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.
Solve this system of equations by graphing. First graph the equations, and then type the solution.3x+2y=6y=–5/2x+1
System of equations:
[tex]3x+2y=6[/tex][tex]y=-\frac{5}{2}x+1[/tex]The solution of the system of equations using the graph is the coordinate in which both functions collide:
In our function, this occurs in (-2, 6).
Answer: ( -2, 6 )
Label the sides of the right triangle.*2 pointsCaptionless ImageA) Hypotenuse = 8 m, Adjacent = 15 m, Opposite = 17 mB) Hypotenuse = 17 m, Adjacent = 8 m, Opposite = 15 mC) Hypotenuse = 15 m, Adjacent = 17 m, Opposite = 8 mD) Hypotenuse = 17 m, Adjacent = 15 m, Opposite = 8 m
Given:
There are given that the right angle triangle, UVW.
Where,
[tex]\begin{gathered} UV=8m \\ VW=15m \\ UW=17m \end{gathered}[/tex]Explanation:
According to the concept:
The hypotenuse is defined as the longest side in the right-angle triangle.
The perpendicular side is defined by the perpendicular base angle.
And,
The adjacent side is defined by the leg of the right-angle triangle.
Final answer:
Hence, the correct option is D.
which conversion factors are used to multiply to 12m/s to get kilometers per minute A. 1000m over 1kmB. 60S Over 1 minC.1 km over 1000mD.1min over 60s
To convert 12 meter per seconds to kilometer per minute
We need kilometer in the denominator and minute in the denomiator
But 1 km = 1000 m and 60 seconds = 1 minute
12m / s x 60s / 1 min x 1km / 1000m
Hence the correct option is;
B and C
Find the equation of the line. Write the equation of the line in standard form Vertical line through (-1,-1)
Solution
We have the following point given (-1, -1)
The equation of a line is given by:
y= mx+b
For this case since we have a vertical line the equation would be:
x= -1
I need help answering it I don’t know howTo do it
Okay, here we have this:
Considering the provided graph we obtain that:
Recall that the slope is undefined when lines are vertical. So in this case we can see that this description is fulfilled, therefore, finally we obtain that the Type of slope is Undefined
The table below shows the birth months for all 25 students in Mr. Battistini's class.Student Birth MonthsWhat is the probability of selecting a student at random from this class who was NOT bornin June?А. 4%B. 16%C.21%D.84%
Given data:
The given table.
The probability that the student not born in june is,
[tex]\begin{gathered} P(J^{\prime})=1-\frac{4}{25} \\ =\frac{21}{25} \\ =0.84 \\ =84\text{ percent} \end{gathered}[/tex]Thus, the option (D) is correct.
George runs hurdles he clears the hurdles 90% of the time which of the following statements applyGeorge clears the hurdles 9/9George clears the 9/100George clears the hurdles 90 /100George clears the hurdles 90/1000
90% = 90/100
answer is the third one
How much must be deposited today into the following account in order to have 40,000 in 6 years for a down payment on a house? Assume no additional deposits are made.An account with annual compounding and an APR of 7%how much should be deposited today? $(Do not round until the final answer. Then round to the nearest cent as needed.)
The formula to calculate the compound interest is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ Where } \\ A\text{ is the total amount at the end of t years.} \\ P\text{ is the initial amount deposited.} \\ r\text{ is the interest rate.} \\ t\text{ is the time.} \end{gathered}[/tex]From the word problem, we have:
[tex]\begin{gathered} A=40,000 \\ P=? \\ r=7\%=\frac{7}{100}=0.07 \\ n=1\Rightarrow\text{ It was compounded once in a year.} \\ t=6 \end{gathered}[/tex]Then, we can replace the above values in the compound interest formula and solve for P.
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 40,000=P(1+\frac{0.07}{1})^{(1)(6)} \\ 40,000=P(1+0.07)^6 \\ 40,000=P(1.07)^6 \\ \text{ Divide by }1.07^6\text{ from both sides} \\ \frac{40,000}{1.07^6}=\frac{P(1.07)^6}{1.07^6} \\ 26,653.69\approx P \\ \text{ The symbol is read 'approximately'.} \end{gathered}[/tex]AnswerYou should deposit today $26,653.69.
