we have the expression
[tex]\frac{9}{7}\div\frac{2}{3}=\frac{9*3}{2*7}=\frac{27}{14}[/tex]The answer is 27/1425. Ally is making a replica of a building that is at ascale of 4 m. to 3 in.The model is 84 in tall. How tallis the building?
We know that in our model 3 inches represent 4 m, to determine how tall the building is with the knowledge that the model is 84 in we can use a rule of three:
[tex]\begin{gathered} 4\text{ m}\rightarrow3\text{ in} \\ x\rightarrow84\text{ in} \end{gathered}[/tex]then:
[tex]x=\frac{84\cdot4}{3}=112[/tex]Therefore, the building is 112 meters tall.
There are a total of 50 questions worth 130 points on Chenille's history exam. Someof the questions are worth five points each, and the other questions are worth twopoints each. Which of the following systems of equations could be used todetermine F, the correct number of five point questions, and t, the correct numberof two point questions answered correctly?
Since F represents the number of five point questions and t represents the number of two point questions, and the total amount of questions is 50, then:
[tex]F+t=50[/tex]F correct answers would give us 5F points, and t correct answers would give us 2t points, for a total of 130 points. Then:
[tex]undefined[/tex]Why aren't there infinitely many semi-regular tessellations?
Regular tessellations use identical regular polygons to fill the plane. The polygons must line up vertex to vertex, edge to edge, leaving no gaps.
Semi-regular tessellations have two properties:
• They are formed by two or more types of regular polygon, each with the same side length
,• Each vertex has the same pattern of polygons around it.
There are 8 semi-regular tessellations in total. We know each is correct because again, the internal angle of these shapes add up to 360.
For example, for triangles and squares, 60 × 3 + 90 × 2 = 360.
(credited)
I want to select average students . If the mean score on the qualifying test is 43.2 and the standard deviation is 8.6. find the score that cutt off the middle 50 percent of all scores
The score that cutt off the middle 50 percent of all scores is 43.2
Explanations:For a normal distribution, the normal value is the mean
It divides the curve in 50%-50%
Mean score, μ = 43.2
Standard Deviation, σ = 8.6
P(X≤a)=0.5
Use Z =(X-μ)/δ ~N(0;1)
b =(a-μ)/σ
P(Z≤b)=0.5
The value is b=0 (the mean for Z)
a=(b*σ)+μ
a=(0*8.6)+43.2
a=43.2
Therefore, the score that cutt off the middle 50 percent of all scores is 43.2
Evaluate the determinant.7 3 28 2 76 8 5A) 212B) -464© -212D860
| 7 3 2|
8 2 7
6 8 5
7(10 - 56) - 3(40 - 42) + 2(64 - 12)
7(-46) - 3(-2) + 2( 52)
-322 + 6 + 104
= -212
A small pool can hold 72.5 gallons of water . The pool is currently 3/4full how many gallons are in the pool ?
If we have that the pool is currently 3/4 full, we need to multiply this fraction by the total the small pool can hold. That is (with no units):
[tex]T=72.5\Rightarrow\frac{3}{4}T=\frac{3}{4}\cdot72.5=54.375[/tex]Therefore, the pool currently has 54.735 gallons (3/4 of its total capacity) (we multiply 3 times 72.5, and then we divide this result by 4).
Which rule describes the transformation used tocreate GHI from DEF?A. (x,y) → (-y, x)B. (x,y) → (-X, -y)C. (x,y) → (x, -y)D. (x,y) → (y, -x)
Explanation:
We can see that the points are mapped as:
[tex]\begin{gathered} G(5,-1)\rightarrow D(-5,1) \\ H(5,2)\rightarrow E(-5,-2) \\ I(-1,2)\rightarrow F(1,-2) \end{gathered}[/tex]Therefore the coordinates of each point change to its opposite.
Answer:
The rule is:
B. (x, y) → (-x, -y)
write an inequality for the graph using x for the variable.
Given:
There are given that the inequality graph.
Explanation:
In the given question, there are given number line graphs, in which the arrow has been shown in a negative direction.
Also,
There are given that the number 2 has not been included in the given graph.
So,
The inequality will be:
[tex]x<2[/tex]Final answer:
Hence, the inequality is shown below:
[tex]x\lt2[/tex]
Which of the following is equal to ? 1/5^-2
25
1) Let's evaluate this expression making use of one exponent property:
[tex](\frac{1}{5})^{-2}=(\frac{5}{1})^2=(5)^2=25[/tex]2) Note that negative exponents reciprocate the base.
