The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean.
What is meant by normal distribution?The probability density function for a continuous random variable in a system defines the Normal Distribution.
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean. This shows that data close to the mean occur more frequently than data far from the mean. On a graph, the normal distribution is represented by a "bell curve."
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the price of a lounge chair is $140 plus 7.5% sales tax.what is the sales tax on the lunge chair in dollors and cents
Given that the price is $140 , and the tax rate is 7.5% (0.075 in decimal form)
we can find the amount in taxes by the product :
0.075 times 140
0.075 * 140 = 10.5
so $10.5 is the amount to be paid in taxes
[tex]undefined[/tex]Determine if the following answers are true or false. If false, justify why it’s not true and find the correct answer(s). If true, justify why they are correct. You must show your step-by-step process to solve each question to receive full credit.
Given the following inequality
[tex]\begin{gathered} \tan ^2(x)>\sqrt[]{5} \\ x\in\lbrack-\pi,\pi\rbrack \\ \end{gathered}[/tex]We need to check if x=0.981 is a solution.
This value is inside of the range, then, we just need to evaluate.
[tex]\tan ^2(0.981)\approx2.2325919107[/tex]Calculating the square root of 5:
[tex]\sqrt[]{5}\approx2.2360679775[/tex]From this, we know that the statement is false, because
[tex]\tan ^2(0.981)<\sqrt[]{5}[/tex]Check PictureGraph the polynomial given below by first selecting the number of points, then moving the points. You will need a point for each x intercept, and one for the y intercept.f(x)=17(x−1)(x+3)(x+7)
ANSWER
Graph:
EXPLANATION
Given:
[tex]f(x)\text{ = }\frac{1}{7}\left(x−1\right)\left(x+3\right)\left(x+7\right)[/tex]Desired Outcome:
Graph the polynomial
Plotting a few selected points using the table below
The local humane society is restocking on cat food to prepare for kitten season. Very young kittens need kitten formula which costs $4.00 per bottle. Older kittens need wet cat food which costs $1.50 per can. Answer numbers 5 and 6. 15) Write an algebraic expression to describe how much the humane society will spend on kitten supplies based on the number of bottles and the number of cans they buy. 16) How much money (before tax) will the humane society spend if they buy 5 bottles of kitten formula and 12 cans of wet cat food? Show your work.
Lets call B the nuber of bottles they will buy and C the number of cans.
Then, if each bottle cost $4, the cost of all the bottles will be 4B.
If each can cost $1.50, then, the total cost of the cans is 1.5C.
If we add this two costs, we have the expression we need:
[tex]\text{Cost}=4B+1.5C[/tex]If they buy 5 bottles of kitten formula and 12 cans of wet cat food, we have B=5 and C=12, and the cost is:
[tex]\text{Cost}=4B+1.5C=4\cdot5+1.5\cdot12=20+18=38[/tex]They will spend $38.
Question 7, pre calc, include the answer in bold please. I have bad WiFi so please finish question if I get disconnected so I can see it, thanks
Given the following function
[tex]f(x)=x^4-x^3+7x^2-9x-18[/tex]We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.
Let's start by dividing by the first factor
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}[/tex]To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)
[tex]\frac{x^4}{x}=x^3[/tex]Then, we ultiply it by the divisor
[tex]x^3(x+1)=x^4+x^3[/tex]Subtracting this result from the dividend, we have
[tex](x^4-x^3+7x^2-9x-18)-(x^4+x^3)=-2x^3+7x^2-9x-18[/tex]This means that our division is
[tex]\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3+\frac{-2x^3+7x^2-9x-18}{x+1}[/tex]Repeating the whole process of division with the second term, we have
[tex]\begin{gathered} x^3+\frac{-2x^3+7x^2-9x-18}{x+1}=x^3-2x^2+\frac{9x^2-9x-18}{x+1} \\ \Rightarrow\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3-2x^2+9x-18 \end{gathered}[/tex]From this result, we can rewrite our function as
[tex]x^4-x^3+7x^2-9x-18=(x+1)(x^3-2x^2+9x-18)[/tex]Repeating this same process with the other know factor, the other division we have to solve is
[tex]\frac{(x^3-2x^2+9x-18)}{x-2}=x^2+9[/tex]Then, our function is
[tex]f(x)=(x^4-x^3+7x^2-9x-18)=(x+1)(x-2)(x^2+9)[/tex]Then, to find the roots we need to solve the following equation
[tex](x+1)(x-2)(x^2+9)=0[/tex]Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system
[tex]\begin{cases}x+1=0 \\ x-2=0 \\ x^2+9=0\end{cases}\Rightarrow\begin{cases}x=-1 \\ x=2 \\ x=\pm\sqrt[]{-9}=\pm3i\end{cases}[/tex]And those are the roots for our function. x = -1, 2, +-3i.
