The top of the lampshade is circular in shape
[tex]\begin{gathered} \text{The circumference of a circle = 2}\pi r \\ \text{where }\pi=3.14,\text{ r= radius of the circle} \\ \text{The radius , r=9 in} \\ \text{Circumference = 2 x 3.14 x }9 \\ \text{Circumference = }56.52\text{ in} \end{gathered}[/tex]The circumference of the top of the shade is 56.52 inches
The difference of 4R and 108
The expression of the mathematical statement given as the difference of 4R and 108 is |4R - 108|
How to rewrite the mathematical statement as an expression?From the question, the mathematical statement is given as
The difference of 4R and 108
In mathematics, the difference of numbers or expressions implies that we subtract one of the numbers from the other number or expression
This in other words means that difference means subtraction
So, we have the following representation
The difference of 4R and 108 ⇒ 4R - 108
However, we do not know the bigger number.
So, the expression can be rewritten as
The difference of 4R and 108 ⇒ 108 - 4R
So, we have two options
4R - 108 and 108 - 4R
When both expressions are combined, we introduce the absolute value symbol i.e. |.....|
|4R - 108|
Hence, the expression represented by the statement is |4R - 108|
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helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(f o g)(x) = 8x³ + 2x - 6
(g o f)(x) = 2x³ + 2x - 12
Step-by-step explanation:
f(x) = x³ + x - 6; g(x) = 2x
(f o g)(x) = f(g(x))
f(g(x)) = (2x)³ + (2x) - 6
f(g(x)) = 8x³ + 2x - 6
(g o f) = g(f(x))
g(f(x)) = 2(x³ + x - 6)
g(f(x)) = 2x³ + 2x - 12
I hope this helps!
Find the measure of all the angles if m<2 = 76°
By opposite angles we know that:
[tex]\begin{gathered} m1\measuredangle=m3\measuredangle \\ m2\measuredangle=m4\measuredangle \\ m5\measuredangle=m7\measuredangle \\ m8\measuredangle=m6\measuredangle \end{gathered}[/tex]By corresponding angles we know that
[tex]\begin{gathered} m5\measuredangle=m1\measuredangle \\ m2\measuredangle=m6\measuredangle \\ m4\measuredangle=m8\measuredangle \\ m7\measuredangle=m3\measuredangle \end{gathered}[/tex]by complementary angles we know that
[tex]\begin{gathered} m1\measuredangle+m2\measuredangle=180º \\ m1\measuredangle+76º=180º \\ m1\measuredangle=104º \end{gathered}[/tex]Using the correspondence and opposite angles:
[tex]\begin{gathered} m1\measuredangle=m3\measuredangle=m5\measuredangle=m7\measuredangle=104º \\ m2\measuredangle=m4\measuredangle=m6\measuredangle=m8\measuredangle=76º \end{gathered}[/tex]For what value of x does 32x93x-4?oo 2o 3o 4
Solution
[tex]3^{2x}=9^{3x-4}[/tex]We can do the following:
[tex]3^{2x}=3^{2(3x-4)}[/tex]And we have this:
[tex]2x=6x-8[/tex][tex]4x=8[/tex][tex]x=\frac{8}{4}=2[/tex]What is the y-intercept of 4x + 8y = 12?
i am stuck on this question. any help would be greatly appreciated
step 1
determine the slope of the given line
y=(3/5)x-17
The slope is m=3/5
Remember that
If two lines are parallel, then their slopes are equal
that means
The slope of the parallel line to the given line is m=3/5 too
step 2
Find out the equation of the line parallel to the given line
y=mx+b
we have
m=3/5
point (-5,15)
substitute and solve for b
15=(3/5)(-5)+b
15=-3+b
b=18
therefore
The equation of the line is
y=(3/5)x+18Is 5/6 equivalent to 0.832
Answer: No
Step-by-step explanation:
1 divided by 6 would be 16 and 4/6. So you would have to multiply 16 and 4/6 by 5, add them together, and then divide by 10 to get the decimal. 16 * 5 = 80. 4/6 * 5 = 20/6. 80/10 = 8. 20/6 divided by 10 = 10/6. 8+10/6 is not equal to .832
Han and clan are stuffing enveloppes Han can stuff 20 envelopes in one minute and Clare can stuff 10 envelopes in one minute. They start working together on a pile of 1000 envelopes. How long does it take them to finish the pile.
uff = Given
Han can stuff 20 envelopes in one minute
Clare can stuff 10 envelopes in one minute
Together they start working on a pile off 1000 envelope.
