Rory works a different number of hours each week. To cover his rent, bills and food costs he needs to a mean average of £268 per week. Week 1 £307. 50, Week 2 £235. 75, Week 3 £287. Rory this he has earned 10% more than the average over the last 4 weeks. Is he correct?

Answer:

C. 5, 9, 12

Step-by-step explanation:

There is a rule in the triangle that if you add any 2 sides measure of the triangle, it must be bigger than the measure of the 3rd side.

Let's Check

A. 19, 6, 13

19 + 6 > 13

6 + 13 = 19

19 + 13 > 6

This is not meet the rule, so this option is wrong.

B. 10, 1, 8

10 + 1 > 8

1 + 8 < 10

This is not meet the rule, so this option is wrong.

C. 5, 9, 12

5 + 9 > 12

9 + 12 > 5

5 + 12 > 9

This meets the rule, so this option is correct.

Answer:

189.36 metres

Step-by-step explanation:

We can use trigonometry to solve this problem.

Let's draw a diagram to help visualize the situation:

```

          |

          |

          |90m

          |

          |

          |

-----------|--------------------

          x

```

We can see that the angle of depression is the angle formed by a horizontal line from the top of the cliff to the boat, and a line of sight from the top of the cliff to the boat. We can also see that the height of the cliff is 90 meters.

Using trigonometry, we can find the distance x between the boat and the foot of the cliff:

tan(26.2°) = opposite / adjacent

tan(26.2°) = 90 / x

To solve for x, we can rearrange the equation:

x = 90 / tan(26.2°)

x ≈ 189.36 meters

Therefore, the boat is approximately 189.36 meters from the foot of the cliff.

Answer:

[tex]b=\frac{r}{9} +a[/tex]

Step-by-step explanation:

To solve this problem, we have to isolate b. The steps are shown below:

Given - [tex]9(b-a)=r[/tex]

Divide both sides by 9 - [tex]\frac{9(b-a)}{9}=\frac{r}{9}[/tex]  → [tex](b-a)=\frac{r}{9}[/tex]

Add a to both sides - [tex](b-a+a)=\frac{r}{9}+a[/tex]  → [tex]b=\frac{r}{9} +a[/tex]

So after doing these steps, we are left with our answer of  [tex]b=\frac{r}{9} +a[/tex].

[tex]b=\dfrac{r}{9}+a[/tex]

Main Concepts:

Concept 1. Solving for a variable

Concept 2. Undoing a multi-step equation

Concept 1. Solving for a variable

To solve any equation ever in mathematics, there are two main steps:

In this case, the variable already appears exactly once, so we can skip ahead to Step 2.

Concept 2. Undoing a multi-step equation

To "Isolate the variable", one must undo the things that are done to it.

To undo something, things must be undone in the reverse order in which they are done.

Looking at the equation, "b" appears on the left side of the equation.  Focusing on the left side, if everything were a number and we were trying to simplify it, Order of Operations would require us to take the "b" and do the following:

1. subtract  by "a" in the parentheses

2. then multiply by 9

To undo these things, we'll need to use the opposite operation of what would have been done in the first place.

To undo the steps above, we undo them in reverse order, so

1. Undo multiplication by 9

2. Then undo the subtraction by "a".

[tex]9(b-a)=r[/tex]

To undo the multiplication, divide both sides by 9

[tex]\dfrac{9(b-a)}{9}=\dfrac{r}{9}[/tex]

simplifying the left side gives

[tex]b-a=\dfrac{r}{9}[/tex]

To undo the subtraction by "a", add "a" to both sides

[tex]b-a+a=\dfrac{r}{9}+a[/tex]

simplifying the left side gives

[tex]b=\dfrac{r}{9}+a[/tex]

The number of text messages teenagers in the United States send each month is,

⇒ =3.24 × 10¹⁰

Given that:

Total teenagers = 27 million

Number of text messages per month = 1200

Total messages sent by teenagers per month = 27 million × 1200

= 32,400,000,000

Decimal point should be after the first significant value from the left.