Jungle Gym Print On the new jungle gym there are 4 ladders that lead to a landing. From the landing you can get to the big platform by climbing up either the rope or the fireman's pole How many different ways are there to get to the big platform?
Answer: 12 ways
Total number of ladder = 4
Yo can get to the platform either by climbing up the rope or fire mans hope
We have two options to get to the big platform
[tex]\begin{gathered} ^nP_r\text{ = }\frac{n!}{(n\text{ - r)!}} \\ ^4P_2\text{ = }\frac{4!}{(4\text{ - 2)!}} \\ =\text{ }\frac{4!}{2!} \\ \text{= }\frac{4\text{ x 3 x 2 x 1}}{2\text{ x 1}} \\ =\text{ 4 x 3} \\ \text{= 12 ways} \end{gathered}[/tex]A line passes through (4,3) and (8,6). Another line has a slope of -3/4. The two lines are parallel. *1 pointTrueFalse
ANSWER
False
EXPLANATION
The formula for the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The slope of the first line is:
[tex]m=\frac{3-6}{4-8}=\frac{-3}{-4}=\frac{3}{4}[/tex]The other line has a negative slope, so the lines are not parallel.
3. From a boat on the lake, the angle of elevation to the top of a cliff is 25.2°. If the base of the cliff is 1384 ft from the boat, how high is the cliff? Round results to an appropriate number of significant digits.
Using trig function Tan to get the height of the cliff;
[tex]\begin{gathered} \tan25.2=\frac{h}{1384} \\ h=tan25.2\times1384 \\ =0.471\times1384 \\ =651.26096 \end{gathered}[/tex]ANSWER
[tex]651.26ft[/tex]Lucas made a recipe that needed five-sixths cup of flour. Sarah's recipe calledfor 1/6 cup of flour. How much moreflour did Lucas need?
Answer:
2/3 cups of flour
Explanation:
Lucas recipe needed 5/6 cup of flour.
Sarah's recipe needed 1/6 cup of flour.
The difference
[tex]\begin{gathered} \text{Difference}=\frac{5}{6}-\frac{1}{6} \\ =\frac{4}{6} \\ =\frac{2}{3}\text{ cups} \end{gathered}[/tex]Therefore, Lucas needed 2/3 cups more of flour.
Use the diagram below to answer the next 4 questions that follow. Lines L1 1 pointand L2 are parallel. Point N is the midpoint of segment GH. If the measureof IHM is 125°, what is the measure of ZIHU? *M3N687
180 - 125 = 55
angle IHJ = 55
IHM + IHJ = 180
Since IHM = 125
Classify the slope as upward downward vertical or horizontal. m = -7
Answer:
downward
Explanation:
A negative slope decreases from left to right.
a line with a negative slope can be thought of as a downward side of a hill. Therefore we classify negative slopes as downward (because our idea of 'upward' is something that increases from left to right).
Therefore, the slope m = - 7 since it is negative is classified as downward.
The upward slope is
a vertical slope is
a horizontal slope is
please solve it and identify what was wrong in solving it the first time
we have that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ABE
A+B+E=180
substitute given values
60+55+E=180
E=65 degrees
so
mRemember that
m by vertical angles
so
mIn the triangle EDC
msubstitute given values
65+85+D=180
D=30 degreesmFind the value of the variable that is not given: V=I w h; Given V = 90,1 = 10, h = 3 (Round the answer to 2 decimal places if necessary)
V= l*w*h
V=90
l=10
h=3
Replace the values in the expression and clear w
V= l*w*h
90=10*w*3
90=30w
w=3
Gloria, an experienced bungee jumper, leaps from a tall bridge and falls toward the river below. The bridge is 200 feet above the water and Gloria's bungee cord is 130 feet long unstretched. When will Gloria's cord begin to stretch? Round your answer to two decimal places.