Find
How long does it take them to finish the pile.
Explanation
as we have given
in one minute , Han can stuff = 20 envelope
in one minute , Clare can stuff = 10 envelope
together in one minute , they can stuff =
[tex]\begin{gathered} 20+10=30 \\ \\ \end{gathered}[/tex]we know that the number of time it will take to finish stuffing would be number of envelope / joint rate = 1000/30
so , time taken to finish the pile =
[tex]\begin{gathered} \frac{1000}{30} \\ \\ \frac{100}{3} \\ \\ 33\frac{1}{3} \\ or \\ 33min20sec \end{gathered}[/tex]Final Answer
Hence , the time taken by them to finish the pile is 33 minutes 20 seconds
The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 72000 miles and a standard deviation of 7000 miles.A. What is the probability that the tire wears out before 60000 miles?Probability = What is the probability that a tire lasts more than 80000 miles? Probability=
a. 0.0436
b. 0.1271
We are given the following:
Distance (x) = 60,000
Mean (u) = 72,000
Standard Deviation(s) = 7,000
We are also told that it is a normal disribution relationship. The formula for ND is as follows:
z = (x - u) / s
Now we can continue with part a and b as follows:
a) P (x < 60,000)
= P (z < (60000 - 72000) / 7000)
= P (z < -1.714)
We can find the corresponding z score by looking at a z score table, and we find th probability to be 0.0436
b) P ( x > 80,000)
= P(z > (80000 - 72000) / 7000)
= P( z > 1.143)
We find the corresponding z score to be 0.8729, now we can substract this from 1 sinsce our probability is larger than the given distance (meaning we are trying to find the area to the right of the z score) to find our final answer:
1 - 0.8729 = 0.1271
true or false 16/24 equals 30 / 45
True.
Given:
The equation is, 16/24 = 30/45.
The objective is to find true or false.
The equivalent fractions can be verified by, mutiplying the denominator and numerator of each fraction.
The fractions can be solved as,
[tex]\begin{gathered} \frac{16}{24}=\frac{30}{45} \\ 16\cdot45=24\cdot30 \\ 720=720 \end{gathered}[/tex]Since both sides are equal, the ratios are equivalent ratios.
Hence, the answer is true.
what is 2x2 and 3x0 and 3x3 and 4x4
the mean salary offered to students who are graduating from coastal state university this year is $24,215, with a standard deviation of $3712. A random sample of 80 coastal state students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is $24,250 or more?
Given that the mean and standard deviation of the population are $24,215 and $3712 respectively,
[tex]\begin{gathered} \mu=24215 \\ \sigma=3712 \end{gathered}[/tex]The sample size taken is 80,
[tex]n=80[/tex]Consider that the salary of students in the sample is assumed to follow Normal Distribution with mean and standard deviation as follows,
[tex]\begin{gathered} \mu_x=\mu\Rightarrow\mu_x=24215 \\ \sigma_x=\frac{\sigma}{\sqrt[]{n}}=\frac{3712}{\sqrt[]{80}}\approx415 \end{gathered}[/tex]So the probability that the mean salary (X) is $24250 or more, is calculated as,
[tex]\begin{gathered} P(X\ge24250)=P(z\ge\frac{24250-24215}{415}) \\ P(X\ge24250)=P(z\ge0.084) \\ P(X\ge24250)=P(z\ge0)-P(0From the Standard Normal Distribution Table,[tex]\begin{gathered} \emptyset(0.08)=0.0319 \\ \emptyset(0.09)=0.0359 \end{gathered}[/tex]So the approximate value for z=0.084 is,
[tex]\emptyset(0.084)=\frac{0.0319+0.0359}{2}=0.0339[/tex]Substitute the value in the expression,
[tex]\begin{gathered} P(X\ge24250)=0.5-0.0339 \\ P(X\ge24250)=0.4661 \end{gathered}[/tex]Thus, there is a 0.4661 probability that the mean salary offer for these 80 students is $24,250 or more.
