Mount Rushmore is a sculpture that was carved using a model with a scale of 1 in :1 ft. If the model of George Washington’s face was 5 ft tall, how tall is his face on Mount Rushmore?
The height of the face is 60 inch.
What is unit conversion?Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.
As 1inch = 1ft,
then to find out how many inches is George Washington’s face.
As there are 12inch in a foot
=12*5
=60inches
Thus , his face is 60ft tall.
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A dart hits the circular dartboard shown below at a random point. find the probability that the dart lands in the shaded square region. the radius of the dartboard is 11in, and each side of the shaded region is 4in.
Answer:
.13 or 13%
Step-by-step explanation:
P = area of shaded region/area of entire board
Entire area: 3.14 * (11 * 11) = 379.94
shaded area: 3.14 * (4 *4) = 50.24
p = 50.24/379.94 = .13 or 13%
The size of angle aob is equal to 132 degrees and the size of angle cod is equal to 141 degrees. find the size of angle dob.
angle AOB = 132 and is also the sum of angles AOD and
DOB. Hence
angle AOD + angle DOB = 132° ---> 1
angle COD = 141 and is also the sum of angles COB and BOD. Hence
angle COB + angle DOB = 141° ---> 2
Now we add the left sides together and the right sides of equations 1 and 2
together to form a new equation.
angle AOD + angle DOB + angle COB + angle DOB = 132 + 141 ---> 3
We should also note that:
angle AOD + angle DOB + angle COB = 180°
Therefore substituting angle AOD + angle DOB + angle COB in equation 3 by 180
and solving for angle DOB:
180 + angle DOB = 132 + 141
angle DOB = 273 - 180 = 93°
A polygon is regular if each of its sides has the same length. Find the perimeter of the regular polygon. It's an octagon with on side 4/3x - 1/3 and another side x+7
To find the perimeter of the regular octagon, set the expressions for the sides equal to each other to find the value of x, substitute this value into either of the expressions for the sides to find the side length, and finally multiply the side length by 8.
Explanation:In mathematics, a regular polygon is a polygon that is equilateral and equiangular. In this case, you have an octagon, which means it has 8 equal sides. If one side is defined as 4/3x - 1/3 and another side is defined as x+7, since it's a regular octagon, all sides must be equal. Therefore, to find the perimeter of the octagon, you need to set the two expressions for the sides equal to each other to find the value of x, and then substitute the value of x into either of the expressions for the sides. Multiply this side length by 8 to get the perimeter.
Here are the steps:
Set the expressions for the sides equal to each other: 4/3x - 1/3 = x + 7Solve for x.Substitute the value of x into either of the side expressions to find the side length.Multiply the side length by 8 to get the perimeter.Learn more about Perimeter of a Regular Polygon here:https://brainly.com/question/19034638
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In a regular polygon, all sides and angles are equal. Given a regular octagon with two sides expressed as 4/3x - 1/3 and x+7, the expressions should be equal since all sides are equal in a regular polygon. Having found x, you can multiply by 8 to find the perimeter of the octagon.
Explanation:Thus, If a polygon is regular, this means all of its sides have the same length. If we're given that one side of the regular octagon is 4/3x - 1/3 and another side is x+7, these two expressions should be equal to each other since it's a regular polygon. This gives us an equation:
4/3x - 1/3 = x + 7
Solving for 'x' will give us the length of one side of the regular polygon. Once you have the length of each side, you can find the perimeter of the regular octagon by multiplying this length by 8 (since an octagon has 8 sides).
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Alan bought a suit on sale for $558. This price was 28% less than the original price. What was the original price?
The risk set by the researcher for rejecting a null hypothesis when it is true is called the
Sets that cover a range of points, including those between isolated points, and cannot be written as lists are called _______ sets.
A. mapping
B. continuous
C. finite
D. discrete
Find the number of possible positive real zeros of 2x^4+14x^3-35x^2
The polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² has one possible positive real zero according to Descartes' Rule of Signs. We observe one change of sign in the coefficients. Thus, there is a maximum of one positive real root.
