Answer:
£6,000 and £15,000.
Step-by-step explanation:
This split works out to 2 fractions: 2 / (2 + 5) = 2/7 and 5/(2+5) = 5/7.
So the required amounts are £21,000 * 2/7 = £6,000 and 5/7 * 21,000
= £15,000.
An Antique Collector want to know the age of a particular chair in a shop Statistical or not statistical
Answer:
[tex]\boxed{\bold{Not \ Statistical}}[/tex]
Step By Step Explanation:
Statistical: A survey, branch or mathematics consisting of data collection, organization, analysis, interpretation and presentation.
A statistical question deals with social problems, people, or something that must be studied and data gained. Statistical questions must have data sets and data gained. They also must have answers that vary from side to side or opinion to opinion, in order to be qualified as a 'statistical question'.
"An Antique Collector wants to know the age or a particular chair in a shop"
V
Statistical Not Statistical
[tex]\boxed{\bold{>}}[/tex] This is not a statistical question because there is no data that needs to be collected, no surveys that need to be filled out and no analysis, interpretation and presentation. The answer to this question does not vary. It is simply a fact.
The conditional relative frequency table below was generated by column using frequency table data comparing the number of calories in a meal to whether the meal was prepared at home or at a restaurant.
A nutritionist attempts to determine an association between where food is prepared and the number of calories the food contains. Which is most likely true?
A. An association cannot be determine because the value 0.55 is similar to the value 0.45
B. There is an association because the value 0.15 is not similar to the value 0.55
C. There is an association because the sum of each column is 1.0.
D. An association cannot ve determined because the sum of the rows going across is not 1.0.
Answer:
B. There is an association because the value 0.15 is not similar to the value 0.55
Step-by-step explanation:
Based on the above picture, for the nutritionist to determine whether there is an association between where food is prepared and the number of calories the food contains, there must be an association between two categorical variables.
The conditions that satisfy whether there exists an association between conditional relative frequencies are:
1. When there is a bigger difference in the conditional relative frequencies, the stronger the association between the variables.
2. When the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.
For the given conditional relative frequency, we can see that there exists a significant difference between the columns of the table in the picture because 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45
We can conclude that there is an association because the value 0.15 is not similar to the value 0.55
Answer:There is an association because the value 0.15 is not similar to the value 0.55.
Step-by-step explanation:
One of the roots of the equation 10x2−33x+c=0 is 5.3. Find the other root and the coefficient c.
Answer:
1. The other root is [tex]-2[/tex]
2. c=-106
Step-by-step explanation:
The given equation is [tex]10x^2-33x+c=0[/tex].
If [tex]5.3[/tex] is a solution to the given quadratic equation, then [tex]x=5.3[/tex] must satisfy this equation.
[tex]10(5.3)^2-33(5.3)+c=0[/tex]
[tex]280.9-174.9+c=0[/tex]
[tex]106+c=0[/tex]
[tex]c=0-106=-106[/tex]
We now substitute [tex]c=-106[/tex] into the given equation to obtain;
[tex]10x^2-33x-106=0[/tex].
Comparing to the general equation;
[tex]ax^2+bx+c=0[/tex], we have a=10, b=-33 and c=-106.
Recall the quadratic formula;
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
We now use the quadratic formula to obtain;
[tex]x=\frac{--33\pm \sqrt{(-33)^2-4(10)(-106)} }{2(10)}[/tex]
This implies that;
[tex]x=\frac{33\pm \sqrt{5329} }{20}[/tex]
[tex]x=\frac{33\pm73}{20}[/tex]
[tex]x=\frac{33-73}{20}[/tex] or [tex]x=\frac{33+73}{20}[/tex]
[tex]x=\frac{-40}{20}[/tex] or [tex]x=\frac{106}{20}[/tex]
[tex]x=-2[/tex] or [tex]x=5.3[/tex]
Hence the other root is [tex]-2[/tex]
How can you represent constraints by absolute value equations?
