The linear scale factor for going from first to second statue will be 2/3 and the weight of the second statue will be 96 2/3 pounds.
How to illustrate the information?It should be noted that the statue is 6 feet tall and weighs about 145 pounds and second model statue is 4 feet tall.
Therefore, the linear scale factor for going from first to second statue will be:
= 4/6
= 2/3
Therefore, the weight of the second statue will be:
= 2/3 × 145
= 96 2/3 pounds.
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For a class project, Henry needs to know how many students at M College think that
climate change is a serious issue. He surveys the students in his classes, and finds that
205 of the 345 students he surveys agree that climate change is a serious issue. There
are 2960 students at M College. Find the estimated number of students at the M College
who agree climate change is a serious issue. What percent of total students is that? What
assumptions are needed, and what are the limitations of his method?
The estimated number of students at the M College who agree climate change is a serious issue is 1759
The percentage of total students is 59.42%
The method used can be biased.
How many students believe climate change is a serious issue?The students surveyed are the sample while the students in the M College are the population. A population is the party of interest in an experiment. A population consists of all the members of the group. A sample is a smaller group of the population.
The limitation of using a sample to estimate for the population is that the sample might be a biased estimate of the population. If the sample is biased, the result of the experiment would be inaccurate.
Estimated number of students at M College = (sample that agree that climate change is a serious problem / total number of people surveyed) x number of students
(205 / 345) x 2960 = 1759
Percentage = (1759 / 2960) x 100 = 59.42%
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PLEASE HELP! DUE IN LESS THAN 2 HOURS! IM STUCK! PLEASE HELP ME! YOU WILL GET 100 POINTS! THANKS QUESTION DOWN BELOW!!! PLEASE SHOW THE WORK!
Answer:
Do you want the equation?
y = [tex]x^{2}[/tex]
Step-by-step explanation:
Answer:
1. One square
2. Four squares
3. Nine squares
4. Sixteen squares
5. Twenty-five squares
6. Thirty six squares
7. 49 squares
8. 64 squares
9. 81 squares
10. 100 squares
Step-by-step explanation:
The pattern is add six squares to the image before the one you’re working.
[tex] \rm If \: \beta = \lim_{x \to0} \frac{ {e}^{ {x}^{3} } - (1 - {x}^{3} {)}^{ \frac{1}3 } + ((1 - {x}^{2} {)}^{ \frac{1}{2} } - 1) \sin x}{x \sin^{2} x} ,\\ [/tex]
then the value of [tex]6 \beta [/tex] is
Expand the limand as
[tex]\dfrac{e^{x^3} - (1 - x^3)^{1/3} + \left((1-x^2)^{1/2} - 1\right) \sin(x)}{x \sin^2(x)} \\\\ ~~~~~~~~ = \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} \cdot \dfrac{x^2}{\sin^2(x)} + \dfrac{(1-x^2)^{1/2} - 1}{x^2} \cdot \dfrac{x}{\sin(x)}[/tex]
Recall that for [tex]a\neq0[/tex],
[tex]\displaystyle \lim_{x\to0} \frac{\sin(ax)}{ax} = 1[/tex]
Then
[tex]\displaystyle \beta = \lim_{x\to0} \left( \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} + \dfrac{(1-x^2)^{1/2} - 1}{x^2}\right)[/tex]
Rationalize the numerators.
