withoutLet "x" represent the two-slices toasters and "y" represent the four-slices toaster.
Each two-slice toaster takes 6hours to make and the four-slices takes 10 hours, you can express the total labor per week as:
[tex]6x+10y=300[/tex]The total capacity production is 40 toasters per week, so if you add the number of two-slice toaster and four-slice toasters made per week, they must add up to at most 40
[tex]x+y\leq40[/tex]To determine how many toasters they can make without exceeding the time restriction, replace the first expression with x=10 to determine the number of toasters you can make with out exceeding the time limit
[tex]\begin{gathered} 6x+10y=300 \\ 6\cdot10+10y=300 \\ 60+10y=300 \\ 10y=300-60 \\ \frac{10y}{10}=\frac{240}{10} \\ y=24 \end{gathered}[/tex]Without exceeding the time limit, the manufacturer can make 24 four-slice toasters.
Now you have to check if the value is within the production restrictions, remember that the manufacturer can produce up to 40 units per week, if the number of two-slice and four-slice toasters add up to 40 or less, then this restriction is not exceeded.
[tex]x+y\leq40[/tex]For x=10 and y=24
[tex]\begin{gathered} 10+24\leq40 \\ 34\leq40 \end{gathered}[/tex]The production limit is not surpassed.
This means that if the manufacturer chooses to produce 10 two-slice toasters, he can produce 24 four-slice toasters without exceeding the time and production restrictions.
A store manager paid 44.00 for a shirt. She marked up the price of the shirt. What was the selling price of the shirt
Answer
Selling Price = 79.2 dollars
Explanation
Markup percentage is given as
[tex]\text{Markup percentage = }\frac{Markup}{Cost\text{ Price}}\times100\text{ percent}[/tex]Then,
Markup = (Selling Price) - (Cost)
For this question,
Markup percentage = 80%
Markup = ?
Cost price = 44 dollars
Selling price = ?
[tex]\begin{gathered} \text{Markup percentage = }\frac{Markup}{Cost\text{ Price}}\times100\text{ percent} \\ 80\text{ = }\frac{Markup}{44}\times100 \\ \text{Markup = 0.8}\times44=35.2\text{ dollars} \end{gathered}[/tex]Markup = (Selling Price) - (Cost)
35.2 = Selling Price - 44
Selling Price = 44 + 35.2 = 79.2 dollars
Hope this Helps!!!
Evaluate the expression: 18_C_4Both the numbers are tiny like small and next to the C. A. 3,060B. 12,240C. 18,360D. 73,440
Given that you need to evaluate:
[tex]_{18}C_4[/tex]Therefore, you need to use the Combination Formula:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Where "n" is the total number of objects of a set and "r" is the number of objects chosen from the set.
In this case, you can identify that:
[tex]\begin{gathered} n=18 \\ r=4 \end{gathered}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]_{18}C_4=\frac{18!}{4!(18-4)!}[/tex][tex]_{18}C_4=\frac{18!}{4!(14)!}[/tex][tex]_{18}C_4=3060[/tex]Hence, the answer is: Option A.
Maria was the understudy in a Broadway show,She performed once a week. Then the lead brokeher arm. Now Maria performs 9 times a week. Whichgraph shows Maria's number of performances?10-10TPerformances5 PNPerformances:6+4+4+:24:27A.1 1 1 2 24 3 3 4 475WeeksB.The 11th15 2 26 3 31 441)Weeks
Answer:
Step-by-step explanation:
Since she performed once a week, the y-axis represents performances and the x-axis represents the number of weeks.
Then, for the first linear relation, the endpoint would be: (1,1)
If the lead broke her arm and now she performs 9 times a week, then the endpoint of Maria's number performances (2,10).
5. Express the polynomial 6x - x + 2x - 4 in standard form.5x + 2x-46x-2x-4-4+ 2x-5X27x2 + 2x - 4
Answer:
The first choice. 5x^2 + 2x -4
Explanation:
The standard form of a polynomial is one in which the terms with the highest exponent are to the left and the lowest to the right.