The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m^s. Find the dimensions.
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the formula for total surface area of cuboid
[tex]\begin{gathered} 2(lb+bh+lh) \\ \text{where l is the length} \\ b\text{ is the breadth} \\ \text{h is the height} \end{gathered}[/tex]STEP 2: Get the dimension of the sides
[tex]\begin{gathered} \text{ Since the dimensions of the cuboid are in the ratio 1:2:3} \\ the\text{ dimensions are given as:} \\ x,2x\text{ and }3x \\ \text{lenght}=x \\ \text{breadth}=2x \\ \text{height}=3x \end{gathered}[/tex]STEP 3: Substitute the dimensions into the formula to get the value of x
[tex]\begin{gathered} 2(lb+bh+lh)=88 \\ By\text{ substitution,} \\ 2((x\cdot2x)+(2x\cdot3x)+(x\cdot3x))=88 \\ \Rightarrow2(2x^2+6x^2+3x^2)=88 \\ \text{Divide both sides by 2} \\ \Rightarrow\frac{2(2x^2+6x^2+3x^2)}{2}=\frac{88}{2} \\ \Rightarrow2x^2+6x^2+3x^2=44 \\ 11x^2=44 \\ \text{Divide both sides by 11} \\ \frac{11x^2}{11}=\frac{44}{11} \\ x^2=4 \\ x=\sqrt[]{4}=2 \\ x=2m \end{gathered}[/tex]STEP 4: Get the other dimensions
[tex]\begin{gathered} \text{breadth}=2x \\ \text{substitute 2 for x} \\ \text{breadth}=2(2)m=4m \\ \\ To\text{ get height} \\ \text{height}=3x \\ \text{substitute 2 for x} \\ \text{height}=3(2)m=6m \end{gathered}[/tex]Hence, the dimensions are:
[tex]2m,4m,6m[/tex]which functions are inverses of each other?A. both pair 1 and pair 2B. pair 1 only C. Pair 2 only D. neither pair 1 nor pair 2
Answer:
The pair one functions are given below as
[tex]\begin{gathered} f(x)=2x-6,g(x)=\frac{x}{2}+3 \\ f(g(x))=2(\frac{x}{2}+3)-6 \\ g(f(x))=\frac{2x-6}{2}+3 \end{gathered}[/tex]Step 1:
From pair 1, substitute the value of x=1 in the
[tex]\begin{gathered} f(x)=2x-6, \\ f(1)=2(1)-6 \\ f(1)=2-6 \\ f(1)=-4 \\ \\ g(x)=\frac{x}{2}+3 \\ g(-4)=-\frac{4}{2}+3 \\ g(-4)=-2+3 \\ g(-4)=1 \end{gathered}[/tex]Step 2:
For pair 2, substitute x=1
[tex]f(x)=7x,g(x)=-7x[/tex][tex]\begin{gathered} f(x)=7x \\ f(1)=7(1) \\ f(1)=7 \\ \\ g(x)=-7x \\ g(7)=-7(7) \\ g(7)=-49 \end{gathered}[/tex]Step 3:
From pair one,
[tex]f(1)=-4,g(-4)=1[/tex]From pair 2,
[tex]f(1)=7,g(7)=-49[/tex][tex]f(x)=y,g(y)=x(\text{inverse)}[/tex]From the above conclusion, we can say that
The final answer is
PAIR 1 ONLY
OPTION B is the right answer
1.) You are buying flower bundles and have
$24 to spend. Rose bundles cost $4. Tulip bundles
cost $6. Write an equation to describe how many
types of each kind of bundle you can buy.
