how do you solve 5y+26=4y-56?

Answers

Answer 1

You must isolate y by putting like terms together.

5y+26=4y-56
Subtract 26 from both sides
5y=4y-82
Subtract 4y from both sides
y= -82

Check:
Substitute the answer in equation
5y+26=4y-56
5(-82)+26=4(-82)-56
-410+26= -328-56
-384 = -384

Hope this helps! :)

Related Questions

Suppose that △ XYZ is isosceles with base YZ . Suppose also that = m ∠ X + 2 x 52 ° and = m ∠ Y + 4 x 34 ° . Find the degree measure of each angle in the triangle.

Answers

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How do I solve this?Help me please!!!

Answers

Given:
Ship M travels E 15 km, then N35E 27 km. Its sub travels down 48° 2 km from that location.

Ship F travels S75E 20 km, then N25E 38 km. The treasure is expected to be at this location 2.18° below horizontal from the port.

Find:
1a. The distance from port to Ship M
1b. The distance from port to the sub
1c. The angle below horizontal from the port to the sub

2a. The distance from port to Ship F
2b. The depth to the expected treasure location
2c. The distance from port to the expected treasure location

Solution:
It can be helpful to draw diagrams. See the attached. The diagram for depth is not to scale.

There are several ways this problem can be worked. A calculator that handles vectors (as many graphing calculators do) can make short work of it. Here, we will use the Law of Cosines and the definitions of Tangent and Cosine.

Part 1
1a. We are given sides 15 and 27 of a triangle and the included angle of 125°. Then the distance (m) from the port to the ship is given by the Law of Cosines as
m² = 15² +27² -2·15·27·cos(125°) ≈ 1418.60
m ≈ 37.66
The distance from port to Ship M is 37.66 km.

1b. The distance just calculated is one side of a new triangle with other side 2 km and included angle of 132°. Then the distance from port to sub (s) is given by the Law of Cosines as
s² = 1418.60 +2² -2·37.66·2·cos(132°) ≈ 1523.41
s ≈ 39.03
The distance from port to the sub is 39.03 km.

1c. The Law of Sines can be used to find the angle of depression (α) from the port. That angle is opposite the side of length 2 in the triangle of 1b. The 39.03 km side is opposite the angle of 132°. So, we have the relation
sin(α)/2 = sin(132°)/39.03
α = arcsin(2·sin(132°)/39.03) ≈ 2.18°
The angle below horizontal from the port to the sub is 2.18°.

Part 2
2a. We are given sides 20 and 38 of a triangle and the included angle of 100°. Then the distance (f) from the port to the ship is given by the Law of Cosines as
f² = 20² +38² -2·20·38·cos(100°) ≈ 2107.95
f ≈ 45.91
The distance from port to Ship F is 45.91 km.

2b. The expected treasure location is at a depth that is 2.18° below the horizontal from the port. The tangent ratio for an angle is the ratio of the opposite side (depth) to the adjacent side (distance from F to port), so we have
tan(2.18°) = depth/45.91
depth = 45.91·tan(2.18°) ≈ 1.748
The depth to the expected treasure location is 1.748 km.

2c. The distance from port to the expected treasure location is the hypotenuse of a right triangle. The cosine ratio for an angle is the ratio of the adjacent side to the hypotenuse, so we have
cos(2.18°) = (port to F distance)/(port to treasure distance)
(port to treasure distance) = 45.91 km/cos(2.18°) ≈ 45.95
The distance from the port to the expected treasure is 45.95 km.

Part 3
It seems the Mach 5 Mimi is the ship most likely to have found the treasure. That one seems ripe for attack. Its crew goes to a location that is 2.18° below horizontal. The crew of the FTFF don't have any idea where they are going. (Of course, the pirate ship would have no way of knowing if it is only observing surface behavior.)

4 friends equally share 1/3 of a pan of brownies. How much of the whole pan of brownies does each friend get?

Answers

the answer will be 1/12 of

The volume of a cylinder is 224π cubic centimeters and its radius is 4 centimeters. What is the height of the cylinder? Enter your answer in the box.

Answers

Put the given information into the formula and solve for the variable of interest.
.. V = π*r^2*h
.. 224π = π*4^2*h
.. 224π/(16π) = h = 14

The height of the cylinder is 14 cm.

_____
You have not provided a box for me to enter my answer. (Please omit such directions.)

The height of the cylinder is 14 centimetres.