For example,
[tex]undefined[/tex]Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Writethe argument in radians and round it to twodecimal places if necessary.-4 - 2i3 + 2iyea
First step is to simplify the expression
-4-2i
------
3+2i
Multiply by the complex conjugate
-4-2i ( 3-2i)
------ * ----------------
3+2i ( 3-2i)
(-4-2i) (3-2i)
------------------
3^2 +2^2
-12 -6i +8i -4
----------------------
9+4
-16+2i
--------
13
Now we can find the magnitude
z = sqrt( a^2 + b^2) where a = real part and b = imaginary part
z = sqrt( 256/139 + 4/139) = sqrt(260/139) = 2 sqrt(65)/13
theta = tan^-1 ( b/a) = tan^-1 ( -2/16) = tan^-1 (-1/8) = .12
z = 2 sqrt(65)/13 ( cos .12 + i sin .12)
A $20 shirt is 40% off. Your trying to figure out if you have enough cash for this. How much is the final price of the shirt?
original price: $20
discount: 40%
[tex]20\cdot0.4=8[/tex]Discount is $8
Final price:
[tex]20-8=12[/tex]The final price is $12
The percentage you are actually paying is 100% - 40% = 60%
The equation that describes this problem is:
[tex]\begin{gathered} A=P\cdot\frac{(100-d)}{100} \\ A=20\cdot\frac{100-40}{100}=12 \end{gathered}[/tex]Where A is the actual price, P is the original price and d is the discount.
Please help with this question! I was given the answer but wasn’t sure how it got to that answer
Answer:
Explanation:
Given:
[tex]\begin{gathered} g(x)=-x^2-ax+3 \\ g(-2)=-9 \end{gathered}[/tex]It is given that g(-2)=-9, so it means that x=-2. We substitute x=-2 into -x^2-ax+3 to get the value of a.
[tex]undefined[/tex]Which is the graph of y = [x]-2?
The given function is,
[tex]f(x)=\lfloor x\rfloor-2[/tex]⌊⌋ is the symbol representing a greatThe greatest integer less than or equal to x is represnted as ⌊x⌋.
(d) Based on your analysis from part c, sketch a graph of what y=9^x could look like.
Given the expression:
[tex]y=9^x[/tex]The graph of the function will be as shown in the following picture:
We will study the behaviour for the following conditions:
x < 0, the function tends to zero
x = 0, the function will be = 1, which represents y-intercept
0 < x < 1 , the function will be in the rangle 1 < y < 9
x = 1 , the function will be = 9
x > 1 , the function tends to infinity
The coordinates of quadrilateral FGHJ are F(-5,-3) G(-3,3) H(3,5) and J(7,-1). Find the midpoint of HJAnswers: A.(1,-2)B.(5,2)C.(0,4)D.(-4,0)
Answer:
B. (5, 2)
Explanation:
The coordinates of a midpoint of a segment that goes from (x1, y1) yo (x2, y2) are
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]So, the midpoint of HJ can be founded replacing (x1, y1) by H(3, 5) and (x2, y2) by J(7, -1)
[tex](\frac{3+7}{2},\frac{5+(-1)}{2})=(\frac{10}{2},\frac{4}{2})_{}=(5,2)_{}[/tex]Therefore, the answer is
B. (5, 2)
Solving a percentage makes your problem using a system of linear equations
For the 1st fruit drink, 220 pints will be used
For the 2nd fruit drink, 40 pints will be used
Explanation:1st type has concentration = 35% = 0.35
2nd type has concentration = 100% = 1
let the amount for the 35% pure fruit = x
Total amount of fruit juice to be made = 260
amount for the 35% pure fruit + amount for the 100% pure fruit = 260
amount for the 100% pure fruit = 260 - x
concentration of mixture = 45% = 0.45
Amount = 260 pints
concentration for the 1st type (amount) + concentration of the 2nd type (amount) = concentration of mixture (amount)
[tex]0.35(x)\text{ + 1}(260\text{ - x})\text{ = 0.45}(260)[/tex]Solve for x:
[tex]\begin{gathered} 0.35x\text{ + 260 - x = 117} \\ 0.35x\text{ - x + 260 = 117} \\ -0.65x\text{ + 260 = 117} \\ -0.65x\text{ = 117 - 260} \end{gathered}[/tex][tex]\begin{gathered} -0.65x\text{ = - 143} \\ divide\text{ both sides by -0.65:} \\ \frac{-0.65x}{-0.65}\text{ = }\frac{-143}{-0.65} \\ x\text{ = 220} \\ \\ Amount\text{ for 35\% pure fruit = 220pints} \end{gathered}[/tex]Amount for the 100% pure fruit = 260 - x
Amount for the 100% pure fruit = 260 - 220 = 40 pints
For the 1st fruit drink, 220 pints will be used and for the 2nd fruit drink, 40 pints will be used
Wesley spent $34.60 at the grocery store. 15%of that was spent on fruit. How much didWesley spent on fruit?
We determine what he spent as follows:
[tex]34.60(0.15)=5.19[/tex]So, he spent %5.19.
