Use the iterative formula below to work out the value of x3, starting with
x₁ = 8.
X1
2
In
Xn+1 = 5-
Give your answer to 3 d.p.
D

Answer:

Step-by-step explanation:

Answer:

x=25

Step-by-step explanation:

60°+95°+X=180°

X=180°-60°+95°

X=180°-155

X=25°

Answer:

178.50

Step-by-step explanation:

8.50 · 7

59.5 · 3

178.50

Aisha earned C178.50 in a week.

First, multiply the number of hours worked per day with the amount earned per hour.

7 × C8.50 = C59.50

Then, use that answer and multiply it by the number of days worked.

3 x C59.50 = C178.50

Answer:

15n - 12

Step-by-step explanation:

18 ----> 3 = 15

3 -15 = -12

Answer:

7.2 cm

Step-by-step explanation:

The adjacent interior angles of a rhombus must be supplementary.

Let ABCD be the rhombus whose area is 40 cm².

Let the diagonals AC and BD intersect at O.

If s is the side, one-half diagonal = s× sin(25) and the other is s× sin(65) = s × cos(25)

Area of a rhombus = ½× (a×b)²× sin(ø)]

side length, a = b

Area of rhombus = ½× s² × sin(25)cos(25)

40 cm² = ½ × s² × sin(25)cos(25)

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)]

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°sin(a)cos(b) = 2[sin(x+y)]

》40 cm² = ½ × s² × 2sin(50)

》40 cm² = s² × sin(50)

\( {s}^{2} = \frac{40}{ \sin(50) } \\ s = \sqrt{ \frac{40}{ \sin(50) } } \)

s = 7.2260841106 cm

Therefore, the length of the side of a rhombus, s is 7.2 cm

Equations

Let's call:

x = time Stanley swam yesterday.

We know he ran for half an hour longer than he swam, thus the time he ran was:

x + 0.5 = time Stanley ran yesterday

We also know he biked for twice the time he ran, thus:

2(x + 0.5) = time Stanley biked yesterday.

The distance covered by Stanley when swimming is

2.5*x

The distance covered by Stanley when running is:

9*(x+0.5)

The distance covered by Stanley while biking is:

16*2*(x + 0.5) = 32(x + 0.5)

The total distance is 64 miles, thus:

2.5*x + 9*(x+0.5) + 32(x + 0.5) = 64

Operating:

2.5x + 9x + 4.5 + 32x + 16 = 64

Simplifying:

43.5x + 20.5 = 64

Subtracting 20.5:

43.5x = 43.5

Thus:

x = 1

Stanley swam for 1 hour, he ran for 1+0.5 = 1.5 hours and biked for 2*1.5=3 hours

Swam: 1 hour, Ran: 1.5 hours, Biked: 3 hours

To determine the landing point, we need to balance the time it takes to row the boat with the time it takes to walk.

The woman's rowing speed is 3 km/h, and her walking speed is denoted as w km/h. Let d be the distance from the island to the landing point, and x be the distance she needs to walk from the landing point to reach the town. The total time for rowing (d/3) should be equal to the total time for walking [(12 - x)/w] in order to arrive at the town.

By rearranging the equation, we find that the landing point should be 12 km minus the distance covered by walking (d * w) divided by 3.

The exact value of x depends on the specific distances involved and the woman's walking speed, which are not provided in the given information.


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Probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.

Convenience sampling is any non sampling technique where units are chosen for the sample based on their accessibility to the researcher.

Thus, probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.

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Answer:

6 games and 3 rides

Step-by-step explanation:

Let the number of games Brianna played be x,

and the number of rides she went on be y.

Total cost for games= 1.25x

Total cost for rides= 3.75y

Since number of games is twice the number of rides,

x= 2y -----(1)

Total costs= cost of games +cost of rides

\(18.75= 1.25x +3.75y\)

Multiply the whole equation by 4 to remove the decimals:

\(75= 5x +15y\)

Simplify by dividing the whole equation by 5:

\(15 = x + 3y\)

Label the equation:

x +3y= 15 -----(2)

Although we can solve these 2 equations by substitution, since the question requires us to graphically solve, we have to graph 2 linear lines.

