The scale factor of model to the tower is 3:1640.
What is scale factor?The scale factor states the scale by which a figure is bigger or smaller than the original figure.
In other words, scale factor is a ratio between two corresponding sides of similar figures.
Therefore, the actual tower is 1,083 feet tall and 410 feet wide at the base.
The scale model currently has a base that is 0.75 feet wide.
Therefore, the scale factor of the model can be calculated as follows;
The scale factor can be written as a ratio or fraction.
The scale factor of the base to the model is the same with the height of the tower to the model.
0.75 : 410
multiply both side by 100
75 : 41000
divide both sides by 25
Therefore,
3 : 1640
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please help me
solve for x. if needed, round your answer to 1 decimal place.
Check the picture below.
[tex]sin(31^o )=\cfrac{\stackrel{opposite}{11}}{\underset{hypotenuse}{x}}\implies x=\cfrac{11}{sin(31^o)}\implies {\Large \begin{array}{llll} x\approx 21.4 \end{array}}[/tex]
Make sure your calculator is in Degree mode.
May you guys/girls please help me I have to submit this befoer mid night and I do not fail because my parents will get me , so may y'all please help me out!?
Answer:
Answer down below!
Step-by-step explanation:
Lets find a point on the graph that we can easily point out to start this problem
We can use the point (0,-3)
From there, we use rise/run to find our answer!
We go up 1 and over 1
Thus, our slope is 1!
Answer:
1
Step-by-step explanation:
slope = rise/run
choose any two points in the graph and count the left/right and up/down to get to that point it's hard to explain u can watch a yt video to completely understand
Please Help!
5|x + 9| < 10
Answer: -7, -11
Step-by-step explanation:
[tex]5|x+9| \leq 10\\\\|x+9| \leq 2\\\\-2 \leq x+9 \leq 2\\\\-11 \leq x \leq -7[/tex]
Answer:
x∈(−11,−7)
Step-by-step explanation:
On Tuesday, the mailman delivers three checks for $5 and two bills for $2 each. If you had a starting balance of $25, what is the ending balance?
Answer:£6
Step-by-step explanation:
First, you need to do 5×3= 15 you times it by three, because there are three checks of £5
Then do 2×2=4 you times it by 2, because there are two checks of £2.
£15+£4=£19
Then Subtract £25-£19= £6
Hope this helps!
Which of the following expressions are equivalent to ( 9 7 8 + 2 4 5 ) − 1 2 (9 8 7 +2 5 4 )− 2 1 left parenthesis, 9, start fraction, 7, divided by, 8, end fraction, plus, 2, start fraction, 4, divided by, 5, end fraction, right parenthesis, minus, start fraction, 1, divided by, 2, end fraction? Choose 2 answers: Choose 2 answers: (Choice A) A 9 7 8 + ( 2 4 5 − 1 2 ) 9 8 7 +(2 5 4 − 2 1 )9, start fraction, 7, divided by, 8, end fraction, plus, left parenthesis, 2, start fraction, 4, divided by, 5, end fraction, minus, start fraction, 1, divided by, 2, end fraction, right parenthesis (Choice B) B 9 7 8 + 2 4 5 + ( − 1 2 ) 9 8 7 +2 5 4 +(− 2 1 )9, start fraction, 7, divided by, 8, end fraction, plus, 2, start fraction, 4, divided by, 5, end fraction, plus, left parenthesis, minus, start fraction, 1, divided by, 2, end fraction, right parenthesis (Choice C) C 9 7 8 − ( − 2 4 5 ) − ( − 1 2 ) 9 8 7 −(−2 5 4 )−(− 2 1 )9, start fraction, 7, divided by, 8, end fraction, minus, left parenthesis, minus, 2, start fraction, 4, divided by, 5, end fraction, right parenthesis, minus, left parenthesis, minus, start fraction, 1, divided by, 2, end fraction, right parenthesis (Choice D) D − ( − 9 7 8 + 2 4 5 ) − 1 2 −(−9 8 7 +2 5 4 )− 2 1 minus, left parenthesis, minus, 9, start fraction, 7, divided by, 8, end fraction, plus, 2, start fraction, 4, divided by, 5, end fraction, right parenthesis, minus, start fraction, 1, divided by, 2, end fraction (Choice E) E 9 7 8 − ( − 2 4 5 − 1 2 ) 9 8 7 −(−2 5 4 − 2 1 )
The equivalent expressions to (9 7/8 + 2 4/5) - 1/2 are given as follows:
a) 9 7/8 + (2 4/5) - 1/2.