Answer:
The absolute number of a number a is written as
|a|
And represents the distance between a and 0 on a number line.
An absolute value equation is an equation that contains an absolute value expression. The equation
|x|=a
Has two solutions x = a and x = -a because both numbers are at the distance a from 0.
To solve an absolute value equation as
|x+7|=14
You begin by making it into two separate equations and then solving them separately.
x+7=14
x+7−7=14−7
x=7
or
x+7=−14
x+7−7=−14−7
x=−21
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.
The inequality
|x|<2
Represents the distance between x and 0 that is less than 2
picture42
Whereas the inequality
|x|>2
Represents the distance between x and 0 that is greater than 2
picture43
You can write an absolute value inequality as a compound inequality.
$$\left | x \right |<2\: or
−2<x<2
This holds true for all absolute value inequalities.
|ax+b|<c,wherec>0
=−c<ax+b<c
|ax+b|>c,wherec>0
=ax+b<−corax+b>c
You can replace > above with ≥ and < with ≤.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
Sorry If its not what your looking for but i tried
Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems.
Constraints can be represented by absolute value equations when dealing with inequalities that involve the distance between a variable and a fixed value. Absolute value equations are commonly used to express constraints in mathematical modeling and optimization problems. Here's how you can do it:
Representing Constraints with "less than" or "greater than" inequalities:
Suppose you have a variable "x" and a fixed value "a." If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than some constant "k," you can write it as:
| x - a | < k
For example, if you want to constrain "x" to be within 3 units from 5, you write:
| x - 5 | < 3
Representing Constraints with "less than or equal to" or "greater than or equal to" inequalities:
If you want to impose a constraint that the absolute value of the difference between "x" and "a" is less than or equal to some constant "k," you can write it as:
| x - a | ≤ k
For example, if you want to constrain "x" to be within 2 units from 8, you write:
| x - 8 | ≤ 2
Using absolute value equations allows you to handle situations where the variable needs to be close to a certain value or within a specific range, regardless of whether it is greater or smaller than that value. This flexibility is particularly useful in various mathematical and optimization problems, including linear programming and constrained optimization.
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What is 6x^2-12x+y+13=0 in vertex form of parabolas
Answer:
[tex]y=-6(x-1)^{2}-7[/tex]
Step-by-step explanation:
we have
[tex]6x^{2} -12x+y+13=0[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+13=-6x^{2} +12x[/tex]
Factor the leading coefficient
[tex]y+13=-6(x^{2} -2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y+13-6=-6(x^{2} -2x+1)[/tex]
[tex]y+7=-6(x^{2} -2x+1)[/tex]
Rewrite as perfect squares
[tex]y+7=-6(x-1)^{2}[/tex]
[tex]y=-6(x-1)^{2}-7[/tex] -----> equation of the parabola in vertex form
The vertex is (1,-7) is a maximum, the parabola open downward
To convert 6x^2 - 12x + y + 13 = 0 to vertex form, follow the steps to complete the square and rewrite the equation as (x - 1)^2 = -y/6 - 7/6.
Explanation:The equation 6x^2-12x+y+13=0 is in the general form of a quadratic equation. To convert it into the vertex form, we need to complete the square.
First, let's group the x terms together: 6x^2 - 12x = -(y + 13).
Next, let's complete the square: 6(x^2 - 2x) = -(y + 13).
Now, we can add (2/2)^2 = 1 to both sides to complete the square: 6(x^2 - 2x + 1) = -(y + 13) + 6.
Simplifying further, we get 6(x - 1)^2 = -y - 7.
Finally, we can write the equation in vertex form by dividing both sides by 6: (x - 1)^2 = -y/6 - 7/6.
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6....................
