A designer builds a model of a bicycle. The finished model is exactly the same shape as the original, but smaller. The scale factor is 2:7. (a) Find the ratio of the height of the model to the height of the original. (b) Find the ratio of the surface area of the model to the surface area of the original. (c) Find the ratio of the volume of the model to the volume of the original. Write these ratios in the format m:n.
Answers
Given
Scale Factor of 2:7
When the scale factor is a:b
Recall the following
[tex]\begin{gathered} \text{The ratio of the sides is} \\ a:b \\ \; \\ \text{The ratio of the area is} \\ a^2:b^2 \\ \; \\ \text{The ratio of the volume is} \\ a^3:b^3 \end{gathered}[/tex]Given that the ratio is is 2:7 then we have the following
[tex]\begin{gathered} \text{The ratio of the height of the model to the height of the original is} \\ 2:7 \\ \; \\ \text{The ratio of the surface area of the model to the surface area of the original is} \\ 2^2:7^2\Longrightarrow4:49 \\ \; \\ \text{The ratio of the volume of the model to the volume of the original is} \\ 2^3:7^3\Longrightarrow8:343 \end{gathered}[/tex][tex]undefined[/tex]
Related Questions
Can you please do this step by step.
Answers
The resulting exponent form is, 1/9¹⁰
Exponent:
Exponent is used to show repeated multiplication of a number by itself. For example,
7 × 7 × 7 can be represented as 7³
Here, the exponent is ‘3’ which stands for the number of times the number 7 is multiplied.
Given,
Here we have the exponent form is,
9⁻⁸x9⁻²
Here we have to use the product property and then we have to get rid of negative exponents.
First step is to use the product property,
We know that, the product property states that,
for any non-zero term a,
yᵃ x yᵇ = yᵃ⁺ᵇ
where a and b are real numbers.
So, the given expression is written as,
=> 9⁻⁸⁺⁽⁻²⁾
=> 9⁻⁸⁻²
=> 9⁻¹⁰
Now the second step is to get rid of the negative components,
As per the rule, the exponent is negative, we can change the exponent into positive by writing the same value in the denominator and the numerator holds the value 1.
So, the value is,
=> 9⁻¹⁰ = 1/ 9¹⁰
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Find the standard form of the graph
Answers
The Standard form is y = [tex]x^{2}[/tex] + 6x - 16
Given,
A quadratic function n standard form whose graph has the given characteristics.
and, passes through (-8, 0), (-6, -16), (2,0).
To find the y =?
Now, According to the question:
Because the graph of a quadratic goes through point (-8 ,0) and point (2, 0)
So, supposing the equation of the quadratic function is
y = a [x - (-8)] (x - 2) = a (x + 8)(x - 2)
The graph passes through the point (-6, 16)
So, -16 = a(-6 + 8)(-6 -2)
=> -16 = a x 2 x (-8)
=> a = 1
So, y = (x + 18)(x - 2)
y = [tex]x^{2}[/tex] + 8x - 2x - 16
y = [tex]x^{2}[/tex] + 6x - 16
Hence, The Standard form of y = [tex]x^{2}[/tex] + 6x - 16
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Given the radius r of a sphere, calculate it's volume V using the formula V = Calculate V when r = 2 feet and use 7 = 3.14. Round your answer to two decimal
Answers
Solution
The volume of a sphere is given by:
[tex]V=\frac{4}{3}r^3\pi^{}[/tex]And replacing the info given we got:
[tex]V=\frac{4}{3}\cdot(2ft)^3(3.14)=33.49ft^3[/tex]Then the final answer would be 33.49 ft3
Help please need answer
Answers
17Given:
The smaller triangle is,
Find the length of the hypotenuse,
[tex]\begin{gathered} \text{hypotenuse}^2=4^2+1^2 \\ =16+1 \\ =17 \\ \text{hypotenuse}=\sqrt[]{17} \end{gathered}[/tex]The larger traingle is,
[tex]\begin{gathered} \text{Hypotenuse}^2=12^2+3^2 \\ =144+9 \\ =153 \\ \text{Hypotenuse}=3\sqrt[]{17} \end{gathered}[/tex]Now, find all the trigonometric functions for a smaller triangle.