[tex]\dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} = \dfrac{e^{3x^3} - (1 - x^3)}{x^3 \left(e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}\right)} \\\\ ~~~~~~~~~~~ = \left(\dfrac{e^{3x^3} - 1}{x^3} + 1\right) \cdot\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}}[/tex]
and observe that
[tex]\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}} \to \dfrac13[/tex]
[tex]\dfrac{(1-x^2)^{1/2}-1}{x^2} = \dfrac{(1-x^2) - 1}{x^2 \left((1-x^2)^{1/2} + 1\right)} \\\\ ~~~~~~~~ = -\dfrac1{(1-x^2)^{1/2} + 1} \to -\dfrac12[/tex]
This leaves us with
[tex]\displaystyle \beta = \lim_{x\to0} \frac{e^{3x^3} - 1}{3x^3} - \frac16[/tex]
The remaining limit is the derivative of [tex]e^{3x^3}[/tex] at [tex]x=0[/tex], so its value is 1, and we find
[tex]\beta = 1 - \dfrac16 = \dfrac56 \implies 6\beta = \boxed{5}[/tex]
solve 6/58 x -1 2/5 -371/40 -6 1/4 1 1/2 371/40
The simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
6 5/8 x -1 2/5
Convert the mixed fractions to improper fractions
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/8 x 1/5
Evaluate the product of the denominators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/40
Hence, the simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
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the lengths of the four sides as a quadrilateral (in feet) are consecutive integers if the perimeter is 86 ft find the value of the longest of the four side lengths
Let x be the shortest side
Let x+1 be the second side
Let x+2 be the third side
Let x+3 be the fourth and longest side
[tex]perimeter = s_{1} + s_{2} + s_{3} + s_{4} \\ 86 = x + (x + 1) + (x + 2) + (x + 3) \\ 86 = x + x + 1 + x + 2 + x + 3 \\ 86 = 4x + 6 \\ 4x = 80 \\ x = 20[/tex]
Shortest side is 20 cm
Longest side is x+3 so 20+3=23
Answer: 23What is the midpoint of the segment shown below?
-10
(-8,-7)
10
(-7,-8) 10-
10
O A. (-15, -15)
OB. (-¹5-15)
O C. (-15, -15)
O D. (-1/5, -1¹/5)
SUBN
The midpoint of the segment where the segment has the endpoints (-8,-7) and (-7,-8) is (-15/2, -15/2)
How to determine the midpoint of the segment shown below?On the segment, we have the following endpoints
(-8,-7) and (-7,-8)
The midpoint of the segment is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
Where
(x1, y1) = (-8,-7)
(x2, y2) = (-7,-8)
Substitute the known values in the above equation
So, we have
Midpoint = 1/2 * (-8 + -7, -7 - 8)
Evaluate the difference in the above equation
So, we have
Midpoint = 1/2 * (-15, -15)
Evaluate the product in the above equation
So, we have
Midpoint = (-15/2, -15/2)
Hence, the midpoint of the segment where the segment has the endpoints (-8,-7) and (-7,-8) is (-15/2, -15/2)
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I need help with 4 and 5
4. The two triangles are similar by virtue of the AAA triangle congruence theorem as a result of the corresponding angles which have equal measures.
5. The length of segment CE to the nearest tenth is; 46.7 in.
What is the length of segment CE as required in the task content?4. The ∆CBD and ∆CAE are similar (congruent) following the fact that angle C is common to both triangles and the angles A and E have equal measures as E and D respectively by virtue of corresponding angles theorem. Ultimately, the two triangles; ∆CBD and ∆CAE are congruent since all three angle measures are the same in the triangles.
The corresponding angles in discuss is due to the fact that the lines ED and AE are parallel lines.
5. Also, upon establishing the congruence of the two triangles, it follows that the ratio of their corresponding sides is same for all three sides.
Therefore, we can establish that;
BD/AE = CD/CE
6/14 = 20/CE
CE = (14 × 20)/6
CE = 140/3
CE = 46.667 in.
Ultimately, the length of segment CE to the nearest tenth is; 46.7 in.
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investment will pay $332,640 at the end of next year for an investment of $220,000 at the start of the year. If the market interest rate is 8% over the same period, should this investment be made?
A.
Yes, because the investment will yield $85,536 more than putting the money in a bank.
B.
Yes, because the investment will yield $76,032 more than putting the money in a bank.
C.
Yes, because the investment will yield $95,040 more than putting the money in a bank.
D.
No, because the investment will yield $95,040 less than putting the money in a bank.
Based on the amount the investment would pay at the end of next year, and the market interest rate, C. Yes, because the investment will yield $95,040 more than putting the money in a bank.
How to know if the investment should be made?The investment of $220,000 at the market rate of 8% would earned:
= 220,000 x 8%
= $17,600
The amount that the investment would make instead is:
= 332,640 - 220,000
= $112,640
The difference is:
= 112,640 - 17,600
= $95,040
In conclusion, the investment should be made.
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A turtle was swimming 2 feet below the surface of a pond. While looking for food, he went down 7 more feet
Look for acute, obtuse, and right angles in your environment or find one of each online. Post an image of each. Can you find all three in one spot?
Identify the acute, obtuse, and right angles in your image or images.
Answer: Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.