Determining the Number of Possible Positive Real Zeros:
To determine the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x², we can use Descartes' Rule of Signs. This rule helps us to count the number of sign changes in the polynomial and thus infer the number of positive real roots.
First, let's observe the original polynomial:
[tex]2x^{4}[/tex] + 14x³ - 35x²
We examine the coefficients: 2, 14, and -35. By running our eye across these coefficients:
From 2 to 14: No sign change (positive to positive).From 14 to -35: One sign change (positive to negative).The polynomial has one sign change. According to Descartes' Rule of Signs, there is a maximum of one positive real root.
Therefore, the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² is one.
Susu is solving the quadratic equation 4x2 – 8x – 13 = 0 by completing the square. Her first four steps are shown in the table.
In which step did Susu first make an error?
Step 1
Step 2
Step 3
Step 4
The given Quadratic equation is
[tex]4x^2- 8x - 13 = 0\\\\4(x^2- 2 x - \frac{13}{4}) = 0\\\\ (x-1)^2-1^2- \frac{13}{4}=0\\\\ (x-1)^2=\frac{\sqrt{17}}{4}\\\\ x-1=\pm\frac{\sqrt{17}}{4}\\\\ x=1 +\frac{\sqrt{17}}{4} \text{or} x=1-\frac{\sqrt{17}}{4}[/tex]
These are the steps to determine the roots as well as solve the quadratic equation.
You can find the mistake by looking at the procedure of solving the quadratic equation by completing the square solved above.
Answer:
step 3
Step-by-step explanation:
George and Carmen went on a bicycle trip. They took a bus to their starting point, and then biked the rest. They traveled 275 kilometers in total, and they biked 55 kilometers more than they were bussed. Let x = kilometers traveled by bike and y = kilometers traveled by bus. Find how many kilometers they traveled by bike.
Which method(s) can be used to solve a system of equations? Select all that apply.
distributing
graphing
substitution
formulas
addition
modeling
Answer:graphong, substitution, addition
Step-by-step explanation:
Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.
Answer:
The sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
Step-by-step explanation:
The given expression is
[tex]3n+3[/tex]
For n=1,
[tex]3(1)+3=6[/tex]
For n=2,
[tex]3(2)+3=9[/tex]
For n=3,
[tex]3(3)+3=12[/tex]
The required AP is
[tex]6, 9, 12, ...[/tex]
Here first term is 6 and common difference is 3.
The sum of n terms of an AP is
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{13}=\frac{13}{2}[2(6)+(13-1)(3)][/tex]
[tex]S_{13}=\frac{13}{2}[12+36][/tex]
[tex]S_{13}=312[/tex]
Therefore the sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
Write an equation in point-slope form of the line having the given slope that contains the given point. m=5m=5, (4,3)
Please help! Geometry.
In a community fitness group, 40% of members run for exercise and 36% of members run and play a sport. What percentage of members who run for exercise also play a sport?
By dividing the percentage of community fitness group members who run and play a sport (36%) by those who run for exercise (40%), we find that 90% of the members who run for exercise also play a sport.
To determine the percentage of community fitness group members who run for exercise and also play a sport, we can use the information provided. The question states that 40% of members run for exercise and 36% of members run and play a sport. To find what percentage of members who run also play a sport, we need to find the proportion of runners who are also sport players.
To do this, we divide the percentage of members who run and play a sport by the percentage who only run:
Percentage of runners who also play a sport = (Percentage of members who run and play a sport) / (Percentage of members who run for exercise)
So,
Percentage of runners who also play a sport = 36% / 40% = 0.9
We then multiply by 100 to convert this to a percentage:
0.9 × 100 = 90%.
Therefore, 90% of the members who run for exercise also play a sport.
the _____ of a central angle are two radii of the circle.
A. sides
B. arcs
C. verticals
D. measures
Answer:
A.Sides.
Step-by-step explanation:
The central angle is the angle made by any arc at the center of the circle.Central angle is formed by two rays from the centre which cuts the circle at two points .The part of the two rays which lie inside the circle is the radius of the circle .