Answer:
[tex]4r+6t \leq 24[/tex]
Step-by-step explanation:
The cost of money spent on a rose bundle can be represented by 4r, where 4 is the cost of one rose bundle and r is the number of rose bundles purchased.
The cost of money spent on a tulip bundle can be represented by 6t, where 6 is the cost of one tulip bundle and t is the number of rose bundles purchased.
The amount spent on rose bundles added to the amount spent on tulip bundles must be equal to or less than $24, since that's all you have to spend. This can be represented using this equation:
[tex]4r + 6t \leq 24[/tex]
:)
the difference between the number c and the quotient of a and b in a mathematical expression.
Answer:
no difference
step by step explanations
because a/b=c
these means c(b) and a(1)
cb=a this means
cb/b=a/b
b cancle by b
and c=a/b
How to solve problem 31? Solve for x y and z using ratios
The Solution:
Given:
Required:
Find the values for x, y, and z.
By the Similarity Theorem:
[tex]\Delta BAD\cong\Delta CBD[/tex]So,
[tex]\begin{gathered} \frac{x}{36}=\frac{36}{6x} \\ \\ \frac{x}{36}=\frac{6}{x} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} x^2=36\times6 \\ \\ x=\sqrt{36\times6}=6\sqrt{6} \end{gathered}[/tex]Find y by applying the Pythagorean Theorem on the right triangle CBD:
[tex]\begin{gathered} y^2=36^2+(6\sqrt{6)}^2 \\ \\ y=6\sqrt{42} \end{gathered}[/tex]Find z:
By the Pythagorean Theorem:
[tex]\begin{gathered} z^2=(42\sqrt{6})^2-(6\sqrt{42})^2 \\ \\ z=36\sqrt{7} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=6\sqrt{6} \\ \\ y=6\sqrt{42} \\ \\ z=36\sqrt{7} \end{gathered}[/tex]How much will the account be worth in 46 months?
In the question we are given the following parameters
Principal = $5100
Rate = 16.87% compounded semi-annually
Time = 46 months = 3yrs 10 months = 3 5/6 years
Explanation
We can solve the question using the formula below
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]"nt" is the number of months the principal accrues interest twice a year.
Therefore we have;
[tex]\begin{gathered} A=5100(1+\frac{16.87\div100}{2})^{\frac{23}{6}\times2} \\ A=5100(1+0.08435)^{\frac{23}{3}} \\ A=5100(1.08435)^{\frac{23}{3}} \\ A=9488.62 \end{gathered}[/tex]Answer:$9488.62
Find the zeros of the following logarithmic function: f(x) = 2logx - 6.
What is the gcf of 16 and 28
Answer:
4
Step-by-step explanation:
Drag the measurements to the containers to show equal length
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is meant by measurements?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
An equation exists an expression that indicates the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd × 36 in per yd = 540 in
195 ft = 195 ft × 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.
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Find the average rate of change of f(x)=x2−x+2 on the interval [1,t].
The average rate of change of the function x²-x+2 on the interval [1,t] is t .
The Average Rate Of Change of the function g(x) on the interval [a,b] is given by the formula
Average rate of change = (g(b)-g(a))/(b-a) .
the function is given as x²-x+2
interval is given as [1,t] .
so a=1 and b=t .
f(a) = f(1) = 1²-1+2 = 1-1+2 = 2
f(b) = f(t) = t²-t+2
and , b-a = t-1
Substituting the values in the average rate of change formula , we get
Average rate of change = (t²-t+2-2)/(t-1)
= (t²-t)/(t-1)
taking t common from the numerator , we get
= t(t-1)/(t-1)
= t .
