Answer:
Yellow: 4
blue: 2
red: 12
green: 2
Help with a composition of two functions! 20 pts for a solution!
The function (fog)(x) would be (x^4 + 10x² + 27). Also, the domain of (fog)(x) is all the real numbers.
What is a function?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.
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Translate this sentence into an equation. Craig's savings decreased by 23 is .55
Answer:
x-23=.55
Step-by-step explanation:
Answer: 0.55 = x - 23
Step-by-step explanation:
let his savings = x
(c) Nicole has a part-time job entering data in a computer. Her pay at the end of the week C
is affected by the amount of data she enters each hour. What is the dependent
variable?
Answer:
the dependent variable is the data because it's the one that changes
please help me with this problem ! would appreciate it!!!
[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]
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find the least common denominator 3/2x+4 and -11/3x+6
Answer: 6x+12
Step-by-step explanation: Both denominators can be multiplied to create 6x + 12.
2x + 4
2x(3) + 4(3)
6x+12
3x + 6
3x(2) + 6(2)
6x+12
I hope this helps!
6. 0, 16, 32, 48, 64, ______, ______, ______
what is the next 3 numbers.
Answer:
Step-by-step explanation:
Remark. Since 6 has a decimal after it, I take it that is the question number.
y = 16x is the basic formula. x starts at 0. Then you add 16 to each number to get the next number in the sequence. Or you could do it the way I propose it.
x 0 1 2 3 4 5 6 7
y 0 16 32 48 64 80 96 112
Circumference and area of a piece of glass cabinet which has a diameter of 1.8m
Answer:
circumference: 5.65 m
area: 2.54 m
Step-by-step explanation:
here are some relationships between measurements of a circle:
C = π d
(Circumference = pi · diameter)
A = π r²
(Area = pi · radius²)
[π / pi is the ratio of a circle's circumference to its diameter. this ratio is actually a constant across all circles, which is where we derive our circumference and area formula from. π ≈ 3.14159]
so, let's work on finding the circumference first.
C = π d
we know the diameter = 1.8, and we know that π ≈ 3.14159
so, if we multiply these two numbers together, we will get the circumference
[this equation makes sense if you read my explanation of pi]
1.8 × 3.14159 = 5.654862
We can round this number to 5.65
So, the circumference of our circle = 5.65 m
now, let's find the area
A = π r²
we know that π ≈ 3.14159, but we still haven't found "r"
r, or radius, is the measurement from the center of a circle to any point of the circle. Because the diameter is the measurement from one side of a circle to the opposite side, diameter = twice the radius
this means we can take our diameter, 1.8, and divide it by 2 to find our radius.
1.8 / 2 = 0.9
now, we can solve for area.
π ≈ 3.14159 , r = 0.9
A = π r²
A = π (0.9)²
A = (3.14159) (0.81)
A = 2.5446879
we can round this area to 2.54
so, the area of our circle = 2.54 m
What is the median of these figure skating ratings?
5.0 6.0 7.0 7.5 8.0 9.0 10.0
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..
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.
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.
Jessica received a $70 gift card for a coffee store. She used it in buying some coffee that cost $7.26 per pound. After buying the coffee, she had $48.22 left on her card. How many pounds of coffee did she buy?
Packs of stickers
Buy for €1.50a pack
Sell For £2.25 a pack
Media buys 5 pack's and sells them all
How Much profit does she
Make ?
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
Sum of 1/2*3 +1/3*4 +1/4*5 ..1/99*100
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.
In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6965 subjects randomly selected from an online group involved with ears. There were 1302 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than 20%. Use the P-value method and use the normal distribution as an approximation to the binomial distribution
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%
What is the claim that the return rate is less than 20% by using a statistical hypothesis method?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%
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Use the Polygon tool to draw an image of the given polygon under a dilation with a scale factor of 14 and center of dilation (0, 0).
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)
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A group of students at Brunel university took a test in marketing and they needed to score 50 to pass. The results showed that the final grades have a mean of 62 and a standard deviation of 8. Suppose we approximate the distribution of these grades by normal distribution. Based on this information, you are required to perform the following; a) what percetage(to 3 decimals) of the students scored more than 78? B) what percentage of the students to 3 decimal places scored under 50? And c) what percentage to 3 decimal places of the students scored between 60 and 80?
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%
Please solve this for me
Answer:
f(x) = square root of x
g(x) = 4x - 1
Step-by-step explanation:
Prepare the journal entry to record each of the following four separate insurances of stock a. corporation issue 4000 share of 5$ par value common stock for 35000 cash
The preparation of the journal entry to record the accounting transaction can be seen in the table below.