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}}=\frac{1}{\sqrt[]{17}} \\ \cos \theta=\frac{Adjacent\text{ side}}{\text{hypotenuse}}=\frac{4}{\sqrt[]{17}} \\ \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}=\frac{1}{4} \\ co\sec \theta=\frac{\text{hypotenuse}}{opposite\text{ side}}=\frac{\sqrt[]{17}}{1}=\sqrt[]{17} \\ \sec \theta=\frac{\text{hypotenuse}}{adjacent\text{ side}}=\frac{\sqrt[]{17}}{4} \\ \cot \theta=\frac{adjecent\text{ side}}{\text{opposite side}}=\frac{4}{1}=4 \end{gathered}[/tex]For the larger triangle,
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{\text{hypotenuse}}=\frac{3}{3\sqrt[]{17}}=\frac{1}{\sqrt[]{17}} \\ \cos \theta=\frac{Adjacent\text{ side}}{\text{hypotenuse}}=\frac{12}{3\sqrt[]{17}}=\frac{4}{\sqrt[]{17}} \\ \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}=\frac{3}{12}=\frac{1}{4} \\ co\sec \theta=\frac{\text{hypotenuse}}{opposite\text{ side}}=\frac{3\sqrt[]{17}}{3}=\sqrt[]{17} \\ \sec \theta=\frac{\text{hypotenuse}}{adjacent\text{ side}}=\frac{3\sqrt[]{17}}{12}=\frac{\sqrt[]{17}}{4} \\ \cot \theta=\frac{adjecent\text{ side}}{\text{opposite side}}=\frac{12}{3}=4 \end{gathered}[/tex]Therefore, the value of the function is the same because the triangles are similar so, corresponding sides are proportional.
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 4 h, and Car B traveled the distance in 4.5 h. Car B traveled 5 mph slower than Car A. (The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.) How fast did Car B travel? Enter your answer in the box.
Answers
Car B travelled with the rate of speed of 40mph .
In the question ,
it is given that ,
Car B travelled 5mph slower than Car A .
let the rate of speed at which Car B travelled be x mph.
So , the rate of speed of Car A is = (x+5) mph
Car A travelled the distance in 4 h , with the speed of (x+5) mph ,
the value of T = 4 h and R = (x+5) mph
So, by the formula R*T=D ,
we get ,the distance travelled by Car A = 4(x+5) miles .
Car B travelled the distance in 4.5 h , with the speed of x mph .
the value of T= 4.5h and R = x mph
So, by the formula R*T=D,
we get , the distance travelled by Car B = 4.5*x = (4.5x) miles .
Since , both the cars travelled the equal distance ,
we get ,
4(x+5) = 4.5x
4x+20=4.5x
4.5x-4x = 20
0.5x= 20
x = 40
Therefore , the rate of speed of Car B is 40 mph.
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The revenue for selling x units of a product is R = 113.95 x. The cost of producing x units is C = 93 x + 750. In order to obtain a profit, the revenue must be greater than the cost. For what values of x will this product produce a profit? (Enter a number. Round your answer up to the nearest whole unit.)
Answers
To make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.
As given in the question,
The revenue for selling x units of a product is R = 113.95 x.
The cost of producing x units is C = 93 x + 750
To make a profit, the revenue must be greater than the cost.
R > C
113.95x > 93x +750
Subtract 93x from both the sides
113.95x -93x +93x-93x +750
⇒20.95x > 750
⇒x > 750/20.75
⇒x>35.799
Value of x to produce a profit is 36units
Therefore, to make a profit with the revenue of R=113.95x and cost of C =93x + 750 the value of x is 36units.
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The skeletal system is not responsible for which of the following?
Answer now
Answers
Answer:
D
Step-by-step explanation:
D is managed by the circulatory system; all the others are done by skeletal system (blood cells are made in the bone marrow BTW).
My new music player has a capacity of 360 gigabytes.
Rewrite the following statement using a number in scientific notation.
Answers
Answer: My new music player has a capacity of 3.6*10^11 bytes.