T is in seconds and L is the length of the pendulum in centimeters. Find the period of the pendulum of the given lengths. Give your answer to two decimal places using 3.14 for π. Show and explain your work below. a. L = 23 cm b. L = 192 cm
The period of the pendulum in each case is given as follows:
a. L = 23 cm: 0.96 s.
b. L = 192 cm: 2.78 s.
Period of pendulumThe period of a pendulum is defined according to the following equation:
P = 2π sqrt(L/g)
In which the parameters are as follows:
L is the length of the pendulum which we want to find the period.g = 9.8 m/s² is the acceleration of the pendulum due to the gravity.For a length of 23 cm = 0.23m, in item a, considering 3.14 for π, the period is calculated as follows:
P = 6.28 x sqrt(0.23/9.8) = 0.96 s.
In item b, the length is of 192 cm = 1.92 m, as each cm has 100 m, hence the period is given by:
P = 6.28 x sqrt(1.92/9.8) = 2.78 s.
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Use the times and corresponding closing prices of the stock to create coordinate pairs. Let X represent the number of weeks since the first at a point, and Y represent the closing price of each time. So, X equals zero represents the data point from five years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since five years ago, when X equals zero. Fill in the table to represent your data as coordinate pairs
Combining both tables we get:
Enter the correct answeach column.5. Bellatrix Lestrange keeps her money in GringottsWizarding Bank. She decided to take $100,000out of her vault and split it among three differentaccounts. She placed part in a savings accountpaying 3% per year, twice as much in Wizard bondspaying 5.5%, and the rest in a mutual fund thatreturned 4%. Her income from these investmentsafter one year was $4,480. How much did Bellatrixplace in each account?11223334.44HOW MUCH DID BELLATRIX PLACE IN THEMUTUAL FUND?556670N (0088
Assum,e that she put x in the account of 3%
So in wizard bonds, she put twice so it is 2x
The rest in the account of 4%
The rest is 100,000 - x - 2x = 100,000 - 3x
The rule of the investment is :
[tex]I=\text{prt}[/tex]I is the interest, P is the money she invested, r is the rate and t is the time
We will make equation for each account
[tex]\begin{gathered} I_1=x(\frac{3}{100})(1)=0.03x_{} \\ I_2=(2x)(\frac{5.5}{100})(1)=0.11x \end{gathered}[/tex][tex]I_3=(100,000-3x)(\frac{4}{100})(1)=4000-0.12x[/tex]The sum of the interest is 4,480, so add them and equate the sum by 4,480 to find the value of x
0.03x + 0.11x + 4000 - 0.12x = 4,480
Add like terms in the left side
0.02x + 4000 = 4,480
Subtract 4000 from both sides
0.02x + 4000 - 4000 = 4,480 - 4000
0.02x = 480
Divide both sides by 0.02
x = 24,000
The value in the mutual fund is 100,000 - 3x, so substitute s by 24,000
The mutual fund = 100,000 - 3(24,000) = 100,000 - 72,000 = 28,000
The mutual fund = $28,000
A teacher gets snacks for the class for $50 and also purchases 6 boxes of pencils. The teacher spent a total of $62. Write an equation that models the situation with x, the cost of one box of pencils.
Answer:
50 + 6x = 62
Explanation:
If x represents the cost of one box of pencils and the teacher got snacks for $50, purchased 6 boxes of pencils, and spent a total of $62, we can write the equation that models the above situation as shown below;
[tex]50+6x=62[/tex]The table shows the total cost c for the number of aquarium tickets purchased t. Write an equationthat can be used to find the cost c oft aquarium tickets. Use the equation and complete the table tofind the cost of 7 tickets.7Number of Tickets, tCost, cWrite an equation3$29.2510 12$97.50 $117.00(Use the operation symbols in the math palette as needed. Use integers or decimals for any numbers in the equatioDo not include the $ symbol in your answer.)
