(1)
Mrs Tan had $3756 to spend on furniture. She bought a sofa set for $1195 and 6 chairs at $128 each.

(a) How much did she spend altogether?

(b) How much money did she have left?

(Marshall Cavendish/ Pupil's book My Pals Are Here! Maths 4A 3rd Edition)

The function (fog)(x) would be (x^4 + 10x² + 27). Also, the domain of (fog)(x) is all the real numbers.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

f(x) = x² + 2

g(x) =  x² + 5

so, to take the composition of f and g (fog) replace the x in f(x)  with g(x);

(fog)(x) = (x² + 5)² + 2

(fog)(x) = (x^4 + 25 + 10x² )+ 2

(fog)(x) = (x^4 + 10x² + 27)

Also, the domain of (fog)(x) is all the real numbers.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ1

Answer:

≈ 47.2 m

Step-by-step explanation:

let the height from the sea to the base of lighthouse be h₁

let the height from the sea to the top of the lighthouse be h₂

using the tangent ratio in the right triangle

tan55.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h_{1} }{610}[/tex] ( multiply both sides by 610 )

h₁ = 610 tan55.1°

tan56.5° = [tex]\frac{h_{2} }{610}[/tex] ( multiply both sides by 610 )

h₂ = 610 tan56.5°

then

height of lighthouse = h₂ - h₁        

                                  = 610 tan56.5° - 610 tan55.1°

                                  = 610(tan56.5° - tan55.1° )

                                 ≈ 47.2 m ( to the nearest tenth )

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{Option D, y = 2x - 3}[/tex]

-------------------------------------------------------------------------------------------------------------

Given: [tex]\textsf{The graph}[/tex]

Find: [tex]\textsf{The equation in slope intercept form}[/tex]

Solution: Looking at the graph, we can see that the line intersects the y-axis at -3 therefore that is the y-intercept.  All we need to do now is find a second point so we can determine the slope.  The line crosses at (1, -1) so we will use that as the second point.  Then we just plug all of the values into the slope intercept form.

Determine the slope

Plug in the values

Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.

Answer:

€3.75

Step-by-step explanation:

1. Formulate:

5×(2.25 - 1.5)

2. Calculate:

5×(2.25-1.5)

5× 0.75

=3.75

Answer

3.7/ €3.7

Answer:

The answer is 5/21 water left in the jug after 2 days.

Step-by-step explanation:

First convert 1 2/3 into a improper fraction. This will turn it into 5/3. After this, find a common denominator between 5/7 and 5/3. This common denominator is 21. Now, convert both fractions into a fraction with 21 as the denominator. This will transform 5/7 into 15/21, and 5/3 into 35/21. So we know from the equation that 15/21 is drank every day. So we multiply 15/21 by 2, which will make it 30/21. 35/21 will stay the same. Now we do 35/21 - 30/21, which gives you the final answer of 5/21 water left in the jug after 2 days.

Hope this helps!

Answer:

Mean: 19.366666666667

Step-by-step explanation:

Mean: Average of the Data set

If you add the numbers below and divide them by the amount of numbers there are, you will get the average of the data set.

14,14,14,15,15,15,15,15,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25

Average= sum/count

Mean= 1162 / 60

Mean= 19.366666666667

Rounded to the nearest tenth: 19.4

Rounded to the nearest hundredth: 19.37

Answer:

4 X 60 = 240 minutes

Step-by-step explanation:

there are 60 minutes in each hour

The length of the rectangle is 100cm.

The breadth of the rectangle is 4cm.

The square encloses more area than the rectangle.

The first step is to determine the area of the square.

Area of a square = length² = 50² = 2500 cm²

Area of a rectangle = length x width

length = area / width

2500 / 25 = 100cm

The first step is to determine the perimeter of the square.