How do you prepare a journal entry to record an account?Initially, when preparing a journal, you have to read the transaction carefully and comprehend it. Discover which accounts need to be credited and debited before entering a journal entry.
From the given information:
The common stock par value = no of shares × par value of shares
The common stock par value = 4000 shares × $5/ share
The common stock par value = $20000
However, the amount paid in capital excess of the par value for the common stock is:
= $35000 - $20000
= $15000
Therefore, the Journal entry can be computed as follows:
Date Account Title Post Ref Debit ($) Credit ($)
Cash 35,000
Paid-in capital in excess of par
value, common stock 20,000
(To record the insurance of common stock)
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A jug of drinking water contained 1 2/3 gallons. If 5/7 gallon is drinked each day, how much water was left in the jug after 2 days?
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!
In 2010, the number of clown costumes sold at a single costume shop was 11. By 2015, that number had grown to 23. Assuming a constant increase in clown costume sales, calculate the average rate of change (the slope) from 2010 to 2015.
The average rate of change = 109%
What is the meaning of Rate of Change ?Rate of Change is the measure of the increase or decrease in the value with respect to the initial value.
It is given that
No of clown sold in 2010 = 11
No of clown sold in 2015 = 23
The average rate of change = ((23-11)/11 ) *100 %
The average rate of change = 109%
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Write and simplify the equation you would use to solve the problem below.
A farmer builds a rectangular pen with a perimeter of 116 feet. If the length is 5 feet more than the width, what is the width?
A.w + 5 = 116
B.4w + 10 = 116
C.2w + 5 = 116
D.2w + 10 = 116
need a hand i cant figure this one out
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
Which statement is correct when a scatterplot is constructed?
The independent variable is the input variable and should be represented by the x-axis.
The independent variable is the input variable and should be represented by the y-axis.
The dependent variable is the input variable and should be represented by the x-axis.
The dependent variable is the input variable and should be represented by the y-axis.
Option A is the correct answer.
The independent variable is the input variable and should be represented by the x-axis.
What is Variable?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.
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Solve for B -9/3+ B equals -1
Answer:
-2
Step-by-step explanation:
-9/3=-3
-3+b=-1
b=-1+3
b=-2
Please assist with the following questions
The answers for following questions are;
i. $244.64
ii. $ 5314.64
What is future value?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
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Charlotte practices the piano for 4 hours each week. How many minutes does she practice each week?
Answer:
4 X 60 = 240 minutes
Step-by-step explanation:
there are 60 minutes in each hour
What is the solution to the following equation?
3( x - 4 ) - 5 = x - 3
A. x = 8
B. x = 3
C. x = 12
D. x = 7
Answer:
x = 7
Step-by-step explanation:
3(x - 4) - 5 = x - 3
3x - 12 - 5 = x - 3
2x = -3 + 12 + 5
2x = 14
x = 7
world problem in length (trigonometry) geometry not chemistry
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 )
What is the slope intercept of the line below
-------------------------------------------------------------------------------------------------------------
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
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{-1 - (-3)}{1 - 0}[/tex][tex]m = \frac{-1 + 3}{1}[/tex][tex]m = \frac{2}{1}[/tex][tex]m = 2[/tex]Plug in the values
[tex]y = mx + b[/tex][tex]y = 2x - 3[/tex]Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.
What is 2(x+3) / 4(x+1)
Answer:
x² + 4x + 3
---------------
2
---- => fraction line
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.
y = 7.5x
y = 5.5x + 10
1. Substitute: 7.5x = 5.5x + 10
Angle PQT and Angle SQR are supplementary angles. If the measure of PQT is (3x+43)° and the measure of Angle SQR is (6x-25)°, what is the numeric measure of Angle PQT and Angle SQR?
Answer:
∠PQT = 97°
∠SQR = 83°
Step-by-step explanation:
Supplementary angles sum to 180°
⇒ ∠PQT + ∠SQR = 180°
Given:
∠PQT = (3x + 43)°∠SQR = (6x - 25)°Therefore:
⇒ (3x + 43) + (6x - 25) = 180
⇒ 3x + 6x + 43 - 25 = 180
⇒ 9x + 18 = 180
⇒ 9x = 162
⇒ x = 18
Substitute the found value of x into the expression for each angle:
⇒ ∠PQT = (3x + 43)°
⇒ ∠PQT = (3(18) + 43)°
⇒ ∠PQT = 97°
⇒ ∠SQR = (6x - 25)°
⇒ ∠SQR = (6(18) - 25)°
⇒ ∠SQR = 83°
Check
⇒ ∠PQT + ∠SQR = 97° + 83° = 180°