Step-by-step explanation:
4x + 3 - x = [?]x + [ ]
Answer:
3x + 3
Step-by-step explanation:
4x + 3 - x can be expressed as:
x + x + x + x + 3 - x
If we combine like terms:
x + x + x + x - x + 3
x + x + x + 3
3x + 3
Find the area of the semicircle. (Take pi=22/7) Diameter=14
Area of semicircle is 77.
What is semicircle?
A semicircle is defined as half circle formed by cutting the circle into two halves.
Given that;
Diameter of semicircle = 14
Radius of semicircle = 14/2 = 7
Now, Area of semicircle = 1/2 (πr²)
Substitute π = 22/7 and r = 7, we get;
Area of semicircle = 1/2 (πr²)
= 1/2 × (22/7) × 7 × 7
= 77
So, Area of semicircle is 77.
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If m∠3 = 4x + 10 and m∠4 = 5x, find x.
The value of x is 10.
Given m∠3 = 4x+10 and m∠4 = 5x
Now, we need to determine what value of x it is.
We know that in quadrilateral four angles are there in that two angles are equal it is said to be as Rhombus.
Two angles are given in this question. We assume those are equal angles.
∴ m∠3 = m∠4
By substituting the values of two angles, we get
4x+10 = 5x
By deducting '4x' on both sides, we get
4x+10-4x = 5x - 4x
10 = x
∴ x = 10
The final value for x is 10.
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the graph shows two points from the table representing a proportional relationship. Which point corresponds to the last entry in the table?
Answer:
Step-by-step explanation: second point correspond to the last entry in the table
The ratio of males to females at a basketball game was 4:5 suppose there were 80 females at the basketball game how many people were at the game all together
Using ratio, we concluded that there are total 144 people at the basketball game.
How do we calculate ratio?Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
Let x be the number of people at the basketball game.
4x = number of males
5x = number of females
Total females = 80
⇒ 5x = 80
⇒ x = 16
4x = 4 × 16
⇒ 64
∴ Total males = 64
Total people present = number of males + number of females
⇒ 64 + 80
⇒ 144
∴Total people at basketball game are 144
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Solve the absolute value inequality |-2z+30| ≤ 30
The answer of the above question is [0,30]
An absolute value inequality is one with an absolute value sign and a variable inside.
An important point to remember: | x |= {x if x ≥ 0 }
| x |= {x if x< 0}
taking the expression |-2z+30| ≤ 30
Write the equivalent compound inequality.
-30≤ -2z+30 ≤ 30
= -30-30 ≤ -2z ≤ 30-30
= -60≤ -2z ≤ 0
= -60/2 ≤ -z ≤ 0
= -30 ≤ -z ≤ 0
Solve the compound inequality.
= 0 ≥ z ≥ 30 (reversing of signs)
Hence, the solution using interval notation [0,30].The check is left to you.
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There is a 6m long pool and there are logs that are 1\2 a meter long. How many logs does she need?
Six 3 digit numbers contain the digit 4, 6 and 8. What are they?
Answer:
468
486
648
684
846
864
For Exercises 1 and 2, use the table. It shows the types of
and prices of Jolly Juice Orange Juice.
Bottles of Jolly Juice Orange Juic
Containers
Price
8 oz
$0.96
16 oz
$1.60
32 oz
$2.56
64 oz
$3.84
1. Find the unit rate for an 8-ounce
container of Jolly Juice. Explain your
answer.
2. Find the unit rate for each size. Then order the sizes from least to greatest unit rate
Answer:
I have 5 apples and give u 2 how much I have
A copy machine makes 91 copies in 3 minutes and 15 seconds. How many copies does it make per minute?
copies per minute
X
5
Find the value of X then find the measure of each labeled angle.
The value of the angle x is 108 degree.
According to the statement
We have to find that the value of the x in the adjacent angle.
So, For this purpose, we know that the
The adjacent angles is the two angles are said to be adjacent angles when they share the common vertex and side.
From the given information:
When we extend line AB to E
Then ∠EBC is created
Since BC is parallel to AD
So, ∠EBC =∠BAD = x° (corresponding angles are equal )
Linear pair : Two angles are said to be linear if they're adjacent angles formed by two intersecting lines. The measure of a angular unit is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Now With the linear pair property
x+(x-36) = 180
2x - 36 = 180
2x = 180+36
2x = 216
x = 216/2
x = 108.