b) 9 7/8 + 2 4/5 + (-1/2).
What are equivalent expressions?Equivalent expressions are expressions that have the same result.
In this problem, the expression a is equivalent to the given expression, as the only difference is the order of the operations being applied, as the subtraction of 2 4/5 and -1/2 is applied before the addition of 9 7/8 + 2 4/5.
Expression b is also equivalent to the given expression, as an addition with the negative number in the fraction is made. However, the addition sign means that the sign inside the parenthesis is kept, which is negative, hence no change is made to the expression.
The remaining expressions involve changes to the signals of each term, hence they are not equivalent to the presented expressions.
Missing informationThe problem is given by the image at the end of the answer.
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Z23w1120х23YWhat is the measure of angle Z?
We are given a trapezoid and we are asked to determine one of its angles. To do that we need to have into account that the following angles are equal:
[tex]\begin{gathered} \angle W=\angle X \\ \angle Z=\angle Y \end{gathered}[/tex]Also, the sum of two different angles must be equal to 180, therefore, we have the following relationship:
[tex]\angle W+\angle Z=180[/tex]Replacing the value of angle W:
[tex]112+\angle Z=180[/tex]Subtracting 112 to both sides:
[tex]\begin{gathered} \angle Z=180-112 \\ \angle Z=68 \end{gathered}[/tex]Therefore, the measure of angle Z is 68.
The assets and liabilities of a landscaping business are listed below.
What is the net worth of the landscaping company?
$126.790
$187.205
$282.799
$470.004
The net worth of the landscaping company is given by:
$187.205.
How to calculate the net worth?The net worth of a company or of a person is given by the sum of all assets of the person subtracted by the sum of all debts of the person.
In the context of this problem, the assets, and it's values, of the company are given as follows:
Owned Inventory: $48,760.Cash: $126,790.Savings account: $32,436.Owned equipment: $20,700.Accounts receivable: $15,640.Property value: $225,678.Hence the sum of the assets is given by:
Assets = 48760 + 126790 + 32426 + 20700 + 15640 + 225678 = $469,994.
The debts of the company, with it's values, are given as follows:
Small Business Loan: $76,400.Building Mortgage: $189,429.Other debt: $16,970.Hence the sum of the debts is given by:
Debts = 76400 + 189429 + 16970 = $282,799.
Then the net worth of the company is:
Net worth = Assets - Debt = 469,994 - 282,799 = $187,205.
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The sloth travels 1/3 meters in 1/10 minute. What is the sloth’s running speed? Includes unit of measure. Round to the nearest tenth, if needed.
The sloth speed of running is 10/3 meters per minute
Distance travelled = 1/3 meters
Time taken to travel the distance = 1/10 minute
The formula for speed is given:
The distance travelled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction. A faster rate of movement is indicated by a higher speed. It is travelling more slowly if the speed is lower.
Speed = Distance/ Time
Speed of the sloth = (1/3)/(1/10)
= 1/3*10/1
= 10/3 meters per minute
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Type the correct answer in each box.What values of a and b make this equation true?(4 + v=49) – 2(/(-4)2 + v=324) = a + bia =b =ReseNext
Problem
Solution
For this case we can do the following:
[tex](4+\sqrt[]{-49})-2(\sqrt[]{(-4)^2}+\sqrt[]{-324})\text{ }[/tex]We also know that :
[tex]\sqrt[]{-1}=i[/tex]Using this property we got:
[tex](4+7i)-2(4+18i)[/tex]Now we can distirbute the terms and we got:
4+7i -8 -36 i
And distributing the terms we got:
(7-36)i +(4-8)
-29 i -4
And then our solution would be:
a= -29
b= -4
Joel digs a hole at a rate of 35 feet every 10 minutes. After digging for 30 minutes, Joel places a bush in the hole that fills exactly 12 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
The elevation of the hole after placing the bush in the hole is 93 feet
This is a problem from the unitary method. We can easily solve this problem by following a few steps.