The table below shows the probability distribution of a random variable X. X P(X) -20 0.53 -19 0.11 -18 0.26 -17 0.09 -16 0.01 What is the expected value of X? Write your answer as a decimal.
ANSWER
[tex]E(X)=-19.06[/tex]EXPLANATION
We want to find the expected value of x.
To do this, we need to find the product of each value with its corresponding proabibilty and then find the sum.
That is:
[tex]E(x)=\Sigma\mleft\lbrace xP(x)\mright\rbrace[/tex]Therefore, we have:
[tex]\begin{gathered} E(X)=(-20\cdot0.53)+(-19\cdot0.11)+(-18\cdot0.26)+(-17\cdot0.09)+(-16\cdot0.01)_{} \\ E(X)=(-10.6)+(-2.09)+(-4.68)+(-1.53)+(-0.16) \\ E(X)=-19.06 \end{gathered}[/tex]That is the expected value.
Which is a graph for the inequality x>=2
The inequality is:
[tex]x\ge2[/tex]Graph:
How long will it take for $4700 compounded semiannually at anannual rate of 1.5% to amount to $6200?
Given:
[tex]A=\text{ \$6200 ; P= \$4700 ;R=1.5\%}[/tex][tex]A=P(1+\frac{R}{n})^{nt}[/tex][tex]6200=4700(1+\frac{0.015}{2})^{2t}[/tex][tex]\frac{6200}{4700}=(2.015)^{2t}[/tex][tex]t=18.5[/tex]It takes 18 years and 6 months to reach the amount $6200
Solve the Perfect Square Trinomial Expression.x2 – 16x + 64-
we have the expression
[tex]x^2-16x+64[/tex]Complete the square
[tex]\begin{gathered} (x^2-16x)+64=0 \\ (x^2-16x+8^2-8^2)+64 \\ (x^2-16x+8^2)+64-8^2 \\ rewrite\text{ as perfect square} \\ (x-8)^2 \end{gathered}[/tex]in training for a swim meet Logan swim 750 m in 1/3 of an hour. His swimming partner Mila swim 2/3 of Logan's distance and in 1/4 of an hour. What is Logan's average swimming speed?
Average speed
The average speed can be computed as the ratio of the distance over the time take to cover that distance. Being d the distance and t the time, we have:
[tex]v=\frac{d}{t}[/tex]Logan swims 750 m in 1/3 of an hour. Let's work in meters and in minutes to make calculations easier. The time taken by Logan is 1/3 of an hour. Since one hour has 60 minutes:
t = 1/3*60 = 20 minutes
The distance is 750 m. Let's calculate the average speed
[tex]v=\frac{750\text{ m}}{20\text{ min}}=37.5\text{ m/min}[/tex]Logan's average swimming speed is 37.5 m/min
A city currently has 137 streetlights. As part of a urban renewal program, the city council has decided to install 3 additional streetlights at the end of each week for the next 52 weeks.How many streetlights will the city have at the end of 31 weeks?
Answer:
[tex]y=\text{ 230 streetlights}[/tex]Step-by-step explanation:
This situation can be represented as a linear equation since it has an initial value and a constant rate of change per week. Remember that linear equations are given as:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{ constant rate of change} \\ b=\text{ initial value} \end{gathered}[/tex]Then, to determine how many streetlights the city will have at the end of 31 weeks, substitute x=31 into the following equation;
[tex]\begin{gathered} y=3x+137 \\ y=3(31)+137 \\ y=\text{ 230 streetlights} \end{gathered}[/tex]Help me pls Match each expression with the type of factoring that applies
3) Difference of Squares:
The difference of squares formula is
[tex]a^2-b^2=(a+b)(a-b)[/tex]We can identify that on the expression:
[tex]x^2-25[/tex]Applying the difference of square we have
[tex]x^2-25=(x+5)(x-5)[/tex]4) Difference of Cubes
Here the formula is quite different from what we have on the difference of squares.
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)^{}[/tex]Now we identify it on
[tex]x^3-1[/tex]The factoring will be
[tex]x^3-1=(x-1)(x^2+x+1)[/tex]5) Sum of Cubes
We have a very similar formula as 4), the difference will be
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)^{}[/tex]We just have to change some signals.
Then
[tex]x^3+27[/tex]We can write as a sum of cubes
[tex]x^3+27=(x+3)(x^2-3x+9)[/tex]6) Grouping
Here we have a quite different technique, we don't have the formula to apply, therefore, let's see the expression and how to group it
[tex]3x^3+15x^2+2x+10[/tex]Here we must factor and find two equal factors, that's the most difficult part, after that we just group them.