I will choose 3 points to plot on the graph for each equation:

x= 2y -----(1)

\(\begin{tabular}{|c|c|c|c|}

\cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\

\cline{1-4}y & 1 &2&3\\

\cline{1-4}

\end{tabular}\)

x +3y= 15 -----(2)

x= -3y +15

\(\begin{tabular}{|c|c|c|c|}

\cline{1-4}x & -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\

\cline{1-4}y & 1 &2&3\\

\cline{1-4}

\end{tabular}\)

Let's plot these points on a graph paper. Then, join them with a straight line for each straight line graph. Please see the attached picture for the graph.

From (1): y= ½x

From (2): 3y= 15 -x

y= 5 -⅓x

From the graph, the solution of the equation is (6,3). The solution is the point on the graph in which the 2 lines intersect.

x- coordinate: 6

y- coordinate: 3

Thus, Brianna played 6 games and went on 3 rides.

Answer:

6 games=$7.5  3 rides=$11.25

1.25*6=7.5

3.75*3=11.25

7.5+11.25=18.75

Answer:

The square root of 58 is a rational number if 58 is a perfect square.

Step-by-step explanation:

It is an irrational number if it is not a perfect square. Since 58 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 58?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.

is this what you needed or

The square root of the number is A = √58 is not a rational number

Given data ,

Let the first number be represented as p

where the value of p = 58

Now , the square root of the number is expressed as

A = √58

The radical form of a number refers to expressing a number using a radical symbol (√) to represent a root.

It is used to express the roots present in the number.

So , A = √58

On simplifying , we get

A = 7.6157731058639082856614110271583...

On further simplification , we get

A = the square root of 58 is not a rational number

Hence , the square root of 58 is an irrational number because it cannot be expressed as a fraction of two integers

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Answer:

≈ 15 ft

Step-by-step explanation:

There is a right triangle formed by the ground, the building and the ladder.

The ground and the height the ladder is up the wall are the legs and the ladder is the hypotenuse.

let x be the distance from the base of the building to the bottom of the ladder.

Using Pythagoras' identity in the right triangle

x² + 26² = 30²

x² + 676 = 900 ( subtract 676 from both sides )

x² = 224 ( take the square root of both sides )

x = \(\sqrt{224}\) ≈ 15 ft ( to the nearest foot )

The values of x and y are 30° and 120° respectively

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

Sum of angles at a point is 360°.

Also the sum of angles on a straight line is 180°.

This means that;

x+x+y = 180

2x+y = 180

and;

x +y +30 = 180°

therefore ;

2x +y = x+y +30

2x -x = y-y +30

x = 30°

2(30) +y = 180

y = 180-60

y = 120°

Therefore the values of x and y are 30° and 120° respectively

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Answer:

circumference 69.08 area 379.94

Step-by-step explanation:

Answer:

2.29 rads

Step-by-step explanation:

The  length of the arc of a circle of radius r is given by;

l = rθ            ---------------------------(i)

Where;

l = length of the arc

θ = central angle o that intercepts that arc and measured in radians.

From the question:

l = 16ft

r = 7ft

Substitute these values into equation (i) as follows;

16 = 7θ

Make θ subject of the formula

θ = \(\frac{16}{7}\)

θ = 2.29    

Therefore, the radian measure of the central angle is 2.29 rads

The area of a trapezoid is one-half the product of the length of an altitude and the sum of the lengths of the bases: A = ½ h(b1 + b2).

Answer:

r=3

Step-by-step explanation:

|r+2|=|3r-4|

-r-2=-3r+4

2r-2=4

2r=6

r=3

In the given model, the intercept for the regression model is 70.

The intercept in the given simple linear regression model is 70. This means that when the independent variable (x) is zero, the predicted value of the dependent variable (y) is 70. The intercept represents the starting point or the y-value when x is zero in the regression equation.

In a simple linear regression model, the equation takes the form: y = β0 + β1x + ϵ, where β0 represents the intercept, β1 represents the coefficient of the independent variable (x), and ϵ represents the error term.