Joel digs a hole at a rate of 35 feet every 10 minutes. So, we have to calculate the rate at 1 min.
Joel digs a hole at a rate of 35 feet every 10 minutes
Joel digs a hole at a rate of 35/10 feet every 1 minute
[ Work done for unit minute = Total work done / total time period ]
Now we have to calculate the total work done for 30 minutes.
For a unit minute work done is 35/10, then for 30 minutes the total work done is, (35/10 × 30 ) feet = 105 feet.
Joel places a bush in the hole that fills exactly 12 feet of the hole.
Therefore, the actual elevation is ( 105 feet - 12 feet ) = 93 feet.
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A dance school offers classes in ballet folklórico. There is a one-time registration fee and a fee
for each class. The total cost of classes, y, is a linear function of the number of classes,
Three classes cost $36. Seven classes cost $68.
What is the rate of change and what does it represent?
The most appropriate choice for equation of line in slope intercept form will be given by-
Rate of change is 8 and rate of change represents slope of the line
What is equation of line in slope intercept form?
Equation of line in slope intercept form is written as y = mx +c
m is the slope of the line and c is the y intercept of the line.
The distance between the origin and the point where the line cuts the x axis is the x intercept
The distance between the origin and the point where the line cuts the y axis is the y intercept
Here,
Let the number of classes be x
Total cost of classes = y
Let the equation of line be y = mx + c
Three classes cost $36
Putting x = 3, y = 36
36 = 3x + c .............. (1)
Seven classes cost $68
Putting x = 7, y = 68
68 = 7x + c ............... (2)
Subtracting equation (2) from (1),
4x = 32
[tex]x = \frac{32}{4}[/tex]
x = 8
Putting the value of x in (1)
[tex]3 \times 8 + c = 36\\24 + c = 36\\c = 36 - 24\\c = 12[/tex]
Equation of line is y = 8x + 12
Now coefficient of x in y = mx + c is the slope of the line and that is the rate of change
so, rate of change is 8 and rate of change represents slope of the line.
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Answer:
$8 per classthe cost of each classStep-by-step explanation:
Given school costs of $36 for 3 classes and $68 for 7 classes, you want to know the rate of change and its meaning.
Rate of changeThe "rate of change" in this context is the change in cost for one additional class. It can be found by ...
rate of change = (change in classes) / (change in cost)
rate of change = ($68 -$36)/(7 classes -3 classes) = $32/(4 classes)
rate of change = $8/class
Interpretation
This "rate of change" is the additional cost for the addition of one class. It is the cost per class.
solve for t
125,000 = 45,000 (1 + .021/365) (365t)
If the equation be 125000 = 45000( 1 + 0.021/365[tex]$) ^{365t[/tex] then simplifying we get the value of t exists 7.61 x [tex]10^{-6}[/tex].
How to simplify an equation?Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.
Let the equation be 125000 = 45000( 1 + 0.021/365[tex]$) ^{365t[/tex]
simplifying the above equation, we get
t = [tex]$\frac{125000}{ 45000( 1+ \frac{0.021}{365} ) 365}[/tex]
t = 7.61 x [tex]10^{-6}[/tex].
Therefore, the value of t exists 7.61 x [tex]10^{-6}[/tex].
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PLEASE HELP !!! QUICKKK !!
A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.
The rate of change will be 3/4.
What is meant by linear function?A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function. Here, a stands for the line's gradient, and b for the y-axis intercept (which is sometimes called the vertical intercept).