We can model the cost and number of tickets by a linear equation of the form
[tex]c=mt+b[/tex]Where c is the cost, t is the number of tickets.
m is the slope of the equation and b is the y-intercept.
First, let us find the slope which is given by
[tex]m=\frac{c_2-c_1}{t_2-t_1}[/tex]You can take any two pairs of values from the table.
[tex]m=\frac{117-97.50}{12-10}=\frac{19.5}{2}=9.75[/tex]The slope is 9.75 and the equation becomes
[tex]c=9.75t+b[/tex]Now we need to find the y-intercept (b)
Choose any one pair of values from the table and substitute them into the above equation and solve for b.
Let's choose (12, 117)
[tex]\begin{gathered} c=9.75t+b \\ 117=9.75(12)+b \\ 117=117+b \\ b=117-117 \\ b=0 \end{gathered}[/tex]The y-intercept is 0 so the equation is
[tex]c=9.75t[/tex]Now to find the cost of 7 tickets, simply substitute t = 7 into the above equation
[tex]\begin{gathered} c=9.75t \\ c=9.75(7) \\ c=68.25 \end{gathered}[/tex]Therefore, the cost of 7 tickets is $68.25
If the distance from the too of the building to the tip of its shadow is 150ft, what is the length of the buildings shadow
In order to know the length of the shadow, we will use a trigonometric function in this case for the data given and the distance we want to find we will use the sine
[tex]\sin (75)=\frac{S}{150}[/tex]we isolate S
[tex]S=\sin (75)\cdot150=144.89[/tex]the length of the shadow is 144.89ft
A system of equations is shown below. Solve for x.
y = x² - 6x + 4
y = x + 1
The value of x in the given quadratic equations is either -2.7 or -11.3.
What are quadratic equations?A quadratic equation is a second-degree algebraic equation in x. ax² + bx + c = 0, where a and b are coefficients, x is the variable, and c is the constant term, is the quadratic equation in its simplest form.
Given first equation, y = x²- 6x + 4 second equation, y = x +1
Put the value of y in the first equation to get
x + 1 = x² - 6x + 4
Solving this equation
x² - 7x + 3 = 0
Using quadratic formula,
x = - b ± [tex]\frac{\sqrt{(b^{2}- 4ac)}}{2a}[/tex]
x = - 7 ± [tex]\frac{\sqrt{(-7)^{2}- 4(3)}}{2}[/tex]
x = - 7 ± 4.3
Therefore in the given quadratic equations, the value of x can be either -2.7 or -11.3
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8. Anna withdrew $50 from her checking account. She spent $28 on a pair of shoes. What fraction of her money does Anna have left?
Explanation:
If she spent $28 of the $50 she withdrew, she now has:
[tex]50-28=22[/tex]$22
The fraction is:
[tex]\frac{22}{50}=\frac{11}{25}[/tex]Answer:
Anna has 11/25 of her money left.
The area in square millimeters of a wound has decreased by the same percentage every day since it began to heal. The table shows the wound's area at the end of each day.