Count the number of digits remaining after the decimal point

= 3.24 × 10¹⁰

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We can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data

First, we can plug in the value of 28 for Age in the regression line equation to get the estimated average number of sick days for an employee who is 28 years old:

Next, we can use the standard error to calculate the margin of error for a 90% confidence interval:

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the estimated average number of sick days:

Confidence interval = 7.079032 ± 2.767462 = (4.31157, 9.84649)

Therefore, we can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data.

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Complete Question:

The estimated regression line and the standard error are given. Sick Days=14.310162−0.2369(Age) se=1.682207 Find the 90% confidence interval for the average number of sick days an employee will take per year, given the employee is 28. Round your answer to two decimal places.

Employee 1 2 3 4 5 6 7 8 9 10

Age 30 50 40 55 30 28 60 25 30 45

Sick Days 7 4 3 2 9 10 0 8 5 2.

A) Where the calibration of the graph represents a unit each, the approximate coordinates of the points  of intersection of the two graphs is (4.5, 3)

This means that after after a given number of days, the area covered by both types of mold were the same.

b) given the function, the number days it takes for the mold to cover 1000 square millimeters is 46 days.

A) this is observed by exploring the graph.

b) Let A(d) = 1000
⇒ 1000 = 100 x [tex]e^{0.05d}[/tex]

If we divide both sides by 100 to simplify, we will get

[tex]e^{0.05d}[/tex] = 10

To solve for d we need to compute the natural log of both sides, so we get

ln [tex]e^{0.05d}[/tex] = ln (10)

Recall that ln (eˣ) = x so

ln [tex]e^{0.05d}[/tex] = ln (10)

⇒ 0.05d = ln (10)

Divide both sides by 0.05

d = ln10/0.05

d = 2.30258509299/0.05

d = 46.0517018599

d ≈ 46 days.

thus,

it will take about 46 days for the mold to cover 1000 millimeters.

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To represent the value of the collection after 3 years if it appreciates at a rate of 3% per year, we can use the following equation:

V = P(1 + r)^t

Where:

V = the value of the collection after 3 years

P = the initial value of the collection, which is $390 in this case

r = the annual appreciation rate, which is 3% or 0.03 as a decimal

t = the number of years, which is 3 in this case

Substituting the given values, we get:

V = $390(1 + 0.03)^3

Simplifying the equation, we get:

V = $390(1.03)^3

V = $390(1.0927)

V = $426.99 (rounded to the nearest cent)

Therefore, the equation that represents the value of the collection after 3 years if it appreciates at a rate of 3% per year is:

V = $390(1.03)^3

V = $426.99

a) The length of its edge is; 8 units.

b) The volume of the sphere is; 268.083 cubic units.

c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage is 52.4 %.

A. We have been given that the volume of the cube is 512 cubic units.

We have to find the length of its edge. So, Let the length of an edge of a cube be a units.

Then, the volume of the cube = (length of edge)3

the volume of the cube = 512 cubic units.

So, (length of edge)3 = 512 cubic units

So,Length of edge = Cube root of 512 cubic units = 8 units

Thus, the diameter of the sphere = 8 units.

Hence, the radius of the sphere = 8 / 2 = 4 units

B. The volume of the sphere = (4 / 3)πr36

= (4 / 3) × π × 4^3

= 4/3 × 3.14 × 64= 268.08 cubic units

C. The fraction of the cube that is taken up by the sphere = volume of sphere/volume of cube

= 268.08 / 512= 67 / 128

So, the percentage of the cube taken up by the sphere is,

= (67 / 128) × 100= 52.34% (approx)

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True. Stokes' theorem states that if we have a surface r whose boundary is a curve c, and f is a vector field, that provided that c and r are oriented compatibly, the circulation of f around c is equal to the flux of the curl of f through r.

Stokes' theorem states "for surface R whose boundary is a curve C, and F is a vector field, then provided that C and R are oriented compatibly, the line integral of F around C is equal to the surface integral of the curl of F over R."

This theorem relates the circulation of a vector field around a closed curve to the flux of its curl through the enclosed surface.

