James and Elizabeth buy some clothes.
James buys 5 shirts and 4 jumpers. He pays £163.
Elizabeth buys 3 shirts and 2 jumpers. She pays £89.
Assume that each shirt has the same cost and that each jumper has the same
cost.
Work out the cost of one shirt and the cost of one jumper.

Cost of one shirt £
Cost of one jumper £

The cost for the sheet is $22.60 and a discount of 30% is given.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, the brand of sheets is on sale 30% off with a regular price of $18.00 per sheet.

Therefore, the cost for the sheet will be:

= $18 - (30% × $18)

= $18 - $5.40

= $12.60

The cost for the brand of sheet is $22.60.

Note that the information was incomplete and the calculation was based on the information given.

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The exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20) is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

In this problem we must determine the exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), whose formula is described below:

y = A · [tex]e^{B\cdot x}[/tex]

Where:

If we know that (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), then the values of constants are:

4 / 5 = A · [tex]e^{-B}[/tex]

20 = A · [tex]e^{B}[/tex]

If we divide the latter expression by the former, then:

25 = [tex]e^{2\cdot B}[/tex]

㏑ 25 = 2 · B

B = (1 / 2) · ㏑ 25

B ≈ 1.609

And the value of A is:

A = 20 / [tex]e^{1.609}[/tex]

A ≈ 4.002

The exponential function is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].

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The mistake happens when computing 70-64. The result is not 4, but should be 6 instead.

The correct long division is shown below.

This means [tex]\frac{15}{8} = 1.875[/tex] in which you can use your calculator to verify this.

The relation between a and r is 2r

According to the given information

a varies directly with r

a = 8

r = 4

a is directly proportional to r

a ∝ r

a = k r

where k is constant of proportionality

k =  [tex]\frac{a}{r}[/tex]

k = [tex]\frac{8}{4}[/tex]

k = 2

so,

a = k r

putting the value of k in the above equation

we get

a = 2r

The relation between a and r is 2r

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Answer:

x = 12/5

Step-by-step explanation:

3 (3x − 1) − 3 (5x − 3) = − (x + 6)

9x − 3 − 15x + 9 = − x − 6

9x − 15x + x = 3 − 9 − 6

− 5x = − 12

5x = 12

x = 12/5

Answer:

[tex]x=\dfrac{12}{5}[/tex]

Step-by-step explanation:

Given equation:

[tex]3(3x-1)-3(5x-3)=-(x+6)[/tex]

Distribute:

[tex]\implies 3 \cdot 3x + 3 \cdot (-1) - 3 \cdot 5x - 3 \cdot (-3)=-x-6[/tex]

[tex]\implies 9x-3-15x+9=-x-6[/tex]

Collect and combine like terms on the left side of the equation:

[tex]\implies 9x-15x+9-3=-x-6[/tex]

[tex]\implies -6x+6=-x-6[/tex]

Add 6x to both sides:

[tex]\implies -6x+6+6x=-x-6+6x[/tex]

[tex]\implies 6=5x-6[/tex]

Add 6 to both sides:

[tex]\implies 6+6=5x-6+6[/tex]

[tex]\implies 12=5x[/tex]

[tex]\implies 5x=12[/tex]

Divide both sides by 5:

[tex]\implies \dfrac{5x}{5}=\dfrac{12}{5}[/tex]

[tex]\implies x=\dfrac{12}{5}[/tex]

By using the concept of compounded interest, it can be calculated that

$9549.02 has to be invested  at 4.3% interest compounded continuously to have $19,000 after 16 years

First option is correct

What is compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.

Let the principal be $p

Rate= 4.3 %

Time = 16 years

[tex]19000 = pe^{\frac{4.3}{100} \times 16}\\19000 = pe^{0.688}\\19000 = p \times 1.989732\\p = \frac{19000}{1.989732}\\[/tex]

p = $9549.02

First option is correct

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To decide whether to use the normal or the Student’s t distribution, for an x distribution that is mound-shaped:

Use the normal distribution if the standard deviation is known. Use the Student's t - distribution when the standard deviation is not known.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a bell curve.

For small sample numbers or unidentified variances, population parameters are estimated using a form of probability function called a t-distribution.

Hence t-distribution is suitable when the variance which is standard deviation squared is unknown

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The value of the function (f⋅g)(3) = 1

The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. It is denoted by the letter f or f(x).  