3) Hence, the answer is 25
Convert 15 gal to quarts
The conversion rate for a gallon to quart is given as
[tex]1\text{ ga }\to4\text{ quart}[/tex]This means that to get the number of quarts in a given measure in gallons, we multiply the number by 4.
The question asks us to convert 15 gallons to quarts.
This can be calculated as
[tex]\begin{gathered} 15\times4 \\ =60\text{ quarts} \end{gathered}[/tex]Therefore,
[tex]15\text{ gal }\to60\text{ quarts}[/tex]Given the functions:Evaluate the function for . Write your answer in exact simplified form. Select "Undefined" if applicable.
Given:
[tex]\begin{gathered} f(x)\text{ = x}^3\text{ + 6x} \\ g(x)\text{ = }\sqrt{2x} \end{gathered}[/tex]Explanation:
The required function is given as,
[tex]undefined[/tex]Describe how you can use the factors of a quadratic function to find its zeroes. (Please try to answer it specifically)
Oce we have the factors, we must equal each factor to zero, then we solve for x to find the zeroes of the equation.
Ex.
(x - 3)(x + 2) = 0
the factors are (x - 3) and (x + 2)
Equal to zero
x - 3 = 0 x + 2 = 0
Solve for x
x = 3 x = -2 and these are the zeroes of the
equation.
Answer:
To find de ceros you can take each factor and use the 0 product property, then you solve to find the value of the cero.
107. Cranky mower To start her old lawn mower, Rita has
S to pull a cord and hope for some luck. On any partic-
ular pull, the mower has a 20% chance of starting.
(a)
Find the probability that it takes her exactly 3 pulls to
start the mower.
(b) Find the probability that it takes her more than 6
pulls to start the mower.
108. 1-in-6 wins Alan decides to use a different strategy for
the 1-in-6 wins game of Exercise 90. He keeps buying
one 20-ounce bottle of the soda at a time until he gets
a winner.
Find the probability that he buys exactly 5 bottles.
(b) Find the probability that he buys at most 6 bottles.
Show
your work.
According to the binomial distribution, there is a 0.128 = 12.8% chance that it will take her precisely 3 pushes to start the mower.
she will need to start the mower more than 10 times.There are just two possible results for each pull. The lawnmower either starts or it doesn't. The binomial distribution is employed to answer this question since the likelihood that the mower will start on a pull is independent of all other pulls.Binomial distribution of probabilitiesThe conditions are: x is the total number of victories.The number of trials is n.P represents the likelihood that a trial will be successful.It has a 20% chance of starting on any given pull, therefore
Item
a:This probability is P(X = 0) when n = 2, multiplied by 0.2, which is the probability that it starts on the third, and it is that it doesn't start on the first two. Hence:
It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.
Item b:When n = 10, this probability is none on the first 10 and is hence P(X = 0):
Her chances of needing more than 10 pushes to start the mower are 0.1074, or 10.74%.
It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.
Item b:On the first, there is no chance in this.
learn more about this theorem click here:
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Part 1 - FlooringFor the most part, the floors in Rachel's new house are in good shape. However, there are a couple of rooms that Rachel wants to redo right away. She plans to put new carpet in the family room and living room, and fresh hardwood floors in the foyer and kitchen. She also needs to put a new tile floor in the breakfast nook and mud room. Rachel (with your help) plans to install all the flooring herself, so there are no labor costs. However, she does need to buy the materials.Rachel has already scoped out the local home improvement store and priced out the cost of each material. She found that the carpet she wants will cost $1.80 per square foot, the hardwood flooring will cost $4.50 per square foot, and the tiles will cost $2.30 per square foot.a. How many square feet of carpet does Rachel need?b. How many square feet of hardwood does Rachel need?c. How many square feet of tile does Rachel need?d. How much will the total cost of materials for the re-flooring project be?