If we look at the expression we will see that we can group:
[tex](3x^3+15x^2)+(2x+10)[/tex]If the factor 3x² on the left ( ) and factor 2 on the right ( ) we get
[tex]3x^2(x+5)+2(x+5)[/tex]Look that now we have (x+5) on both terms, then we group them!
[tex](x+5)(3x^2+2)[/tex]That's the final form, hence
[tex]3x^3+15x^2+2x+10=(x+5)(3x^2+2)[/tex]1) GCF (greatest common factor)
Here we must identify one factor that appears on all terms, look at
[tex]2x^2+6x[/tex]See that "2x" appears on both terms, then it's the greatest common factor:
[tex]2x^2+6x=2x(x+3)[/tex]See that if we do the distribution we will get the other form again.
2) Unfoil
Here we must find two numbers that the sum is 6 and the product is 8, these two numbers are 4 and 2.
The generic formula is
[tex]x^2+bx+c=(x+x_1)(x+x_2)_{}[/tex]Where x₁ and x₂ are the numbers we find doing the sum and the product, in our case it's 4 and 2, then
[tex]x^2+6x+8=(x+4)(x+2)[/tex]Final answer:
2 - Unfoil - x² + 6x + 8
1 - GCF - 2x² + 6x
3 - Difference of Cubes - (x³ - 1)
4 - Sum of Cubes - (x³ + 27)
5 - Grouping - (3x³ + 15x² + 2x + 10)
6 - Difference of Squares - (x² - 25)
What is the decimal form of-4 7/8?A -4.625 B -4.875 C -4.9375 D -4.75
answer: B
Huai takes out a 3100 student loan at 6.1% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and borrows another 12,100 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate 7.6% of . Find the total amount of interest that will accrue until payments begin. find the total amount of interest that will accrue for loan 1
In linear equation, p = $65.47 per month is the total amount of interest .
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y).Huai takes out a 3100 student loan at 6.1% to help him with 2 years of community college.
The monthly payment on loan1 can be finding as
3100 = p [ 1 - ( 1 + 0.066/12)⁻⁴/0.066/11
3100 = p[ 1 - ( 1.0055)⁻⁵⁵/0.0055
3100 = p [ 1 - 0.73958/0.0055 ]
3100 = p [ 0.26041/0.0055 ]
3100 = p [ 47.34886 ]
p = 3100/47.34886
p = 65.47148
p = $65.47 per month
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A circular fountain, 20 meters in diameter, has a 2 meters wide gravel walkway around it. What is the approximatearea of the walkway in square meters?a.100
The area of the gravel walkway with a fountain of 20 meters is 263.76m².
What is the area of the circle?The area of a circle seems to be the region of a two-dimensional plane occupied by the circle. It is simple to calculate using the formula A = πr², (Pi x r-squared), where r seems to be the circle's radius. The square unit, like m2, cm2, and so on, is the unit of area.The area of a circle is:
Area = πr²Here given the circular fountain:
Diameter = 20mSo radius = diameter /2 = 20/2Radius = 10mGravel walkway has a radius of 2m, so diameter = 4m
The gravel walkway area = circular fountain area.
The gravel walkway area is equal to the area of the big circle less than the area of the inner circle:
(3.14 x 10²)-(3.14 x 4²)314 - 50.24= 263.76 m²Therefore, the area of the gravel walkway with a fountain of 20 meters is 263.76m².
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The jet flies 175 miles in 7 minutes . It’s constant speed is 25 miles in one minute. At the same rate, how far would the jet fly in 75 minutes? How could you use the table from Example 1 to find how far the jet would fly in 75 minutes?
Answer
[tex]\frac{25\text{ mi }\times\text{ 75 }}{1\text{ min }\times\text{ }75}=\frac{1875\text{ miles}}{75\text{ minutes}}[/tex]The jet would fly 1,875 miles in 75 minutes at this rate.
Explanation
We have been given that the speed of the jet is 25 miles per minute.
And the jet flies 175 miles in 7 minutes.
We are then asked to find how far the jet would fly in 75 minutes.
175 miles = 7 minutes
25 miles = 1 minute
Let the number of miles the jet will fly in 75 minutes be x miles
So,
25 miles = 1 minute
x miles = 75 minutes
We can form a mathematical relationship by cross multiplying
(x) × 1 = 25 miles × 75 minutes
x = 1,875 miles
So, we can write the bubble as
[tex]\frac{25\text{ mi }\times\text{ 75 }}{1\text{ min }\times\text{ }75}=\frac{1875\text{ miles}}{75\text{ minutes}}[/tex]Hope this Helps!!!
if you vertically shift the square root parent function, F(x)=/x, up nine units, what is the equation of the new function?