In the given regression model, the intercept (β0) is stated as 70. This means that when x is zero, the predicted value of y is 70. The intercept captures the inherent value of y that is not explained by the independent variable. It represents the baseline value of y when there is no influence from x.

Therefore, in the given model, the intercept is 70.

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√48 = 4√3

Click on the photo to view full solution

If mark and Alexis work together on a particular truck, they can load all of the packages in 90 minutes.

It will take 90 minutes for both Mark and Alexis to load all of the products.

Given,

that Mark can load a truck with items in 120 minutes and Alexis can do the same in 240 minutes, the average time for the two of them is as follows:

Average = (120 + 240) ÷ 2

= 360 ÷ 2

= 180

In this case, the term "Average" refers to the value that should be used to represent the sample. By dividing the total number of values in a particular set by the sum of all the values in that set, the average is determined. also known as the arithmetic mean.

Since there were two parties engaged, our calculation is 180 ÷ 2 = 90.

Hence, in this case, it is concluded that the correct answer is option B. 90 minutes.

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the probability that the salesman will make more than $1500 on any given day is practically zero.

The probability that the salesman will sell at least one policy on a randomly selected day can be found by summing the probabilities of selling one or more policies, which is the complement of the probability of selling zero policies. Thus, P(Z≥1) = 1 - P(Z=0). Using the given probability distribution, we find that P(Z=0) = 0.2, so P(Z≥1) = 1 - 0.2 = 0.8.
The expected value of Z, E(Z), is the weighted average of the possible outcomes of Z, where the weights are their respective probabilities. Thus, E(Z) = 0(0.2) + 1(0.3) + 2(0.4) + 3(0.1) = 1.6.
The salesman's expected earnings, E(earnings), can be found by multiplying E(Z) by the earnings per policy, which is $800. Thus, E(earnings) = E(Z)($800) = 1.6($800) = $1280.
To find the probability that the salesman will make more than $1500 on any given day, we need to use the expected value and standard deviation of Z. The standard deviation of Z is the square root of the variance, where the variance is the weighted average of the squared deviations from the mean. Using the formula for variance, we find that Var(Z) = (0-1.6)²(0.2) + (1-1.6)²(0.3) + (2-1.6)²(0.4) + (3-1.6)²(0.1) = 0.64. Thus, the standard deviation of Z is \(\sqrt{(0.64) }\) = 0.8.
To find the probability that the salesman will make more than $1500, we need to standardize the value of $1500 using the formula z = (x - E(Z))/SD(Z), where x is the value we want to standardize. Thus, z = (1500 - 1280)/0.8 = 275/4 = 68.75. Using a standard normal distribution table or calculator, we find that the probability of Z being greater than 68.75 is essentially zero, since it is beyond the range of practical values.

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The distance between two lines measured along a perpendicular line to the line is always the same is called as equidistant .

Given :

The distance between two lines measured along a perpendicular line to the line is always the same.

What is Equidistant ?

Distances between two points from a common points are equal then it is called as equidistant .

Formulas :

Midpoint = ( x1 + x2 / 2 , y1 + y2 / 2 )

Distance = \(\sqrt{(x2 - x1 )^2 - (y2 - y1)^2 }\)

These are two main formulas are used to find whether equidistant or not.

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Answer:

Interest rate increases by 100%+n%

n% = 1.5%

100%+1.5%=101.5%=1+0.015=1.015^x

so its y = 2000(1.015)^x

Answer:

144

Step-by-step explanation:

Answer:

Step-by-step explanation:

f is (-2,-3)

Answer:

Step-by-step explanation:

Answer:

is mechanistic in nature.

Step-by-step explanation:

Answer:

-80 Degrees

Step-by-step explanation:

I just subtracted both of the numbers.

Answer:

-80 degrees F

Step-by-step explanation:

All you have to do is subtract the two. Because the question says "The lowest temperature in U.S history is 52°F lower than Albany's record low temperature", we know that the lowest temp in US history is even lower than that of Albany's record. Just perform subtraction: -28 - 52 = -80