Answer: 56
Step-by-step explanation:
Given: An astronomer wishes to measure on a photograph the distance between the image of a certain star and three other star images nearby.
The total number of images nearby = 8
The number of images chosen by astronomer = 3
Then, the number of choices of the three stars without being in order is given by :-
[tex]^8C_3=\frac{8!}{3!(8-3)!}=\frac{8\times7\times6\times5!}{3!5!}=56[/tex]
Hence, he has 56 choices .
ABC has coordinates of A (-8, -8), B(4, -2) and C (2, 2). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 1.5
1. A(-12, -8), B(6, -2), C(3, 2)
2. A(-12,-12), B(6, -3), C(3, 3)
3. A(-8, -8), B(4, -2) C(2, 2)
4. A(-5.33, -5.33), B 2.67, -1.33), C(1.33, 1.33)
The coordinates of the image after dilation with a scale factor of 1.5 are A(-12, -12), B(6, -3), and C(3, 3).
Explanation:To find the coordinates of the image after a dilation, we need to multiply the coordinates of each point by the scale factor. The scale factor is 1.5, so multiplying the x-coordinate and y-coordinate of each point by 1.5 will give us the new coordinates.
For point A (-8, -8), the new x-coordinate is -8 * 1.5 = -12 and the new y-coordinate is -8 * 1.5 = -12. So the image of A is (-12, -12).
Using the same process, we can find the new coordinates for points B and C as well. The correct answer is option 2: A(-12, -12), B(6, -3), C(3, 3).
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True or false: Dilating a triangle changes the angles and side length of the triangle
Answer:
Statement is false.
Step-by-step explanation:
Dilating of a triangle produces another triangle having properties as
(1) Corresponding angles of parent and dilated triangle will be same
(2) Corresponding sides of both the triangles will be in the same ratio. They can not measure equal.
Therefore, given statement is false.
Solve for L. p=2L+2w
In 4 hours, a car travels 200 miles. What is the speed of the car
Answer:
50 miles per hour
Step-by-step explanation:
200 ÷ 4 = 50
200 = miles in 4 hours
50 = miles in 1 hour
Final answer:
The speed of the car is calculated by dividing the distance traveled (200 miles) by the time taken (4 hours), resulting in a speed of 50 miles per hour.
Explanation:
To determine the speed of the car, we use the formula for speed, which is distance traveled divided by the time taken. In this case, the car travels 200 miles in 4 hours. Plugging in numbers, we calculate the speed as follows:
Divide the distance by the time:Therefore, the speed of the car is 50 miles per hour (mph).
Find the volume of the composite solid.
A. 420 ft^3
B. 530 ft^3
C. 630 ft^3
D. 840 ft^3
Answer:
[tex]V=630ft^3[/tex]
Step-by-step explanation:
This solid is composite by a triangular prism and a rectangular prism. So, let:
[tex]V_1=Volume\hspace{3}of\hspace{3}the\hspace{3}rectangular\hspace{3}prism\\V_2=Volume\hspace{3}of\hspace{3}the\hspace{3}triangular\hspace{3}prism[/tex]
Hence, the volume of the composite solid is:
[tex]V=V_1+V_2[/tex]
The volume of the rectangular prism is given by:
[tex]V_1=l*w*h[/tex]
Where:
[tex]l=length=8ft\\w=width=7.5ft\\h=height=7ft[/tex]
So:
[tex]V_1=8*7.5*7=420ft^3[/tex]
The volume of the triangular prism is given by:
[tex]V_2=\frac{1}{2} l*b*h[/tex]
Where:
[tex]l=Distance\hspace{3} between\hspace{3} the\hspace{3} triangular \hspace{3}faces=8ft\\b=length\hspace{3}of\hspace{3} one\hspace{3} side \hspace{3}of\hspace{3} the \hspace{3}triangle=7.5ft\\h=length \hspace{3} of \hspace{3} an \hspace{3}altitude \hspace{3} drawn \hspace{3} to \hspace{3} that \hspace{3}side=7ft[/tex]
So:
[tex]V_2=\frac{8*7.5*7}{2} =210ft^3[/tex]
Therefore:
[tex]V=420ft^3+210ft^3=630ft^3[/tex]
Why is it preferable to measure a penny in millimeters?
Millimeters are preferred for measuring a penny because they offer greater precision and accuracy, enabling us to measure the dimensions of small objects like a penny with closer to exact measurements.