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To find the limit of cos(x)/(1-sin(x)) as x approaches (π/2)+, we can use l'Hospital's Rule.

First, we can take the derivative of both the numerator and denominator with respect to x: lim cos(x)/(1 − sin(x)) x → (π/2)+ = lim [-sin(x)/(cos(x))] / [-cos(x)] x → (π/2)+ = lim sin(x) / [cos(x) * cos(x)] x → (π/2)+

Now, plugging in (π/2)+ for x, we get: lim sin(π/2) / [cos(π/2) * cos(π/2)] x → (π/2)+ = 1 / (0 * 0) = undefined

Since the denominator approaches 0 as x approaches (π/2)+, and the numerator is bounded between -1 and 1, the limit does not exist.

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Results:

(i)The amount Willow would lose in profit per mug if she uses the printing company = $12.50.

(iii) the total profit she would lose after selling all 65 mugs at $22 per mug = $812.50

To calculate the profit Willow would lose per mug, we use the formula:

Profit (P) lost per mug = Selling price (SP) per mug - Cost Price (CP) per mug:

$22 - $9.50 = $12.50

Thus, Willow will lose $12.50 in profit per mug if she uses the printing company.

To calculate the total profit, she would lose after selling all 65 mugs, we  multiply the profit lost per mug by the number of mugs:

$12.50 x 65 = $812.50

Therefore, Willow would lose $812.50 in profit after selling all 65 mugs at $22 per mug using the printing company instead of her own printing press.

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Answer:

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

The 2 parts of 1 seg multiplied = 2 parts of other seg multiplied

3(x+5)=4(2x)

3x+15=8x

15=5x

x=3

Answer:

[tex] {3}^{2} + {4}^{2} = {5}^{2} [/tex]

[tex] {(3 \times 2)}^{2} + {(4 \times 2)}^{2} = {(5 \times 2)}^{2} [/tex]

[tex] {6}^{2} + {8}^{2} = {10}^{2} [/tex]

3-4-5 is a Pythagorean triple.

Multiplying each of these numbers by 2, we obtain 6-8-10, which is a Pythagorean triple.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the distributive property to simplify the expression inside the parentheses first, then combine like terms:

2x + 6 + 5x - 7 = 4x - 8

7x - 1 = 4x - 8 (combine like terms)

7x - 4x = -8 + 1 (subtract 4x from both sides)

3x = -7 (combine constants)

x = -7/3

Therefore, the solution to the equation 2(x + 3) + 5(x - 1) = 4(x - 2) - 8 is x = -7/3.

Answer:

4 cm by 9

Step-by-step explanation:

Let's assume that the length of the rectangular ink pad is x cm and the width is y cm.

We know that the perimeter of a rectangle is the sum of the lengths of all sides, which in this case is given as 26 cm. Therefore, we can write:

2(x + y) = 26

x + y = 13

We also know that the area of a rectangle is the product of its length and width, which in this case is given as 36 square cm. Therefore, we can write:

xy = 36

We now have two equations with two variables. We can solve for one variable in one equation and substitute it into the other equation to solve for the other variable.

Let's solve for y in the first equation:

y = 13 - x

We can substitute this expression for y into the second equation:

x(13 - x) = 36

Expanding the left side of the equation, we get:

13x - x^2 = 36

Rearranging terms, we get:

x^2 - 13x + 36 = 0

This is a quadratic equation that can be factored as:

(x - 4)(x - 9) = 0

Therefore, the solutions for x are x = 4 and x = 9. We can plug these values back into the equation y = 13 - x to find the corresponding values of y:

If x = 4, then y = 13 - x = 9.

If x = 9, then y = 13 - x = 4.

Therefore, the dimensions of the rectangular ink pad are 4 cm by 9 cm or 9 cm by 4 cm.

Answer:

**9 cm by 4 cm** or **4 cm by 9 cm**.

Step-by-step explanation:

Let's call the length of the ink pad "l" and its width "w". We know that the perimeter of a rectangle is given by the formula `2(l+w) = 26` which simplifies to `l+w = 13`. We also know that the area of a rectangle is given by the formula `lw = 36`.