ANSWERS
a. 863.08 ft²
b. 474 ft²
c. 249 ft²
d. $4,259.24
EXPLANATION
Given:
• Rooms with ,carpet,: Family room and living room
,• Rooms with ,hardwood,: kitchen and foyer
,• Rooms with ,tiles,: breakfast nook and mudroom
• Cost ,carpet,: $1.80 per square foot
,• Cost ,hardwood,: $4.50 per square foot
,• Cost ,tiles,: $2.30 per square foot
First, we have to find the area of each of the mentioned rooms,
a. The family room is in the shape of a square whose sides are all 20 feet and a semicircle whose diameter is 20 feet. The area of the family room is the sum of the areas of each of these figures,
[tex]A_{family-room}=(20ft\cdot20ft)+(\frac{1}{2}\cdot\pi\cdot(20ft/2)^2)[/tex]As shown above, the area of the semicircle is half the area of the full circle with the same diameter. Solve,
[tex]A_{family-room}\approx(400ft^2)+(157.08ft^2)=557.08ft^2[/tex]The living room is in the shape of a rectangle with side lengths 15ft and 22ft, but a right triangle is cut out from the corner. The area of the living room is the area of the mentioned rectangle minus the area of the triangle of the corner,
The side lengths of the triangle are 15ft - 9ft = 6ft and 22ft - 14ft = 8ft. The area of the triangle is,
[tex]A_{triangle}=\frac{6ft\cdot8ft}{2}=24ft^2[/tex]So, the area of the living room is,
[tex]A_{living-room}=(22ft\cdot15ft)-24ft^2=330ft^2-24ft^2=306ft^2[/tex]The area that Rachel wants to cover with a new carpet is,
[tex]A_{carpet}=A_{family-room}+A_{living-room}=557.08ft^2+306ft^2=863.08ft^2[/tex]Hence, the area to be covered with carpet is 863.08 ft².
b. The kitchen is a rectangle with dimensions 24 ft and 15 ft, so its area is,
[tex]A_{kitchen}=24ft\cdot15ft=360ft^2[/tex]The foyer is in the shape of a rectangle with dimensions 10ft and 15ft. However, assuming that the stairs won't be covered with hardwood and that they cover that part of the foyer's floor, to find the area we have to subtract the area the stairs occupy in that room.
The rectangle where the stairs are has dimensions 9ft and (10ft - 6ft ) = 4ft. The area of the Foyer is,
[tex]A_{foyer}=(10ft\cdot15ft)-(9ft\cdot4ft)=(150ft^2)-(36ft^2)=114ft^2[/tex]The area Rachel wants to be covered by hardwood is the sum of the two,
[tex]A_{hardwood}=A_{kitchen}+A_{foyer}=360ft^2+114ft^2=474ft^2[/tex]Hence, the area to be covered with hardwood is 474 ft².
c. The mudroom is in the shape of a rectangle with dimensions 15 ft and 7 ft, so its area is,
[tex]A_{mudroom}=15ft\cdot7ft=105ft^2[/tex]The breakfast nook is in the shape of a trapezoid, where the height is 8ft and the lengths of the bases are 24ft and 12ft. Its area is,
[tex]A_{breakfast-nook}=\frac{(12ft+24ft)}{2}\cdot8ft=\frac{36ft}{2}\cdot8ft=18ft\cdot8ft=144ft^2[/tex]The area Rachel wants to cover with tiles is the sum of these two areas,
[tex]A_{tiles}=A_{mudroom}+A_{breakfast-nook}=105ft^2+144ft^2=249ft^2[/tex]Hence, the area to be covered with tiles is 249 ft².
d. Finally, we have to find the cost of flooring with each material,
[tex]Costs=\begin{cases}C_{carpet}=A_{carpet}\cdot p_{carpet}=863.08ft^2\cdot1.80=1,553.54 \\ C_{hardwood}=A_{hardwood}\cdot p_{hardwood}=474ft^2\cdot4.50=2,133 \\ C_{tiles}=A_{tiles}\cdot p_{tiles}=249ft^2\cdot2.30=572.70\end{cases}[/tex]The total cost of the project is the sum of the three,
[tex]C_{project}=C_{carpet}+C_{hardwood}+C_{tiles}=1,553.54+2,133+572.70=4,259.24[/tex]Hence, the total cost of the re-flooring project will be $4,259.24.
Wich expression is equivalent to a+(c+7)
Given the expression:
[tex]a+(c+7)[/tex]To determine an equivalent expression, the first step is to open the bracket.
Therefore:
[tex]undefined[/tex]Which of the following things is not contained at the plane B?
Related with the picture and your question, you should notice that an element is not contained in a set, that in your case is the plane B, when any of its points is outside of this one.
Then by the picture we could notice that the line q is not contained at the plane B, because the point G is inside q but it is not in B.
