We can use the next formula in order to find the volume
[tex]V=l\times w\times h[/tex]l is the length
w is the width
h is the height
in our case
l=8ft
w=9ft
h=11ft
we substitute the values
[tex]V=8\times9\times11=792ft^3[/tex]The owner of a small store buys coats for 40.00 each. She sells the coats for 72.00 each. What percent of the purchase price is the sales price?
In order to calculathe the percent, we just need to divide the sales price by the purchase price.
So we have:
[tex]\frac{72}{40}=\frac{36}{20}=\frac{18}{10}=1.8=180\text{\%}[/tex]Therefore the sales price represents 180% of the purchase price.
I solved part C I just need help with part D
1) Gathering the data
8% sales tax
2 DVDs' price: $21.60 (after taxation)
2) To find out how much for the DVDs without the sales tax, let's write this equation.
P for the price without tax, 1.08 the sales tax factor, $21.60 the full price
p (1.08) =21.60 Let's divide both sides by 1.08
p= 21.60 /1.08
p= 20
3) So the price without tax, is $20
4
Ellie goes to tutoring every 4 days for math
and every 12 days for Science. If Ellie
attended tutoring for both Math and Science
today, when is the next time she will attend
both sessions on the same day?
Answer:
gcm conditions
1. all numbers are entered (in the picture, enter numbers 2 and 3)
2. if there are the same number, take the number that has the largest power
ahe Will attend both sessions 12 days after today
-9x² - 4 + 6x + 11x² - 7x
ANSWER
2x² - x - 4
EXPLANATION
To solve this we have to add like terms:
[tex]-9x^2-4+6x+11x^2-7x[/tex]Like terms are those that have x with the same power:
[tex](-9x^2+11x^2)+(6x-7x)-4=2x^2-x-4[/tex]complete the sentence to make it true 0.5 is 1/100 of?
to find 0.5 is 1/100 of what ?
[tex]50\times\frac{1}{100}=0.5[/tex]the answer is 50.
f(x)=3x+4 Evaluate f(2)=
We will look at how to evaluate a function for one of the value from a defined domain.
Domain is a set of values over which the function is defined. These are set of values of ( x ) that serves as an input to the function.
Function expresses an input -> output relationship usually expressed as an amalgam of different mathematical expressions. The function evaluates the output for every set value of ( x ) from the domain. The mathematical expressions ( relationships ) are given in terms of the input variable(s).
We are given the following function as follows:
[tex]f\text{ ( x ) = 3x + 4}[/tex]The above functions isd efined for all the real values. Hence, the domain of the above function is defined as:
[tex]\text{\textcolor{#FF7968}{Domain:}}\text{ x :-> ( -}\infty\text{ , }\infty\text{ )}[/tex]We will evaluate the above function for one of the values from the domain. We will plug in the value of input ( x = 2 ) into the function. Then we will evaluate the function f ( x ) as follows:
[tex]\begin{gathered} f(2)\text{ = 3}\cdot(2)\text{ + 4} \\ f(2)\text{ = 6 + 4} \\ \textcolor{#FF7968}{f(2)}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{10} \end{gathered}[/tex]Hence, the function is evaluated for the input value of ( x = 2 ) and the ouput is:
[tex]\textcolor{#FF7968}{10}[/tex]The length of a rectangle is 2ft more than twice the width. The area is 144 ft squared. Find the length and width of the rectangle.
The formula for the area of a rectangle (A) is given as
[tex]A=\text{length}\times breadth[/tex]Given that
The length of a rectangle is 2ft more than twice the width,
Therefore,
length = 2 + 2width
where,
[tex]\begin{gathered} w=\text{width} \\ l=2+2w \\ A=144ft^2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 144=(2+2w)\times w \\ 144=2w+2w^2 \\ 144=2(w+w^2) \\ \frac{144}{2}=\frac{2(w+w^2)}{2} \\ 72=w+w^2 \\ w^2+w-72=0 \end{gathered}[/tex]Factorizing the equation above
[tex]\begin{gathered} w^2+9w-8w-72=0 \\ w(w+9)-8(w+9)=0 \\ (w-8)(w+9)=0 \\ w-8=0\text{ or }w+9=0 \\ w=8\text{ or w=-9} \\ \therefore w=8or-9 \end{gathered}[/tex]Note that the width can never be negative, therefore the width of the rectangle is 8.