We are given that Gloria jumps from a bridge using a bungee cord. The quadratic expression that models an object falling freely is the following:
[tex]h=h_0+v_0t-\frac{1}{2}gt^2[/tex]Where:
[tex]\begin{gathered} h_0=\text{initial height} \\ v_0=\text{initial velocity} \\ g=\text{acceleration of gravity} \\ t\text{ = time} \end{gathered}[/tex]A representation of the problem is the following:
If we assume that the initial velocity is zero, we get the following values:
[tex]\begin{gathered} h_0=200 \\ h=200-130 \\ g=32 \\ \end{gathered}[/tex]The height is equivalent to the total height of the bridge minus the longitude of the cord. The value for "g" is a constant equivalent to 32 feet per second.
Replacing we get:
[tex]200-130=200-\frac{1}{2}(32)t^2[/tex]Now we solve for "t", first by subtracting 200 to both sides:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Solving the operation:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Multiplying both sides by -2:
[tex]260=32t^2[/tex]Dividing both sides by 32:
[tex]\frac{260}{32}=t^2[/tex]Taking square root on both sides of the equation:
[tex]\sqrt[]{\frac{260}{32}}=\sqrt{t^2}[/tex]Solving the operations:
[tex]2.85=t[/tex]Therefore, the cord starts stretching at 2.85 seconds.
Triangle 1 is a scale drawing of Triangle 2 as shown below. Based on the information shown in these triangles, what is the length of the side x? A. 9 B. 15.75 c. 7
x = 7
Explanations:Since triangle 1 is a scale drawing of triangle 2, the ratio of corresponding sides will be the same.
Therefore:
[tex]\frac{4}{6}=\text{ }\frac{x}{10.5}[/tex]Cross multiply:
4(10.5) = 6x
42 = 6x
6x = 42
x = 42/6
x = 7
The table below shows data for a class's mid-term and final exams:
Mid-TermFinal
96 100
95 85
92 85
90 83
87 83
86 82
82 81
81 78
80 78
78 78
73 75
Which data set has the smallest IQR? (1 point)
Group of answer choices
They have the same IQR
Mid-term exams
Final exams
There is not enough information
The interquartile range is a measure of where the “middle fifty” is in a data set, where the bulk of the values lies.
The interquartile range formula is the first quartile subtracted from the third quartile:
[tex]IQR=Q_3-Q_1[/tex]IQR of the Mid-Term
Step 1: Arrange the numbers in order
[tex]73,78,80,81,82,86,87,90,92,95,96[/tex]Step 2: Find the median
[tex]Median\Rightarrow86[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=80[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=92[/tex]Step 4: Calculate the IQR
[tex]IQR=92-80=12[/tex]IQR of the Final
Step 1: Arrange the numbers in order
[tex]75,78,78,78,81,82,83,83,85,85,100[/tex]Step 2: Find the median
[tex]Median\Rightarrow82[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=78[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=85[/tex]Step 4: Calculate the IQR
[tex]IQR=85-78=7[/tex]ANSWER
The data with the smallest IQR is the FINAL.
The Fancy Marble Company makes one type of spherical marble with a radius of 2 cm. The maximum error in measurement is 0.1 cm for the radius. Which of the following is closest to the minimum .volume of one of these marbles? A 7.95 cm B. 8.79 cm C. 28.72 cm D. 38.77 cm
hello
to solve this question, we need to find the volume of a sphere
the formula is given as
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ r=2\pm0.1 \\ \pi=3.14 \end{gathered}[/tex]the minimum volume of the sphere is would be as a result in reduction of the radius of the sphere
[tex]\begin{gathered} R=r-0.1 \\ R=2.0-0.1 \\ R=1.9\operatorname{cm} \end{gathered}[/tex]we can use this radius to calculate the volume of the sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi R^3 \\ v=\frac{4}{3}\times3.14\times1.9^3 \\ v=28.716\cong28.72\operatorname{cm}^3 \end{gathered}[/tex]from the calculations above, the minimum volume of the sphere is 28.72cm^3 which corresponds to option C
Part 2: Consider this word problem: "Professor has several tarantulas and frogs. She counts 104 legs and 80 eyes in the room (not including her own). How many of each creature does she have?" Answer the question in a paragraph form. Answer the following: • What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up orpull some information from the back of your head?• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!)