The rate of change of y with respect to x, can be calculated utilizing any two of the pairs of values of the table, say, (3, -5) and (7, -2).
Rate of change [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]
Let, (3, -5) = (x1, y1) and (7, -2) = (x1, y1).
Rate of change [tex]$=\frac{(-5)-(-2)}{7-3}$[/tex]
Rate of change = 3/4.
Therefore, the correct answer is option c) 3/4.
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the length of a base of an isosceles triangle is xthe length of a leg is 2x - 2 the perimeter of the triangle is 56 find x
The perimeter of the triangle is computed adding the length of each side. That is,
P = (2x - 2) + (2x - 2) + x
P = (2x + 2x + x) + (-2 - 2)
P = 5x - 4
Substituting with P =56 and solving for x:
56 = 5x - 4
56 + 4 = 5x
60 = 5x
60/5 = x
12 = x
How much money is pictured below?
Answer:
The amount of money pictured below is one dollar
Answer:
Step-by-step explanation:
1 quarter= 25 cents
1 nickel = 5 cents
9 mickels total= 9x5= 45
1 quarter= 25 + 45= 70
and then you have one dollar
so 1 dollar and 70 cents
1.70$
Please help me with this question !!!
Answer:
composition about loyalty
how do you mak y squared equal 169
Answer:
13
Step-by-step explanation:
y^2 = 169
y = [tex]\sqrt{169}[/tex]
y = 13
12
3 4
5 6
78
In the figure, a || b, and both lines are intersected by transversal t. Complete the statements to prove that m²1 = m25.
a | b (given)
m21+ m23 = 180° (Linear Pair Theorem)
m25+ m26 = 180° (Linear Pair Theorem)
m21+ m23 = 25 + 26 (
m23= m26 (
m21= m25 (Subtraction Property of Equality)
The angle value of m is m∠7 = m∠3 = 125° in linear pair.
What linear pair?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair always has an angle total of 180 degrees.m∠1 = 180° - 55° = 125°
m∠2 = 55° [ vertical angle ]
m∠3 = m∠1 = 125° [ vertical angle ]
m∠4 = 180° - m∠3 = 180 - 25 = 55°
m∠5 = m∠1 = 125°
m∠6 = m∠2 = 55°
m∠7 = m∠3 = 125°
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in a G.P the 7th term is 16 times the 3rd term and the sum of the 2nd term and the 6th term is 102.if the common ratio(r) is positive .find the
1 common ratio
2 first term
3 sum of the 8th term
1. Common ratio of the G.P is 50
2. First term of the G.P is -100
3. Sum of the 8th term is 250.
Given,
In a Geometric progression,
7th term is 16 times the 3rd term
Sum of 2nd and 6th term is 102
Common ratio is positive.
Now,
Take a as first term.
r as common ratio
Then,
2nd term = a + r
6th term = a + 5r
So,
a + r + a + 5r = 102
Then,
2a + 6r = 102
2a = 102 - 6r
a = (102 - 6r) / 2
Now,
1. Common ratio:
Consider any term,
Here, 3rd term = a + 2r
Substitute a here.
a + 2r = (102 - 6r) / 2 + 2r
102 - 6r + 4r = 2
102 - 2 = 6r - 4r
100 = 2r
r = 100/2 = 50
That is,
The common ratio of the G.P is 50.
2. First term:
Consider,
7th term is 16 times the 3rd term
That is,
3rd term = a + 2r
7th term = 16(a + 2r)
r = 50
Then,
a + 50 × 2 = 16(a + 50 × 2)
a + 100 = 16(a + 100)
a + 100 = 16a + 1600
100 - 1600 = 16a - a
15a = -1500
a = -1500/15
a = -100
Therefore,
The first term of the G.P is -100
3. Sum of the 8th term.
8th term = a + 7r = -100 + 7 × 50 = -100 + 350 = 250
That is,
The sum of the 8th term is 250.