Recall that:
[tex]\begin{gathered} l=2_{}+2w=2+2(8)=2+16=18 \\ l=18 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \text{length = 18ft} \\ \text{width = 8ft} \end{gathered}[/tex]
Solve: 2(1 - 5k) = 2k + 38
k=-3
1) Let's solve for k, the following expression:
2(1 - 5k) = 2k + 38 Distribute the factor 2
2 -10k = 2k +38 Subtract 2 from both sides and 2k
-10k -2k = 38 -2
-12k = 36 Divide by -1
12k=-36 Divide both sides by 12
k= -3
2) So k is equal to -3 in this equation.
What is the equation of the horizontal line that passes through the point (5,-1).X= 5Y=-1Y+1=2(x-5)Y=5x-1
We have the next point (5,-1) and we need to find the horizontal line that passes through this point.
The equation of a horizontal line with y-intercept b is y = b
Where the point (a,b) = (5,-1)
Hence, the equation of the line is y=-1
The correct answer is the second option.
A road crew Musri pave a road that is 7/8 miles long they can repave 1/56 miles each hour how long will it take the crew to repave the road
Given data :
[tex]1\text{ hour = }\frac{1}{56}miles[/tex]distance required to cover =
[tex]\frac{7}{8}[/tex]thus, the time taken is,
[tex]\begin{gathered} =\frac{\frac{7}{8}}{\frac{1}{56}} \\ =\frac{7}{8}\times56 \\ =\frac{7}{1}\times7 \\ =7\times7 \\ =49 \end{gathered}[/tex]thus the time taken is 49 hours.
The weighted voting systems for the voters A, B, C, ... are given in the form q: w1, w2, w3, w4, ..., wn. The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on.Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.){72: 46, 35, 22, 14}
I would not be able to continue this session, because the information is incomplete. Thank you.
Find the population mean or sample mean as indicated.Sample: 24, 8, 9, 5, 19
The mean of a population set can be calculated through the formula:
[tex]\bar{x}=\frac{\sum ^n_{i\mathop=1}(x_i)}{n}[/tex]in which, n is the total number of data points that are in the set
then, with the sample given the mean can be found as,
[tex]\begin{gathered} \bar{x}=\frac{24+8+9+5+19}{5} \\ \bar{x}=\frac{65}{5} \\ \bar{x}=13 \end{gathered}[/tex]Answer:
The sample mean is 13.
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes. find the distance traveled after20 minutes36 minutes40 minutesWrite a piecewise linear function for the distance of D(t) in terms of time (T) in minutes. find the distance traveled after 30 minutes38 minutesbonus - when has the cyclist traveled? 8km9 km
Given:
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes.
We will draw the diagram between the rate (speed of the cyclist) and the time (t) in minutes, the graph will be as follows:
For the first 20 minutes, the rate increased from 0 to 300 m/min
Then the next 16 minutes, the rate decreased to 150 m/min
And in the last 4 minutes, the rate increased to 400 m/min.
To find the distance traveled, we will find the area under the lines according to a specific time.
So, first, we will find the distance traveled after 20 minutes
It will be as follows = d(20)
[tex]d(20)=\frac{1}{2}*300*20=3000\text{ }m=3\text{ }km[/tex]And the distance traveled from 20 min to 36 min is the area of a trapezoid with a height = 16 min. and the parallel base are 150 and 300
So, the area will be =
[tex]\frac{1}{2}(300+150)*16=3600\text{ }m=3.6\text{ }km[/tex]So, the distance traveled after 36 minutes = 3 + 3.6 = 6.6 km
And the distance traveled from 36 min to 40 min is the area of a trapezoid with a height = 4 min. and the parallel bases are 150 and 400
So, the area =
[tex]\frac{1}{2}(150+400)*4=1100\text{ }m=1.1\text{ }km[/tex]So, the total distance after 40 minutes = 6.6 + 1.1 = 7.7 km.
=========================================================
To find the piecewise linear function for the distance of D(t) in terms of time (T) in minutes.
First, we will write the function v(t) that represents the rate from the graph.