Answer:
option (a)
x - √7x / x - 7
Step-by-step explanation:
Given the expression in the question
√x / (√x + √7)
There are 3 steps to follow
Multiply numerator and denominator by a radical that will get rid of the radical in the denominator. Make sure all radicals are simplified. Simplify the fraction if needed.Step 1Multiply by √x - √7
√x (√x - √7) / (√x + √7)(√x - √7)
√x .√x - √7.√x / (√x + √7)(√x - √7)
Step 2a² - b² = (a+b)(a-b)
√x² - √7x / √x² - √7²
Step 3x - √7x / x - 7
Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. x + y > 3 x + y < -4
Answer:
The graph for the following system of inequalities is attached below.
Step-by-step explanation:
The given system of inequalities is
[tex]x+y>3[/tex] .... (1)
[tex]x+y<-4[/tex] .... (2)
From inequality (1) and (2) it is clear that (x+y) is greater than 3 adn 3 is not less than -4. So, the given system of inequality has no feasible reason or solution.
The related equation of first inequality is
[tex]x+y=3[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=3\Rightarrow y=3[/tex]
The y-intercept is 3.
Put y=0 to find the x-intercept.
[tex]x+0=3\Rightarrow x=3[/tex]
The x-intercept is 3.
The related equation of second inequality is
[tex]x+y=-4[/tex]
Put x=0 to find the y-intercept.
[tex]0+y=-4\Rightarrow y=-4[/tex]
The y-intercept is -4.
Put y=0 to find the x-intercept.
[tex]x+0=-4\Rightarrow x=-4[/tex]
The x-intercept is -4.
The related lines are dotted line because the sign of inequalities are > and <.
Check each inequality be (0,0).
[tex]0+0>3[/tex]
[tex]0>3[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
[tex]0+0<-4[/tex]
[tex]0<-4[/tex]
This statement is false. So the shaded region of first inequality is opposite sides of the origin.
The graph for the following system of inequalities is attached below.
Answer:
This is the correct graph on Odyssey :)
6/10+39/100 find the sum
The answer is-
Exact form: 99/100
Decimal form: 0.99
Please !!! Someone help me
answer is the last one D
pls mark brainliest
The answer is D good luck
Javier’s Bakery sells donuts in packages of 3 and cookies in packages of 5 today the backers sold the same number of donuts and cookies . What is the smallest number of donuts that the bakery could have sold?please help me
The answer is A.) 5 because it’s the smaller number
Which of the following rules is true for all values in the input-output table below?
A x + 1 = y
B x + 2 = y
C 2x = y
D 3x − 2 = y
Answer:
The answer is b
thank you
whats the answer
(5+3i)+(2-2i)
Answer: 7 + i
Step by step:
Remove parentheses.
5 + 3i + 2 - 2i
Add 5 and 2
7 + 3i - 2i
Subtract 2i and 3i
7 + i
The sum of the complex numbers (5+3i) and (2-2i) is 7+i. You add the real parts to get 7 and the imaginary parts to get i, then combine them.
Adding two complex numbers: (5+3i)+(2-2i). To perform this addition, we simply add the real parts and the imaginary parts separately. The real parts are 5 and 2, and when we add them together we get 7. The imaginary parts are 3i and -2i, which sum up to 1i (or just i). Hence, the result of the addition of these two complex numbers is 7+i.
To further clarify with an example similar to the student's question: (3+4i) + (−2+7i) = (3 - 2) + (4 + 7)i = 1 + 11i. The process is straightforward—add the real numbers, add the imaginary numbers, and combine them into one complex number.
Which expression is equivalent to (cd)^5
Answer:
c^5 *d^5
Step-by-step explanation:
Point P is the image of P -2,-2 under a translation by 1 unit to the left and 3 units down.
Answer:
(- 3, - 5)
Step-by-step explanation:
A translation of 1 unit left, subtract 1 from x- coordinate
A translation of 3 units down, subtract 3 from y- coordinate
The translation rule is
(x, y) → (x - 1, y - 3), hence
(-2, - 2) → (- 2 - 1, - 2 - 3) → (- 3, - 5)
Find the missing number: 8.4(1.5 + 2.3) = 12.6 +
Answer:
19.32
Step-by-step explanation:
One way to find the missing number is to get the value of the left side of the equation first.
