You have to multiply:
[tex]-5\frac{1}{2}\cdot7\frac{5}{6}[/tex]First write the compound fractions as impropper fractions.
To do so, divide the whole number by one to express it as a fraction and add both fractions:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{5}{1}+\frac{1}{2}\to\text{ common denominator 2} \\ \\ \frac{5\cdot2}{1\cdot2}+\frac{1}{2}=\frac{10}{2}+\frac{1}{2}=\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} 7\frac{5}{6}=\frac{7}{1}+\frac{5}{6}\to\text{ common denominator 6} \\ \frac{7\cdot6}{1\cdot6}+\frac{5}{6}=\frac{42}{6}+\frac{5}{6}=\frac{47}{6} \end{gathered}[/tex]Rewrite the multiplication using the corresponding impropper fractions:
[tex]-\frac{11}{2}\cdot\frac{47}{6}[/tex]And solve the multiplication, numerator * numerator and denominator*denominator:
[tex]-\frac{11}{2}\cdot\frac{47}{6}=-(\frac{11\cdot47}{2\cdot6})=-\frac{517}{12}[/tex]Use the formula for n^P_r to evaluate the following expression.
Use the following formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]Then, for 11P6:
[tex]\begin{gathered} _{11}P_6=\frac{11!}{(11-6)!}=\frac{11!}{5!}=\frac{5!\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11}{5!} \\ _{11}P_6=6\cdot7\cdot8\cdot9\cdot10\cdot11=332640 \end{gathered}[/tex]Hence, the result is 332640
Review the proof. Which step contains an error? step 2 step 4step 6step 8
Answer
Option C is correct.
Step 6 contains the error.
Explanation
Looking through the steps, we can see easily that the mistake occurs at the 6th step, specifically when the process moves from step 5 to step 6
-1 + cos θ = -2 sin² (θ/2)
If one multiplies through by -1
1 - cos θ = 2 sin² (θ/2)
NOT 1 + cos θ = 2 sin² (θ/2)
Hope this Helps!!!
We have seen the isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use information to the right to help the measure of angles 1, 2, 3, 4, and 5.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
triangle diagram
Step 02:
angles:
we must analyze the diagram to find the solution
angle 1:
angle 1 = 180° - 155° = 25°
angle 2:
angle 2 = angle 1 = 25°
angle 3:
angle 3 = 180° - 25° - 25° = 130°
angle 4:
angle 4 = 155°
angle 5:
angle 5 = 180° - 25° = 155°
That is the full solution.
A publisher for promising new novel figures fixed costs at $61,000 and variable cost at $1.50 for each book produced if the book is sold to distributors for $15 each how many must be produced and sold for publisher to break even?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} For\text{ the cost price function:} \\ Fixed\text{ cost=\$61,000 = constant} \\ Variable\text{ cost = \$1.50 }\times\text{ number of books} \\ Let\text{ x be the number of books produced} \end{gathered}[/tex]The function for the cost price becomes:
[tex]61000+1.5x[/tex]STEP 2: Get the function for the selling price
The function for the selling price becomes:
[tex]\text{ \$}15x[/tex]STEP 3: Calculate the number of books required to break even
To get the breakeven, the cost price will be equal to selling price. Therefore,
[tex]\begin{gathered} 61000+1.5x=15x \\ Subtract\text{ 1.5x from both sides} \\ 61000+1.5x-1.5x=15x-1.5x \\ 61000=13.5x \\ Divide\text{ both sides by 13.5} \\ \frac{61000}{13.5}=\frac{13.5x}{13.5} \\ 4518.518519=x \\ x\approx4519 \end{gathered}[/tex]Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519
Remi and Pam start at the same point and begin jogging in different directions. Remi is jogging east at a speed of 3 miles per hour. Pam is jogging south at a speed of 4 miles per hour. After how many hours will they be exactly 15 miles apart?
The number of hours (time) after which both Remi and Pam would be exactly 15 miles apart is 3 hours.
How to determine the number of hours (time)?First of all, we would have to determine the amount of distance (d) covered by both Remi and Pam.