To find the height of the cylinder, we use the formula for the volume of a cylinder, which is given by [tex]$ V = \pi r^2 h $,[/tex] where V is the volume, r is the radius, and h is the height.

Given that the volume V is [tex]224\pi[/tex] cubic centimetres and the radius r is 4 centimetres, we can substitute these values into the formula to solve for the height h:

[tex]\[ 224\pi = \pi (4)^2 h \][/tex]

Simplifying the equation by dividing both sides [tex]$ \pi $ and $ (4)^2 $,[/tex]we get:

[tex]\[ \frac{224\pi}{\pi \cdot 16} = h \][/tex]

[tex]\[ \frac{224}{16} = h \][/tex]

[tex]\[ 14 = h \][/tex]

Therefore, the height h of the cylinder is 14 centimetres.

how dpyou find the area of a trapizoid

Answers

It usually works to use the formula for the area of a trapezoid.
A = (1/2)×(b₁ +b₂)×h
where b₁ and b₂ are the lengths of the parallel bases, and h is the height (the perpendicular distance between the bases)

_____
This is one of several area formulas it pays to memorize.

Answer:

add the parallel sides and divide by 2

then multiply it by the perpendicular side so

Step-by-step explanation:

A=side one+side two x2

Luke purchased a motorcycle for $8,765. It depreciates about 5.3% each year. What is the value of the motorcycle after five years?

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &8765\\ r=rate\to 5.3\%\to \frac{5.3}{100}\to &0.053\\ t=\textit{elapsed time}\to &5\\ \end{cases} \\\\\\ A=8765(1-0.053)^5\implies A=8765(0.947)^6[/tex]

To find the number of centimeters in 10 inches, multiply the number of inches given (10) by _____.

3.04

2.54

2.78

2.44

Answers

we have that 1 in----- 2.54 cm
10 in--------X
x=10*2.54=25.4 cms

the answer is 2.54 cms

what you must do for this case is to know the conversion of inches to centimeters:
1 inch = 2.54 centimeters
We can make the following rule of three:
1 ---> 2.54
10 ----> x
Clearing x:
x = (10/1) * (2.54)
x = 25.4 cm
Answer:
multiply the number of inches given by
2.54

the average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes with a standard deviation of 3.6 minutes assume the variable is normally distributed what is the probability that a patron Will Wait less than 18 minutes or more than 25 minutes

Answers

Look it up on google

To determine the probability of a patron waiting less than 18 minutes or more than 25 minutes at a restaurant, we calculate the Z-scores for each time, look up the corresponding probabilities in a standard normal distribution table, and add the probabilities together.

To find the probability that a patron will wait less than 18 minutes or more than 25 minutes at a restaurant with an average waiting time of 23.5 minutes and a standard deviation of 3.6 minutes, assuming a normal distribution, we need to calculate two separate probabilities and then add them together.

First, we calculate the Z-score for 18 minutes, which is (18 - 23.5) / 3.6. Then, we find the corresponding probability from the standard normal distribution table. This gives us the probability of waiting less than 18 minutes.

Secondly, we calculate the Z-score for 25 minutes, which is (25 - 23.5) / 3.6. The corresponding probability gives us the probability of waiting more than 25 minutes. However, we want the probability of waiting longer, so we subtract this probability from 1 to find the probability of waiting more than 25 minutes.

Adding both probabilities gives us the total probability of a patron waiting either less than 18 minutes or more than 25 minutes.

Which function has an inverse that is also a function?

Answers

The function that has an inverse that is also a function will have no repeated y-values. The appropriate choice is the third one.
{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

Answer:

C){(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

Step-by-step explanation:

The one-to-one function has inverse where the inverse is also function.

That is, there should be unique output for each input values.

Look at the options, Option C) only has unique output for each input values.

Therefore, the answer C){(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

Hope this will helpful.

Thank you.

Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?

Answers

A)496.30, hope this helped

Question:

Evaluate each expression:

1. 9x + 8y, when x = 4 and y = 5

2. 2x + 8x, when x = 3

3. 4y + 7y, y = 5

4. 10x + 18y, when x = 4 and y = 5

5. x + 8y, when x = 2 and y = 1/4

6. 9x + 8y, when x = 1/3 and y = 1/4

7. 3x + 7y, when x = 8 and y = 4

8. 12x + 16y, when x = 1/4 and y = 5

Answers

1.) 9(4) + 8(5)

36 + 40 = 74

2.) 2(3) + 8(3)

6 + 24 = 30

3.) 4(5) + 7(5)