It is preferable to measure a penny in millimeters because millimeters provide a more precise and accurate measurement due to their smaller size compared to centimeters. The standard width of a penny is 1.9 cm, which is equivalent to 19 mm. Since scientists have established the convention of using the degree of precision dependent on the measuring device, millimeters are more appropriate for small objects like a penny to get an accurate measurement. A millimeter allows us to report the size of the penny to the nearest millimeter, facilitating a precise estimation.
When choosing a unit of measurement, one must consider the object's size and the necessary precision. For very small objects like a paper clip or a penny, millimeters would give the most accurate measurement, compared to centimeters, which are 10 times bigger and could provide a less accurate measurement. Therefore, for tasks requiring precise measurements of small dimensions, millimeters are preferred.
What number can you multiply by π to get a rational number?
Select each correct answer.
0
1π
−π
2
Solution:
0 is the correct option.
Explanation:
We have been given the number π, which is an irrational number. The value of π is 3.14
Now, let us multiply the number π with the given numbers in option and see what type of number we get.
[tex]0\times \pi = 0\\\\1\pi \times \pi = \pi^2\\\\-\pi \times \pi = -\pi^2\\\\2\times \pi = 2\pi[/tex]
Among all the above result, only 0 is a ration number.
Hence, when we multiply 0 with π then the result will be a rational number.
Answer:
A/0
Step-by-step explanation:
Shirt cost $20 each and ties cost $12 each. Write an expression for the cost of s shirts and t ties
Answer:
The cost of "s" shirts and "t" ties = $20s + $12t
Step-by-step explanation:
Given:
Shirt cost = $20 each
Ties cost = $12 each.
The number of shirts represented by "s" and the number of ties represented by "t"
Cost = $20*the number of shirts + $12*the number of ties
so, the cost of "s" shirts and "t" ties = 20s + 12t
Example:
If we want to find the cost 2 shirts and 3 ties, we need to plug s = 2 and t= 2 in the above expression.
The cost of 2 shirts and 3 ties = 20*2 + 12*3
= 40 + 36
= $76
The cost of 2 shirts and 3 ties is $76.
An architect built a scale model of a shopping mall. On the model, a circular fountain is 27 inches tall and 63 inches in diameter. If the actual fountain is to be 6 feet tall, what is its diameter?
14 ft
12 ft
2.6 ft
42 ft
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Why do have to ignore the absolute value sign while solving differential equation?
Can someone help me please? (Math)
The rectangular piece of property measures 10 mi by 4 mi. find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.
A store offers a 15% discount on all items in the store during a sale. All store employees get an additional 10% employee discount. In the equation below, C represents the cost of an item for an employee including tax and x represents the original price of the item:
C = 0.765x + 0.06(0.765x)
Chris is an employee at the store. He plans to buy a coat during the sale. The price of the coat before the discount is $100. How much will Chris pay for the coat during the sale? Remember, do not include the $ symbol.
Answer for Blank 1:
If 7 sandwich rolls cost $1.54, how much will 30 rolls cost?
A line is to be graphed through the point (–3, 0). which points can be used to create a line with an undefined slope through (–3, 0)? check all that apply. (–5, –3) (–3, –6) (–3, 2) (–1, 0) (0, –3) (3, 0)
Answer:
[tex](-3,-6)[/tex]
and
[tex](-3,2)[/tex].
Step-by-step explanation:
The given point is [tex](-3,0)[/tex].
If we want to use a point to create a line with an undefined slope through [tex](-3,0)[/tex], then that point must have the same x-coordinates as the given point.
Since the given point, [tex](-3,0)[/tex] has an x-coordinate of [tex]-3[/tex], we check all the points that have an x-coordinate of -3.
The correct answers are;
[tex](-3,-6)[/tex]
and
[tex](-3,2)[/tex].
These point will make the slope undefined, because it will result in division by zero.
If 5 ib of pasta salad serves 14 people how much pasta salad should you bring to a picnic with 49 people
Final answer:
To determine how much pasta salad is needed for 49 people when 5 pounds serves 14 people, calculate the proportion based on ounces, resulting in 17.5 pounds needed for 49 people.
Explanation:
If 5 pounds of pasta salad serves 14 people, the amount needed for 49 people can be calculated by setting up a proportion because the number of people and the amount of pasta salad are directly proportional. First, we convert 5 pounds of pasta salad to ounces, since the standard conversion is 1 pound = 16 ounces, so 5 pounds equals 80 ounces.
