Sally works for 38 hours per week.
Her weekly wage is £355.68
She receives a pay increase of 23p per hour.
Work out her new weekly wage.
Give your answer in £

Step-by-step explanation:

hope it is helpful to you

Answer and Step-by-step explanation:

To find the length of HP, we must use the Pythagorean Theorem.

This theorem helps us solve for the sides of any right triangle.

The equation for the Pythagorean Theorem is:

\(a^{2}+ b^{2} = c^{2}\), in which a and b are the legs, while c is the hypotenuse.

Let's plug in our values into the equation to find the length of HP.

We will use the variable x to represent HP.

\(9^{2}+ 12^{2} = x^{2} \\\\\\Square.the.9.and.the.12.\\\\\\81 + 144 = x^2\\\\\\Add.\\\\\\225 = x^2\\\\\\Square.both.sides.\\\\\\\sqrt{225} = \sqrt{x^2} \\\\\\15 = x = HP\)

So, we get our answer to be 15.

The length of HP is 15.

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A) The amount of interest he will earn in a year is $3,000.

B) The amount he spent on furniture is $600.

Part A: To calculate the interest Alex will earn in one year, use the formula for simple interest:

Interest = Principal × Rate × Time.

In this case, Principal = $30,000, Rate = 10% (0.10), and Time = 1 year. So,

Interest = $30,000 × 0.10 × 1 = $3,000.

Part B: Alex spends 20% of the interest on furniture. To calculate this amount, multiply the interest by 20% (0.20): $3,000 × 0.20 = $600.

Therefore, in one year, Alex will earn $3,000 in interest. He will spend $600 on furniture for his new house.

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The statement "A disadvantage of electronic questionnaires is that this way of surveying is relatively expensive." is: B. False.

In Science, a sample survey simply refers to a type of observational study that uses various data collection methods such as questionnaires and interviews, which favors it in revealing correlations between two data variables.

In Science, a question can be defined as a group of words or sentence that are developed, so as to elicit an information in the form of answer from an individual such as a student.

In conclusion, an advantage of of electronic questionnaires is that it is a form of sample survey that is relatively less expensive in comparison with other forms of survey.

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The solutions of the equation:

(n-3)(n+6)(n+5)=0

are n = 3, -6, -5

Here we want to solve the equation below:

(n-3)(n+6)(n+5)=0

Remember that the product between any number x and 0 is always zero:

x*0 = 0

Then the expression (n-3)(n+6)(n+5) will be equal to zero if any of the factors is zero, that means that if:

n - 3 = 0

n = 3

if:

n + 6 = 0

n = -6

if

n + 5 = 0

n = -5

These are the 3 solutions.

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Answer:

Part A) $9.96

Part B) $7.47

Step-by-step explanation:

Given:

If 2 Ice cream = $4.98

Step:

Then Let's find how much is 1 Ice cream.

To find the cost of 1 Ice cream divide the $4.98 by 2

which gives you 2.49

Now:

Part A) How much will 4 pints of ice cream cost?

2.49 x 4 = $9.96

Hence, 4 pints of ice cream cost → $9.96

Part B) How much will 3 pints of ice cream cost?

2.49 x 3 = $7.47

Hence, 3 pints of ice cream cost → $7.47

[RevyBreeze]

Answer: I'm not the best at this so you might wanna wait for another answer but I think you just half 152??? so 76 :))) but I feel like you shouldn't trust me haha

Step-by-step explanation:

Answer: No the ratios are NOT related  

Step-by-step explanation:

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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No hay una relación clara entre la frecuencia con la que alguien come comida rápida en una semana y la forma en que la persona consigue trabajo cada día. Estos dos aspectos no parecen estar directamente relacionados entre sí.

La forma en que alguien consigue trabajo cada día puede depender de factores como la industria en la que trabaja, la ubicación geográfica, la economía local, el nivel de educación, la experiencia laboral y las habilidades de la persona, entre otros. Mientras que la frecuencia con la que alguien come comida rápida en una semana puede depender de sus preferencias personales, hábitos alimenticios, disponibilidad y accesibilidad a opciones de comida, y su estilo de vida en general.

Aunque es posible que algunos factores subyacentes, como el nivel socioeconómico, puedan estar relacionados tanto con la frecuencia de consumo de comida rápida como con la forma en que alguien consigue trabajo, no se puede asumir automáticamente que existe una relación directa entre estos dos aspectos sin una evidencia específica y verificación rigurosa.