Therefore , the average rate of change of function x²-x+2 on the interval [1,t] is t .
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Consider the function, Find the zeros or x-intercepts of f(x).
To find the x-intercepts, equate the function with zero as follows:
[tex]\begin{gathered} f(x)=0 \\ -16x^2+25x+10=0 \\ x=\frac{-25\pm\sqrt[]{(25)^2-4\times10\times-16}}{2\times-16} \\ x=\frac{-25\pm\sqrt[]{625+640}}{-32} \\ x=\frac{-25\pm35.5668}{-32} \\ x=-0.3302,1.8927 \end{gathered}[/tex]Hence the intercepts are -0.3302 and 1.8927
The intercepts are at points (-0.3302,0) and (1.8927,0)
1. The sliders for y = ax + b have been set to create the following graph. What are possible values for a and b?
The slope of the line is m = 2 and the y-intercept b = 2
Therefore, the equation for the graph is
[tex]y=-2|x|+2[/tex]meaning a = -2 and b = 2.
(The negative sign in front of the absolute value drags the graph below the y = 0 )
PLS HELP ASAP I WILL GIVE BRAINLIEST
Answer: I think the answer is [tex]\frac{2/3}{1}\\[/tex] and [tex]\frac{3}{1}[/tex]
Step-by-step explanation: I hope this helps. Correct me if I am wrong.
What is the image of the point (-7,-3) after a rotation of 90° counterclockwise about the origin?
The new point after rotation of point (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).
What is meant by coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x, y).
Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.
Given: the Point A be (-7, -3)
After rotation, this point moves to a unique coordinate (x, y) which exists as point B
Let's say the origin is O
Slope of line segment AO = (-3-0)/(-7-0) = 3/7
Slope of line segment BO = (y - 0)/(x - 0) = y/x
Since both lines exist perpendicular to each other so
Slope AO × Slope BO = -1
3/7 × y/x = -1
⇒ 3y = -7x
If we observe the result then it will be clear that if we put x = 3 then y = -7 will be the new coordinate.
Therefore, the new point after rotation of point (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).
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I need help with this practice problem solving It asks to divide
ANSWER
[tex]-\frac{5}{13}-\frac{14i}{13}[/tex]EXPLANATION
We want to divide the given complex fraction:
[tex]\frac{4+i}{-2+3i}[/tex]To do this, we have to rationalize the denominator of the fraction by multiplying the given fraction by another fraction made up of the conjugate of the denominator of the given fraction:
[tex]\frac{4+i}{-2+3i}\cdot\frac{-2-3i}{-2-3i}[/tex]Simplifying this, we have:
[tex]\begin{gathered} \frac{(4+i)(-2-3i)}{(-2+3i)(-2-3i)} \\ \Rightarrow\frac{-8-12i-2i+3}{4+6i-6i+9} \\ \frac{-8+3-12i-2i}{13}=\frac{-5-14i}{13} \\ \Rightarrow-\frac{5}{13}-\frac{14i}{13} \end{gathered}[/tex]That is the solution of the division.