Here we have

f(x) = − 3x − 2  

g(x) = − x + 2

=> (f · g) = f(g(x))

Now Take x = − x + 2 in f(x)

=> f(g(x)) =  − 3(− x + 2)x − 2  

=  3x − 6 − 2      

=  3x − 8  

From the above calculations,

(f⋅g)(x) =  3x − 8    

Now we need to calculate the value of (f⋅g)(3) as given below

=> (f⋅g)(3) =  3(3) − 8 = 9 − 8 = 1

Therefore,

The value of the function  (f⋅g)(3) = 1

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Answer:

m= -3

Step-by-step explanation:

5(2m+1)-3m=-16

5(2m)+5(1)-3m= -16

10m+5-3m= -16

7m+5= -16

     -5.   -5

7m= -21

/7.    /7

m= -3

Hopes this helps please mark brainliest

And :-3

process:

5(2m + 1) - 3m = - 16

10m+5-3m=-16

7m=-16-5

m=-21/7

m=-3

Answer: 1

Let's solve your equation step-by-step.

3x+2=5

Step 1: Subtract 2 from both sides.

3x+2−2=5−2

3x=3

Step 2: Divide both sides by 3.

3x/3 = 3/3

(3x divided by 3 cancels the 3 in 3x making it just x)

x=1

Answer: 1.49 x [tex]10^{-5}[/tex]

Step-by-step explanation:

The part (a) is not correct i.e. The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.

What is Regression analysis ?

Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The result variable is sometimes referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".

Given, tail length = (3 × weight) + 20

(a) Here, The slope is 3 which indicates that a mouse's length is the sum of 3 times the weight and 20. So, the statement is not correct.

(b) If weight is 38 gm, then

    tail length = 38 × 3 + 20

                     = 114 + 20 = 134mm.

So, the statement is correct.

(c) We've  tail length = (3 × weight) + 20

we can see that the relationship between the two is positive because when the weight is increased, the tail length also increases.

So, the given statement is correct.

(d) The slope is 3 when the tail length is being measured in millimeters.

Now, If we measure it in centimeter = 3/10 = 0.3 cm

∵ 1 mm = 1/10 cm.

So, the given statement is correct.

(e) when a mouse has weight of 29 grams and tail length of 100 mm.

    When the weight is 29 grams, it should have tail length as :

             tail length = 29 × 3 + 20

                              = 107 mm.

  but, tail length is given as 100 mm.

So, the residual for the mouse is -7 i.e. (100 - 107)

Hence, The given statement is correct.

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$1,556.72 is required to deposit in the account each month.

72% of interest is earned.

a)

It is a classic Ordinary Annuity saving plan. The general formula is

FV = P((1+r)^n-1)/r)--------(1)

where  

FV is the future value of the account.  

P is the monthly payment (deposit).

r is the monthly percentage yield presented as a decimal.

n is the number of deposits (= the number of years multiplied by 12, in this case).

From this formula, you get the monthly payment:

P=FV(r/(1+r)^-1)----------(2)

Under the given conditions,

FV = $800,000

r = 0.04/12

n = 25*12.  

So, according to formula (2), the monthly payment is

P=800000(0.04/12(1+0.04/12)^25*12-1)

P=800000(0.003/1.713)

P=$1.556.72

Note that of the projected $800,000 the total you deposit will be only  25*12 times $1.556.72 i.e. about 25*12*1.556.72 = 467016 dollars.                    

The rest is what the account will earn/accumulate over the 25 years.

b)

You will earn:  

(8000000-467016/467016)*100

72% of interest is earned.

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The dependent variable, y from the given situation is 15

The total number of exercises the individual needs, y = 3x/3

Where,

So,

y = 3x/3

substitute the value of x into the equation

y = 3(15) / 3

open parenthesis

y = 45 /3

y = 15

In conclusion, the value of the dependent variable is 15

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The coordinate of the vertices of △A'B'C' are A'(3,6), B'(9,-3), and C'(-12, 6). Since the scale factor is 3.

What is coordinate of a point?

The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph.

The coordinate of △ABC are A(1,2), B(3,-1) and C(-4,2).

The scale factor is k = 3.

The x-coordinate of A is 1.

The y-coordinate of A is 2.

The x-coordinate of B is 3.

The y-coordinate of B is -1.

The x-coordinate of C is -4.

The y-coordinate of C is 2.

To find the vertices of △A'B'C', multiplying x-coordinate and y-coordinate by 3.

The x-coordinate of A' is 1 × 3 = 3.

The y-coordinate of A' is 2 × 3 = 6.

The x-coordinate of B' is 3 × 3= 9.

The y-coordinate of B' is -1 × 3 = -3.

The x-coordinate of C' is -4 × 3 = -12.

The y-coordinate of C' is 2 × 3 = 6.

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The inequality that represent each situations are:

a. 6(n + 3) ≥ 42.

b. 6(n + 3) ≤ 42

c. 6(n + 3) < 42

d. 6(n+3) > 42.