20 + 35 = 55

4.) 10(4) + 18(5)

40 + 90 = 130

5.) 2 + 8(1/4)

2 + 2 = 4

6.) 9(1/3) + 8(1/4)

3 + 2 = 5

7.) 3(8) + 7(4)

24 + 28 = 52

8.) 12(1/4) + 16(5)

4 + 80 = 84

What is the slope of a line that is perpendicular to the line shown? (0, 2) (3, 0)

Answers

(0, 2) (3, 0)
slope = (2-0)/(0-3) = -2/3

perpendicular lines, slope is opposite and reciprocal

so the slope of a line that is perpendicular to the line is 3/2

answer
3/2

Which system of linear inequalities is represented by the graph?

x – 3y > 6 and y > 2x + 4
x + 3y > 6 and y > 2x – 4
x – 3y > 6 and y > 2x – 4
x + 3y > 6 and y > 2x + 4

Answers

The blue line has a slope of 2 and a y-intercept of +4. Its equation is
y = 2x +4
The shaded area is above the line, so it is the boundary of the inequality
y ≥ 2x + 4

The red dashed line has a slope of -1/3 and a y-intercept of 2. Its equation is
y = -1/3x + 2
The shaded area is above the line, so it is the boundary of the inequality
y > -1/3x + 2
or
x +3y > 6

The graph seems to represent the inequalities
x +3y > 6 and y ≥ 2x +4

Answer:

So the answer is D

Step-by-step explanation:

How do I convert 12 ounces into grams. Please help

Answers

1 oz = 28.35 grams

To find out how many grams equals 12 ounces, multiply 28.35 by 12.
Final answer should be 340.2 grams = 12 oz.

1 ounce equals 28.35 grams so 12 ounces would equal 340.194 grams
Hopefully this helps!
:)

a fish is 12 meters above the surface of the ocean. what is its elevation

Answers

we have that

the level of the surface of the ocean is level zero
therefore
the elevation of the fish is = 0+12=+12 meters (the positive sign tells me that it is above the surface of the ocean)

the answer is 12 meters

which equation represents an exponential function with an initial value of 500

Answers

Your answer would be the third option: f(x) = 500(2)^x

f(x) = 500(2)^x number 3

In this problem we consider an equation in differential form mdx+ndy=0. the equation (4y+(5x^4)e^(?4x))dx+(1?4y^3(e^(?4x)))dy=0 in differential form m˜dx+n˜dy=0 is not exact. indeed, we have m˜y?n˜x= for this exercise we can find an integrating factor which is a function of x alone since m˜y?n˜xn˜= can be considered as a function of x alone. namely we have ?(x)= multiplying the original equation by the integrating factor we obtain a new equation mdx+ndy=0 where m= n= which is exact since my= nx= are equal. this problem is exact. therefore an implicit general solution can be written in the form f(x,y)=c where f(x,y)= finally find the value of the constant c so that the initial condition y(0)=1. c= .

Answers

Taking a wild guess as to what those question marks are supposed to encode... If the ODE is

[tex]\underbrace{(4y+5x^4e^{-4x})_{M(x,y)}\,\mathrm dx+\underbrace{(1-4y^3e^{-4x})}_{N(x,y)}\,\mathrm dy=0[/tex]

then the ODE will be exact if [tex]M_y=N_x[/tex]. We have

[tex]M_y=4[/tex]
[tex]N_x=16y^3e^{-4x}[/tex]

and so indeed the equation is not exact. So we look for an integrating factor [tex]\mu(x,y)[/tex] such that

[tex]\mu M\,\mathrm dx+\mu N\,\mathrm dy=0[/tex]

is exact. In order for this to occur, we require

[tex](\mu M)_y=(\mu N)_x\implies\mu_yM+\mu M_y=\mu_xN+\mu N_x[/tex]
[tex]\implies\mu_yM-\mu_xN=\mu(N_x-M_y)[/tex]

Now if [tex]\mu[/tex] is a function of either [tex]x[/tex] or [tex]y[/tex] alone, then this PDE reduces to an ODE in either variable. Let's assume the first case, so that [tex]\mu_y=0[/tex]. Then

[tex]\mu_x N=\mu(M_y-N_x)\implies\dfrac{\mathrm d\mu}\mu=\dfrac{M_y-N_x}N\,\mathrm dx[/tex]