We can use these two equations to solve for "l" and "w". Let's solve for "w" in terms of "l" using the first equation: `w = 13 - l`. We can substitute this expression for "w" into the second equation to get: `l(13-l) = 36`. Expanding this expression gives us a quadratic equation: `l^2 - 13l + 36 = 0`. We can solve this equation using the quadratic formula: `l = (13 ± sqrt(13^2 - 4(1)(36))) / (2(1))`. This simplifies to `l = (13 ± 5) / 2`. So we have two possible values for "l": `l = 9` or `l = 4`.

If we use `l = 9`, then we can find "w" using the expression we derived earlier: `w = 13 - l = 4`. So the dimensions of the ink pad are **9 cm by 4 cm**.

If we use `l = 4`, then we get `w = 13 - l = 9`. So another possible set of dimensions is **4 cm by 9 cm**.

Therefore, there are two possible sets of dimensions for the ink pad: **9 cm by 4 cm** or **4 cm by 9 cm**.

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Answer:

x= 6

x= 1

Step-by-step explanation:

First we must factor the equation by finding two numbers which when multiplied equal 6, and when added equal -7

-6 * -1 = 6 and -6 - 1 = 7, so our numbers are -6 and -1.

We will then write this factored form as (x - 6)(x - 1)=0

Because of the zero product property (anything multiplied by zero will equal zero), we know that either x - 6 equals zero, or x - 1 equals zero.

This means there will be two solutions.

First, we will do x - 6 = 0. We can simply move the 6 to the other side by adding 6 to both sides. This gets x = 6.

Then, we will do x - 1 = 0. By adding 1 to both sides, we will get x = 1

So finally, we know that x = 6 and x = 1

To solve this expression, we can first simplify the expression inside the parenthesis by combining like terms:

(x + 2y) + (x + 2y)^2 = (x + 2y) + x^2 + 4xy + 4y^2

Now we can distribute the A to each term inside the parenthesis:

A(x + 2y) + A(x^2 + 4xy + 4y^2)

Next, we can simplify each term:

A(x + 2y) = Ax + 2Ay

A(x^2 + 4xy + 4y^2) = Ax^2 + 4Axy + 4Ay^2

Putting these simplified terms back together, we get:

Ax + 2Ay + Ax^2 + 4Axy + 4Ay^2

This is the final simplified expression.

The statements that are true about Triangle HNR are;

a. The value of x is 2,

b. The value of y is 6 and

e. The length of KH is 7.6

To find the value of y for triangle HRN, we have to pick out coordinates that have y value in them and they are;  KR = (0.5y + 3.2) and KW = (2y - 8.9). The centroid divides the medians of a triangle into segments with a 2:1

KW : KR = 1:2

(2y - 8.9)/ (0.5y + 3.2) = 1/2

We multiply KW by 2 for the cross exchange, it becomes

4y - 17.8 = 0.5y + 3.2

3.5y = 21

We divide 3.5 and 21 by 3.5 to find the value of y

y = 6

We can then look for the length of KN which is

0.5 x 6 + 3.2 = 6.2

Therefor KR is 6.2

To find the value of x, we take the coordinates that have x in them.

KN = (5x -5.2), KT = (7.1x - 11.8)

7.1 x - 11. 8/ 5x - 5.2 = 1/2
14.2x - 23.6 = 5x -5.2

9.2x = 18.4

x = 2

To find the length of KN, we say

KN = 5 × 2 - 5.2 = 4.8

To find the value of w, we take the coordinates with w values and they are  KD = (9w -23.2) and KH = (4.5w - 5.9).