Let t represent the number of hours (time) to cover these distances. Let r represent the distance covered (traveled) by Remi.Let p represent the distance covered (traveled) by Pam.Mathematically, the distance covered (traveled) by a physical body (object) can be calculated by using this formula:
Distance = speed × time
For the distance covered (traveled) by Remi, we have:
r = 3 × t
r = 3t.
For the distance covered (traveled) by Pam, we have:
p = 4 × t
p = 4t.
Also, the amount of distance (d) covered by both Remi and Pam forms a right-angled triangle as they both jogged East and South respectively. Therefore, there distances can be modeled by Pythagorean theorem:
d = r² + p²
Substituting the parameters into the formula, we have;
15² = 3t² + 4t²
225 = 9t² + 16t²
225 = 25t²
Dividing both sides by 25, we have:
t² = 225/25
t² = 9
t = √9
Time, t = 3 hours.
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Sally deposits $2,500 at 8% interest for 3 years . How much can she withdraw at the end of that period
ANSWER
$3100
EXPLANATION
Sally deposits $2500 at 8% interest for 3 years.
We want to find the amount she can withdraw at the end of the period.
To know this, we have to first find the interest.
Simple Interest is given as:
[tex]\begin{gathered} SI\text{ = }\frac{P\cdot\text{ R }\cdot\text{ T}}{100} \\ \text{where P = principal = \$2500} \\ R\text{ = rate = 8\%} \\ T\text{ = 3 years} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} SI\text{ = }\frac{2500\cdot\text{ 8 }\cdot\text{ 3}}{100} \\ SI\text{ = }\frac{60000}{100} \\ SI\text{ = \$600} \end{gathered}[/tex]Therefore, after 3 years the interest will be $600.
The amount she can withdraw after this period is therefore the sum of the principal and the interest:
$2500 + $600 = $3100
She can withdraw $3100 at the end of the period.
Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 3 years?
Answer:
The amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]Explanation:
Given that Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. for the first 3 years;
[tex]\begin{gathered} \text{ Principal P = \$500} \\ \text{rate r = 6\% = 0.06} \\ \text{time t = 3 years} \end{gathered}[/tex]Recall the simple interest formula;
[tex]i=P\times r\times t[/tex]substituting the given values;
[tex]\begin{gathered} i=500\times0.06\times3 \\ i=\text{ \$90} \end{gathered}[/tex]Therefore, the amount of interest she will be paid in the first 3 years is;
[tex]\text{ \$90}[/tex]Joan uses the function C(x) = 0.11x + 12 to calculate her monthly cost for electricity.• C(x) is the total cost (in dollars).• x is the amount of electricity used (in kilowatt-hours).Which of these statements are true? Select the three that apply.A. Joan's fixed monthly cost for electricity use is $0.11.B. The cost of electricity use increases $0.11 each month.C. If Joan uses no electricity, her total cost for the month is $12.D. Joan pays $12 for every kilowatt-hour of electricity that she uses.E. The initial value represents the maximum cost per month for electricity.F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Answer:
The correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Step-by-step explanation:
Notice that the given function is the equation of a line in the slope-intercept form:
[tex]C(x)=0.11x+12[/tex]From this interpretation, we'll have that the correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
The figure below shows two parallel lines, k and f, cut by a transversal. What is the value of x?
A 25
B 35
C 45
D 65
Answer:
x=65 0r in other words D
Step-by-step explanation:
110=2x-20
+20 +20
130=2x
/2 /2
65=x
HELLPPPPLLPPPPPPPPPPPPPPP
Answer:
a²+13a+40
Step-by-step explanation:
Now the x in the function has been replaced into (a+5) :
(a+5)²+3(a+5) =
(a²+10a+25)+(3a+15) =
a²+13a+40
Hope this helped and have a good day
For each ordered pair, determine whether it is a solution to 4x - 5y = -13.Is it a solution?x$(x, y)YesNo(-7, -3)(3, -4)OO(-2, 1)oO(6, 7)0
The equation is 4x - 5y = -13.
Substitute -7 for x and -3 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-7)-5\cdot(-3)=-13 \\ -28+15=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation so point (-7,-3) is solution of equation.
Substitute 3 for x and -4 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot3-5\cdot(-4)=-13 \\ 12+20=-13 \\ 32\ne-13 \end{gathered}[/tex]The ordered pair not satisfy the equation. So point (3,-4) is not a solution of the equation.