So in our case we might consider using

[tex]\dfrac{\mathrm d\mu}\mu=\dfrac{4-16y^3e^{-4x}}{1-4y^3e^{-4x}}\,\mathrm dx=4\,\mathrm dx[/tex]
[tex]\implies\displaystyle\int\frac{\mathrm d\mu}\mu=4\int\mathrm dx[/tex]
[tex]\implies\ln|\mu|=4x[/tex]
[tex]\implies\mu=e^{4x}[/tex]

Our new ODE is guaranteed to be exact:

[tex](4ye^{4x}+5x^4)\,\mathrm dx+(e^{4x}-4y^3)\,\mathrm dy=0[/tex]

so we can now look for our solution [tex]f(x,y)=C[/tex]. By the chain rule, differentiating with respect to [tex]x[/tex] yields

[tex]\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dx}+\dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dx}=0[/tex]
[tex]\implies\dfrac{\partial f}{\partial x}+\dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dx}=0[/tex]
[tex]\implies\dfrac{\partial f}{\partial x}\,\mathrm dx+\dfrac{\partial df}{\partial y}\mathrm dy=0[/tex]

Now,

[tex]\dfrac{\partial f}{\partial x}=\mu M=4ye^{4x}+5x^4[/tex]
[tex]\implies f=ye^{4x}+x^5+g(y)[/tex]

Differentiating with respect to [tex]y[/tex] gives

[tex]\dfrac{\partial f}{\partial y}=\mu N[/tex]
[tex]\implies e^{4x}+\dfrac{\mathrm dg}{\mathrm dy}=e^{4x}-4y^3[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy}=-4y^3[/tex]
[tex]\implies g(y)=-y^4+C[/tex]

So the general solution is

[tex]f(x,y)=ye^{4x}+x^5-y^4+C=C[/tex]
[tex]\implies f(x,y)=ye^{4x}+x^5-y^4=C[/tex]

Given that [tex]y(0)=1[/tex], we get

[tex]f(0,1)=1-1^4=0=C[/tex]

so the particular solution is just

[tex]ye^{4x}+x^5-y^4=0[/tex]

Suppose u = f(x, y) with x = r cos θ and y = r sin θ. find ∂u ∂r .

Answers

ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

Weights were recorded for all nurses at a particular hospital, the mean weight for an individual nurse was 135 lbs. with a standard deviation of 15. If 19 nurses are selected at random, find the probability that the mean weight is between 125 and 130 lbs

Answers

[tex][/tex]Given:
population mean, μ =135
population standard deviation, σ = 15
sample size, n = 19

Assume a large population, say > 100,
we can reasonably assume a normal distribution, and a relatively small sample.
The use of the generally simpler formula is justified.

Estimate of sample mean
[tex]\bar{x}=\mu=135[/tex]

Estimate of sample standard deviation
[tex]\s=\sqrt{\frac{\sigma^2}{n}}[/tex]
[tex]=\sqrt{\frac{15^2}{19}}=3.44124[/tex] to 5 decimal places.

Thus, using the normal probability table,
[tex]P(125<X<130)[/tex]
[tex]=P(\frac{125-135}{3.44124}<Z<\frac{130-135}{3.44124})[/tex]
[tex]=P(-2.90593<Z<-1.45297)[/tex]
[tex]=P(Z<-2.90593)=0.0018308[/tex]
[tex]=P(Z<-1.45297)=0.0731166[/tex]

Therefore
The probability that the mean weight is between 125 and 130 lbs
P(125<X<130)=0.0731166-0.0018308
=0.0712858

What is the fifth term of the sequence?

an=5⋅2n−1

Enter your answer in the box.

a5=

Answers

Answer:

The fifth term of the sequence is:

Step-by-step explanation:

We are given the general term([tex]n^{th}[/tex] term) of the sequence as:

an=5.2n-1

We have to find the fifth term

i.e. we have to find the value of an for n=5

a5=5×2×5-1

=50-1

=49

Hence, the fifth term of the sequence is:

math hw..................

Answers

Arc AB = 63 * 2 = 126 degrees

Mia bought 10 1/9 lb of flour. She used 2 3/4 lb of flour to bake a banana cake and some to bake a chocolate cake. After baking two cakes, she had 3 5/6 lb of flour left. How much flour did she use to bake the chocolate cake?

Answers

We know that she started with 10 1/9 pounds and after the two cakes she was left with 3 5/6. So if we subtract what she started with minus what she is left with we will get what she used.