Step-by-step explanation: Scientific notation of a number is going to be in the form of a*10^b where a is a number greater than 1 but less than 10 which is then multiplied by the appropriate power of 10 so that the numbers are equal. This allows us to see numbers concisely without getting distracted by the sheer number of zeroes in some numbers. For 360, since 3.6 is between 1 and 10, we use that for a. To get 3.6 to equal 360 you have to move the decimal two places to the right, or multiply by 10^2, so b=2. Since this is in gigabytes, and giga=10^9, to express the answer in bytes we just multiply 10^2 to 10^9=10^11
Hope this helps
how could you use the relationship between addition and subtraction with counting up to find 3 1/4 - 1 3/4
Answers
Answer:
1 1/2
Explanation:
We can illustrate the relationship between addition and subtraction using the following example:
If we have 5 - 3 = 2, then we can say that 2 + 3 = 5
So, in this case, the result of 3 1/4 - 1 3/4 is a number that added to 1 3/4 is equal to 3 1/4. Then, the answer will be 1 2/4 because:
[tex]1\frac{3}{4}+1\frac{2}{4}=\frac{7}{4}+\frac{6}{4}=\frac{13}{4}=3\frac{1}{4}[/tex]Because 1 3/4 is equivalent to 7/4 and 1 2/4 is equivalent to 6/4.
Finally, 2/4 is equivalent to 1/2, so we can rewrite the result 1 2/4 as follows:
1 2/4 = 1 1/2
Therefore, the answer is 1 1/2
A plot of land measure 25m by 12cm .A portion of this plot measuring 8m by 8m is used for cultivation of vegetable find the area of the plot not cultivated.
Answers
Answer
is ur question right
30in 10in 10in 30in 20in area of irregular figures
Answers
Answer:
Explanation:
he arrow comprises of two sshapes
• A rectangle with dimensions 30 inches by 20 inches.
,• A triangle with a base of 40 inches and a height of 30 inches.
Thus:
[tex]\begin{gathered} \text{Area}=\text{Area of Rectangle+Area of Triangle} \\ =(l\times w)+(\frac{1}{2}bh) \\ =(30\times20)+(\frac{1}{2}\times40\times30) \\ =600+600 \\ =1200\; in^2 \end{gathered}[/tex]The area of the arrow is 1200 square inches.
What number is 0.5% of 8
Answers
Answer:
0.5%=0.5/100
0.5/100×8=0.04
The depth of a local lake averages 26 ft, which is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|. What is the difference between the depths in February and July?
21 feet
23 feet
8 feet
13 feet
Answers
The difference between the depths in February and July is D. 13 feet.
How to illustrate the information?According to the information supplied, the symbol for the average depth of a nearby lake, which is 26 feet, is |26|. It was 5 feet deep in February, or |5|, and 18 feet deep in July, or |18|. As a result, it is important to remember that the depth in July is -18.
Consequently, the variation in depth between February and July will be
= -5 - (-18)
= -5 + 18
= 13
The depth is 13 feet as a result.
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Suppose you're conducting a hypothesis test for one mean, the significance level is , and the P-value is 0.30. Should you reject or fail to reject , and why?
Answers
The significance level is less than p-value, so we will fail to reject the hypothesis test.
Given,
Conducting a hypothesis test for one mean
The significance level, α = 0.05
The p-value = 0.30
We have to find the test is reject or fail to reject.
If the significance level is greater than p-value, we will reject the hypothesis test.
If the significance level is less than p-value, we will fail to reject the hypothesis test.
Here,
The significance level, α is 0.05 and the p-value is 0.30
Lets see,
The significance level is less than the p-value.
That is,
0.05 < 0.30
So, we will fail to reject the hypothesis test
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Question is stated in picture. Don’t forget to round to nearest tenth.
Answers
In order to calculate the volume of the cone, we can use the formula:
[tex]V=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Where r is the base radius and h is the height.
So, using r = 3 and h = 4, we have:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot3^2\cdot4 \\ V=37.68 \end{gathered}[/tex]Therefore the volume is 37.68 units³.
A mixture of alcohol and water contains a total of 35oz of liquid. There are 7oz of pure alcohol in the mixture. What percent of the mixture is water? What percent is alcohol?
Answers
The mixture has two components, this means that we can calculate the percentages if we divide the portion of water or alcohol by the total amount of the mixture.