Okay, here we have this:
Considering the provided information we are going to calculate how many of each creature does she have, so we obtain the following:
• What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up or
pull some information from the back of your head?:
The missing information of the exercise is the amount of legs and eyes of each type of animal
• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?:
The mathematical concept that we apply to solve this exercise will be the systems of equations of two equations by two incognites.
• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!):
According to the given information we obtain the following systems of equations:
8x+4y=104 (Equation of the legs)
8x+2y=80 (Eye equation)
"X" corresponds to the number of tarantulas and "y" to the number of frogs.
Solving:
We will clear x in the second equation:
8x+2y=80
8x=80-2y
x=(80-2y)/8
x=10-2y/8
Replacing in the first equation:
8x+4y=104
8(10-2y/8)+4y=104
80-2y+4y=104
80+2y=104
2y=24
y=24/2
y=12
Using this value of y in the equation of x:
x=10-2y/8
x=10-2(12)/8
x=10-24/8
x=10-3
x=7
Finally we obtain that she has 7 tarantulas and 12 frogs.
1. Solve the given system of equations. X + y + z = 9 x - z = 5 X + y = 6the solution is: x = y = and z =
x=8
y=-2
Z=3
Explanation
Step 1
Let
[tex]\begin{gathered} x+y+z=9\text{ Equation (1)} \\ x-z=5\text{ Equation(2)} \\ x+y=6\text{ Equation(3)} \end{gathered}[/tex]Step 2
isolate x from equation (1) , (2) and (3)
[tex]\begin{gathered} x+y+z=9 \\ x=9-y-z\text{ Equation (4)} \end{gathered}[/tex][tex]\begin{gathered} x-z=5 \\ x=5+z\text{ equation (5)} \\ \\ x+y=6 \\ x=6-y\text{ equation(6)} \\ \end{gathered}[/tex]Step 3
combining equation (4) and (5)
[tex]\begin{gathered} 9-y-z=5+z \\ 9-y-2z=5 \\ -y-2z=5-9 \\ -y-2z=-4\text{ Equation(7)} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} x=x \\ \text{equation (5) = equation (6)} \\ 5+z=6-y\text{ equation (8)} \end{gathered}[/tex]Step 5
using equation(7) and (8) find y and z
[tex]\begin{gathered} -y-2z=-4\text{ (7)} \\ 5+z=6-y(8) \\ \text{isolate y from equation (7)} \\ -y=-4+2z \\ y=4-2z \\ \text{replace in equation (8)} \\ 5+z=6-4+2z \\ 5+z=2+2z \\ z-2z=2-5 \\ -z=-3 \\ z=3 \end{gathered}[/tex]replace the value of z= 3 in equation (7) to find y
[tex]\begin{gathered} -y-2z=-4 \\ -y-2\cdot3=-4 \\ -y-6=-4 \\ -6+4=y \\ y=-2 \end{gathered}[/tex]finally, replace the value of y in equation (3) to find x
[tex]\begin{gathered} x+y=6 \\ x-2=6 \\ x=6+2 \\ x=8 \end{gathered}[/tex]I hope this helps you
How is the function in the following picture graphed on a chart?
Okay, here we have this:
Find the area and perimeter of each polygon:
6
5
4
8
Area:
unit2
Perimeter:
unit2
OK
Part a
The area of the figure is equal to the area of two rectangles
Area of the top rectangle
A=(6)*(5)=30 unit2
Area of the bottom rectangle
A=(8)*(4)=32 unit2
therefore
The total area is
A=30+32
A=62 unit2Part b
Find out the perimeter
To find out the perimeter adds all the length sides
so
P=8+4+(8-6)+5+6+5+4
P=34 unitsHow many solutions does this equation have? Solve on paper and enter your answer on Zearn.
