The linear velocity of a point on the tip of the outer edge of the circular saw blade is 0.429 miles per hour.
Explanation:To find the linear velocity of a point on the tip of the outer edge of the circular saw blade, we can use the formula:
Linear velocity = 2 * π * radius * angular velocity
Where the radius is half of the diameter. Given that the diameter is 7 1/4 inches, the radius is 7 1/4 / 2 = 3 5/8 inches or 3.625 inches. Converting this to feet, we get 3.625 / 12 = 0.302 feet. To convert the angular velocity from revolutions per minute to radians per second, we multiply by 2 * π / 60. Substituting these values into the formula, we get:
Linear velocity = 2 * π * 0.302 * (2500 * 2 * π / 60) = 37.699 feet per minute.
To convert this to miles per hour, we divide by 5280 (since there are 5280 feet in a mile) and multiply by 60 (since there are 60 minutes in an hour):
Linear velocity = (37.699 / 5280) * 60 = 0.429 miles per hour.
16 increased by twice a number is -56
Pauline spent $7.50 every day for 3 days. Which expression is the best choice to help her determine the total amount of money she spent?
A. (7.50) × (−3) = −22.50; She spent $22.50.
B. (−7.50) × (3) = −22.50; She spent $22.50.
C. (−7.50) × (−3) = 22.50; She spent $22.50.
D. (7.50) × (3) = 22.50; She spent $22.50.
If the area of a square is 196 square meters, what is its perimeter
Rachel deposited $6,449.82 into a savings account with an interest of 6.9% compounded annually. About how long will it take for the accout to be worth $8,000?
Answer:
3 years and 3 months.
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A= P(1+\frac{r}{100})^t[/tex]
Where,
P = principal amount,
r = rate per period,
t = number of periods,
Here, A = $ 8,000, r = 6.9%, P = $6,449.82,
By substituting the values,
[tex]8000 = 6449.82(1+\frac{6.9}{100})^t[/tex]
[tex]\frac{8000}{6449.82}=(1+\frac{6.9}{100})^t[/tex]
[tex]\ln (\frac{8000}{6449.82})=t\ln(1.069)[/tex]
[tex]\implies t = \frac{\ln (\frac{8000}{6449.82})}{\ln(1.069)}=3.228[/tex]
Hence, it would be take 3.228 years or 3 years and 3 months.
Which number is a composite number?
17
27
37
47
Dale drove 845 miles in 13 hours. at the same rate, how long would it take him to drive 585 miles?
Convert the complex number from rectangular form to polar form. z = -14 + 8i
Final answer:
To convert z = -14 + 8i to polar form, calculate the magnitude as √(260)≅17, and the argument by adding π to the arctan(8/-14), which accounts for the angle being in the second quadrant. Express the number in polar form using these values.
Explanation:
To convert the complex number z = -14 + 8i from rectangular form to polar form, we start by finding the magnitude (r) and the argument (θ) of the complex number. The magnitude is given by √(x² + y²), which in our case is √((-14)² + 8²) = √(196 + 64) = √(260)≅17. The argument θ is the angle with respect to the positive x-axis which can be found using the arctan function: θ = arctan(y/x). However, since our x is negative and y is positive, our complex number is in the second quadrant, so we need to add π radians (or 180 degrees) to the arctan(y/x) value to obtain the correct argument in the complex plane.
θ = arctan(8/-14) + π ≅ arctan(-4/7) + π. We then get the polar form: z = r(cos(θ) + i sin(θ)) or z = r eˣiθ. Substituting the magnitude and argument into this formula, we find the polar form of the complex number z.
What %of 200 miles is 150 miles
Which of the f-values satisfy the following inequality? f+8≤12 Choose all answers that apply:
A
f = 4
B
f = 5
C
f = 6
Ray's gym charges an initial sign-up fee of $25.00 and a monthly fee of $15.00.
Write a function that describes the gym's total membership fee for x months.
You need at least 5000 points to earn a gift card from your bank. You currently have 2700 points. What inequality represents the number of points you need to earn a gift card.
The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function h(t)=300-16t2. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall.
Answer:
-96 feet/sec.