To write the inequality for each of the situations, translate each statement into algebraic expressions and use the appropriate inequality sign where necessary.

Thus, let the unknown number be represented as n.

a. The statement, "at least 42" means not less 42, which is the same as "greater than or equal to 42".

Therefore, the first statement is represented by the inequality, 6(n + 3) ≥ 42.

b. "6 times n and 3 is at most 42" is written as, 6(n + 3) ≤ 42

c. "6 times n and 3 is less than 42" would be translated as: 6(n + 3) < 42

d. "6 times n and 3 is more than 42" would be, 6(n+3) > 42.

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Step-by-step explanation:

6(n+3)>42

this is your answer

arlynn

The value of x in simplest radical form is x = [tex]\sqrt{17}[/tex]

Explain Pythagoras theorem.

The Pythagorean Theorem (also known as the Pythagorean Theorem) is an important topic in mathematics that describes the relationship between the sides of a right triangle. The sides of a right triangle are also called Pythagorean numbers.

The Pythagorean theorem is basically used to find unknown side lengths and triangle angles. Using this theorem, we can derive the formulas for the base, perpendicular and hypotenuse.

Using Pythagoras theorem in both the triangles,

Find the hypotenuse in above triangle

[tex]h^2=P^2+B^2[/tex]

[tex]h^2=4+4=8[/tex]

h = [tex]2\sqrt{2}[/tex]

Now, using Pythagoras theorem in below triangle,

[tex]h^2=P^2+B^2[/tex]

[tex]5^2 = x^{2} + 8[/tex]

25 = [tex]x^{2}[/tex] + 8

[tex]x^{2}[/tex] = 25 - 8 = 17

x = [tex]\sqrt{17}[/tex]

Therefore, x = [tex]\sqrt{17}[/tex]

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Answer:

2/27 or 0.074 or 7.4%

Step-by-step explanation:

Step 1: Roll a fair 6-sided die 27 times. The following outcomes are obtained. 

roll-

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27

outcome-

2,2,2,5,6,4,5,3,4,3,2,1,2,1,3,6,6,1,4,3,2,6,3,5,4,2,5

Step 2: Make a table for the frequency of each distinct outcome. 

Outcome-

1,2,3,4,5,6

Frequency:

3,7,5,4,4,4

Step 3:  The probability of rolling a two on the die is obtained using the classical probability formula as follows,

P(X=2)= factorable cases/total cases

from the frequency distribution table,

P(X=2)= 2/27= 0.074=7.4%

How would you express the area of he rectangle using the Distributive Property?

area = length * width

area using Distributive Property: 3 (x + 5)

4 is the constant of proportionality of given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

The graph of the relationships ( dogs,cost) is a line that contains the points(0,0) (3,12) and (6,24).

We need to find the constant of proportionality

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

To find the constant of proportionality, we have to divide the value of y by x.

12/3=4

24/6=4

Hence, 4 is the constant of proportionality of given graph.

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Answer:

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

It is assumed you need to add 5 and square root of 4:

The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Now,

Since, The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Hence, We get;

⇒ 7 × 5/8 = 35 / 8

Thus, The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

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Answer:

10

Step-by-step explanation:

Because if you line up the numbers 10 is the least common factor of 110,40,120

Answer: b 10

Step-by-step explanation:

the prime factorization of 110: 2 * 5 * 11

the prime factorization of 40: 2^3 * 5

the prime factorization of 120: 2^3 * 3 * 5

the factor they all share is only 2, and they all share 5 but they dont all share 11 and 3. Multiply 2 * 5 = 10. SO 10 is the GCF (Greatest Common Factor) of 110, 40, and 120.

hope this helps!

Answer: 12 symmetries

Step-by-step explanation:

just draw the lines on the star.

The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Data provided in the question:

Total amount to be invested = $140000

Stock                          X       Y

Expected return       14%     10%

Beta                          1.42     1.18

Expected return of portfolio = 17.6%

Now,

let the weight invested n stock X be W

therefore,

Weight of Stock Y = 1 - W

thus,

( W × 14% ) + (1 - w) × 10% = 17.6 %

14W + 10% - 10W = 17.6%

4W = 7.6

W = 1.9

Therefore,

weight of Y = 1 - 1.9 = -0.9

Amount investment in Sock Y = Total amount to be invested × Weight

= 140,000 × ( - 0.9 )

= - $126,000 i.e short Y

Beta of portfolio = ∑ (Beta × Weight)

Beta of portfolio= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]

Beta of portfolio= 2.698 - 1.062

Beta of portfolio= 1.636

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Answer:

The vendor sold 212 sodas and 34 hot dogs.

Step-by-step explanation:

Subtract 34 from 246 for the number of sodas sold.