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Carson would have approximately $268111 in his account when Makayla's money has tripled in value.

To solve this problem, we'll need to calculate the amount of money in Carson's account when Makayla's money has tripled in value.

First, let's determine the time it takes for Makayla's money to triple. We'll use the formula for compound interest:

\(A=P(1+\frac{r}{n} )^{nt}\)

Where

A is the final amount

P is the principal amount

r = interest rate

n is the number of times interest is compounded per year

t is the time in years

For Makayla's investment:

P = $80,000

r = 4 7/8% = 0.04875 (convert to decimal form)

n = 365 (compounded daily)

t is the unknown we need to find

We want to solve for t when A = 3 * P (triple the initial amount):

3 * P = \(P(1+\frac{r}{n} )^{nt}\)

3 = \((1+\frac{r}{n} )^{nt}\)

Taking the natural logarithm of both sides:

ln(3) = \(ln((1+\frac{r}{n} )^{nt})\)

ln(3) = (n*t) * ln(1 + r/n)

Solving for t:

t = ln(3) / (n * ln(1 + r/n))

Substituting the given values:

t = ln(3) / (365 * ln(1 + 0.04875/365)

Using a calculator, we find:

t = 22.5 years

Now, we can calculate the amount of money Carson would have in his account after approximately 22.5 years. The continuous compounding formula is:

A = \(Pe^{rt}\)

Where:

A is the final amount

P is the principal amount

r = interest rate

t is the time in years

For Carson's investment:

P = $80,000

r = 5 3/8% = 0.05375 (convert to decimal form)

t = 22.5 years

Using the formula:

\(A = 80000\times e^{0.05374\times 22.5}\)

Using a calculator, we find:

A = $268111.15

Rounding to nearest dollar

= $ 268111

Therefore, Carson would have approximately $268111 in his account when Makayla's money has tripled in value.

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Answer:

The practice of using brass rings to stretch the neck, also known as neck elongation or neck stretching, is traditionally associated with the Padaung ethnic group from Myanmar (formerly known as Burma).

From a sociological perspective, the use of brass rings to stretch the neck can be seen as an example of deviance, which refers to behavior that violates social norms and expectations. Deviance can be either criminal or non-criminal, depending on the specific behavior in question and the cultural context in which it occurs.

In the case of Padaung women, the use of brass rings to elongate the neck is a form of non-criminal deviance, as it does not violate any laws. However, it does violate cultural norms and expectations in many other societies, where elongated necks are not seen as desirable or attractive.

Therefore, the practice of neck elongation among Padaung women can be seen as a form of cultural deviance, in which members of a particular group engage in behavior that is not considered acceptable or desirable by the larger society in which they live. At the same time, it can also be seen as an expression of cultural identity and tradition, as the practice has been passed down through generations and is an important part of Padaung culture and heritage.

The number of rows needed to reach a seating capacity of 1197 are 14.

1st row = 17 seats

2nd row = 17 + 4 = 21 seats

3rd row = 21 + 4 = 25 seats

4th row = 25 + 4 = 29 seats

The total number of seats in the first n rows, we can use the arithmetic series formula:

Sum = (n/2) × (first term + last term)

where n is the number of terms (rows),

The first term is 17,

The last term is 17 + (n-1) × 4

We need to find the number of rows (n) such that the sum of seats is equal to 1197

(n/2) × (17 + 17 + (n-1) × 4) = 1197

Simplifying the equation

(n/2) × (34 + 4n - 4) = 1197

(n/2) × (4n + 30) = 1197

2n² + 15n - 1197 = 0

n = \(\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\)

b = 15, c = -1197, a = 2

n = -15 ± √5013/4

n = 13.9

n = 14

Therefore, the architect must use 14 rows in the theater design to achieve a seating capacity of 1197.

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The 1/3000 square mile does Xacier now for every 1 square mile Bao mows, so we can set up a proportion using the given information.

The amount of area that Xavier mows "X" and the amount of area that Bao mows "B". We know that for every 1/150 square mile that Xavier mows, Bao mows 1/20 square mile. So we can set up the following proportion:

X / (1/150) = B / (1/20)

To solve for X in terms of B, we can cross-multiply and simplify:

X = (1/150) * B * (1/20)

X = B / 3000

This means that for every 1 square mile that Bao mows, Xavier mows 1/3000 square miles. To find the amount of area that Xavier mows for every 1 square mile that Bao mows, we can simply divide X by B:

X / B = (1/3000) / 1

X / B = 1/3000

Therefore, Xavier mows 1/3000 square miles for every 1 square mile that Bao mows.