For alcohol:
[tex]\frac{7oz}{35oz}\times100=0.2\times100=20\%[/tex]For water:
[tex]\frac{35oz-7oz}{35oz}\times100=0.8\times100=80\%[/tex]Answer:
The mixture is 20% alcohol and 80% water
<<<<< >>>>
How much is +7 - 4?
Number line: -15 to +15
A.3
B.11
C.-11
D.-3
_________
What is the value of +3 - 8?
Number line: -15 to +15
A.-11
B.-5
C.5
D.11
________
What is the value of 5 - 12?
Number line: -15 to +15
A.7
B.-17
C.17
D.-7
______What integer is the result of moving 10 units in a positive direction, starting at -6?
Number line: -15 to +15
A.-16
B.4
C.16
D.-4
Answers
Answer:
1. 3
2. -5
3. -7
4. 4
Step-by-step explanation:
prove me wrong
Hello, can you help me with problem? To understand it I need help thanks
Answers
Solution:
The student with the correct objective function and constraints is Dontavious.
her vertices for the correct feasible region is;
[tex](0,8),(3,4),(6,0)[/tex]he minimum cost of transportation for the field trip is; at (3,4) because it follows the constraint;
[tex]\begin{gathered} x+y\le7 \\ \\ \text{Other regions are above 7} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} C=300x+200y \\ C=300(3)+200(4) \\ C=900+800 \\ C=\text{ \$1700} \end{gathered}[/tex]Therefore, the minimum cost is $1,700
PLEASE HELP I DONT UNDERSTAND
Answers
(a) The angles are exterior angles.
(b) The angles are alternate exterior angles and are equal to each other.
(C) The value of x is 6 and the measure of angle 27x - 5 is equal to 130°.
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Two parallel lines and a transversal cutting them are given. The two angles are 130° and 27x - 5.
Both angles are exterior angles.
The angles 130° and 27x - 5 are alternate exterior angles and are equal.
Now,
130° = 27x - 5
Adding 5 on each side.
27x - 5 + 5 = 130 + 5
27x = 135
Dividing each side by 27
x = 5°
Therefore, substituting the value of x.
27x - 5 = 27(5) - 5 = 135 - 5 = 130°
Hence, the measure of angle 27x 0 5 = 130°
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Please help me with my calculus homework, thanks so much!
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Use geometry to evaluate:
[tex]\int ^2_0(\sqrt[]{4-x^2}\text{ ) }dx[/tex]Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
[tex]\pi\text{ -- OPTION B}[/tex]On a coordinate plane, point A is located (-2,2) and point B is located at (6,-1). Determine the coordinates of the point that is 7/8 of the distance from a to b
Answers
The coordinates of the point that is 7/8 of the distance from A to B is (5, -5/8)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
point A is located (-2,2) and point B is located at (6,-1). Let O(x, y) represent the point that is 7/8 of the distance from a to b, hence:
x = (7/8)(6 - (-2)) + (-2) = 5
y = (7/8)(-1-2) + 2 = -5/8
Point O = (5, 5/8)
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What is the gradient of the straight line shown
below?
Answers
Answer:
Gradient = 1.
Step-by-step explanation:
Note that it passes through the points (6, 6) and (0, 0)
So, the gradient is (6-0)/(6-0)
= 1.
The city is issuing bonds to raise money for a building project. You obtain a $4100 bond that pays 6% interest annually that matures in 8 years. How much interest will you earn?
Answers
rather its multiplication,division,adding, and subtraction I will give four answers
Answers: I think its 718320000
The function g(r) represents the shift of the
function f(x) five units to the right. If f(x)=
It +5, which of the following is g(x)?
Answers
A shipping box is 36 inches by 24 inches by 18 inches; how many cubic ft. can it hold?
A) 8 D) 12
B) 9 E) 15
C)10
Answers
The volume that the shipping box which measure 36 inches by 24 inches by 18 inches can hold is 9 cubic feet.
What is the volume of the shipping box with the given dimensions?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Given the data in the question;
Length l = 36 in = ( 32/12 )ft = 3ftWidth w = 24 in = ( 24/12 )ft = 2ftHeight h = 18 in = ( 18/12 )ft = 1.5ftVolume V = ?Plug the given values into the formula above and solve for the volume V.