This is easiest done by converting the mixed numbers into improper fractions, finding a common denominator and subtracting (subtract the numerators and keep the denominator) as follows:

[tex]10 \frac{1}{9}-3 \frac{5}{6}= \frac{91}{9}- \frac{23}{6} =\frac{182}{18}- \frac{69}{18}= \frac{113}{18} [/tex]

That's how much flour she spent on both cakes. If we subtract from this what she spent on the banana cake 2 3/4 we will be left with what she used for the chocolate cake.

This is found as follows: [tex] \frac{113}{18} -2 \frac{3}{4} = \frac{113}{18} - \frac{11}{4} = \frac{226}{36} - \frac{99}{36} = \frac{127}{36}=3 \frac{19}{36} [/tex]

She used [tex]3 \frac{19}{36} [/tex] pounds of flour on the chocolate cake.

Mia used [tex]3\frac{19}{36}[/tex] lb of flour to bake the chocolate cake.

Further Explanation

Given:

Total flour [tex]10\frac{1}{9}[/tex] lbs

She used:

[tex]2\frac{3}{4}[/tex] for banana cake

x lbs for chocolate cake

Flour left [tex]3\frac{5}{6}[/tex] lbs

How much flour did she use to bake the chocolate cake?

so the flour that Mia use for banana cake is total flour subtract the flour that she used plus the left over.

x =Total flour - flour for banana cake - left over

[tex]\boxed {= 10\frac{1}{9} - 2\frac{3}{4} - 3\frac{5}{6} } \\[/tex]

I am going to put this into improper fraction

[tex]\boxed { = \frac{91}{9} - \frac{11}{4} - \frac{23}{6} }[/tex]

because the denominator is different, we are going to find the common denominator for 9, 4 and 6 which is 36

[tex]\boxed {= \frac{364-99-138}{36} }\\ \boxed {= \frac{127}{36} }\\\boxed {= 3\frac{19}{36} }[/tex]

So the flour that she use to bake the chocolate cake is [tex]3\frac{19}{36}[/tex] lbs

Learn More

Part to whole relationship https://brainly.com/question/11677654

Math word problem brainly.com/question/997374

Mixed fraction brainly.com/question/745462

Keyword: mixed fraction, subtraction, improper fraction, part to whole relationship

What is the measure of

Answers

<ABC = 1/2(45+75)
<ABC = 120 / 2
<ABC = 60

answer
A. 60

The measure of the angle formed by 2 chords that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs.

m∠ABC = (75+45)/2 = 60°

A box of 25 light bulbs is shipped to a hardware store.when it arrives,four of the bulbs are broken.predict the number of broken light bulbs in an order of 125 bulbs

Answers

First you need to divide 125 / 25 which is 5 then you do subtraction 21 x 5 which is 105, then you subtract again 125 - 105 which is 20, 20 light bulbs will be broken. Or you could have just multiplied 5 by 4 which is the amount of light bulbs that were broken which is a lot easier...

Final answer:

The prediction method for the number of broken light bulbs in an order is based on a proportional relationship. Using the ratio from a smaller sample, it's calculated that an order of 125 light bulbs would result in 20 broken bulbs, assuming the breakage rate stays constant.

Explanation:

Given that 4 out of 25 light bulbs are broken in the initial order, we can predict the number of broken light bulbs in a larger order of 125 bulbs. The ratio of broken bulbs to total bulbs in the initial order is 4 broken bulbs for every 25 bulbs.

To find the predicted number of broken bulbs in a larger order, you multiply the total number of bulbs in the larger order by the ratio of broken bulbs in the smaller order. The calculation for the larger order of 125 bulbs would be:

(4 broken bulbs / 25 total bulbs) × 125 total bulbs in the larger order = 20 broken bulbs

Therefore, if 25 light bulbs yield 4 broken ones, an order of 125 light bulbs is predicted to have 20 broken bulbs, assuming the rate of breakage remains consistent.

What is the least whole number that has exactly 9 factors, including 1 and itself?

Answers

If the whole number has exactly 9 (odd number) factors, it will have to be a perfect square.
All squares of primes have exactly three factors.
So start with perfect squares (skipping perfect squares of primes)
4^2=16 {1,2,4,8,16} 5 factors.
6^2=36 {1,2,3,4,6,9,12,18,36} 9 factors.

Answer: 36 is the least whole number that has exactly 9 factors.

In the 2005 regular season, the Chicago White Sox won 28 more games than the Detroit Tigers. Together, they won a total of 170 games. How many games did each team win?

Answers

Final answer:

In the 2005 regular season, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.