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The length of the rectangle is found as 7 feet.

For the stated question;

Let the length and the width of the rectangle be 'L' and 'B'.

Then, width is given as;

W = L-2

Area = 35 square feet

A = LW = 35

Put the value of W

L(L-2) = 35

L² -2L - 35 = 0

L² -2L - 35 =0

(L-7)(L+5) = 0

L > 0 so, L=7 is solution

Thus, the length of the rectangle is found as 7 feet.

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The correct question is-

A rectangle is drawn so that the width is 2 feet shorter than the length. the area of the rectangle is 35 square feet. find the length of the rectangle.

f(x)>=-7

Functions:

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.

If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x

Given :

f(x) = -3|x+1|-4

using the table of values for g(x) = |x|

Solution :

f(x) = -3|x+1|-4

f(x) = -3|g(x)+1|-4

f(x) = -3||x|+1|-4

which means |x| is always positive |x|>0

f(x) = -3||x|+1|-4

f(x) = -3x-3-4

f(x) = -3x-7

f(x)>=-7

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By answering the presented question, we may conclude that Therefore, trigonometry the given identity is true.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.  

= 1/sin x

= √(1/sin²x - 1) / (1/sin²x)

= √(1 - sin²x) / sin x

= √(cos²x) / sin x

= √(1 - sin²x) / cos x

= √(csc²x - 1) / cos x

cos x = √(csc²x - 1) / cos x

cos²x = csc²x - 1

cos²x + sin²x = csc²x

1 = csc²x

Therefore, the given identity is true.

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The line in slope intercept form is y=x-6.

From the given graph, (0, -6) and (6, 0).

The standard form of the slope intercept form is y=mx+c.

Slope (m) = (0+6)/(6-0)

= 6/6

= 1

Substitute m=1 and (x, y)=(0, -6) in y=mx+c, we get

-6=1(0)+c

c=-6

So, slope intercept form is y=x-6

Therefore, the line in slope intercept form is y=x-6.

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To derive the state-space representation, we introduce state variables x1 and x2. The state equations are x1' = x2 and x2' = -2x1 - x2 - 2x3 - 4x4 - x, with the output equation y = x1. Answer : y = [ 1   0   0   0 ] [ x1 ]

The state equations describe the dynamics of the system and can be obtained by expressing the derivatives of the state variables. In this case, we have:

x1' = x2

x2' = -2x1 - x2 - 2x3 - 4x4 - x

The output equation relates the output variable y to the state variables. In this case, the output equation is:

y = x1

Therefore, the state-space representation of the system is as follows:

State equations:

x1' = x2

x2' = -2x1 - x2 - 2x3 - 4x4 - x

Output equation:

y = x1

In matrix form, the system can be represented as:

[ x1' ]   [ 0   1   0   0 ] [ x1 ]   [ 0 ]

[ x2' ] = [ -2 -1  -2  -4 ] [ x2 ] + [ -1 ]

          [ 0   0   0   0 ] [ x3 ]

          [ 0   0   0   0 ] [ x4 ]

Output equation:

y = [ 1   0   0   0 ] [ x1 ]

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Answer:

y = -1/2 | x+3|

Step-by-step explanation:

y = f(x + C)  C > 0 moves it left

                 C < 0 moves it right

y = Cf(x)   C > 1 stretches it in the y-direction

                0 < C < 1 compresses it

y = −f(x)  Reflects it about x-axis

Our parent function is

f(x) = |x|

We want it 3 units left

y = f(x + 3)

y = |x+3|

Then reflected across the x axis

y = −f(x)

y = -|x+3|

Then shrink by 1/2 vertically

y = Cf(x)

y = -1/2 | x+3|

Answer:

y = -1/2 | x+3|

Step-by-step explanation:

Given that the average time spent by a consultant with each customer is 10 minutes.We have been given the following data:

[\begin{aligned}\mu &=1 \\L_{q} &=? \\w_{q} &=?\end{aligned}\].

The given data doesn't give a clear picture of the service goal, therefore we need to find out the service goal.

This is nothing but the waiting time of the customer.

To calculate the waiting time of the customer we need to first find the average number of customers in the queue and then the average waiting time in the queue.