Then one angle is of 108 degree and second angle is 72 degree.
So, The value of the angle x is 108 degree.
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A square window has an area of 9 square feet. What is the perimeter of the window?
Answer:
12
Step-by-step explanation:
help me do this plroblem
Answer: $640
Step-by-step explanation:
Answer:
640
Step-by-step explanation:
16. Vocabulary A number written in
expanded form is written as the sum
of each …..
.Write 39,005
in expanded form...
HELP PLEASE? THE PICTURE IS ATTACHED FOR ANYONE THAT WANTS TO HELP, I’D APPRECIATE IF SOMEONE HELP ME ANSWER THIS
Answer:
$32.00
Step-by-step explanation:
The easiest way of calculating discount is, in this case, to multiply the normal price $80 by 40 then divide it by one hundred. So, the discount is equal to $32. To calculate the sales price, simply deduct the discount of $32 from the original price $80 then get $48 as the sales price.
HELP PLEASE? THE PICTURE IS ATTACHED FOR ANYONE THAT WANTS TO HELP, I’D APPRECIATE IF SOMEONE HELP ME ANSWER THIS
Answer:
40% Of 80 is 32
8.G.A.1- I can verify the properties of rotations, reflections, and translations
Describe the transformation that occurred to get from the figure ABCD to EFGH. Include all necessary components of the transformation (angle of rotation, direction, center of rotation, how many units and in what direction, line of reflection, etc)
The transformation that occurred to get from the figure ABCD to EFGH, including the necessary terminologies is as follows:
Step 1: Reflection
The reflection using the y axis as the line of reflection at point C After the reflection the points changed A = E, D = H, C = G, and B = F
Step 2: Rotation
The rotation occurred with point A now E as the center of rotation. The angle of rotation is 90 degrees anticlockwise direction.
Step 3 Translation
The quadrilateral is now moved 4 units to the left to arrive at the new position.
What is transformation?Transformation is a term used in mathematics to describe some technical movements that objects makes. This objects are usually plotted to ensure that every movement can be calculated.
Some terms in transformation are reflection, rotation, translation and so on. Reflection produces mirror image of the object, Rotation is achieved using a specified angle and the direction is specified with either clockwise or anticlockwise then Translation is more of a straight forward movement.
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I need help to find the degree
Answer:
Step-by-step explanation:
Find the degree, leading term, and leading coefficient.
Polynomial Degree:
2
Leading Term:
5x²
Leading Coefficient:
5
-6(w +5 ) +9<-51
Solve the inequality
Answer:
w>5
Step-by-step explanation:
Go onto symbolab it's a website good for solving math problems like this
The leg of a right triangle is 8 ft in length while
the hypotenuse is 15 ft in length. Find the missing
side of the triangle. Write the answer in simplified
radical form
Answer:
[tex]\sqrt{161}[/tex] ft
Step-by-step explanation:
According to the pythagorean theorem, in a right-angle triangle, the sum of of the squared legs is equal to the hypotenuse squared.
In simpler words, if we have legs [tex]a[/tex] and [tex]b[/tex], as well as hypotenuse [tex]c[/tex], then [tex]a^2 + b^2 = c^2[/tex].
In our case, we know that [tex]a = 8[/tex] and [tex]c = 15[/tex], therefore, we should try and find b.
[tex]8^2 + b^2 = 15^2\\\to 64 + b^2 = 225 \text{ // Subtract by 64}\\\to b^2 = 161 \text{ // Take the square root of both sides}\\\to b = \sqrt{161}[/tex]
6. BUILDING A horse farm is developing a new indoor arena in a rectangular building. They want the width of the building to be 2y feet and the length to be 4y – 9 feet. Write an expression in simplest form to represent the area A of the building in terms of y.
The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.
Here, we are given the dimensions of a rectangular arena, which are as follows-
Length = 4y - 9 feet
width = 2y feet
The area of a rectangle is given by the formula-
Area of a rectangle = length x breadth
Thus, in this case, area (A) can be calculated as follows
A = (4y - 9) * 2y
Now, we simplify the equation-
A = (4y)(2y) - 9(2y)
A = 8 - 18y
Thus, the area of the rectangular arena can be represented by the following equation- A = (8 - 18y) square feet.
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