Explanation:

In the 2005 regular season, let's denote the number of games won by the Chicago White Sox as 'x' and the number of games won by the Detroit Tigers as 'y'. We know that the Chicago White Sox won 28 more games than the Detroit Tigers, so we can write x = y + 28.

Together, they won a total of 170 games, so we can write x + y = 170.

Now we can solve the system of equations:

Substitute the value of x from the first equation into the second equation: (y + 28) + y = 170
Combine like terms: 2y + 28 = 170
Subtract 28 from both sides: 2y = 142
Divide by 2: y = 71
Substitute the value of y into the first equation to find x: x = 71 + 28 = 99

Therefore, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.

Final answer:

The Chicago White Sox won 99 games and the Detroit Tigers won 71 games in the 2005 regular season.

Explanation:

To find out how many games each team won, we need to set up a system of equations using the given information. Let x represent the number of games won by the Chicago White Sox and y represent the number of games won by the Detroit Tigers.

We are given two pieces of information:

1. The White Sox won 28 more games than the Tigers, so we have the equation x = y + 28.

2. Together, both teams won a total of 170 games, so we have the equation x + y = 170.

We can use these equations to solve for the values of x and y. Substituting the first equation into the second equation, we get (y + 28) + y = 170. Combining like terms, we have 2y + 28 = 170. Subtracting 28 from both sides, we get 2y = 142. Dividing both sides by 2, we find that y = 71.

Now we can substitute the value of y back into the first equation to find x. x = 71 + 28, so x = 99. Therefore, the Chicago White Sox won 99 games and the Detroit Tigers won 71 games.

#8 surface area please explain

Answers

The problem is asking you to solve for the surface area of the triangular prism. You know that the prism is made up of two triangles and three square surfaces. Adding these surface together, will give you the surface area.

Solving for the surface area:

Surface area of 2 triangles (top and bottom) + Surface area of 3 rectangles (sides)

2 [1/2 (2.6)(3.9)] + [ (4.3)(3.9) + (4.3)(2.6) + (4.3)(5.2) ] = 60.45 cm^2 surface area

a book normally costs $21.50. today it was on sale for 15.05. what percentage discount was offered during the sale?

Answers

To find the discount %, we must use the equation below.

Discounted Price / Original Price = 1 - Discount %

15.05 / 21.5 = 1 - Discount %

Subtract 15.05 / 21.5 from both sides and add Discount % to both sides to get the following equation.

Discount % = 1 - 15.05 / 21.5 = 1 - 0.7 = 0.3 = 30% discounted

Final answer:

To calculate the percentage discount of a book, subtract the sale price from the original price, divide by the original price, and multiply by 100. The detailed calculation shows that the book had a 30% discount during the sale.

Explanation:

The question asks how to calculate the percentage discount of a book that has been reduced from its normal price to a sale price. To find the percentage discount, we subtract the sale price from the original price, and then divide this difference by the original price. Finally, we multiply by 100 to get the percentage.

Step-by-Step Solution:

Calculate the difference in price: $21.50 (original price) - $15.05 (sale price) = $6.45 (amount discounted).Divide the discount by the original price: $6.45 / $21.50.Convert the result to a percentage: ($6.45 / $21.50) × 100 = 30%.

The percentage discount offered on the book during the sale was 30%.

Miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle?

Answers

People will need to go through more than one obstacle at locations 1, 2, and 3 on the course.

let's break it down:

Tires: Appear every sixth of the course.

Cones: Appear every third of the course.

Hurdles: Appear every half of the course.

To find where people need to go through more than one obstacle, we need to find the common multiples of these fractions.

Tires (1/6 of the course):

Locations of tires: 1/6, 2/6, 3/6, 4/6, 5/6, 6/6 (which is the end)

Locations: 1, 2, 3, 4, 5, 6

Cones (1/3 of the course):

Locations of cones: 1/3, 2/3, 3/3 (which is the end)

Locations: 1, 2, 3

Hurdles (1/2 of the course):

Locations of hurdles: 1/2, 2/2 (which is the end)

Locations: 1, 2

Now, let's find where there are overlaps:

Location 1: There's a tire, a cone, and a hurdle.

Location 2: There's a tire and a cone.

Location 3: There's a tire and a cone.

Location 4: There's a tire.

Location 5: There's a tire.

Location 6: There's a tire.

So, people need to go through more than one obstacle at locations 1, 2, and 3.

how many different combinations of 1 odd number and 1 shape are possible

Answers

3 and a Triangle becuase they are both odd numbers or have odd sides.

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