I need help with his practice problems from my ACT prep guidePlease show your work in steps
Answer:
[tex]-\sqrt[]{6}+1[/tex]Explanation:
Given the below expression;
[tex]\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)[/tex]Recall that;
[tex]\begin{gathered} \sec x=\frac{1}{\cos x} \\ \sin x=\cos (\frac{\pi}{2}-x) \end{gathered}[/tex]So we can rewrite the expression as;
[tex]\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\cos(\pi-\frac{7\pi}{4})}-\frac{1}{\cos(-\pi)} \\ \frac{\tan(-\frac{2\pi}{3})}{\cos(-\frac{5\pi}{4})}-\frac{1}{\cos(-\pi)} \end{gathered}[/tex]Also, recall that;
[tex]\begin{gathered} \cos (-x)=\cos x \\ \tan (-x)=-\tan x \end{gathered}[/tex]So we'll have;
[tex]\frac{-\tan (\frac{2\pi}{3})}{\cos (\frac{5\pi}{4})}-\frac{1}{\cos (\pi)}[/tex]From the Unit circle, we have that;
[tex]\begin{gathered} \cos \pi=-1 \\ \cos (\frac{5\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \tan (\frac{2\pi}{3})=-\sqrt[]{3} \end{gathered}[/tex]Substituting the above values into the expression and simplifying, we'll have;
[tex]\begin{gathered} \frac{-(-\sqrt[]{3})}{\frac{-\sqrt[]{2}}{2}}-\frac{1}{-1}=\frac{\sqrt[]{3}}{\frac{-\sqrt[]{2}}{2}}+1=-\frac{2\sqrt[]{3}\sqrt[]{2}}{\sqrt[]{2}\cdot\sqrt[]{2}}+1 \\ =-\sqrt[]{6}+1 \end{gathered}[/tex]What is the solution to x^2 – 9x < –8?A. x < 1 or x > 8B. x < –8 or x > 1C. 1 < x < 8D. –8 < x < 1
INFORMATION:
We have the next inequality
[tex]x^2-9x<-8[/tex]And we must find its solution
STEP BY STEP EXPLANATION:
To solve it, we must:
1. Move all terms aside
[tex]x^2-9x+8<0[/tex]2. Factor x^2-9x+8
[tex](x-8)(x-1)<0[/tex]3. Solve for x
[tex]x=8\text{ or }x=1[/tex]4. From the values of x, we have these 3 intervals to test
[tex]\begin{gathered} x<1 \\ 18 \end{gathered}[/tex]5. Choose a test point for each interval
For the interval x < 1:
[tex]\begin{gathered} \text{ Using x }=0, \\ 0^2-9(0)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
For the interval 1 < x < 8:
[tex]\begin{gathered} \text{ Using x }=2, \\ 2^2-9(2)<-8 \\ -14<-8 \end{gathered}[/tex]which is true. So, the interval is maintained
For the interval x > 8:
[tex]\begin{gathered} \text{ Using x = 9,} \\ 9^2-9(9)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
Finally, the solution would be the interval that was maintained: 1 < x < 8.
ANSWER:
C. 1 < x < 8
Answer:
C. 1 < x < 8
Step-by-step explanation:
x² - 9x < -8
we will suppose some values for x to check which values will satisfy this inequality:
for x = 1
1(1-9) < -8 which is wrong
for x = 2
2(2-9) < -8 this is satisfying the inequality
for x = 8
8(8-9) < -8 which is wrong
let's take any negative value now,
let x = -2
-2(-2-9) < -8 which is wrong
thus x is the positive value which will always be greater than 1 and less than 8 for the given inequality.
[tex]4\sqrt[3]{16} /2\sqrt[3]{2}[/tex]
The expression 4∛16/2∛2 has a value of 4when simplified
How to evaluate the expression?From the question, the expression is given as
4∛16/2∛2
From the above parameter, we can see that the factors of the expression uses the cube root symbol
This means that the expression is a radical expression
Next, we have
4∛16/2∛2 = 4∛16/2∛2
Divide 4 by 2 in the equation
So, we have
4∛16/2∛2 = 2∛16/∛2
Solving further, we combine the cube roots (or radicals)
This is represented as
4∛16/2∛2 = 2∛(16/2)
Evaluate the quotient of 16 and 2
So, we have the following equation
4∛16/2∛2 = 2∛8
Take the cube root of 8
4∛16/2∛2 = 2 x 2
Evaluate the product
4∛16/2∛2 = 4
The expression cannot be further simplified
Hence, the solution to the expression 4∛16/2∛2 is 4
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a polynomial function has four turning points and two zeros. it’s degree could be ___? select all that apply 4567
SOLUTION
A polynomial function with real coefficients has four turning points and two zeros could be a degree 6 or any higher even degree because a polynomial with degree n has at most (n - 1) turning points.
So, it cannot be a degree 4.