(9w -23.2)/(4.5w - 5.9) = 1/2

18w - 46.4 = 4.5w - 5.9

13.5w = 40.5

w = 40.5/13.5

w = 3

The length of KH becomes

4.5 × 3 - 5.9

KH = 7.6

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[tex]\textit{volume of a rectangular prism}\\\\ V=Lwh ~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=150\\ w=120\\ V=288000 \end{cases}\implies 288000=(150)(120)h \\\\\\ \cfrac{288000}{(150)(120)}=h\implies 16=h[/tex]

Answer: 3.5 cm

Step-by-step explanation:

SA for cone = [tex]\pi[/tex]rs + [tex]\pi[/tex]r²        r=radius=9     s=slant height (not height)

A(cone) = 9[tex]\pi[/tex]s + 81[tex]\pi[/tex]

SA for a cylinder = 2[tex]\pi[/tex]rh +2[tex]\pi r^{2}[/tex]      r=6     h = 18

A(cyl) = 2([tex]\pi[/tex])(6)(8) + 2([tex]\pi[/tex])6²

           = 96[tex]\pi[/tex] + 72[tex]\pi[/tex]

           =168[tex]\pi[/tex]

Set the 2 areas equal to each other to solve for slant height

9[tex]\pi[/tex]s + 81[tex]\pi[/tex] = 168[tex]\pi[/tex]

9[tex]\pi[/tex]s=87[tex]\pi[/tex]

s=87/9

this is slant height, now you use pythagorean to solve for h

(87/9)²=9²+h²

h=3.5

The probability that a randomly selected passenger car gets more than 35 mpg is approximately 38.4%.

To find the probability that a randomly selected passenger car gets more than 35 mpg, we need to use the normal distribution with a mean of 33.7 mpg and a standard deviation of 4.4 mpg.

First, calculate the z-score for 35 mpg using the formula:

z = (X - μ) / σ

where X is the value (35 mpg), μ is the mean (33.7 mpg), and σ is the standard deviation (4.4 mpg).

z = (35 - 33.7) / 4.4
z ≈ 0.295

Now, we use a z-table or calculator to find the probability for a z-score of 0.295. The table shows the probability to the left of the z-score, so we need to find the complement to get the probability of a car getting more than 35 mpg.

P(Z > 0.295) = 1 - P(Z ≤ 0.295)
P(Z > 0.295) ≈ 1 - 0.616
P(Z > 0.295) ≈ 0.384

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Answer:

a) The mode is 6 (which occurs the most times--18).

b) Since there are 50 observations, the median is the value halfway between observations 25 and 26 when the data are arranged in order. That value is 6.

c) (4(2) + 5(10) + 6(18) + 7(14) + 8(6))/50 =

312/50 = 6.24 peas/pod

Answer:

20,000 mL

Step-by-step explanation:

Liter = 1000 mL

She bought 10 two liter bottles, so in total:

10 * 2 = 20 liters

20 L * 1000 mL/L = 20,000 mL

Answer: 68

Step-by-step explanation:

All the angles of a triangle add up to 180

so 32 + 80 + x = 180  or 180-32-80=x

x = 68

Answer:

x= 68

Step-by-step explanation:

80+ 32+ x= 180

112 +x= 180

x= 180-112

x= 68

The slope of the line of best fit to Tara's data is equal to 3.6 and it indicates a positive rate of change with respect to the data.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models the line is represented by this mathematical equation;

y = mx + c

y = 3.6x + 17.6

By comparison, we have the following:

mx = 3.6x

Slope, m = 3.6.

Initial value or y-intercept, c = 17.6.

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Using only addition, how can you use eight '8's to get 1,000? 8 added 125 times=1000. 888+88+8+8+8=1000.

Answr: C

Step-by-step explanation:

...

The requried equation is true, which means that y = x is indeed the solution to the equation.

When Sherron inputs the equation 5 + 6x = 9y + 2 + 3(1 - y), we can simplify it as follows:

5 + 6x = 9y + 2 + 3 - 3y

5 + 6x = 6y + 5

6y = 6x

y = x

So the solution to the equation is y = x.

We can also check the solution by substituting y = x back into the original equation:

5 + 6x = 9y + 2 + 3(1 - y)

5 + 6x = 9x + 2 + 3(1 - x)

5 + 6x = 9x + 2 + 3 - 3x

5 + 6x = 6x + 5

Thus, the equation is true, which means that y = x is indeed the solution to the equation.

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Answer:The y-intercept is (0,10)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (ln(11),0)

y-intercept(s): (0,10)