Given the table showing the number of days since wound began to heal and area of wound in square millimeters
To determine the statement that are correct from the option provided
From the table shown it can be seen that as the day increases by 1, the area of wound in square millimeters decreases by a common ratio of
[tex]\frac{20}{25}=\frac{16}{20}=\frac{12.8}{16}=\frac{10.24}{12.8}=0.8[/tex]Suppose that an expression to represent the area of wound is
[tex]ab^c[/tex]The modelled expression from the table is
[tex]\begin{gathered} a=25 \\ b=0.8 \\ c=n-1 \\ \text{Therefore, we have} \\ 25(0.8^{n-1}) \end{gathered}[/tex]Let us use the modelled expression to verify each of the given conditions
The modelled expression can be simplified as shown below:
[tex]\begin{gathered} 25(0.8^{n-1}) \\ \text{Note},\text{ using indices rule} \\ \frac{a^n}{a}=a^{n-1} \\ \text{Therefore:} \\ 0.8^{n-1}=\frac{0.8^n}{0.8} \end{gathered}[/tex]Then, we have the modelled expression becomes
[tex]25(0.8^{n-1})=25\times\frac{0.8^n}{0.8}=\frac{25}{0.8}\times0.8^n=31.25(0.8^n)[/tex]From the two modelled expression we can see that
[tex]\begin{gathered} \text{when:} \\ c=n-1,a=25,b=0.8 \\ c=n,a=31.25,b=0.8 \end{gathered}[/tex]Then we can conclude that the two conditions that are true from the options are
If the value of c = n, the value of a is 31.25, and
If the value of c = n, the value of b is 0.8
Let f(x)=5x.Let g(x)=5x−7.Which statement describes the graph of g(x)with respect to the graph of f(x)? g(x)is translated 7 units down fromf(x).g(x)is translated 7 units left fromf(x).g(x)is translated 7 units right from f(x).g(x)is translated 7 units up fromf(x).
Given
[tex]\begin{gathered} f(x)=5x \\ g(x)=5x-7 \end{gathered}[/tex]According to rules of transformation:
f(x)+c shift c units up and f(x)-c shift c units down.
For the given function g(x) = 5x-7, 7 is being subtracted from 5x.
Where 5x is represented by f function.
Therefore, we could apply the rules of transformation f(x)-c shift c units down.
Here the value of c is 7.
Answer: g(x) is translated 7 units down from f(x)
Under certain conditions, the velocity of a liquid in a pipe at distance r from the center of the pipe is given by V = 400(3.025 x 10-5--2) where Osrs5,5x10 -3. Writeras a function of V.r=where the domain is a compound inequality(Use scientific notation. Use integers or decimals for any numbers in the expression.)Le
Solving the equation for r:
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-r^2) \\ r^2=9.025\cdot10^{-5}-\frac{V}{400} \\ r=\sqrt[]{9.025\cdot10^{-5}-\frac{V}{400}} \end{gathered}[/tex]With the first equations, we can establish some limits for V:
With the lowest value for r (r=0):
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-0^2) \\ V=400(9.025\cdot10^{-5}) \\ V=3.61\cdot10^{-2} \end{gathered}[/tex]With the highest value for r (r=9.5x10^-3)
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-(9.5\cdot10^{-3})^2) \\ V=400(9.025\cdot10^{-5}-9.025\cdot10^{-5}) \\ V=400(0) \\ V=0 \end{gathered}[/tex]According to the radius range, velocity can be between 0 and 3.61x10^-2
It is also necessary to check the domain of the function considering it is a square root. The argument of an square root cannot be less than 0. Then:
[tex]\begin{gathered} 9.025\cdot10^{-5}-\frac{V}{400}\ge0 \\ 9.025\cdot10^{-5}\ge\frac{V}{400} \\ V\leq400(9.025\cdot10^{-5}) \\ V\leq3.61\cdot10^{-2} \end{gathered}[/tex]This is the same limit for velocity obtained before. Then, we can say for velocity that:
[tex]0\leq V\leq3.61\cdot10^{-2}[/tex]help please A sandwich shop has three kinds of bread, seven types of meat, and four types of cheese. How many different sandwiches can be made using one type of bread, one meat, and one cheese?
Types of combinations of
Bread, Meat , CHeese
How many combinations of B M CH can be made.
There are 3, 7 and 4 types of food , respectively
Made a tree of possibilities
Then, for every 3 , there are 7 possibilities. Multiply both
3 x 7 = 21
And for every 7 , there are 4 possibilities . Multiply then
3x 7 x 4 = 84 possible type of sandwiches
Graph the equation and find the x-coordinate of the x-intercept:1.5x - 3y = 7Round to the nearest hundredth
We can begin by finding the x-intercept. This is the point at which the graph crosses the horizontal axis. This point is given when the y-value of the function is 0, then, we can solve the equation for y = 0 and find the value for x:
[tex]\begin{gathered} 1.5x-3y=7\to y=0 \\ 1.5x-3\cdot(0)=7 \\ 1.5x=7 \\ x=\frac{7}{1.5} \\ x\approx4.67 \end{gathered}[/tex]The x value of the x-intercept of the equation is approximately 4.67.