Perimeter = 4 x length

4 x 5 = 20cm

Perimeter of a rectangle = 2(length + width)

breadth = (perimeter / 2) - length

(20 / 2) - 6

10 - 6 = 4cm

Area of the square = 5 x 5 = 25

Area of the rectangle = 6 x 4 = 24

To learn more about the perimeter of a rectangle, please check: https://brainly.com/question/3205029

#SPJ1

[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]

Answer: correct radical forms are:

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

Step-by-step explanation:

Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.

therefore,  

radical form of given values are :

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

learn more about radical forms at

https://brainly.com/question/18864104

#SPJ10

Answer:

A. B. C. D.

Step-by-step explanation:

because Which statement describes the end behavior of the function f(x)= |x-7| -7?

A. As x approaches negative infinity, f(x) approaches negative infinity.

B. As x approaches negative infinity, f(x) approaches positive infinity.

C. As x approaches positive infinity, f(x) is no longer continuous.

D. As x approaches positive infinity, f(x) approaches negative infinity.

The hypothesis test shows that we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

The claim that the return rate is less than 20% is p < 0.2. From the given information, we can compute our null hypothesis and alternative hypothesis as:

[tex]\mathbf{H_o :p =0.2}[/tex]

[tex]\mathbf{H_i:p < 0.2}[/tex]

Given that:
Sample size (n) = 6965

Sample proportion [tex]\mathbf{\hat p = \dfrac{x}{n} = \dfrac{1302}{6965} \sim0.1869}[/tex]

The test statistics for this data can be computed as:

[tex]\mathbf{z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}}[/tex]

[tex]\mathbf{z = \dfrac{0.1869 -0.2}{\sqrt{\dfrac{0.2(1-0.2)}{6965}}}}[/tex]

[tex]\mathbf{z = \dfrac{-0.0131}{0.0047929}}[/tex]

z = -2.73

From the hypothesis testing, since the p < alternative hypothesis, then our test is a left-tailed test(one-tailed.

Hence, the p-value for the test statistics can be computed as:

P-value = P(Z ≤ z)

P-value = P(Z ≤ - 2.73)

By using the Excel function =NORMDIST (-2.73)

P-value = 0.00317

P-value ≅ 0.003

Therefore, we can conclude that since P-value is less than the significance level at ∝ = 0.01, we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

Learn more about hypothesis testing here:

https://brainly.com/question/15980493

#SPJ1

Step-by-step explanation:

1. True

2. False

3. True

5. Falsw

6.True

7.True

8.False

10.True

15. always

17. always

Answer:

11∗2+13∗4+15∗6+⋯+199∗100=?

=(1−12)+(13−14)+(15−16)+⋯+(199−1100)

=(1+13+15+17+⋯+199)−(12+14+16+⋯+1100)

=(1+13+15+17+⋯+199)−12(1+12+13+⋯+150)

=∑k=15012k−1−∑k=15012k

Continue further.

Answer: the answer is a

Step-by-step explanation:

The answers for following questions are;

i. $244.64

ii. $ 5314.64

Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value is important to investors and financial planners, as they use it to estimate how much an investment made today will be worth in the future.

Here, future value or amount;

          A = P(1 + r)ⁿ

Where,

A = future value = ?

P = principal = $ 12,300

r = interest rate = 6%/12 = 0.06/12 = 0.005

n = number of periods = 12 X 6 years = 72

A = P(1 + r)ⁿ

= 12,300(1 + 0.06/12)⁷²

= 12300 (1 + 0.005)⁷²

= 12300 (1.005)⁷²

= 12300 (1.4384)

= 17,614.64

Each monthly payment = Total payment / number of months

= $17,614.64 / 72

= $ 244.64

Total amount of interest = Total payment - Principal payment

                                          =   17,614.64 - 12300

                                          =   $ 5314.64

Thus, The answers for following questions are;

i. $244.64

ii. $ 5314.64

Learn more about Interest from:

https://brainly.com/question/13324776

#SPJ1

Answer:

Just put it into a calculator

0.97053528353

[tex]\text{Let's find the sine of -105 degrees}\\\text{Start by typing -105 into our calculator}\\\text{and click the sin button}\\\text{It gives us an irrational number, which is the sine of -105 degrees}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The value is end less, it would take an eternity to type it here,}\\\text{ but I will round it to the nearest 100th}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{-0.97}[/tex]

Answer:

Step-by-step explanation:

-3 +2 +-1 +-2 +-3 +1 = -6 yards total

-6 / 6 =  -1 yard per play average

Answer:

My answer: 15.87%

Step-by-step explanation:

The Final grades follows normal distribution.