Substitute -2 for x and 1 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-2)-5\cdot1=-13 \\ -8-5=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation. So point (-2,1) is solution of equation.
Substitute 6 for x and 7 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot6-5\cdot7=-13 \\ 24-35=-13 \\ -11\ne-13 \end{gathered}[/tex]The orderedpair not satisfy the equation. So point (6,7) is not a solution of the equation.
The average of 13, 15, 20 and x is 18. What is the value of x?
x will be equal to 24.
Given,
There are 4 numbers:
13, 15, 20, and x.
Average of all numbers = 18.
We know that,
Average = ( sum of all numbers) / ( total numbers)
In this case,
Average = ( 13 + 15 + 20 + x) / 4
According to the question,
18 = (48 + x) / 4
=> 72 = 48 + x
=> x = 72 - 48
=> x = 24.
So, in order to make the average equal to 18, x should be equal to 24.
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what is 40+56 in GCF
The GCF stands for greatest common factor. To represent a sum by its GCF we need to use the distributive property and we need to first find the GCF of the numbers. Let's break each number by its factors:
[tex]\begin{gathered} 40=2\cdot2\cdot2\cdot5 \\ 56=2\cdot2\cdot2\cdot7 \end{gathered}[/tex]We now multiply the numbers that appear on both.
[tex]\text{GCF}=2\cdot2\cdot2=8[/tex]We now apply the distributive property:
[tex]8\cdot(5+7)[/tex]A wheel is rotating 600 times per minute. Through how many degrees does a point in the edge of the wheel move in 1/2 seconds.
The wheel is rotating 600 times per minute, find how many times rotate in 1 second:
1 minute = 60 seconds
[tex]600\frac{times}{\min}\cdot\frac{1\min}{60s}=10\frac{times}{s}[/tex]Then, if in 1 second it rotates 10 times in 1/2 seconds it rotates:
[tex]\frac{10\frac{times}{s}}{2}=5\text{times}[/tex]Multiply the number of times it rotates (5 times) by 360 (a wheel has 360º)
[tex]5\text{times}\cdot\frac{360º}{1\text{time}}=1800º[/tex]Then, a point moves 1800º in 1/2 secondsIf the LM follows the reference trajectory, what is the reference velocity vref (t) ?
Answer:
Explanation:
A music store has 40 trumpets, 39 clarinets, 24 violins, 51 flutes, and 16 trombones in stock. Write each ratio in simplest formTrumpets to violins
SOLUTION
Given the question in the question tab, the following are the solution steps to get the ratio of Trumpets to violins
Step 1: Write the given data
40 trumpets
39 clarinets
24 violins
51 flutes
16 trombones
Step 2: Write the ratio of trumpets to violins
Trumpets=40
Violins=24
[tex]\begin{gathered} \text{ratio}=40\colon24=\frac{40}{24} \\ By\text{ s}implification, \\ \frac{40}{24}=\frac{5}{3} \end{gathered}[/tex]Hence, the ratio of trumpets to violin in its simplest from is:
[tex]5\colon3[/tex]Using this formula and other formulas, find Q1,Q2, Q3 the midquartile, and the interquartile range for the data set.51, 62, 73, 92, 97, 100, 104
Given:
The given set of data is 51, 62, 73, 92, 97, 100, 104.
The objective is to find Q1,Q2, Q3 the midquartile, and the interquartile range.
Explanation:
The given set of data is already arranged in increasing oder.
To find Q2:
The quartile Q2 represents the middle term of the set of data arranged in increasing order.
The number of terms in the set of data is N = 7.
Then, the middle term of the set of data is 92, which is Q2.
To find Q1:
The quartile 1 represents the middle term of the left side of the Q2.
The left side of Q2 contains 51, 62, 73.
Thus, the middle term of the left side of Q2 is 62, which is Q1.
To find Q3:
The quartile 3 represents the middle temr of the right side of the Q2.
The right side of Q2 contains 97, 100, 104.
Thus, the middle term of the right side of Q2 is 100, which is Q3.
To find midquartile:
The midquartile is termed as the average of highest and lowest value of the set of data.
The highest value in the given set of data is 104 and the lowest value in the given set of data is 51.