Answer:
The new function is;
[tex]G(x)=\sqrt[]{x}+9[/tex]Explanation:
Given the parent function;
[tex]f(x)=\sqrt[]{x}[/tex]To move it up 9 units.
Then we will need to add 9 units to the right-hand side of the equation;
[tex]\begin{gathered} G(x)=f(x)+9=\sqrt[]{x}+9 \\ G(x)=\sqrt[]{x}+9 \end{gathered}[/tex]Therefore, the new function is;
[tex]G(x)=\sqrt[]{x}+9[/tex]Given the triangle below identify which trig function we must use, solve for the anglesTrig Function:
Since we have a right triangle, we can solve the sides of the triangle using cos(x), sin(x), or tan(x).
To fin
What is the interquartile range of the number of days represented on Kelly's line plot? Be sure to show your work and explain your reasoning.
The ordered list of the given plot is:
0, 0, 2, 2, 2, 3, 4, 4, 5, 5, 5, 7, 7
The first interquartile is given by:
IQ = Q3 - Q1
Where Q3 and Q1:
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1) \\ Q_3=\frac{3}{4}(n+1) \end{gathered}[/tex]where n = 8 is the total number of data.
[tex]\begin{gathered} Q_1=\frac{1}{4}(8+1)=\frac{1}{4}(9)=\frac{9}{4} \\ Q_3=\frac{3}{4}(8+1)=\frac{3}{4}(9)=\frac{27}{4} \end{gathered}[/tex]Then, the interquatile range:
IQ = 27/4 - 9/4 = 18/4
Hence, the interquartile range is 18/4
find the percent markup. Cost of a microphone $99.50, selling price 124.38
Let's begin by listing out the information given to us:
Percent markup (m) = ?, Cost (c) = $99.50, Selling price (p) = $124.38
The formula for percent markup is given by:
[tex]\begin{gathered} \text{\% }Markup=\frac{SellingPrice-Cost}{Cost}\cdot100\text{ \%} \\ m=\frac{p-c}{c}\cdot100\text{ \%}=\frac{124.38-99.50}{99.50}\cdot100\text{ \%} \\ m=25.005\text{\%}=\text{ }25\text{ \%} \\ m=25\text{ \%} \end{gathered}[/tex]The percent markup is 25%
Select the correct answer from the drop-down menu.A box contains shirts in two different colors and two different sizes. The numbers of shirts of each color and size are given in the table.SizeShirt ColorLarge Medium TotalRed424890Blue354075Total7788165From the data given in the table, we can infer thatResetNext
First option
P(red shirt | large shirt) = P(large shirt)
From conditional probability: P(A | B) = n(A ∩ B) / n(B)
n is "the number of..."
So: P(red shirt | large shirt) = n(red shirt ∩ large shirt) / n(large shirt)
Where:
A 90% confidence interval for a proportion is found to be (0.52, 0.58). What isthe sample proportion?A. 0.56B. 0.54C. 0.55D. 0.58
Sarai, if the confidence interval is (0.52, 0.58), therefore:
0.52 + 0.03 = 0.55
0.58 - 0.03 = 0.55
The sample proportion is C. 0.55
Sarai, the definition of a confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. In our question, the margin of error is 0.03, that is added and subtracted from the sample proportion to calculate the upper and lower limits of the confidence interval.
Using a confidence level of 90%, we got a margin of error of 0.03
Using a different confidence level, we should get a different margin of error.
The formula of the margin of error is:
Explanation:
L = lower bound
U = upper bound
The confidence interval (L, U) is (0.52, 0.58)
Find the midpoint of L and U
(L+U)/2 = (0.52+0.58)/2 = 0.55
The exact middle of the confidence interval is the location of the point estimate, which in this context is the sample proportion.
Extra info: the margin of error is 0.03 since 0.55-L = 0.55-0.52 = 0.03 and also U - 0.55 = 0.58 - 0.55 = 0.03
Use a graphing calculator to solve the equation to the nearest tenth.2x^2 - 4x -10=0; x between 3 and 4
Given the equation:
[tex]2x^2-4x-10=0;x\in(3,4)[/tex]We will use a graphing calculator to solve the equation
The graph of the equation will be as shown in the following figure:
As shown the intersection between the given equation and the x-axis is a point between 3 and 4 which = 3.4495
Rounding to the nearest tenth
So, the answer will be the solution to the equation:
[tex]x=3.4[/tex]