This is a linear equation, to build the graph we just need 2 points and join them with the line.
The x-intercept is the point (4.67, 0). Another easy point to find and build the graph can be the y-intercept, which is given when x = 0. Replacing in the equation:
[tex]\begin{gathered} 1.5x-3y=7\to x=0 \\ 1.5\cdot(0)-3y=7 \\ -3y=7 \\ y=\frac{-7}{3} \\ y\approx-2.33 \end{gathered}[/tex]With this, the other point we can use to graph the equation is (0, -2.33).
Drawing both points on a cartesian plane:
Both points (x and y-intercepts) are drawn in red.
Graph the line with the given slope m and y-intercept b.
m = 4,b=-5
The graph of the linear equation can be seen in the image at the end.
How to graph the linear equation?
The general linear equation is.
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we know that m = 4 and b = -5, so we have:
y = 4*x - 5
To graph this line, we need to find two points.
Evaluating in x = 0 we get:
y = 4*0 - 5 = -5
Evaluating in x = 2 we get:
y = 4*2 - 5 = 8 - 5 = 3
So we have the points (0, -5) and (2, 3), so now we need to graph these points and connect them with a line, the graph can be seen below:
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food cost for your restaurant is about $.38 on the dollar. that means for every dollar in sales, you spend 38 cents in food cost.figure out the food cost for the following days’ sales:monday:$3,459.00tuesday:$2,976.81wednesday:$3,185.32thursday:$3,562.91friday:$4,582.13saturday:$4,820.36
The Solution.
Monday's sales is $3459.00
The food cost for Monday is
[tex]\text{ Food cost = 0.38}\times3459=\text{ \$1314.42}[/tex]Tuesday's sales is $2976.81
The food cost for Tuesday is
[tex]\text{Food cost = 0.38}\times2976.81=\text{ \$}1131.19[/tex]Wednesday's sales is $3185.32
The food cost for Wednesday is
[tex]\text{ Food cost = 0.38}\times3185.32=\text{ \$}1210.42[/tex]Thursday's sales is $3562.91
The food cost for Thursday is
[tex]\text{Food cost = 0.38}\times3562.91=\text{ \$}1353.91[/tex]Friday's sales is $4582.13
The food cost for Friday is
[tex]\text{Food cost = 0.38}\times4582.13=\text{ \$}1741.21[/tex]Saturday's sales is $4820.36
The food cost for Saturday is
[tex]\text{Food cost = 0.38}\times4820.36=\text{ \$}1831.74[/tex]Write the tangent ratios for LP and 4Q. If needed, reduce!P12R160Not drawn to scaletan P=tan Q =
Given: The right triangle PQR as shown
To Determine: The tangents of P and Q
Solution
Given a right triangle, the tangent of any angle can be determine
Note that the side facing the right angle is the hypothenuse, the side facing the angle is the opposite and the other side is the adjacent.
Determine the opposite and the adjacent for angle P in the triangle PQR given
[tex]\begin{gathered} Note; \\ tan\theta=\frac{opposite}{adjacent} \\ tanP=\frac{16}{12} \\ tanP=\frac{4}{3} \end{gathered}[/tex]I need to help finding the length of the arc shown in red..
We have the next formula to find the length is
[tex]\text{arc length }=\text{ 2}\pi r(\frac{\theta}{360})[/tex]where
r=10
theta=45°
[tex]\begin{gathered} \text{arc length=}2\pi(10)\frac{45}{360}=\frac{5}{2}\pi \\ \end{gathered}[/tex]the arc length is 5/2 pi cm
Which equation shows a proportional relationship? options: O y = x O y + 1 = 7x O y - 2 = x + 8 O x = y + 5
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = kx
for some constant k , called the constant of proportionality . This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
From the given options, the baove property is satisfied by,
[tex]y=\frac{2}{3}x[/tex]Thus, the correct option is A.
