water in the tank at any time t.

The initial condition is V (0) = 300 gallons. As dV/dt = 4 - 2V(t), dV / (4 - 2V(t)) = dt. Integrating both sides, ∫dV / (4 - 2V(t)) = ∫dt. On integrating, we get-1/2 * ln|4 - 2V(t)| = t + C where C is the constant of integration. Rewriting this,|4 - 2V(t)| = e^(-2t - 2C)Multiplying both sides by -1 and removing the modulus sign,4 - 2V(t) = ±e^(-2t - 2C)Solving this equation for V(t),V(t) = 2 - 2e^(-2t - 2C)The initial condition V(0) = 300 gives C = -ln(1/3).Thus, the volume V(t) of water in the tank at any time t is given by V(t) = 2 - 2(1/3) e^(-2t) or V(t) = 2/3 + (4/3) e^(-2t).

(b) Set up an initial value problem for Q(t), the amount of salt (in lbs.) in the tank at any time t. Solving the differential equation, we get Q(t) = 80 - 40e^(-3t)

Q(t) be the amount of salt (in lbs) in the tank at any time t. Let C(t) be the concentration of salt in the tank at any time t. The concentration of salt is defined as C(t) = Q(t) / V(t)The volume of water in the tank at any time t is given by V(t) = 2/3 + (4/3) e^(-2t). The initial volume is V (0) = 300.The amount of salt initially is Q (0) = 40. The rate of inflow of salt is 4 lbs/min. The rate of outflow of salt is given by Q(t)/V(t) * 2. The initial value problem for Q(t) is Q'(t) = 4 - 2Q(t) / (2/3 + (4/3)e^(-2t)) and Q(0) = 40.

(c) Yes, the function Q(t) makes sense for all positive t values. As t → ∞, the volume of the tank approaches 2/3 gallons.

Will the function Q(t) that you would solve for make sense for describing this physical tank for all positive t values? If so, determine the long-term behavior (as t → ∞) of this solution. If not, determine the t value when the connection between the equation and the tank breaks down, as well as what happens physically at this point in time. Yes, the function Q(t) makes sense for all positive t values. As t → ∞, the volume of the tank approaches 2/3 gallons.

As a result, the concentration of salt in the tank approaches 2 lb /gal. The rate of inflow of salt is 4 lbs/min. The rate of outflow of salt is Q(t) / V(t) * 2. Therefore, we can write the differential equation as Q'(t) = 4 - 2Q(t) / (2/3) and Q(0) = 40. Solving the differential equation, we get Q(t) = 80 - 40e^(-3t). Therefore, the long-term behavior of Q(t) is that it approaches 80 lbs. at t = ∞. The connection between the equation and the tank breaks down when the volume of the tank is 0 gallons. This occurs at t = ln(2/3) / 2 = 0.24 min. At this point, the concentration of salt in the tank is infinite, which is not physically possible.

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To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)

where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.

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The factorized polynomial 6x² + 15xy -14x -35y is given as (2x + 5y) (3x - 7)

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

To solve this problem, we simply need to factorize the polynomial given.

\(6x^2 + 15xy - 14x - 35y\)

\(6x^2 + 15xy - 14x - 35y\\(2x + 5y) (3x - 7)\)

This is the the reduced or factorized form of the given polynomial.

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Answer: 5+d

Step-by-step explanation:

More means adding and it doesn't matter which order you put it in in adding.

Step-by-step explanation:

We know that HK and GL are congruent by Given. We can also see that GK is congruent to itself on both sides because of reflexive property. A works, because it corresponds and might fit into SAS. B doesn't, because the two angles don't correspond. C is the same as A, so it will work as well. D's angles correspond, but don't fit SAS.

This means that angle KHG and angle GLK will be congruent, as well as angles GHK and KLG (They're the same angles though).

To prove that \(\triangle GHK \cong \triangle KLG\) by the SAS Congruence Theorem, the additional information we need is: D. ∠HKG ≅ ∠LGK

Recall:

Given the image showing \(\triangle GHK $ and $ \triangle KLG\), the following are known:

\(HK \cong GL\\\\GK \cong GK\)

However, for us to prove that both triangles to be congruent, we need an additional information that tells us an included angle in one triangle is congruent to a corresponding included angle in the other.

Therefore, to prove that \(\triangle GHK \cong \triangle KLG\) by the SAS Congruence Theorem, the additional information we need is: D. ∠HKG ≅ ∠LGK

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