9x +7x+8=-4+4(3x+5)
No solutions
One solution
Infinitely many solutions
Answer: One solution
Step-by-step explanation:
Simplify to find x:
9x +7x+8=-4+4(3x+5)
16x + 8 = -4 +12x +20
4x = -4 +20 -8
4x = 8
x=2
jacobs school is selling tickets to a fall musical. On the first day of ticket sales the school sold 2 senior citizens tickets and 6 child tickets for a total of $26. The school took in $54 on the second day by selling 12 senior citizen tickets and 2 child tickets. Find the price of senior citizen ticket and the price of a child ticket.
Let s and c represent the prices of the senior citizen and the child tickets respectively
Then the problem can be modelled as follows:
[tex]\begin{gathered} 2s+6c=26--------------------(1) \\ 12s+2c=54--------------------(2) \\ We\text{ will now solve the simultaneous equation by elimination method} \\ \text{equation (1) }\times6\colon \\ 12s+36c=156---------------------(3) \\ 12s+2c=54-----------------------(2) \\ ---------------------------------------- \\ \text{equation (3) - equation (2):} \\ 34c=102 \\ \Rightarrow c=\frac{102}{34}=3 \\ \text{Substituting the value of c into equation (1), we have:} \\ 2s+6(3)=26 \\ 2s+18=26 \\ \Rightarrow2s=26-18=8 \\ \Rightarrow s=\frac{8}{2}=4 \end{gathered}[/tex]Hello I really need help with this question I’m not understanding it
The subset of the event " The two spins have a sum of 5 " is { (2,3), (3,2), (1,4) and (4,1) }
It is given that the sum of Jae's two spins was 5.
S is the sample space of spinning the spinner twice.
The collection of all the possible outcomes is termed the sample space
Subset: If every element in set A is also an element in set B, then set A is a subset of set B. Set A is therefore contained within set B.
Now, the subset of the event " The two spins have a sum of 5 "
In the spinner, there are 1, 2, 3, and 4.
So, the values that would give us a 5 are (2,3), (3,2), (1,4), and (4,1)
These are the terms that will be in the required subsets,
So, Required subset = { (2,3), (3,2), (1,4) and (4,1) }
To read more about subsets, visit https://brainly.com/question/17514113
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What is the area, in square inches, of the shape below? 8.4 in 9.7 in
Problem:
The area of the triangle is
[tex]A\text{ = }\frac{bxh}{2}[/tex]here, b is the base of the triangle and the variable h is its height so :
[tex]A\text{ = }\frac{bxh}{2}\text{ = }\frac{9.7\text{ in x 8.4 in}}{2}\text{ = }\frac{81.48in^2}{2}=40.74in^2[/tex]We can conclude that the area of the shape is 40.74 in^2
Which inequality is true when the value of c is −11?−c−4≤−3c-4≥3-c-4≤3c-4≤3
In order to find which inequality is true, let's use the value of c in each one and check if they are true or false:
[tex]\begin{gathered} -c-4\le-3 \\ 11-4\le3 \\ 7\le-3\text{ (false)} \\ \\ c-4\ge3 \\ -11-4\ge3 \\ -15\ge3\text{ (false)} \\ \\ -c-4\le3 \\ 11-4\le3 \\ 7\le3\text{ (false)} \\ \\ c-4\le3 \\ -11-4\le3 \\ -15\le3\text{ (true)} \end{gathered}[/tex]Therefore the correct option is the fourth one.
Find the next 3 terms of the arithmetic sequence 5, 9, 13, 17
You have the following arithmetic sequence:
5, 9, 13, 17
due to the it is an arithmetic sequence, difference between consecutive numbers is constant.
In fact, when you calculate the difference between consecutive numbers you have:
9 - 5 = 4
13 - 9 = 4
17 - 13 = 4
To determine the next three terms it is necessary to sum 4 (the previous result) to each previous term, just as follow:
17 + 4 = 21
21 + 4 = 25
25 + 4 = 29
Hence, 21, 25 and 29 are the next three terms