Then, the midquartile can be calculated as,
[tex]\begin{gathered} \text{Midquartile}=\frac{104+51}{2} \\ =77.5 \end{gathered}[/tex]To find interquartile:
The
231231312312312312311
Answer: 3456765432345
Step-by-step explanation:
2345676543456
Hi, can you help me answer this question please, thank you!
Consider that you have a population greater than 30, then, you can use the normal distribution to determine the margin of error.
Use the following formula:
[tex]\bar{x}\pm Z_{\frac{\alpha}{2}}\frac{s}{\sqrt[]{n}}[/tex]where:
x: mean = 33
s: standard deviation = 2
n = 31
Z: z-value for 98%
The value of Z can be found on a table for the normal distribution. For a margin of error at 98%, you get for Z:
Z = 2.326
Replace the previous values of the parameters into the formula for the margin of error (confidence interval):
[tex]\begin{gathered} 33\pm(2.326)\frac{2}{\sqrt[]{31}}= \\ 33\pm0.83 \end{gathered}[/tex]Then, the margin of error is:
(33.00 - 0.83 , 33.00 + 0.83) = (32.17 , 33.83)
Calculate the slope of the given line using either the slope formula m = y 2 − y 1 x 2 − x 1 or by counting r i s e r u n . Simplify your answer. You can choose your method.
The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with the points (-8, 3) and (0,1) we get:
[tex]m=\frac{1-3}{0-_{}(-8)}=\frac{-2}{8}=-\frac{1}{4}[/tex]Use the strategy to simplify 4/576Write the prime factorization of the radicand.442834O42/2832O 4./283²O4. 2882
To simplify the fraction we will need to facto
Cheng-Yu ordered a book that cost $24 from an online store. Hertotal with the shipping charge was $27. What was the percent ofmarkup charged for shipping?
Given:
Cost of book = $24
Total cost of book (shipping charge inclusive) = $27
The shipping charge is:
Total cost - cost of book = $27 - $24 = $3
The shipping charge is $3
To find the percentage markup charged for shipping, use the formula:
[tex]\frac{ship\text{ charge}}{Total\text{ cost}}\ast100[/tex][tex]\frac{3}{27}\ast100\text{ = }0.111\text{ }\ast\text{ 100 = }11.1percent^{}[/tex]Therefore, the percent of markup charged for shipping is 11.1%
ANSWER:
11.1%
sin(theta) = .754
What is theta
Answer: I believe it is representing the angular position of a vector
In short, it is a symbol to represent a measured angle.
What is the probability that a randomly chosen marble is red or small?
We have the next formula
[tex]P\mleft(RorS\mright)=P\mleft(R\mright)+P\mleft(S\mright)-P\mleft(RandS\mright)[/tex]P(R)=0.7
P(S)=0.9
P(RandS)=0.6
The probability that randomly chosen marbñe is red or small is
[tex]\begin{gathered} \\ P(RorS)=0.7+0.9-0.6=1 \end{gathered}[/tex]Find the exact value of the expression. No decimal answers. Show all work.Hint: Use an identity to expand the expression.
Given the expression:
[tex]\cos (\frac{\pi}{4}+\frac{\pi}{6})[/tex]You can expand it by using the following Identity:
[tex]\cos \mleft(A+B\mright)\equiv cos(A)cos(B)-sin(A)sin(B)[/tex]You can identify that, in this case:
[tex]\begin{gathered} A=\frac{\pi}{4} \\ \\ B=\frac{\pi}{6} \end{gathered}[/tex]Then, you can expand it as follows:
[tex]\cos (\frac{\pi}{4}+\frac{\pi}{6})=cos(\frac{\pi}{4})cos(\frac{\pi}{6})-sin(\frac{\pi}{4})sin(\frac{\pi}{6})[/tex]By definition:
[tex]\cos (\frac{\pi}{4})=\frac{\sqrt[]{2}}{2}[/tex][tex]\cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2}[/tex][tex]\sin (\frac{\pi}{4})=\frac{\sqrt[]{2}}{2}[/tex][tex]\sin (\frac{\pi}{6})=\frac{1}{2}[/tex]Then, you can substitute values:
[tex]=(\frac{\sqrt[]{2}}{2})(\frac{\sqrt[]{3}}{2})-(\frac{\sqrt[]{2}}{2})(\frac{1}{2})[/tex]Simplifying, you get:
[tex]\begin{gathered} =(\frac{\sqrt[]{2}}{2})(\frac{\sqrt[]{3}}{2})-(\frac{\sqrt[]{2}}{2})(\frac{1}{2}) \\ \\ =\frac{\sqrt[]{6}}{4}-\frac{\sqrt[]{2}}{4} \end{gathered}[/tex][tex]=\frac{\sqrt[]{6}-\sqrt[]{2}}{4}[/tex]Hence, the answer is:
[tex]\frac{\sqrt[]{6}-\sqrt[]{2}}{4}[/tex]when a graph is a smooth curve it means that there is not a definite law connecting the two quantities which are plotted true or false
Question:
When a graph is a smooth curve it means that there is not a definite law connecting the two quantities which are plotted.
