Answer:
£15 and £22
Step-by-step explanation:
let,the cost of one shirt be X and one jumper be y.Then according to question,
5x+4y=163-----(1)
also,
3x+2y=89------(2)
Now, multiplying eqn (2) by 2 and then subtracting from (1),we get
5x+4y=163
6x+4y=178
- - -
_________
-x=-15
:.x=15
Putting value of X in eqn (1),
5×15+4y=163
or,4y=163-75
or,y=88/4
:.y=22
Hence cost of one shirt is £15 and one jumper is £22.
Find a formula for the exponential function passing through the points(-1,4/5) and (1 , 20)
y=
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].
How to derive the exponential function containing two given points
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:
x - Independent variable.y - Dependent variable. A, B - Constants.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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Write a function describing the relationship of the given variables.
A, varies directly with, r, and when r = 4, A = 8
A=______
The relation between a and r is 2r
How to write a function describing the relationship of the given variables?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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Suppose you want to have $800,000 for retirement in 25 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
b) How much interest will you earn?
$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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Another brand of sheets is on sale 30% off with a regular price of $18.00 per sheet. Which is a better deal, the previous example or this one? Explain. (2 points)
30% OFF EACH SHEET!
The cost for the sheet is $22.60 and a discount of 30% is given.
How to calculate the value of the sheets?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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What is the greatest common factor of 110, 40, and 120?
a
40
b
10
c
220
d
1
pls help
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!
Given the following functions, find and simplify (f⋅g)(3). f(x)=−3x−2 g(x)=−x+2 Do not include "(f⋅g)(3)=" in your answer.
The value of the function (f⋅g)(3) = 1
What are Functions: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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Find the value of x. Leave your answer in simplest radical form.
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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To test m for an x distribution that is mound-shaped using
sample size n 30, how do you decide whether to use the normal or the
Student’s t distribution?
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.
What is normal distribution?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.
What is t distribution?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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Aspen incorrectly converted 15/8 to a decimal using long division. Check her work carefully to find the error. Select the digit where she first made a mistake.
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.
A group of 8 students was asked, "How many hours did you watch television last week?" Here are their responses.
7,5, 4, 5, 9, 8, 11, 7
Find the median and mean number of hours for these students.
If necessary, round your answers to the nearest tenth.
Need ASAP PLEASE
take your die and roll it the number of times that is equal to your age 26 in years. Create a table below to document each roll of the die. Use this trial data to determine the experimental probability of rolling a two on the die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places) and a percentage (rounded to one decimal place).
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%
Write an inequality to represent the situation.
six times a number and three is at least forty-two
six times a number and three is at most forty-two
six times a number and three is less than forty-two
six times a number and three is more than forty-two
6(n + 3) ≤ 42
6(n + 3) ≥ 42
6(n+3) > 42
6(n + 3) < 42
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.
How to Write an Inequality for a Situation?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
For what value of x would 3 (3x − 1)− 3 (5x − 3)= − (x + 6)?]
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]
Solve 5(2m + 1) − 3m = −16.
m equals negative 16 over 30
m equals negative 21 over 30
m = −3
m = −0.33
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
Select from the drop-down menu to correctly complete the statement. The product of 7 and 5/8 is Choose... because 5/8 is less than 1.
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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At a baseball game, a vender sold a combined total of 246 sodas and hot dogs. The number of hot dogs sold was 34 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
The vendor sold 212 sodas and 34 hot dogs.
Step-by-step explanation:
Subtract 34 from 246 for the number of sodas sold.
Write this number in scientific notation.
.0000149
Answer: 1.49 x [tex]10^{-5}[/tex]
Step-by-step explanation:
Mugs can be packed with up to 6 mugs in each box how many boxes are needed to pack 1528
5 and square root of 4
Answer:
7-------------------
It is assumed you need to add 5 and square root of 4:
[tex]5+\sqrt{4} =5+\sqrt{2^2} =5+2=7[/tex]An individual is teaching a class on Excel macros. The individual plans to break the class up into groups of 3 and wants each group to have a different exercise to practice on. Solve for the dependent variable (y) if the independent variable is 15.
The dependent variable, y from the given situation is 15
Solve for the dependent variableThe number of groups = 3Number of exercises each group practice on = 3The total number of exercises the individual needs, y = 3x/3
Where,
y = independent variable x = dependent variable = 15So,
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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How much money has to invested at 4.3% interest compounded continuously to have $19,000 after 16 years?
A. $ 9549.02
B. $ 9584.15
C. $ 9618.91
D. $ 9560.77
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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Nicholas is typing a book report at an average speed of 40 words per minute. Which equation could Nicholas use to find t, the amount of time in minutes he will spend typing, if his report has [w] words?
A. t = 40w
B. w = 40t
C. t = w + 40
D. w = t + 40
Please help ASAP I've been stuck on this question
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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send help i need help please whta is the answer
How would you express the area of he rectangle using the Distributive Property?
area = length * width
area using Distributive Property: 3 (x + 5)
How many reflection symmetries does a twelve-pointed star have? How many rotational symmetries does a twelve-pointed star have?
Answer: 12 symmetries
Step-by-step explanation:
just draw the lines on the star.
The graph of the relationships ( dogs,cost) is a line that contains the points(0,0) (3,12) and (6,24). What is the constant of proportionality?
4 is the constant of proportionality of given graph.
What is 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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Solve 3x + 2 = 5. hurry pls
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
16x¹9y8
8x11 ⁹ what is the solution
You have $108,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.0 percent. Stock X has an expected return of 12.6 percent and a beta of 1.15, and Stock Y has an expected return of 9.8 percent and a beta of .86.
The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.
What is an expression?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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Choose the best answer. For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is predicted tail length = 20 + 3
\times
×
weight. Which of the following is not correct? (a) The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length. (b) The predicted tail length of a mouse that weighs 38 grams is 134 millimeters. (c) By looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive. (d) If you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been 3/10 = 0.3. (e) One mouse weighed 29 grams and had a tail length of 100 millimeters. The residual for this mouse is -7.
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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