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Answer the questions based upon the table:
1- What is the independent variable? (hint- it is the input),
2- What is the dependent variable? (hint- it is the output)
3-
Is the relation a linear function? (hint- if it has a consistent difference between the
consecutive output values, then YES)
4- What is the slope of the function?
5- What is the domain?
6- What is the range?
7- What is the y-intercept? (hint- x = 0 at the y-intercept)
8- What is the x-intercept? (hint-y = 0 at the x-intercept)
The features of the relation are given as follows:
1. Independent variable: number of weeks.
2. Dependent variable: money saved.
3. Yes, the relationship is linear.
4. The slope is of 40.
5. The domain is: {0, 1, 2, 3, 4, 5, 6, 7}.
6. The range is: {50, 90, 130, 170, 210, 250, 290, 330}.
7. The y-intercept is of $50.
8. The table has no x-intercept.
Dependent and independent variablesThe output variable is a function of the input, hence the output is the dependent variable and the input is the independent variable.
The input and the output in this problem are given as follows:
Input: number of weeks -> Independent variable.Output: money saved -> Dependent variable.Linear relationIn a linear relation, the rate of change of the output relative to the input is constant, and is called slope.
In the context of this problem, the money saved has a constant increase of $40 each week, hence:
The relation is linear.The slope is of $40.Domain and rangeThe domain is the set containing the input values of the function, hence the number of weeks, as follows:
{0, 1, 2, 3, 4, 5, 6, 7}.
The range is the set containing the output values of the function, hence the money saved, as follows:
{50, 90, 130, 170, 210, 250, 290, 330}.
InterceptsThe y-intercept is the value of y when x = 0, hence, from the table, it is of:
y = 50.
The x-intercept is the value of x when y = 0. From the given table, y never assumes a value of 0, hence the function has no x-intercept.
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A machine factory makes two and one 4th pounds of nails in one and a half hours at what rate in
pounds per hour does the machine make nails
The machine make nails at a rate of 8th pounds per hour
How to determine the rate of making machine?From the question, the given parameters are:
Amount of pounds of nails = 4th poundsNumber of time = half an hourThe rate in pounds per hour the machine make nails is then calculated as
Rate of making nails = Amount of pounds of nail/Number of time
Substitute the known values in the above equation
So, we have
Rate of making nails = 4th pounds/0.5 hour
Evaluate
Rate of making nails = 8th pounds per hour
Hence, the rate of making nails is 8th pounds per hour
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simplify the expression using the order of operations 4+(5-11) over 2^4 minus 14
You must show all your work.
Answer:
-1
Step-by-step explanation:
BEDMAS
[tex]\frac{4+(5-11)}{2^{4}-14 }\\\frac{4+(-6)}{16-14 }\\\frac{-2}{2}\\-1[/tex]
Hope that helps
Math please its in the picture and show solution please
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
Explain about the simplify?No, to simplify is to reduce anything to its most basic form without figuring out what the letter 'x' or other letters are. Finding the meaning of the 'x' or other letters is known as solving.
Overview. Making something simpler refers to making it simpler to do or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. We accomplish this by dividing the denominator and numerator by the highest possible number.
It has the same precise meaning. The phrase "expand the brackets" means the same thing as "multiply out the brackets," with the added indication that when we do so, we are multiplying everything inside by everything outside the brackets.
The answer for a is x
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please help me complete the blank spots in the sentence!
The full sentence relating to the function in the tabulated data is;
"The x-intercept shows that if Ronald buys only apples, he can buy 12 pounds (lb). The y-intercept shows that if Ronald buys only eaches, he can buy 10 pounds (lbs). Hence the complete sentence."
What is a math function?It is to be noted that in mathematics, a function is an expression, rule, or law that describes the connection between one variable (the independent variable) and another variable (the dependent variable).
Tabular data has the following characteristics: They are made up of rows and columns. A table contains rows and columns and is used to organize everything tabular. Typically, sports statistics are provided in a tabular manner. A table is a type of graphic that arranges data into rows and columns. Tabular data is presented in a table format.
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Question 5 of 5
Compare 7/8 and 8/9 by converting each fraction to a decimal. Which is larger?