Match the equation in Column I with the correct description in Column II
As given by the question
There are given that the equations:
Now,
According to the given question,
The correct matching values are;
[tex]\begin{gathered} (a)\rightarrow E \\ (b)\rightarrow D \\ (c)\rightarrow C \\ (d)\rightarrow B \\ (e)\rightarrow A \end{gathered}[/tex]MAH ~ WCF what is the value of x?picture will be sent in messages
Since both triangles are congruent, the proportion between their sides is the same, so we can write:
[tex]\frac{MA}{MH}=\frac{WC}{WF}\Longrightarrow\frac{62}{92}=\frac{15.5}{x}\Longrightarrow62x\text{ = 92 }\cdot\text{ 15.5 = }1426\Longrightarrow\text{ x = 1426/62 =}23[/tex]x = 23
Answer:
x = 23
Express the following as an algebraic function of x.sin(sin-'(x) – cos-'(x))
Hello there. To solve this question, we'll have to remember some properties about inverse trigonometric functions.
Given the expression:
[tex]\sin (\sin ^{-1}(x)-\cos ^{-1}(x))[/tex]We want to express it as an algebraic function of x.
For this, imagine the following triangle:
Now, we find the missing leg of the triangle applying Pythagoras theorem:
[tex]\begin{gathered} 1^2=x^2+?^2 \\ 1-x^2=?^2 \\ ?^{}=\sqrt[]{1-x^2} \end{gathered}[/tex]Now, finding the sine and cosine of the angles alpha and beta, we get:
First, remember the sine of an angle is equal to the ratio between the opposite side to the angle and the hypotenuse of the triangle. The cosine of the same angle is equal to the ratio between the adjacent side to the angle and the hypotenuse of the triangle.
Therefore, we have:
[tex]\begin{gathered} \sin (\alpha)=\frac{x}{1}=x \\ \cos (\beta)=\frac{x}{1}=x \\ \sin (\beta)=\frac{\sqrt[]{1-x^2}}{1}=\sqrt[]{1-x^2} \\ \cos (\alpha)=\frac{\sqrt[]{1-x^2}}{1}=\sqrt[]{1-x^2} \end{gathered}[/tex]This means that:
[tex]\begin{gathered} \alpha=\sin ^{-1}(x) \\ \beta=\cos ^{-1}(x) \end{gathered}[/tex]Now, the expression we had earlier turns into:
[tex]\sin (\alpha-\beta)[/tex]For this, we'll use the angle sum formula:
[tex]\sin (u-v)=\sin (u)\cos (v)-\sin (v)\cos (u)[/tex]Which gives us:
[tex]\sin (\alpha)\cos (\beta)-\sin (\beta)\cos (\alpha)_{}[/tex]Plugging the results we got earlier, this is simply:
[tex]x\cdot x-\sqrt[]{1-x^2}\cdot\sqrt[]{1-x^2}[/tex]As x > 0, because we're using it as a triangle side (but it could be negative considering inverse sine and cosine as functions), we get:
[tex]\begin{gathered} x^2-(1-x^2) \\ x^2-1+x^2 \\ 2x^2-1 \end{gathered}[/tex]Devin owes $26,000 in students loans for college. The interest rate is 8.75% and the loan will be paid off over 15 years. How much will Devin pay altogether?$60,125$72,123$3,412,500$8,125
Answer:
$60,125
Explanation:
We'll use the below formula to determine how much Devin will pay altogether;
[tex]A=P(1+rt)[/tex]where A = final amount = ?
P = principal amount = $2600
r = interest rate in decimal = 8.75/100 = 0.0875
t = time in years = 15 years
Substituting the given values into our formula and solving for A, we'll have;
[tex]\begin{gathered} A=26000(1+0.0875\times15) \\ =26000(2.3125) \\ =60,125 \end{gathered}[/tex]Therefore, Devin will pay $60,125 altogether.
The Fishers ate out at a restaurant and paid a total of $68.22, including the tip. If the Fishers tipped 20%, what was the cost of the meal?
Explanation:
Multiply 68.22 by 1.2 to get 81.864 or $81.86
find the solution to the system of equations given below x=-4 5x+4y=-16
We have the following system of equations:
[tex]\begin{gathered} x=-4\ldots(A) \\ 5x+4y=-16\ldots(B) \end{gathered}[/tex]Solving by substitution method.