V = w × h × l
V = 2ft × 1.5ft × 3ft
V = 3ft² × 3ft
Volume V = 9ft³
Therefore, the volume of the rectangular prism is 9 cubic feet.
Option B is the correct answer.
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You purchase $7,000 from a store offering 10% down, no interest if paid in full by three months.
$5,000 is paid before deadline, how much is owed if monthly interest is 2.49%?
Owed: $____________
Answers
The $7,000 worth of purchase and payment of $5,000 before the three months deadline gives the amount owed at 2.49% monthly compound interest rate as $2,153.15
Owed: $2,153.15
What is a compound interest rate?Compound interest accounts for the interest that is earned on an interest, such that the interest rate is compounded on an initial amount.
The given parameters are;
The amount of the items purchased from the store = $7,000
The amount of down payment required = 10%
The amount paid in three months = $5,000
Monthly interest on amount owed after three months = 2.49%
Required;
The amount owed after payment of $5,000 before three months
Solution;
Using the compound interest formula, we have;
[tex] \displaystyle{A = P \cdot \left(1 + r \right)^{n} }[/tex]
Where;
A = The amount owed
P = The amount loaned = $7,000 - $5,000 = $2,000
r = Monthly interest rate = 2.49%
n = The number of months = 3 months
Which gives;
[tex] \displaystyle{A = 2000 \times \left(1 + 0.0249 \right)^{3} \approx 2153.1509}[/tex]
The amount owed (for the 3 months period) is approximately $2,153.15
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57⁰
Diagram not
drawn accurately
(i) Work out the size of the angle marked p.
Answers
The measure of angle p is 213 degrees
How to determine the measure of the angle?The possible question is added at the end of the solution and as an attachment
From the attached figure, we have the following angles
Angle 1: Angle pAngle 2: Angle with a measure of 57 degreesAngle 3: Angle with a measure of 90 degrees i.e. a right-angled triangleAlso, from the attached figure:
We can see that the three angles named above are formed by lines that meet at a point (say the point of origin)
When multiple lines meet at a point, the sum of the angles formed at this point is 360 degrees
This means that
Angle 1 + Angle 2 + Angle 3 = 360
Substitute the known values in the above equation
So, we have
p + 57 + 90 = 360
Evaluate the sum in the above equation
So, we have
p + 147 = 360
Evaluate the like terms in the above equation
So, we have
p = 213
Hence, the value of the angle with the name p is 213 degrees
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Possible question
Diagram not drawn accurately
Work out the size of the angle marked p.
See attachment
If P is the midpoint of __. SP = x + 4, and ST = 4x, determine the length of __.
Answers
we have the segment ST
see the attached figure to better understand
ST=SP+PT -----> by addition segments postulate
P is the midpoint
that means
SP=PT
therefore
ST=2SP
substitute given values
4x=2(x+4)
4x=2x+8
4x-2x=8
2x=8
x=4
the length of segment ST is 4(4)=16 units
therefore
the answer is
If P is the midpoint of ST. SP = x + 4, and ST = 4x, determine the length of ST.
ST=16 units
SP=8 units
I went to Old Navy and found a pair of pants on sale for $24. This price was 15% off the original price. What was the original price?
Answers
The original price of the pants is $28.23
Let the original price of the pants be 100x
Then, the discount given will be 15x
and the sale price would be 85x
According to the question, the sale price given is 24
So,
85x = 24
x = 24÷85
x= 0.2823
Therefore,
100x = 100*0.2823
= 28.23
Hence, the original price of the pants is $28.23
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A truck is carrying tomato juice, orange juice, and cherry juice bottles in a ratio of 4:3:4. If there are 30 orange juice bottles, then how many juice bottles in total are there.
Answers
We know that there are tomato juice, orange juice, and cherry juice bottles in a ratio of 4:3:4, respectively.
As you can observe in the given ratio, to get 30 orange juice, we have to multiply it by 10. So, if we multiply the whole ratio, we obtain the following
[tex]\begin{gathered} 4\times10\colon3\times10\colon4\times10 \\ 40\colon30\colon40 \end{gathered}[/tex]This means that 30 orange juice bottles are in the same ratio as 40 tomato juice bottles and 40 cherry juice bottles.
Hence, the total number of juice bottles is 40+30+40 = 110.