We know that the distribution of customers arriving at the consultant follows Poisson's distribution.  

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The salesman used 460 order forms in total, when he used three types of order forms: a, b, c.

Given that,

A salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b

A = 50

B = 4A + 0.5C = 200+ 0.5C  .......... (i)

C =  A +  0.5B =  50 + 0.5 B  .......... (ii)

multiply (ii) with 2

B = 2C -50              .......... (iii)

B = 0.5C + 160        ...........(i)

subtract (i) from (iii)

0 = 1.5C -210

C = 420/3 = 140

put in (i)

B = 200 + 0.5(140) = 270

Total forms = A+B+C = 50 + 270 + 140 = 460

Therefore, he used 460 forms altogether.

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A closed under addition can be proved if the sum of any two members of the set also belongs to the set.

We can take any two even integers and add them together. The result is an even integer. A set is closed under scalar multiplication if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.

For example,

A = {( x, y) , y = 0 }

B= { (x, y) , x+ y = 1 }

Typical elements of A are (1,0), (2,0). The element (1,1) is an element not in A. Typical elements of B are (1,0), (1/2,1/2). The element (1,1) is an element not in B. Now A and B carry an addition that is  (x, y)+(x', y')=(x + y, x' + y')). Saying that A is closed under addition just means that whenever you take two elements in A, the sum of those elements is again in A. Let's check if this is the case: two elements in A have the form (x, 0) and (x', 0). The sum of those elements is (x + x', 0), and this is again in A. Thus A is closed under addition.

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Answer:

13 for 5 bags.

Step-by-step explanation:

Dani spends 5.20 in total for 2 bags. You would do 5.20/2 to get 2.60 which tells us that 2.60 is the cost per bag. Then you would do 2.60 x 5 to get 13.

Answer:

\(2\sqrt{3}\) or 2 square roots of 3

Step-by-step explanation:

The figure shown is a 30 - 60 - 90 degree special right triangle

The image below shows the properties of a 30 - 60 - 90 degree special right triangle

We are asked to find the longer leg (v)

The image tells us that the longer leg is equal to the shorter leg to the square root of 3

so v = 2 to the square of 3

Hence, the answer is the first one

Answer:

37777777777999999999999999

The order of the angles from the least measure to greatest measure is ∠HGB, ∠ECD, ∠FGH and ∠GBH. The solution has been obtained by using the properties of angles.

What is an angle?

When two rays or lines share an endpoint, they form an angle, which is a figure in plane geometry.

We are given that CEFH is a parallelogram. We know that the adjacent angles of a parallelogram are supplementary.

So,

⇒∠FEC + ∠HCE = 180°

⇒124° + ∠HCE = 180°

⇒∠HCE = 56°

We know that angles on a straight line form a linear pair.

So,

⇒∠BCH + ∠HCE + ∠ECD = 180°

⇒90° + 56° + ∠ECD = 180°

⇒∠ECD = 34°

We know that the opposite angles of a parallelogram are equal.

So,

⇒∠FEC = ∠FHC

⇒∠FHC = 124°

Now,

⇒∠FHC + ∠FHG = 180°

⇒∠FHG = 56°

Using the angle sum property of triangle, we get

⇒∠FHG + ∠FGH + ∠GFH = 180°

⇒56° + ∠FGH + 87° = 180°

⇒∠FGH = 37°

∠GHB = 124°     (Vertically opposite angles)

∠CHB = 56°     (Vertically opposite angles)

Using the angle sum property of triangle, we get

⇒∠BCH + ∠CHB + ∠HBC = 180°

⇒90° + 56° + ∠HBC = 180°

⇒∠HBC = 34°

∠GBH = 44°    (Straight line angle)

∠HGB = 12°     (Angle sum property of triangle)

Hence, order of the angles from the least measure to greatest measure is ∠HGB, ∠ECD, ∠FGH and ∠GBH.

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Answer:B. y=0.5x+0.3

Step-by-step explanation:a. p. e. x.

The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation thus option (B) is correct.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given points,

Let's take two-point (1,1)  and (2,1.5)

The slope associated with the above points will be as,

(1.5 - 1)/(2 - 1) = 0.5

Thus, the line will be y = 0.5x + 0.3

Hence "The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation".

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Answer: it is in absolute value form, so when you take it out the signs would change to 7 + 42 = 49

Step-by-step explanation: