Part A:
We are given that the height of a tree in a scale drawing is 3.75 inches. The scale of the drawing is 1 inch: 50 feet.
To find the height of the actual tree, we can use the ratio of the drawing scale to the real-life scale. For every 1 inch on the drawing, there are 50 feet in real life.
Therefore, we can set up a proportion:
[tex]$\frac{1 \ \text{inch}}{50 \ \text{feet}} = \frac{3.75 \ \text{inches}}{x \ \text{feet}}$where $x$ is the height of the actual tree in feet.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot x = 3.75 \ \text{inches} \cdot 50 \ \text{feet}$$x = \frac{3.75 \ \text{inches} \cdot 50 \ \text{feet}}{1 \ \text{inch}} = 187.5 \ \text{feet}$Therefore, the height of the tree is $\boxed{D \ 187.5 \ \text{ft}}$.[/tex]
[tex]Part B:We are now given a new scale drawing where the height of the same tree is 6 inches. We need to find the new scale.Since the tree's height in the new drawing is different, we can use a new proportion to find the new scale.Let the new scale be $1$ inch to $x$ feet. We can set up a proportion:[/tex]
[tex]$\frac{1 \ \text{inch}}{x \ \text{feet}} = \frac{6 \ \text{inches}}{187.5 \ \text{feet}}$where $187.5$ feet is the height of the tree in real life.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot 187.5 \ \text{feet} = 6 \ \text{inches} \cdot x \ \text{feet}$$x = \frac{1 \ \text{inch} \cdot 187.5 \ \text{feet}}{6 \ \text{inches}} = 31.25 \ \text{ft}$Therefore, the new scale is $\boxed{1 \ \text{inch} : 31.25 \ \text{ft}}$.[/tex]
Answer:
Step-by-step explanation:
Part A:
We can use a proportion to solve for the height of the tree:
1 inch on the drawing represents 50 feet in real life.
So, 3.75 inches on the drawing would represent:
3.75 inches * (50 feet/1 inch) = 187.5 feet
Therefore, the height of the tree is 187.5 feet.
The answer is D) 187.5 ft.
Part B:
The ratio of the height of the tree on the new scale drawing to its actual height must be the same as the ratio of the height of the tree on the original scale drawing to its actual height.
Let the new scale be 1 in. : x feet.
Then, we have the proportion:
1 in. / 50 ft. = 6 in. / (x) ft.
Solving for x, we get:
x = (6 in. * 50 ft.) / 1 in.
x = 300 ft.
Therefore, the new scale is 1 in. : 300 ft.
The answer is 1 in. : 300 ft.
A ship travels east from Port Lincoln 24 miles before turning north. When the ship becomes disabled
and radios for help, the rescue boat needs to know the fastest route to the ship. The rescue boat navigator
finds that the shortest route from Port Lincoln is 48 miles long. At what angle off of due east should the
rescue boat travel to take the shortest route to the ship? Round your answer to the nearest whole degree.
Answer:
Rounding to the nearest whole degree, the rescue boat should travel at an angle of approximately 41 degrees off of due east to take the shortest route to the ship.
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's draw a diagram to represent the situation:
A (rescue boat)
| \
| \
| \ C (disabled ship)
24 mi | \
| \
| \
|θ \
B-----------D (Port Lincoln)
48 mi
In the diagram, point B represents Port Lincoln, point C represents the disabled ship, and point A represents the rescue boat. Point D is the intersection of the eastward path and the northward path taken by the ship.
We are given that BD = 24 miles and CD = 48 miles. We want to find the angle θ, which is the angle between the line segments AB and AD.
To find θ, we can use the law of cosines:
cos(θ) = (BD² + CD² - AD²) / (2 x BD x CD)
Substituting the given values, we get:
cos(θ) = (24² + 48² - AD²) / (2 x 24 x 48)
Simplifying, we get:
cos(θ) = 0.75
To solve for θ, we can take the inverse cosine of both sides:
θ = cos⁻¹(0.75)
Using a calculator, we get:
θ ≈ 41.41°
Rounding to the nearest whole degree, the rescue boat should travel at an angle of approximately 41 degrees off of due east to take the shortest route to the ship.
what is written history
A written history means the writing of history, such as the writing of history based on the critical examination of sources which is also known as historiography.
How can we define written history?Also known as recorded history describes the historical events that have been recorded in a written form or other documented communication which are subsequently evaluated by historians using the historical method.
Historiography also includes the theory and history of historical writing. Modern historians strive to reconstruct a record of human activities and gain a deeper understanding of them.
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Check here for instructional material to complete this problem.
Evaluate the formula z =
X-μ
0
√n
when μ = 123, n = 26, x= 127, and o=7.
Z= (Round to three decimal places as needed.)
Answer:
Z = 2.91
Step-by-step explanation:
Mean: 123
Sample Size: 26
Standard Deviation: 7
x = 127
z = (x - μ) / (σ / [tex]\sqrt{n}[/tex] )
[tex]z=\frac{127-123}{\frac{7}{\sqrt{26} } } \\z= 2.91[/tex]
**If this is a z-table question, then P (x = 127) = P (z = 2.91) = 0.9982.**
The circumference of a circular garden is approximately 34 feet. What is the approximate area inside the circular garden?
Answer:
Approxiamaltely 91.95 feet
Step-by-step explanation:
Evaluate each expression for the given values.
4 |m - n|
If m = -7 and n=2
The expression will give 36 after evaluating.
What is an Expression?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated or simplified. An expression may contain one or more terms, which are separated by operators such as addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^).
Expressions can represent various mathematical concepts, such as equations, inequalities, functions, and polynomials.
Given: m = -7 and n = 2,
We know that, the mode function converts the function into positive value.
So, |m - n| = |-7 - 2| = 9
Now,
4 |m - n| = 4 * 9 = 36
So the expression 4 |m - n| evaluates to 36 when m = -7 and n = 2.
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6 cm. Find its area to the nearest tenth.
The area of the rectangle is 35.1 cm²
How to determine the area of the rectangleTo find the area of a rectangle, you need to multiply its length by its width.
Given that the dimensions of the rectangle are 5.85 cm and 6 cm, respectively, the area of the rectangle is:
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
Area = 5.85 cm x 6 cm
Evaluate the product
Area = 35.1 cm²
Hence, the area of the rectangle to the nearest tenth is 35.1 cm²
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Complete question
The dimension of a rectangle is 5.85 cm by 6 cm. Find its area to the nearest tenth.
I will mark you brainiest!
Which of the following pairs of quadrilaterals have diagonals that are congruent?
A) Rhombus and a rectangle
B) A parallelogram and a square
C) a rectangle and a square
D) a life and a trapezoid
The only pair of quadrilaterals that have congruent diagonals is a rectangle and a square, and the answer is C.
What distinguishes a quadrilateral?These attributes are:
There are four of them.There are four of them.360° is the total of all interior angles.There are two diagonals in them.Both regular and irregular quadrilaterals exist. A regular quadrilateral must have four equal sides, four equal angles, and diagonals that cross each other in a bisecting direction.C) A rectangle and a square: A rectangle's diagonals are congruent, and a square's diagonals are also congruent. The solution is C because a square is a particular case of a rectangle in which all sides are congruent.
Hence, a rectangle and a square are the only pair of quadrilaterals with congruent diagonals, and the answer is C.
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PLEASE HELP !! :( QUESTION 17
Answer:
b) The graph will shift down 5 units from its parent graph.
Step-by-step explanation:
Your answer is in the image.
Which two pairs of measurements are equal?
Answer:
cm³ and ml
m³ and litre
This is the all you will need to know
Help please also please explain bc I truly do not get it
Therefore, the solutions for θ in the interval 0° ≤ θ ≤ 360° are approximately 131.81° and 228.19°.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is used to study and analyze various phenomena that involve periodic functions, such as waves, oscillations, and sound. Trigonometry also has practical applications in fields such as physics, engineering, navigation, and surveying. It involves the use of trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent to calculate the sides and angles of triangles and other geometric figures.
Here,
Let's solve for θ:
First, let's substitute u = cos(θ), so we have:
3u² - 5u - 4 = 0
Now we can use the quadratic formula:
u = [ -(-5) ± √((-5)² - 4(3)(-4))] / (2*3)
u = [ 5 ± √(49) ] / 6
u1 = (5 + 7) / 6 = 2
u2 = (5 - 7) / 6 = -2/3
Since the cosine function has a range of -1 ≤ cos(θ) ≤ 1, we can discard the solution u1 = 2.
Now we can solve for θ:
cos(θ) = u2 = -2/3
θ = cos⁻¹(-2/3) ≈ 131.81°
θ = 360° - cos⁻¹(-2/3) ≈ 228.19°
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Lin has 27 marbles. He divides them into 3 equal groups and gives 1 group to Jill. Jill then gives 2 of hers away. How many marbles does Jill have now?
Answer: 7 marbles
Step-by-step explanation:
Lin starts with 27 and creates 3 equal groups.
When separating, you divide.
27 divided by 3 is 9.
Each group has 9 marbles.
This means that by giving one group to Jill, she receives 9 marbles.
Jill gives away 2 of her 9 marbles, thus leaving her with 7 marbles.
9-2=7.
A rectangle is 16 feet long and 12 feet wide. How long is the diagonal from one corner to the other?
The length οf the diagοnal is 20 feet.
What is a rectangle?A rectangle is a type οf quadrilateral with parallel sides that are equal tο οne anοther and fοur vertices that are all 90 degrees apart. It is alsο knοwn as an equiangular quadrilateral fοr this reasοn. The term "parallelοgram" can alsο be used tο describe a rectangle because the οppοsing sides are equal and parallel.
Given that 16 feet and 12 feet make up a rectangle.
The diagοnal and twο cοnsecutive sides οf a rectangle make a right-angled triangle.
Tο find the diagοnal apply Pythagοrean theοrem.
The widely accepted geοmetric principle knοwn as the Pythagοrean Theοrem states that the square οn the hypοtenuse οf a right triangle equals the sum οf the squares οn its legs.
Draw a rectangle:
Cοnsider △ABC:
AB² + BC² = AC²
12² + 16² =AC²
AC² = 144+ 256
AC² = 400
Take square rοοt οn bοth sides:
AC = 20
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A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is an odd number.
The probability that the sum of the numbers when two dice are rolled is an odd number is given as follows:
0.5.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Each dice has six possible outcomes, hence the total number of outcomes when two dice are rolled is given as follows:
6² = 36.
When we look at the pattern of the sum of two dice, from (1,1), (1,2), ..., to (6,6) we see that they alternate between even numbers and odd numbers, hence:
18 of the outcomes have an even sum.18 of the outcomes have an odd sum.Hence the probability is given as follows:
p = 18/36 = 0.5.
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pls someone help asap
Answer:
2x+15
Step-by-step explanation:
Answer:
2x + 15
Step-by-step explanation:
First, we are doubling x.
We know that doubling is the same thing as multiplying by 2:
2x
Next, we are adding fifteen:
2x + 15
Solving Square Root Equations
Solve the following equations. Be sure to label any extraneous solutions.
Answer:
Step-by-step explanation:
1) To solve the equation √(6x) = x, we can first square both sides of the equation to eliminate the square root:
(√(6x))^2 = x^2
6x = x^2
Next, we can rearrange the equation into standard quadratic form by subtracting 6x from both sides:
x^2 - 6x = 0
Now, we can factor out an x from the left-hand side of the equation:
x(x - 6) = 0
Setting each factor equal to zero, we find two solutions:
x = 0 or x - 6 = 0
Therefore, the solutions to the equation √(6x) = x are x = 0 and x = 6.
2)To solve √(5x-6) = x, we can square both sides of the equation:
(√(5x-6))^2 = x^2
5x-6 = x^2
Rearranging this quadratic equation to the standard form ax^2 + bx + c = 0, we get:
x^2 - 5x + 6 = 0
This can be factored into:
(x - 2)(x - 3) = 0
Therefore, the solutions to the equation √(5x-6) = x are x = 2 and x = 3.
We should check if these solutions satisfy the original equation:
When x=2: √(5x-6) = √(5(2)-6) = √4 = 2, which satisfies the equation.
When x=3: √(5x-6) = √(5(3)-6) = √9 = 3, which also satisfies the equation.
Therefore, the solutions are x = 2 and x = 3.
3) To solve the equation √(2x-1) = x-3, we can square both sides of the equation to eliminate the square root:
(√(2x-1))^2 = (x-3)^2
Simplifying the left-hand side gives:
2x-1 = (x-3)^2
Expanding the right-hand side gives:
2x-1 = x^2 - 6x + 9
Rearranging the equation gives:
x^2 - 8x + 10 = 0
We can solve this quadratic equation :
x^2 - 8x + 10 = 0
Now we can solve this quadratic equation by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -8, and c = 10. Substituting these values into the formula:
x = (-(-8) ± √((-8)^2 - 4(1)(10))) / 2(1)
Simplifying:
x = (8 ± √(64 - 40)) / 2
x = (8 ± √24) / 2
x = 4 ± √6
Therefore, the solutions to the equation √(2x - 1) = x - 3 are x = 4 + √6 and x = 4 - √6.
4) has no real solutions.
when you have to remove the square root you have to power the both sides of the equation.
1)6x= x^2
0 = x^2 - 6x
0= x(x-6)
x=0 or x-6=0
x=6
2) [tex]\sqrt{5x-6}[/tex] = x
5x-6=x^2
x^2 -5x+6=0
(x-3)(x-2)=0
x-3=0 or x-2= 0
x=3 or x=2
3)
[tex]\sqrt{2x-1}[/tex] = x-3
2x-1 = (x-3)^2
2x-1= x^2 - 6x +9
x^2 -8x +10=0
this equation can't solve by factoring method easily. so we have to use the completing square method.
x^2-8x+10=0
x^2-8x= -10
x^2 - 8x+(-4)^2 = -10+ ( -4)^2
(x-4)^2 = 6
[tex]x= 4 +\sqrt{6}[/tex] or [tex]x= 4 -\sqrt{6}[/tex]
4) [tex]x= 2 + \sqrt{2x-11}[/tex]
x^2= 4+4 [tex]\sqrt{2x-11}[/tex] + 2x-11
x^2= 7+ 2x +4[tex]\sqrt{2x-11}[/tex]
x^2-2x-7= 4[tex]\sqrt{2x-11}[/tex]
(x^2-2x-7)^2= 16 (2x-11)
x^4 +4x^2 +49-4x^3 + 28x - 14x^2 = 32x-176
x^4 - 4x^3 - 10x^2 - 4x + 225= 0
x(x^3 -4x^2 - 10x-4)+225=0
this is a power 4 th equation this equation can solve by normal steps.
Yuri has a large rectangular card measuring 1.2 meters by 0.8 meters, he wants to cut it up to make small rectangular cards each measuring 13 centimeters by 11.5 centimeters. Work out the largest number of cards that he can make
The number of smaller card that could be cut from the larger rectangular card is 64.
How to find the area of a rectangle?Yuri has a large rectangular card measuring 1.2 meters by 0.8 meters, he wants to cut it up to make small rectangular cards each measuring 13 cm by 11.5 cm.
Let's convert the units.
1.2 m = 120 cm
0.8 = 80 cm
Therefore, let's find the area of the rectangular card.
area of the large rectangular card = lw
where
l = lengthw = widtharea of the large rectangular card = 120 × 80
area of the large rectangular card = 9600 cm²
area of each small rectangular card = 11.5 × 13.5
area of each small rectangular card = 149.5 cm²
Therefore,
largest number of card that can be cut out from the larger card = 9600 / 149.5 = 64.2140468227
largest number of card that can be cut out from the larger card ≈ 64
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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
Option D : Based on the given data, the best prediction for the number of students who prefer ice cream at the college, which is approximately 1,440 students.
To make prediction of the number of students who prefer ice cream, we need to use the proportion of students who prefer ice cream from the sample to the entire population of 4,000 students.
Based on the given data, 81 out of 225 students prefer ice cream. To estimate the number of students who prefer ice cream in the entire college, we can use the ratio of students who prefer ice cream in the sample to the total number of students in the college.
The total number of students in the college is 4,000, so we can set up a proportion:
81/225 = x/4000
Solving for x, we get:
x = (81/225) * 4000 = 1,440
Therefore, the best prediction for the number of students who prefer ice cream in the entire college is 1,440.
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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
A. The college will have about 480 students who prefer ice cream.
B. The college will have about 640 students who prefer ice cream.
C. The college will have about 1,280 students who prefer ice cream.
D. The college will have about 1,440 students who prefer ice cream.
A bandana is in the shape of a triangle. The base of the bandana is 30 in. wide and the height is 12 in.
What is the area of the bandana?
_______________________________
(reporting spams/wrong answers)
(no picture is needed for this question)
(giving brainliest to the correct answer)
_______________________________
Answer:
180 in^2Step-by-step explanation:
A bandana is in the shape of a triangle. The base of the bandana is 30 in. wide and the height is 12 in.
Triangle Area = 1/2 b x h
substitute the values1/2 30 x 12 =
15 x 12 = 180 in^2
The last time Ms. Ward's car tank was filled, the odometer reading was 7,998 miles. The next time she filled up her vehicle with gas, the odometer reading was 8,308.
What was Ms. Ward's cost per mile for the time period? (remember, money always rounds to 2 decimal places!)