Solution:
a smooth curve is by definition a function, so by definition of a function, we have that there is a definite law connecting the two variables (quantities).
Answer: false.
Identify the vertex of the function below.f(x) - 4= (x + 1)2-onSelect one:O a. (-4,1)O b.(1,-4)O c. (-1,-4)O d.(-1,4)
The standard equation of a vertex is given by:
[tex]f(x)=a(x-h)^2+k[/tex]where (h,k) is the vertex.
Comparing with the given equation after re-arranging:
[tex]f(x)=(x+1)^2+4[/tex]The vertex of the function is (-1, 4)
find the coordinates of a point on a circle with radius 18 corresponding to an angle of 190°
The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).
What is transforming coordinates?
Polar coordinates (r,θ) are transformed into Cartesian coordinates (x, y) using the formulas x = r cos(θ), and y = r sin(θ).
This problem is under the concept of transforming polar coordinates (r,θ) to cartesian coordinates (x, y).
For this problem the polar coordinates are r = 18 and θ = 190°.
Convert these polar coordinates into a cartesian coordinates as,
x = r cos(θ) = 18 cos(190°) = -17.73
y = r sin(θ) = 18 sin(190°) = -3.13
The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).
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Me.Hoffman has a doorstop in his classroom shaped like a triangular prism shown
- To determine the perimeter of the base, consider that the length is 5 in and the width is the same as the width of the top face of the prism, that is, 2 in. Then, the perimeters is:
P = 2l + 2w
w = 2 in
l = 5 in
P = 2(5 in) + 2(2 in)
P = 10 in + 4 in
P = 14 in
- The height of the doorstop is 1.2 in
- The area of the base is:
A = wl
A = (2 in)(5 in)
A = 10 in²
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.C=111.1°a=7.1mb=9.6mOption 1: No triangle satisfies the given conditions.Option 2: c=19.6m, A=26.8°, B=42.1°Option 3: c=16.7m, A=30.8°, B=38.1°Option 4: c=13.8m, A=28.8°, B=40.1°
Answer: Option 4: c=13.8m, A=28.8°, B=40.1°
Explanation:
From the information given,
the known sides are a = 7.1 and b = 9.6
the known angle is C = 111.1
We would find side c by applying the cosine rule which is expressed as
c^2 = a^2 + b^2 - 2abCosC
By substituting the given values into the formula,
c^2 = 7.1^2 + 9.6^2 - 2 x 7.1 x 9.6Cos111.1
c^2 = 50.41 + 92.16 - 136.32Cos111.1
c^2 = 142.57 - 136.32Cos111.1 = 191.6448
c = √191.6448 = 13.8436
c = 13.8
To find angle A, we would apply the sine rule which is expressed as
a/SinA = c/SinC
Thus,
7.1/SinA = 13.8436/Sin 111.1
By cross multiplying, we have
13.8436SinA = 7.1Sin111.1
SinA = 7.1Sin111.1/13.8436 = 0.4785
Taking the sine inverse of 0.4785,
A = 28.8
Recall, the sum of the angles in a triangle is 180. Thus,
A + B + C = 180
28.8 + B + 111.1 = 180
139.9 + B = 180
B = 180 - 139.9
B = 40.1
Option 4: c=13.8m, A=28.8°, B=40.1°