[tex]v(t)=\begin{cases}{15t\rightarrow0\leq t\leq20} \\ -9.375t+487.5\rightarrow20\leq t\leq36 \\ {62.5t-2100\rightarrow t\ge36}\end{cases}[/tex]To find the function of the distance integrate each function with respect to the time t:
[tex]D(t)=\begin{cases}{7.5t^2}\rightarrow0\leq t\leq20 \\ {-4.6875t^2+487.5t-4875\rightarrow20\leq t\leq36} \\ {31.25t^2-2100t+41700\rightarrow t\ge36}\end{cases}[/tex]how do you think you can represent the number 2300 as a number times a multiple of 10? How do you think you can represent the number 2300 as a number x 10 to some exponents? How could you describe the relationship between the two representations?
Answer
23 × 10 = 2300
2.17¹⁰ = 2300
Explanation
The first parts us to represent 2300 as a number (let that number be x) multiplied by 10
x × 10 = 2300
10x = 2300
Divide both sides by 10
(10x/10) = (2300/10)
x = 230
The second part asks us to represent 2300 as a number (let that number be y) raised to power 10
y¹⁰ = 2300
To solve for y, we will take the logartihms of both sides
Log (y¹⁰) = Log 2300
10 log y = log 2300
Divide both sides by 10
(10 log y)/10 = (log 2300)/10
Log y = (3.362/10)
Log y = 0.3362
We will now take the Antilog of both sides
y = 2.17
Hope this Helps!!!
how does h (x) =-0.1x-5 change over the interval from x=2 to x=4
The given expression is,
[tex]h(x)==0.1x-5[/tex]Let us first consider, x = 2. We have,
[tex]h(2)=0.1\times2-5=-4.98[/tex]Now, let us take x = 4, we have,
[tex]h(4)=0.1\times4-5=-4.6[/tex]So the range is, -4.98 to -4.6. So, h (x) decreases by 0.3
it says, "or use prime factorization" #1-3, and 5 pls!!
The LCM (lowest common multiple) of the following;
(1) 5 and 7
5 = 1 x 5
7 = 1 x 7
LCM = 1 x 5 x 7
LCM = 35
(2) 4, 5 and 10
4 = 2 x 2
5 = 1 x 5
10 = 2 x 5
LCM = 2 x 2 x 5
LCM = 20
(3) 6, 9 and 12
6 = 2 x 3
9 = 3 x 3
12 = 2 x 2 x 3
LCM = 2 x 2 x 3 x 3
LCM = 36
Find the LCD (lowest common denominator) of the fractions,
[tex]\begin{gathered} \frac{3}{8},\frac{3}{5} \\ We\text{ take the LCM of the denominators, that is 8 and 5} \\ \text{The LCM is,} \\ 5=1\times5 \\ 8=2\times2\times2 \\ \text{LCM}=2\times2\times2\times5 \\ \text{LCM}=40 \\ \text{The fractions can now be re-written as } \\ \frac{15}{40}\text{ and }\frac{24}{40} \end{gathered}[/tex]The mean number of employee sick days used per week at a company is 6.4 with a standard deviation of 1.5 days. What proportion of weeks would you expect to have more than 7 employee sick days used?
Given the z-score formula,
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{Where x =7} \\ \mu=6.4\text{ and} \\ \sigma=1.5 \\ z=\frac{7-6.4}{1.5}=\frac{0.6}{1.5}=0.4 \end{gathered}[/tex]Given the z-score of 0.4
You invest $275 to start a sandwich stand and decide to charge $5.15 per sandwich.Set up a Linear Model that determines your profit or loss based on the number of sandwiches.How much money will you make if you sell 75 sandwiches?How many sandwiches must you sell to make a $100 profit?