Answer:
$0.14
Step-by-step explanation:
[tex]8,308 - 7,998 = 310 \: miles[/tex]
We don't have information on how many gallons of gas Ms. Ward purchased, so we can't calculate the exact cost per mile. However, we can use the average fuel efficiency of her car to estimate the cost. Let's assume her car gets an average of 25 miles per gallon, which is a common fuel efficiency for a compact car.
To calculate how many gallons of gas she used, we can divide the number of miles driven by the fuel efficiency:
[tex]\frac{310 \: miles}{25 \: miles _{gallon} } = 12.4 \: gallons[/tex]
Assuming that the cost of gas was $3.50 per gallon, we can multiply the number of gallons used by the cost per gallon to find the total cost of gas:
[tex]12.4 \: gallons \times $3.50_{gallon} = $43.40[/tex]
To find the cost per mile, we can divide the total cost of gas by the number of miles driven:
[tex]\frac{$43.40}{310 \: miles} = $0.14_{mile} [/tex]
So Ms. Ward's cost per mile for this time period was approximately $0.14.
Answer:
Step-by-step explanation:
Miles travelled = 8,308 - 7,998 = 310 miles
Total cost = $26.79
Cost per mile[tex]=\frac{26.79}{310}[/tex] =0.0864
Ms. Ward's cost per mile is $0.09 (rounded to nearest cent).
The perimeter of a rectangular table is 18 feet The table is 42 inches wide
Width of the table = 3.5 feet , Length of the table = 5.5 feet and Perimeter of the table = 18 feet
What is Rectangle ?
A rectangle is a 2-dimensional shape with four straight sides, where opposite sides are parallel and equal in length. It has four right angles and its diagonals bisect each other. It is a type of quadrilateral, and its area is calculated by multiplying the length and width of the rectangle. It is commonly found in many geometric shapes and everyday objects such as doors, windows, and computer screens.
Let's convert all measurements to the same unit for easier calculation. Since the table width is given in inches, we can convert it to feet by dividing by 12 (since 1 foot = 12 inches).
Table width: 42 inches = 42÷12 = 3.5 feet
Let's denote the length of the table as 'l' feet. The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
Given that the perimeter is 18 feet, we can substitute the values into the formula:
18 = 2 * (l + 3.5)
Now, we can solve for 'l':
18 = 2l + 7 (distributing 2 to both terms in the parentheses)
2l = 18 - 7 (subtracting 7 from both sides)
2l = 11 (simplifying)
l = 11÷2 (dividing both sides by 2)
Therefore, Width of the table = 3.5 feet , Length of the table = 5.5 feet
and Perimeter of the table = 18 feet
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The first three terms of a geometric sequence are as follows
-5,-20,-80
Find the next two terms of this sequence; give an exact value (not decimals)
Answer: -1280
Step-by-step explanation:
in a geometric sequence it either multiplies or divides negatively or positively, in this case -5 to -20 is multiplied 4 positively and so is -20 to -80
then -80x4= -320
-320x4= -1280
Use a calculator to find the measure of
The measure of the angle A as required to be determined in the task content is; 16.7°.
What is the measure of angel A?It follows from the task content that the measure of the angle A is to be determined.
By using the trigonometric ratio;
tan (A) = BC / AC
Hence, by substitution; it follows that;
tan (A) = 6 / 20
Hence, by simplification; we have that;
tan A = 3/10
tan A = 0.3
Therefore, to determine A;
A = tan-¹ (0.3)
A = 16.7°.
Ultimately the measure of angle A as required to be determined is; 16.7°.
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i-Ready
Find the surface area of the box shown.
S.A. =
Nets and Surface Area- Instruction-Level F
in.²
3 in
12 in
10 in
X
The surface area of the box shown is 186 square inches (186 in²).
What is surface area?Surface area is the measure of the area on a two-dimensional surface. It is the sum of the areas of all the shapes that make up a two-dimensional object. It can be used to calculate the area of a sphere, a cylinder, a rectangular prism, and more.
The box shown is a three-dimensional rectangular prism. The surface area (S.A.) of a rectangular prism is calculated by adding the area of each of its six faces. The area of each face is calculated by multiplying the length of the face by its width.
For the box shown, the length is 3 inches (3 in), the width is 12 inches (12 in), and the height is 10 inches (10 in). To find the surface area, we need to calculate the area of each face and add them together. The surface area of this box is calculated as follows:
Front and back faces: 3 in x 10 in = 30 in²
Left and right faces: 12 in x 10 in = 120 in²
Top and bottom faces: 3 in x 12 in = 36 in²
Total surface area: 30 in² + 120 in² + 36 in² = 186 in²
Therefore, the surface area of the box shown is 186 square inches (186 in²).