8.4(1.5 + 2.3) = 31.92
Now we need to take that value and subtract it to the value on the right side of the equation.
31.92 - 12.6 = 19.32
So we have:
8.4(1.5 + 2.3) = 12.6 + 19.32
31.92 = 31.92
Answer:
The required number is 19.32
Step-by-step explanation:
Consider the provided expression.
Let the missing number is x.
[tex]8.4(1.5 + 2.3) = 12.6 +x[/tex]
Add the numbers as shown.
[tex]8.4(3.8) = 12.6 +x[/tex]
Open the parentheses.
[tex]31.92= 12.6 +x[/tex]
Subtract 12.6 from both the sides.
[tex]31.92-12.6= 12.6-12.6 +x[/tex]
[tex]x=19.32[/tex]
Hence, the required number is 19.32
There are bytes in a gigabyte. There are bytes in a megabyte. How many times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive?
Answer: third option.
Step-by-step explanation:
You know that:
- There are 10⁹ bytes in a gigabyte.
- There are 10⁶ bytes in a megabyte.
Then, to know how many times greater the storage capacity of a 1-gigabyte flash drive is than a 1-megabyte flash drive, you must divide 10⁹ bytes by 10⁶ bytes.
Remember the quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
Then:
[tex]=\frac{10^9}{10^6}=10^3=1,000[/tex] times greater
Answer:
1,000
Step-by-step explanation:
mark goes to the mall every 4 days, costco every 2 days, and the grocery store every 3 days.if he goes to all three on the 15th, when will he go to all three again?
Answer:
27th
Step-by-step explanation:
Every 4 days=4m
Every 3days=3s
Costco =2c
When does 4m=D=3s?
When m=0=s and when m=3 and s=4
4•3=12=3•4
Can 2c=12? Yes, when c=6
So 12 days from now, mall, store and Costco will all happen.
15+12=27
Solve for t.
t ÷ 5 1/3 = 3/4
Answer:
t = 4
Step-by-step explanation:
To solve for t, convert the numbers to improper functions. Then multiply by 16/3 on each side.
t ÷ 5 1/3 = 3/4
t ÷ 16/3 = 3/4
t = 16/3 * 3/4
t = 48/12
t = 4
Which ordered pair is a solution of the equation? 7x-2y=-5
answer X= 5 over 7 and 2 over 7y step by step explaination add 2y on both sides u cancelled -2y and positive 2y u bring down 7X u get 7X=-5+3 then u divide and u get that answer yw have a nice day mark me brainliest
Answer:
2y=-x7
Love mORgan
The numbers of hours that 12 students say they typically spend on homework in a week are 2, 0, 10, 8,10, 8, 8, 8, 10, 10, 8, and 8. What is the mean number of hours? What are the outliers in the data set?
Answer:
The mean is 7.5 and the outliers are 0 and 2
Step-by-step explanation:
To find the mean, add all of the numbers together and divide by the amount of numbers.
2 + 0 + 10 + 8 + 10 + 8 + 8 + 8 + 10 + 10 + 8 + 8 = 90
90/12 = 7.5
To see the outliers, look for the numbers far away from the mean.
Help plz !! Need this to graduate
Find the area thanks
16 x 14 = 224
[tex]answer = {224cm}^{2} [/tex]
Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of polynomial division and the quadratic formula.
x3 - 27 = 0
Answer: 3
Step-by-step explanation:
[tex]x^3-27=0\\\\x^3=27\\\\\sqrt[3]{x^3}=\sqrt[3]{27}\\\\x=\sqrt[3]{3\cdot 3\cdot 3} \\\\x=3[/tex]
What is the axis of symmetry for f(x) = 2x2 + 4x + 2?