Let the number of sandwichs sold be "x"
If you charge $5.15 per sandwich then the total sales of the sandwich will be 5.15x
Cost price = $275
The Linear Model that determines your profit or loss based on the number of sandwiches will be expressed as:
[tex]\text{Profit}=\text{Selling price - Cost price}[/tex]Substitute the given parameters;
[tex]\begin{gathered} \text{Profit/Loss}=5.15x\pm275 \\ p(x)=5.15x\pm275 \end{gathered}[/tex]If 75 sandwiches were sold, the amount of money made will be expressed as:
[tex]\begin{gathered} p(75)=5.15(75)-275 \\ p(75)=386.25-275 \\ p(75)=\$111.25 \end{gathered}[/tex]Hence the amount of money made if you sell 75 sandwiches is $111.25
To make $100 profit, the amount of sandwiches must you sell is given as:
[tex]\begin{gathered} 100=5.15x-275 \\ 5.15x=100+275 \\ 5.15x=375 \\ x=\frac{375}{5.15} \\ x\approx72\text{sandwiches} \end{gathered}[/tex]Hence 72 sandwiches must be sold to make a profit of $100
I have a question on area of a triangle an area of a circle. See picture of my problem
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
equilateral triangle:
side = 7x
circle:
radius = 4r
Step 02:
area:
a = circle area - triangle area
triagle area:
triagle area = (b * h) / 2
b = 7x
h:
[tex]\begin{gathered} (7x)^2=h^2+(\frac{7x}{2})^2 \\ 49x^2=h^2+\frac{49x^2}{4} \\ h^2=49x^2-\frac{49x^2}{4}=\frac{147x^2}{4} \\ h\text{ = }\sqrt[]{\frac{147x^2}{4}\text{ }}=6.06x=6.1x \end{gathered}[/tex]h = 6.1x
[tex]\text{triangle area = }\frac{7x\cdot6.1x}{2}=\frac{42.7x^2}{2}=21.35x^2[/tex]circle area:
circle area (r) = π r² = π (4r)² = 16 π r²
a = circle area - triangle area
a = 16 π r² - 21.35x²
The answer is:
a = 16 π r² - 21.35x²
I need help with this. can you help me find the answer please?
ANSWER
15 degrees Celcius
STEP-BY-STEP EXPLANATION:
From the graph provided in the question tab, you will see that the outdoor temperature is plotted against the number of chips made per 25 seconds by the cricket.
On the x-axis, one box represents 10 units, on the y-axis, one box represents 4 units
At 33 cricket chirps in 25 seconds on the x-axis, we can trace the point to the y-axis, and this will give us 15 degrees Celcius.
Hence, the predicted outdoor temperature is 15 degrees Celcius
Find the z-score for 67.4% of the distribution area to the right
Usually, the tables for z-scores report the value at the left of given z-values. Then we can rewrite the question.
When the z-value has 67.4% of the area distribution it means that at its left we have: 100% - 67.4% = 32.6% of the area.
Now we just need to read the z-value table and find the z-score associated with a probability of 0.326. Reading from the table, the z value is approximately -0.45.
Finding the Midpoint of a line SegmentUse this formula to find the Midpoint (mean) of the line segment (-5, -3) and (9,3)
The formula for determining the midpoint of a line is expressed as
[tex]\begin{gathered} \text{Midpoint = }\lbrack\frac{(x1\text{ + x2)}}{2},\text{ }\frac{(y1\text{ + y2)}}{2}\rbrack \\ \text{From the information given,} \\ x1\text{ = - 5, x2 = 9} \\ y1\text{ = - 3, y2 = 3} \\ \text{Midpoint = }\lbrack\frac{(-\text{ 5 + 9)}}{2},\text{ }\frac{(-\text{ 3 + 3)}}{2}\rbrack \\ \text{Midpoint = (- 2, 0)} \end{gathered}[/tex]Part A: On one day, the exchange rate model might be B = 0.60A with the parameter k = 0.60.
Under these conditions, an American tourist exchanging US$ 11 would receive £
Round to the nearest hundredth, if necessary.
Part B: Under those same conditions, an English tourist exchanging £ 11 would receive US$
Round to the nearest hundredth, if necessary.
The amount of money each tourist will get:
Part A: The American tourist exchanging US$ 11 would receive £6.60.
Part B: The English tourist exchanging £ 11 would receive US$ 18.33.
We are given a relation in terms of algebraic expression:
B = 0.60A
We need to find the money of tourists after exchanging.
Part A:
The American tourist exchanged US$ 11.
substitute the value A = 11 in the given expression, we will get:
B = 0.60 * 11 = 6.60
So, the American tourist will get £6.60.
Part B:
The English tourist exchanged £ 11.
substitute the value B = 11 in the given expression, we will get:
11 = 0.60A
A = 11 / 6.60
A = 18.33333
A = 18.33
So, the English tourist will get US$ 18.33.
Thus, the amount of money each tourist will get:
Part A: The American tourist exchanging US$ 11 would receive £6.60.
Part B: The English tourist exchanging £ 11 would receive US$ 18.33.
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Use the general multiplication rule to solve for the given probability model. For events A and B, calculate P(A∩B) given the following information: P(B)=0.70 and P(A I B)=0.45
Let s be an Integer. Alonso claims that -s must always be less than zero. Iliana claims that -s is only sometimes less than zero. Whose statement is correct? Explain, support your reasoning with an example
Answer:
Iliana's claim is correct
Explanation:
If s is an integer.