Next, we set up the proportion as follows:
14 people → 80 ounces of pasta salad
49 people → x ounces of pasta salad
To solve for x, you cross-multiply and divide:
14x = 80 * 49
x = (80 * 49) / 14
x = 280 ounces
Thus, you will need 280 ounces of pasta salad, which is equivalent to 17.5 pounds (since 280 ounces divided by 16 ounces per pound equals 17.5 pounds). Therefore, for a picnic with 49 people, you should bring 17.5 pounds of pasta salad.
A jewelry store is selling necklaces and bracelets. Each necklace yields a profit of $8 and each bracelet yields a profit of $6. It costs $3.50 and 11 minutes to create each necklace and $2.50 and 5 minutes to create each bracelet. The store has 880 available minutes and $330 available for production. The owner also estimates that the total demand will not exceed 120 units.
How many bracelets and necklaces should the owner sell?
n = necklace
b = bracelet
n +b =120
n = 120-b
3.50n + 2.50b = 330
11n + 5b = 880
3.5(120-b) +2.5b=330
420-3.5b + 2.5b = 330
420 -b = 330
-b = -90
B =90
N = 30
3.5*30= 105
2.5*90 = 225
225 +105 = 330
11*30 = 330
90*5 = 450
450 +330 = 780
90 bracelets and 30 necklaces
Simplify 4(6 - 2x) - 3(3 - 4x)
Find the equation (in terms of xx and yy) of the tangent line to the curve r=3sin2θr=3sin2θ at θ=π/6θ=π/6
A suit is on sale for 26% off. the sale price is $629.what is the regular price?
Marisa is walking from her home to her friend Sanjay's home. When she is 12 blocks away from Sanjay's home she looks at her watch. she looks again when she is 8 blocks away from Sanjay's home and finds that 6 minutes have passed?
A.what do you need to assume in order to treat this as a linear situation
B. identified the variables for the linear situation and identify two points on the line explain the meaning of the points in the in the context of the problem
C. find the slope of the line and describe what it means in the context of the problem
D. write an equation in point slope form for the situation and use it to find the number of minutes It takes to reach Sanjay's home. show your work
Final answer:
Marisa walks at a constant speed to Sanjay's home, covering 1.5 blocks each minute.
Two points on the line representing her journey are (12, 0) and (8, 6).
The slope of line is -1.5.
The point-slope form of the equation is y = -1.5x + 18, and it takes 18 minutes to reach home.
Explanation:
To answer the question about Marisa walking to her friend Sanjay's home, we need to treat her journey as a linear situation.
A. Assumptions for a Linear Situation:
We need to assume that Marisa is walking at a constant speed between the two observed points.
In other words, there are no changes in her walking pace between being 12 and 8 blocks away from Sanjay's home.
B. Variables and Points on the Line:
The variables in this linear situation would be distance to Sanjay's home (x) and time passed (y).
Two points on the line are (12, 0) when she starts at 12 blocks away and looks at the watch, assuming 0 minutes have passed, and (8, 6) when she is 8 blocks away after 6 minutes.
C. Slope of the Line:
The slope of the line can be calculated using the formula slope = (y2 - y1) / (x2 - x1).
Hence, the slope equals (6 - 0) / (8 - 12) = 6 / (-4) = -1.5 blocks/minute.
This slope indicates that Marisa covers 1.5 blocks each minute.
D. Equation and Time to Reach Sanjay's Home:
The point-slope form of the equation is y - y1 = m(x - x1).
Using the point (8, 6) and the slope -1.5, the equation is y - 6 = -1.5(x - 8).
Rearranging, we get y = -1.5x + 18.
To find out how many minutes it takes to reach Sanjay's home when x = 0, we plug in the values to get
y = -1.5(0) + 18,
y = 18 minutes.
subtract 6a squared plus 3a minus 4a squared plus 2a
Which statement about the equation is true? 3y – 1 = 13 – 4y The equation has one solution. The equation has no solution. The equation has a few solutions. The equation has many solutions.
Answer:
The equation has one solution
Step-by-step explanation:
Add 4y +1 and divide by 7.
3y -1 = 13 -4y
7y = 14
y = 2
There is one solution.
Answer:
equal to 2
Step-by-step explanation:
The solution to an inequality is given in set builder notation as {x l x > }. What is another way to represent this solution set?
(–∞ , ]
(–∞ , )
(, ∞)
[, ∞)
A set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy. In your case, the set builder notation {x l x > } means that the set consists of all elements that are greater than.