It means =70

The Given standard deviation =10

The normal random variable of a standard normal distribution is called a standard score or a z-score. In Every normal condition, random variable X will be transformed into a z score via the following equation:

z=(X)

But when X is a normal random variable, μ is the mean of X.

For That, it is X=60

Z=(60−70)/10=−1

P(X<60)=P(Z<−1)

=0.1587

Hence percent of students failed in test is 15.87%

It will have little to no effect on the median, but it will make the mean a less useful measure of center.

The initial data elements are given as:

35, 25, 15, 40, 50

When a new data element is added, we have:

35, 25, 15, 40, 50, 95

See that 95 is far from the other data elements.

This means that 95 is an outlier of the data elements

Outliers have effects on the mean and it renders the mean useless.

However, it has little to no effect on the median

Hence, the true statement is (d)

Read more about outliers at:

https://brainly.com/question/3631910

#SPJ1

Answer:

Step-by-step explanation:

it will have little to no effect on the median but will make the mean a less useful measure of center.

The cost price of the table is $40.

Gain is the amount gain by selling the product at a higher price than its cost.

Let the cost of the table is $ x

The percentage gain is x%  (as given in the question)

Cost price = ?

It is known that

Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price

Selling price = 56

Cost Price = $ x

Therefore substituting the value

x = (56 - x) * 100 / x

x² = 5600 - 100x

x² +100x -5600 = 0

Step 2 : Factorizing

x² + 140x - 40 x -5600 = 0

x( x+14 ) -40( x +14) = 0

( x - 40)(x +14) = 0

x = $40

Therefore the cost price of the table is $40.

To know more about Gain

https://brainly.com/question/23385214

#SPJ1

Answer:

4w + 10 = 116

Step-by-step explanation:

Call the width w.

The length is 5 more than that, so the length is w + 5

Perimeter is 2w + 2l

2w + 2(w+5) = 116

Distribute the 2 to the values in the parentheses.

2w + 2w + 10 = 116

Combine like terms

4w + 10 = 116

Answer:

5.0 6.0 7.0 7.5 8.0 9.0 10.0

arranging the following

5.0 , 6.0 , 7.0 , 7.5 , 8.0 , 9.0, 10.0

7.5 is the median..

The points are (168, 168) , (168,56) , (112,0) , (70,112)

Given a scale factor is 14 and the center of dilation (0,0)

We need to find the Points using the scale factor and polygon tool

Now to find the new points the equation is

(old points - dilation center)*scale factor + dilation center

As we know the origin is the dilation center which simplifies to

(old point)*dilation center

(12,12) * 14  =  (168,168)

(12,4) * 14 = (168, 56)

(8,0)*14  =   (112, 0)

(5,8) *14  = (70, 112)

Hence the new points are  (168, 168) , (168,56) , (112,0) , (70,112)

Learn more about center of dilation here

https://brainly.com/question/14101746

#SPJ10

Option A is the correct answer.

The independent variable is the input variable and should be represented by the x-axis.

A variable is a symbol and placeholder for a quantity that may change, or any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

For the Scatterplot, out of given options,

Option A is the correct option which represents The independent variable is the input variable and should be represented by the x-axis.

Thus, The independent variable is the input variable and should be represented by the x-axis.

Learn more about Variable from:

https://brainly.com/question/1511425

#SPJ1

Answer:

x-23=.55

Step-by-step explanation:

Answer: 0.55 = x - 23

Step-by-step explanation:

let his savings = x

Answer:

please help me find em ah and I will be able to do what I can

Answer:

x² + 4x + 3

---------------

       2

---- => fraction line