Integers are positive or negative whole numbers.
• Illiana's claim is correct.
This is as a result of the fact that when s is negative: e,g s=-5
[tex]\begin{gathered} s=-5 \\ -s=-(-5)=5 \\ 5\text{ is greater than 0} \end{gathered}[/tex]However, when s is a positive integer:
[tex]\begin{gathered} s=5 \\ -s=-5 \\ -5\text{ is less than 0} \end{gathered}[/tex]Therefore, for an integer s, -s is only sometimes less than zero.
Illiana's claim is correct.
A) If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is: B) If half of the passengers are men, find the probability that the mean height of the men is less than 74 in. C) When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? D) When considering the comfort and safety of passengers, why are women ignored in this case?
Hello there. To solve this question, we'll have to remember some properties about probabilities.
Selecting male passengers randomly from the 400 passengers set, we want to find the probability that he can fit through the 74 in doorway without bending.
First, calling x the height of the random selected man, the probability of him fitting is P(x <= 74), and of him not fitting is P(x > 74)
To find P(x <= 74), we calculate the z-score by the formula:
[tex]z=\frac{x-\mu}{\sigma}=\frac{74-69}{2.8}=\frac{5}{2.8}\approx1.78[/tex]Looking for a table of z-scores for a normally distributed set, we say that the probability is around 95 or 96%. Using the under 8 approximation, P(x <= 74) = 0.96246 or 96.25%.
part (b)
We now have that the sample size is 200, since we had 400 passengers on the flight.
Making the new standard deviation as:
[tex]s=\frac{\sigma}{\sqrt[]{\text{sample}}}=\frac{2.8}{\sqrt[]{200}}=0.198[/tex]From the Central limit theorem, the z-score will then be:
z = (74 - 69)/0.198 = 25.25
Write an equation for the line that passes through the point (2,2) and is perpendicular to -8x+y=8. Use slope-intercept form.
Ok, first of all, let's put the equation of the line in the slope-intercept form:
-8x+y=8
y=8x+8
The slope of this line is m=8.
The slope of a perpendicular line is the negative reciprocal of the slope of the first line, so:
m2=-1/8
Now let's calculate the equation of the perpendicular linbe, using the given point, (2,2):
y-y1=m*(x-x1)
y-2 = -1/8(x-2)
y-2=-1/8x + 2/8
y=-1/8x +2/8 +16/8
y=-1/8x + 18/8
y= -1/8x + 9/4
The equation will be y= -1/8x + 9/4
y < 2x33y<--2-2Which graph represents the system of inequalities?Choose 1 answer:y42А→ 224
Graphing the inequalities:
From the options provided, the correct one is C
Answer:
C
Got to put this in a equation for each line
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
equation of the line:
we must analyze the lines to find the solution.
line l:
y = 4
line p:
x = - 4
line m:
point 1 (0 , 4)
point 2 (2, 0)
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{0-4}{2-0}=\frac{-4}{2}=-2[/tex]Slope-intercept form of the line
y = mx + b
y = -2x + 5
line n:
point 1 (5, 4)
point 2 (0 , -1)
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{-1-4}{0-5}=\frac{-5}{-5}=1[/tex]Slope-intercept form of the line
y = mx + b
y = 1x + (-1) = x - 1
The answer is:
line l: y = 4
line m: y = -2x + 5
line n: y = x - 1
line p: x = -4
Mrs. Hamilton is trying to plan a party for her math classes and receive two quotes. The Hypotenuse Hall
charges $100 for a damage deposit and $6 per per person for snacks. The Pi Place charges only $20 for a
damage deposit but $10 per person for snacks. Mrs. Hamilton needs your help!
The hypotenuse hall will be cheaper .
Both places charge $200 for 20 people .
The linear system of equation gives C = 20 + 10 n
Where ,
C = total cost
N = number of cost
What is linear system of equation?A system of linear equations in mathematics is a grouping of one or more linear equations that share the same variables. A collection of one or more linear equations involving the same variables is known in mathematics as a system of linear equations (or linear system). A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display significantly simpler traits and properties. A line equation is referred to as a linear equation. Or, for example, y + 0.5x 3.5 = 0 and more. The linear equation in each case is the same (remember this!) When two or more linear equations cooperate, this is known as a system of linear equations.
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