If we substitute equation A into equation B, we get
[tex]5(-4)+4y=-16[/tex]since 5(-4)= -20, we have
[tex]-20+4y=-16[/tex]If we move -20 to the right hand side as +20, we obtain
[tex]\begin{gathered} 4y=-16+20 \\ \end{gathered}[/tex]since -16+20=20-16 = 4, we get
[tex]4y=4[/tex]and finally, y is equal to
[tex]\begin{gathered} y=\frac{4}{4} \\ y=1 \end{gathered}[/tex]Since equation A tells us that x=-4, the solution of the system is
[tex]\begin{gathered} x=-4 \\ y=1 \end{gathered}[/tex]find the value of x then find the measure of both angles
According to the given graph, the angles are linear pairs because they are on a straight angle, so the must sum 180°. Having said that, we express the following.-
[tex](4x+20)+(x-10)=180[/tex]We reduce like terms
[tex]5x+10=180[/tex]Then, we subtract 10 on each side.
[tex]\begin{gathered} 5x+10-10=180-10 \\ 5x=170 \end{gathered}[/tex]At last, we divide the equation by 5.
[tex]\begin{gathered} \frac{5x}{5}=\frac{170}{5} \\ x=34 \end{gathered}[/tex]We use this value to find the angles.
[tex]\begin{gathered} 4x+20=4(34)+20=136+20=156 \\ x-10=34-10=24 \end{gathered}[/tex]Therefore, x is equal to 34, and the angles are 156° and 24°.Question 4 please . Using a graphing utility (geogebra) to graph the function
Problem N 4
we have the function
[tex]f\mleft(x\mright)=x^4-3x^2+2x-1[/tex]Interval (-2,2)
using a graphing tool
Local minimum value at (1,-1)
Local maximum value at (0.37,-0.65)
Increasing functionIntervals (-1.37,0.37) U (1, infinite)
Decreasing functionIntervals (-infinite, -1.37) U (0.37,1)
4p-9=2p+21solve the equation
The given equation is,
[tex]4p-9=2p+21[/tex]The equation can be solved as,
[tex]\begin{gathered} 4p-9=2p+21 \\ 4p-2p=21+9 \\ 2p=30 \\ p=\frac{30}{2} \\ p=15 \end{gathered}[/tex]Thus, the requried value of p is 15.N
suppose s and t are mutually exclusive events. find p (s or t) if p(s)=29% and p(t)=49%
Given:
P(s) = 29%
P(t) = 49%
For us to be able to determine P(S or T), we will be using the following formula:
[tex]\text{ P\lparen S or T\rparen = P\lparen S\rparen + P\lparen T\rparen}[/tex]We get,
[tex]\text{ P\lparen S or T\rparen = 29\% + 49\% = 78\%}[/tex]Therefore, the answer is CHOICE A: 78%
Find the missing angle:
FRT=________
Using the secant-secant theorem,
[tex]m\angle FRT=\frac{140^{\circ}-50^{\circ}}{2}=\boxed{45^{\circ}}[/tex]
Answer: 45 degrees
Step-by-step explanation:
Using the secant-secant theorem
Evaluate each complex number.
√-49=
√-48=
√-5 x √-8=
Answer:
Step-by-step explanation:
1-58. Copy the number line below and place the following probabilities on it
Considering the following:
a) 1/4 chance that you will be the team member who gets supplies tomorrow
b) A 25% chance of snow tomorrow
c) A 0.8 probability of eating vegetables with dinner
d) P(blue marble) = 5/8
e) A 0.10 probability that it will be 85º on Saturday
Then:
1/4 =0.25 and 25% represents the same amount
A 0.8 probability is equivalent to 80% of probability of eating vegetables.
P (blue marble) = 5/8 5: 8 =0.625 what is equivalent to 62.5 if we multiply it by 100
And Finally 0.10 probability is a probability of 10% of 85ºF on Saturday
Placing all this values on a line by increasing order
Roughly sketched.
Remember that Probability is always represented within an interval between 0 and 1
Identify the units you would expect for the given quantity.The price of a bottle of French perfume, found by multiplyingthe unit price of the perfume in euros per milliliter by thevolume of the bottle in milliliters.
Given:
The price of a bottle of French perfume, found by multiplying
the unit price of the perfume in euros per milliliter by the volume of the bottle in milliliters.
the unit of the unit price is: euros per milliliter
And the unit of the volume is: milliliters
By multiplying the two units: the unit of the result will be euros