Choices
x = −3
x = −1
x = 1
x = 3
Answer:
-1
Step-by-step explanation:
to find the axis of symmetry, the formula is X= -b/ 2a
a is the 2 from 2x2
and b is 4 from 4x
then plug them to the formula
-b= -4 because of the negative in -b
and 2a is 2(2)
-4/4 is -1
so x= -1
hope im right
hope it helps
which sequence shows the numbers in order from least to greatest
Answer:
C
Step-by-step explanation:
1/2 is positive unlike the other two so it is obviously last.
Now it's between -3/4 and -2/3
-3/4 = -0.75
-2/3 = -0.67
Since -0.75 < -0.67, -3/4 is first and -2/3 is second.
Answer:
Your answer would be C.
Step-by-step explanation:
Tell how to read the statement f(4)=16. Then interpret what it means in terms of input and output values.
An equation f(4)=16 means that when the input value is 4, the output value is 16.
Explanation:An equation in the form f(4)=16 means that when the input value of the function f is 4, the output value is 16.
For example, if f represents the function that multiplies an input by 4, then f(4)=16 because 4 multiplied by 4 equals 16.
In terms of input and output values, f(4)=16 means that when the input value is 4, the function will return an output value of 16.
Claire made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Claire doesn’t touch the money in her account, she can find the amount she’ll have the next year by multiplying her current amount by 1.03. A) how much money will Claire have in her account after 1 year? After 2 years? B) how much money will Claire have in her account after 5 years? Explain your reasoning. C) Write an expression for the amount of money Claire would have after 30 years if she never withdraws money from that account.
We can make and use the equation: A = 160( 1.03 )^y: A = amount, 160 = amount put in, 1 + .03 = 1.03 = interest, and y as the number of years, as the money is compounded every year. (This is the compound interest equation, but I put in the numbers)
A) 160 * 1.03 = $164.80, 160 * 1.03² = $169.744 ≈ $169.74
B) 160 * 1.03⁵ = 185.48385 ≈ $185.48
The expression is the same as saying (((((160 * 1.03)1.03)1.03)1.03)1.03). This is like multiplying 160 * 1.03, which gives the amount for the first year. Then, that amount is multiplied by 1.03, which is the amount for the second year. This isi repeated until 5 years.
C) 160(1.03)³⁰
Claire will have $164.80 after 1 year and $169.74 after 2 years in her savings account due to the 3% interest rate. After 5 years, she will have $185.86. The expression for the amount after 30 years is $160 × (1.03)³⁰.
Explanation:When Claire deposited $160 into her savings account at a 3% interest rate per year, she initiated a process of compound interest. This means each year, the amount of money in her account will increase by 3% of the amount from the previous year. The way to find out how much money she will have after a certain number of years is to multiply the initial amount by 1.03 raised to the power of the number of years.
Interest After 1 Year
After 1 year: $160 × 1.03 = $164.80
Interest After 2 Years
After 2 years: $160 × (1.03)² = $169.74
Interest After 5 Years
After 5 years: $160 × (1.03)⁵ = $185.86. This is calculated using the formula for compound interest: $160 × 1.03 raised to the fifth power.
Interest After 30 Years
To write an expression for the amount of money she will have in 30 years: $160 × (1.03)³⁰. This follows the general formula for compound interest, which is the initial amount times one plus the interest rate raised to the number of years.
riddle time I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I? if hard text me and i will give you the answer
Answer:
Is it a map? To me that makes the most logical sense.
Answer:
A map
Step-by-step explanation:
A map has cities, mountains, and water. It doesn't show houses, trees, or fish because it doesn't show specific things.
What is the area of this triangle? please help me.
Answer:
6
Step-by-step explanation:
Area of a triangle: bh/2
4*3/2=6
Answer:
6 units²
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = DE = 3 units and
h is the distance from the vertex F to DE = 4 units, hence
A = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 units²
suppose that 17 inches of wire cost $0.85 at the same rate how many inches of wire can be bought for $0.55
Answer:
11 inches
Step-by-step explanation:
17/0.85 * 0.55
20 * 0.55
11.