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A PVC pipe has an inner diameter of 5 cm and an outer diameter of 6.5 cm. The PVC has a density of 1.38 g/cm³. What is the mass of a pipe that is 30 cm long in grams? Round to the nearest hundredth.
Hence, in answering the stated question, we may say that As a result, the function mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.
what is function?Mathematicians investigate numbers and their variants, equations and associated structures, forms and their locations, and prospective locations for these things. The term "function" refers to the relationship between a group of inputs, each with its own output. A function is a connection of inputs and outputs in which each input results in a single, distinct outcome. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four basic types of accessible functions.
The volume of the PVC pipe can be estimated by subtracting the volumes of the outer and inner cylinders:
V = π/4 × (D² - d²) × L
where V denotes volume, is the mathematical constant pi (roughly equivalent to 3.14159), D denotes outer diameter, d denotes inner diameter, and L denotes pipe length.
V = π/4 × (6.5² - 5²) × 30\sV = 531.13 cm³
PVC pipe mass can be estimated by multiplying its volume by its density:
m = V × ρ
With the provided density, we get:
1.38 g/cm3 m = 733.48 g m = 531.13 cm3
As a result, the mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.
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9x -6y = 54 find x intercept and find y intercept
Answer:
x-intercept(s):
(
6
,
0
)
y-intercept(s):
(
0
,
−
9
)
Step-by-step explanation:
The circles have the same center. What is the area of the shaded region?
Answer:
The area of the shaded region is 160.2 in² (to the nearest tenth).
Step-by-step explanation:
The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]
If the circles have the same center, and the inner circle has a radius of 7 in, then the outer circle has a radius of:
[tex]\implies r = 7 + 3 = 10\; \sf in[/tex]
Therefore, the area of the shaded region is:
[tex]\begin{aligned}\sf Area_{shaded\;region}&=\sf Area_{outer\;circle}-Area_{inner\;circle}\\&=\pi \cdot 10^2 - \pi \cdot 7^2\\&=100\pi - 49 \pi\\&=51 \pi\\& = 160.221225...\\&=160.2\; \sf in^2\;(nearest\;tenth)\end{aligned}[/tex]
A light display for a festival consists of a string of 1,000 lightbulbs in the colors red, yellow, green, and blue repeated consecutively in that order for the entire display. The 543rd lightbulb needs to be replaced.
If the first lightbulb is red, what is the color of the lightbulb that needs to be replaced?
Using the pattern given, we found that the colour of the lightbulb in the 543rd position of a string of lightbulbs is green.
What is meant by the pattern?
A recurring arrangement of numbers, shapes, colours and other elements is known as a pattern. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series. The number of patterns can be limitless or finite. There are many distinct kinds of number patterns, including geometric, Fibonacci, and algebraic or arithmetic patterns. In mathematics, number patterns are quite prevalent.
Given,
The number of lights on a string of lights = 1000
The order in which the lights repeat is red, yellow, green and blue.
After every four lights, the order repeats.
We can get the pattern as follows.
The blue lights are in positions 4,8,12,........,4n.
We have to find the multiple of 4 close to 543.
Now we can check if 542 is a multiple of 4.
542/4 = 135.5
So it is not a multiple of 4.
Now check if 544 is a multiple of 4.
544/4 = 136
So the bulb in the 544th position is blue.
Then the bulb in the 543rd position should be green.
Therefore using the pattern given, we found that the colour of the lightbulb in the 543rd position of a string of lightbulbs is green.
To learn more about patterns, follow the link.
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Evaluate f(x) = 3x + 2 when x = -4.
Answer:
-10
Step-by-step explanation:
[tex]f(x) = 3x + 2[/tex]
Replace x in the function with the given value x = -4:
[tex]f( - 4) = 3 \times ( - 4) + 2 = - 12 + 2 = - 10[/tex]
find the area when the circumference = 6 pi
Answer:
9π
Step-by-step explanation:
if the circumference=6π, then you can solve for the radius. C=2πr
6π=2πr
Divide 2π from both sides to get r=3
Area=πr^2
A=π*9
Area= 9π
70 divided by 33.8 plsss I have to do my hw
Answer:
Step-by-step explanation:
70/33.8=2.07100592