Answer:
8.9 is larger
Step-by-step explanation:
7/8 is 0.875 in decimal form
8/9 is 0.88 or 0.89 if you round up.
7/8 < 8/9
Hope this helps! Please have a great day :)
what two numbers multiply to get 30 and add up to get 31
Answer:
1 and 30!
1 times 30 = 30
1 + 30 = 31
Step-by-step explanation:
;p
Answer:
30 and 1
Step-by-step explanation:
You add 1 to 30 to get your answer of 31.
30 + 1 = 31
You can also multiply 30 times 1 to get thirty.
30 * 1 = 30
Have a nice day!
Landon works at a movie theater. yesterday he worked 4 hours and made $48. how much money will he make in 1 hour? how many hours does he need to work to make $156?
The amount of money Landon will make in 1 hour is $12 and he needs to work for 13 hours to make $156.
The amount of money he will make in 1 hour can be calculated by using division.
It can be determined by dividing the total amount earned by him by the total number of hours he worked yesterday. Therefore;
money earned in 1 hour = total amount earned ÷ total number of hours
money earned in 1 hour = 48 ÷ 4
money earned in 1 hour = $12
Now we can calculate the number of hours he needs to work at the movie theater to make $156 by dividing the desired amount by the amount earned in one hour. Therefore;
number of hours required = 156 / 12
number of hours required = 13
Hence, Landon will make $12 in one hour and he will need to work 13 hours to make $156
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Given f(x)=x^2+1 and g(x)=2x−1, find (f−g)(x)
x2−2x−1
x squared minus 2 x minus 1
x2+2x
x squared plus 2 x
x2−2x+1
x squared minus 2 x plus 1
x2−2x+2
The value of (f-g)x is x²-2x+2. Therefore, option C is the correct answer.
The given functions are f(x)=x²+1 and g(x)=2x-1.
What is function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
We need to find the value of (f-g)(x).
Now, f(x)-g(x)= (f-g)(x)
=x²+1 -(2x-1)
=x²+1-2x+1
=x²-2x+2
The value of (f-g)x is x²-2x+2. Therefore, option C is the correct answer.
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I need 23 and 24. The directions for them are solve for x. And assume that lines which appear to be diameters are actual diameters.
Explanation
Question 23
To get the value of x, let us get y as shown below
[tex]\begin{gathered} y+100=180^0(linear\text{ pairs}) \\ y=180-100=80^0 \end{gathered}[/tex]Next, we will make use of the fact tha y and (x+85 ) are vertical angles so that
[tex]\begin{gathered} y=x+85\text{ \lparen linear pairs\rparen} \\ where\text{ y=80} \\ 80=x+85 \\ x=80-85=-5 \\ x=-5 \end{gathered}[/tex]For question 23, x = -5
For question 24
The total angle in a circle is 360 degrees so that
[tex]-38x+4+65+42+95+40=360[/tex]solving for x
[tex]\begin{gathered} -38x+246=360 \\ -38x=360-246 \\ -38x=114 \\ x=\frac{114}{-38} \\ x=-3 \end{gathered}[/tex]For question 24, x =-3
suppose a 95% confidence interval was made to estimate the monthly cost of internet service instead of a 90% confidence interval. how would the interval change?
The 95% confidence interval will be more extensive than the 90% confidence interval
In measurements, the probability that a population boundary will fall between a bunch of values for a specific level of the time is alluded to as a certainty stretch. Investigators every now and again utilize certainty goes that incorporate 95% or the vast majority of expected perceptions. Thus, it could be presumed that there is a 95% probability that the genuine worth falls inside that reach assuming that a point gauge of 10.00 with a 95% certainty time frame - 10.50 is determined utilizing a factual model.
The degree of conviction or vulnerability in a testing cycle is estimated by certainty spans.
Also, they are utilized in relapse examination and speculation testing.
To decide measurable importance, analysts often join certainty spans with p-values.
95% or almost 100% certainty levels are most often utilized in their development.