We say :
The sides of a central angle are two radii of the circle.
what doesThe mathematical expression 2 ∈ V means
For one week at your store, employees worked 200 regular hours and 50 hours of overtime. what percent of the total hours for the week were overtime?
total hours = 200+50 = 250
50 were overtime
50/250=0.20 = 20% of the hours were overtime
In PQR, point S lies on QR. If PS is perpendicular to QR, which term describes PS?A. Perpendicular bisector
B. Angle bisector
C. Median
D. Altitude
What is a tangent of a circle
Determine the quadrant when the terminal side of the angle lies according to the following conditions: cos(t)>0, tan(t)>0
The original price P of an item less a discount of 20% ?
Answer:
0.8 P
Step-by-step explanation:
Let the origional price of P
A discount of 20% is given on the item
The price of item=[P(100-d)]÷100
The price of the item= [tex]\frac{p(100-20)}{100}[/tex]
The price of the item= [tex]\frac{p(80)}{100}[/tex]
The price of the item= 0.8 P
If the discount 20% is given on origional price of the item, than the price will be 0.8 P
Hence, the correct answer is 0.8 P
What is the total amount for an investment of $1,250 invested at 9.6% for 12 years and compounded continuously? ≈ $5006.50 ≈ $6125.25 ≈ $4062.65 ≈ $3955.64
The total amount for the investment is approximately $4062.65.
Explanation:To calculate the total amount for an investment of $1,250 invested at 9.6% for 12 years and compounded continuously, we can use the formula A = P * e^(rt), where A is the total amount, P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate, and t is the number of years. Plugging in the values, we have A = 1250 * e^(0.096 * 12). Using a calculator, we find that A is approximately $4062.65.
If the volume for 3-D pyramid A is 300 cm3 and the volume for 3-D pyramid B is 900 cm3, how many times bigger is the volume of pyramid B than pyramid A?
Answer:
Volume of pyramid B is three times bigger than the volume of pyramid A
Step-by-step explanation:
We are given that:
The volume for 3-D pyramid A is 300 cm³ .
and the volume for 3-D pyramid B is 900 cm³.
We have to tell how many times bigger is volume of pyramid B than volume of pyramid A.
volume of 3-D pyramid B= 900 cm³
= 3×300 cm³
= 3×volume of 3-D pyramid A
Hence, Volume of pyramid B is three times bigger than the volume of pyramid A
Answer:
Step-by-step explanation: 3%
Find the exact value of cos 75 by using a sum or difference formula
The exact value of cos 75 is (√6 - √2)/4 or 0.2588190.
What is Trigonometry?Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.
We have to find the exact value of cos 75.
So, The value of cos 75 degrees in decimal is 0.258819045.
Then,
cos 75°
= cos (1.3089)
= (√6 - √2)/4 or 0.2588190
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What is 7.75×10-1 in standard notation
The length of a rectangle is 3 ft more than twice the width, and the area of the rectangle is 77 ft2 . find the dimensions of the rectangle.
A card is picked from a standard deck of 52 cards. determine the odds against and the odds in favor of selecting a 10
The odds in favor of drawing a '10' from a standard 52-card deck are 1 to 12, and the odds against are 12 to 1.
Explanation:In a standard deck of 52 cards, there are four '10' cards - one each of hearts, diamonds, clubs, and spades. Hence the probability of drawing a '10' is 4 out of 52, or simplified, 1 out of 13.
Therefore, the odds in favor of selecting a '10' (i.e., the probability of selecting a '10' versus not selecting a '10') are 1 to 12 because for each '10' card there are 12 others that are not '10s'.
The odds against selecting a '10' are simply the inverse of the odds in favor. That is, for every one time you may draw a '10', there are 12 other times when you would draw something else, hence the odds against drawing a '10' are 12 to 1.
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The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 00 and 66 minutes. find the probability that a randomly selected passenger has a waiting time greater thangreater than 3.253.25 minutes. find the probability that a randomly selected passenger has a waiting time greater thangreater than 3.253.25 minutes.
The cost of fertilizing a lawn is $0.25 per square foot. find the cost to fertilize the triangular lawn whose base is left parenthesis 8 plus startroot 19 endroot right parenthesis8+19 feet and altitude is startroot 76 endroot76 feet.