It cannot be a degree 5 because it has two real zeros, and then three complex roots. A polynomial function with real coefficients cannot have an odd number of complex roots.
Answer:
6
Step-by-step explanation:
edge 23
Discuss the order of operations to explain why the expressions [(12÷(2+ 2)] ^3 and (12 ÷ 2) + 2^3 do not havethe same value.
The order of operations are different. Hence, the answers are not equal
Explanation:
Oder of operations using PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction)
[(12÷(2 + 2)]³ and (12 ÷ 2) + 2³
we solve seperately:
[(12÷(2+ 2)]³
we solve the parenthesis first:
(12 ÷ 4)³
then we apply division:
= (3)³
Then expand the exponent:
= 27
(12 ÷ 2) + 2³
we solve the parenthesis first:
6 + 2³
we expand the exponent:
6 + 8
we apply addition:
14
The order of operations are differnt. Hence, the answers are not equal
Divide the polynomial by the monomial (63xy^3+ 56x^2y^4)/(7xy)
ANSWER
9y² + 8xy³
EXPLANATION
To divide this polynomial by the given monomial, we can distribute the denominator into the sum,
[tex]\frac{63xy^3+56x^2y^4}{7xy}=\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}[/tex]Then, each coefficient simplifies with the coefficient of the monomial, since both are multiples of 7. Also, in the first term, x cancels out, and we have to subtract 1 from the exponent of y. In the second term, we subtract 1 from both the exponents of x and y,
[tex]\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}=9y^2+8xy^3[/tex]Hence, the result is 9y² + 8xy³.
Write the phrase "8 more than 10 divided by x is 12" as a variable expression:
Answer:
10/x + 8 = 12
Step-by-step explanation:
10 divided by x = 10/x
8 more than 10 divided by x = 10/x + 8
A company plans a major investment and theamount of profit is uncertain, but researchersgive the following estimate for the distribution.1.5210Profit(inmillions)Probability0.10.20.40.20.1What is the expected value of the profit?[?] million dollars
The expected value is the return you expect from some kind of investment/action.
When we are presented with probabilty of an action, we can take the expected value of the whole table [investment] by taking the sum of the products of probability and the action.
Here, we want products of "probability" and "profit". Then we sum it. Shown below:
[tex]\begin{gathered} E=(0.1)(1)+(0.2)(1.5)+(0.4)(2)+(0.2)(4)+(0.1)(10) \\ E=3 \end{gathered}[/tex]Expected value of profit = 3 million dollarsMelissa works as a tutor for S12 an hour and as a waitress for S11 an hour. This month, she worked a combined total of 105 hoursat her two jobs.Lett be the number of hours Melissa worked as a tutor this month. Write an expression for the combined total dollar amount sheearned this month.
From the question
Melissa earns $12 an hour as a tutor
And $11 an hour as a waitress
Also,
This month, she worked a combined total of 105 hours
at her two jobs.
Let t be the number of hours Melissa worked as a tutor this month
Let w be the number of hours Melissa worked as a waitress this month
This implies
[tex]t+w=105[/tex]Since Melissa worked t hours as a tutor this month then
Total money earned as a tutor = $12t
Also,
Since Melissa worked w hours as a waitress this month then
Total money earned as a waitress this month = $11w
Therefore, the total combined earnings for the month is
[tex]\text{ \$12t }+\text{ \$11w}[/tex]a museum wants to use equal rows to arrange the African baskets. which list shows all the different possible arrangements so that all the rows have the same number. Assume that an arrangement such as 4 x 20 is the same as 20 x 4.
Answer:
(B)1 x 80,2x 40,4 x 20,5 x 16,8 x 10
Explanation:
The number of African Baskets = 80
The list of all possible arrangements so that all the rows have the same number will be a list that contains all the positive product of factors of 80.
Factors of 80 are: 1,2,4,5,8, 10, 16,20,40,80
The list is, therefore:
[tex]1\times80,2\times40,4\times20,5\times16,8\times10[/tex]The correct choice is B.