Consider number line. Plot the point as unfilled circle that goes after > sigh and shade the ray that goes from this point to the right. Then another way to represent this solution is
( ,∞).
Answer: correct choice is C
Final answer:
The correct alternative representation of the set builder notation { x | x > A } in interval notation is ( A, ∞ ), which includes any number greater than A up to positive infinity, but does not include A itself.
Explanation:
The solution to an inequality given in set builder notation as { x | x > A } can be represented in interval notation in several ways, depending on the specifics of the inequality. If the set includes all numbers greater than A, but does not include the number A itself, the interval notation is ( A, ∞ ). This means that the solution set includes any number greater than A, extending to positive infinity, but it does not include A because of the use of the parenthesis.
Interval notation such as [ A, ∞ ) would mean that the set includes the number A and extends to positive infinity. However, this is not the correct representation if the initial set builder notation specifies that x is greater than A, not greater than or equal to A. Similarly, intervals ( -∞ , A ] and ( -∞ , A ) represent sets that include numbers less than or equal to A, and less than A, respectively, which again isn't the case here.
Therefore, the correct answer is 2nd option
What is the angle of rotation of this regular octagon? what is the measure of an interior angle?
Final answer:
The angle of rotation of a regular octagon is 45°, and the measure of an interior angle of a regular octagon is 135°.
Explanation:
The angle of rotation for a regular octagon can be found by dividing the full circle of 360 degrees by the number of sides, which is 8 for an octagon. Therefore, the angle of rotation is 360° / 8 = 45°.
The measure of an interior angle of a regular octagon is determined by the formula (n-2) × 180° / n, where 'n' is the number of sides. Substituting 8 for 'n', the measure of an interior angle is (8-2) × 180° / 8 = 6 × 180° / 8 = 135°.
Write the number in scientific notation. 322,000,000
Answer:
[tex]3.22\times 10^{8}[/tex]
Step-by-step explanation:
In scientific notation we write a very large or very small number as the product of a number between 0 to 9 and the exponent of 10,
Here, the given number,
[tex]322,000,000[/tex]
[tex]=3.22\times 10^{8}[/tex]
Hence, the scientific notation of the given number is [tex]3.22\times 10^{8}[/tex]
Sam buys one bag of flour for $2.50, three packages of shredded cheese for $3.00 each, and two packages of mushrooms for $3.50 each. How much does Sam pay in all?
Answer:
The Answer is 18.5 which could also be 18.50
Step-by-step explanation:
The amount that Sam pay should be $18.50
Given that,
Sam buys one bag of flour for $2.50, three packages of shredded cheese for $3.00 each, and two packages of mushrooms for $3.50 each.Based on the above information, the calculation is as follows:
[tex]= (1 \times \$2.50) + (3\times \$3) + (2\times \$3.50)[/tex]
= $2.50 + $9 + $7
= $18.50
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A metallurgist needs to make 12.4 lb. of an 10) alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold.How much of each should he use?
Look at the rectangle and the square:
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Finding the Length of the Diagonals
Rectangle PQSR
Diagonal SQ, using the Pythagorean Theorem (a^2 + b^2 = c^2), would be equal to:
14^2 + 7^2 = c^2 (Where c is the hypotenuse;)
196 + 49 = c^2
Square root of 245 = c
15.6 inches.
Square LMON
Diagonal OM, using the Pythagorean Theorem (a^2 + b^2 = c^2), would be equal to:
7^2 + 7^2 = c^2 (Where c is the hypotenuse;)
49 + 49 = c^2
Square root of 98 = c
9.9 inches.
Finding the Diagonal Relation
9.9 * 2 = 19.8
19.8 is not equal to diagonal SQ.
9.8 is therefore not two times the length of 15.6, so Anna is incorrect.
Anna says that the length of diagonal SQ is two times the length of diagonal OM which is incorrect.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Look at the rectangle and the square:
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
The diagonal is given by the Pythagoras theorem.
Diagonal SQ will be
SQ² = QR² + SR²
SQ² = 7² + 14²
SQ = 15.65 inches
Diagonal OM will be
OM² = ON² + MN²
OM² = 7² + 7²
OM = 9.899 inches
Twice of OM will be
⇒ 2 x OM
⇒ 2 x 9.899
⇒ 19.798 which is not equal to SQ.
Anna says that the length of diagonal SQ is two times the length of diagonal OM which is incorrect.
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Write an equation of the line that passes through the points (-3,4) and (-5,1)