Step-by-step explanation:
The height h of a falling object after t second when it is dropped from a platform 300 feet above the ground is modeled by the function h (t) = 300 - 16t²
Then speed or average rate by which the object falls from height h will be [tex]\frac{d[h(t)]}{dt}=\frac{d(300-16t)^{2} }{dt}[/tex]
Speed = [tex]\frac{d}{dt}(300)[/tex] - [tex]\frac{d}{dt}(16t^{2} )[/tex]
= -16 (2t)
Speed = -32t
After 3 second speed of object will be
Speed = -32(3)
= -96 feet/second
Therefore, the average rate will be -96 feet/sec. during the first 3 seconds of its fall.
You need to bake some banana bread and some zucchini bread for a fund raiser at school. You plan to bake at least 4 and at most 12 loaves of bread. You need at least twice as many loaves of banana bread as zucchini bread.
The problem is an algebraic translation of a real-life situation using inequalities. The number of loaves, for both banana and zucchini bread, must be between 4 and 12, with banana bread needing to be twice as many as zucchini.
Explanation:This question deals with the concept of inequality and translating word problems into algebraic expressions. In this question, if x represents the number of zucchini bread loaves you bake and y represents the number of banana bread loaves, then the inequalities can be written as:
4 ≤ x + y ≤ 12y ≥ 2xThese inequalities mean that the total number of loaves of bread, including both banana and zucchini, should be no fewer than 4 and no more than 12, and the number of banana bread loaves should be at least twice the number of zucchini bread loaves.
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If a 30-foot tree casts a 12-foot shadow, find the length of the shadow cast by a 28-foot tree.
Final answer:
To calculate the length of the shadow cast by a 28-foot tree, we use proportional relationships, which yield a shadow length of approximately 11.2 feet.
Explanation:
Shadow Length Calculation
To find the length of the shadow cast by a 28-foot tree, we can use the concept of similar triangles. The relationship between the height of an object and the length of its shadow is proportional provided the sun's rays are coming at the same angle.
In this case, a 30-foot tree casts a 12-foot shadow.
We can set up a proportion to compare the two trees to find the unknown shadow length for the 28-foot tree.
Let's set up the proportion: Since the shadows are proportional to their respective tree heights, we can express this as follows:
(Shadow length of 28-foot tree) / 28 feet = 12 feet / 30 feet
By cross-multiplying and solving for the unknown shadow length, we would get:
(Shadow length of 28-foot tree) × 30 = 28 × 12Performing this calculation:
(Shadow length of 28-foot tree) = 336 / 30So, a 28-foot tree will cast a shadow that is approximately 11.2 feet long.
The correct answer is that the length of the shadow cast by a 28-foot tree is 11.2 feet.
To solve this problem, we can use the concept of similar triangles. The tree and its shadow form a right-angled triangle with the ground, and the angle of elevation of the sun is the same for both trees. Therefore, the triangles formed by the trees and their respective shadows are similar.
Let's denote the height of the first tree as [tex]\( h_1 = 30 \)[/tex] feet, the length of its shadow as [tex]\( s_1 = 12 \)[/tex] feet, the height of the second tree as [tex]\( h_2 = 28 \)[/tex] feet, and the length of its shadow as [tex]\( s_2 \)[/tex], which we want to find.
Since the triangles are similar, the ratios of the corresponding sides are equal:
[tex]\[ \frac{h_1}{s_1} = \frac{h_2}{s_2} \][/tex]
Substituting the known values:
[tex]\[ \frac{30}{12} = \frac{28}{s_2} \][/tex]
Now, we solve for [tex]\( s_2 \)[/tex] :
[tex]\[ s_2 = \frac{28 \times 12}{30} \][/tex]
[tex]\[ s_2 = \frac{336}{30} \][/tex]
[tex]\[ s_2 = 11.2 \][/tex]
6 ( y + 8 ) = 3 ( 2y - 7 )
Convert 2 3/25 as a decimal/
which graph has a slope of 4/5?
The only graph with a slope of 4/5 is;
Graph 2
The slope of the graph is simply rise divided by run or defined as the change in y-coordinates divided by the corresponding change in x-coordinate.
Thus; m = (y₂ - y₁)/(x₂ - x₁)
Graph 1; Let us pick two coordinates;
(1, 2) and (2, 3)
m = (3 - 2)/(2 - 1)
m = 1
Graph 2; Let us pick two coordinates;
(-1, 1 ) and (4, 5)
m = (5 - 1)/(4 - (-1))
m = 4/5
Graph 3; Let us pick two coordinates;
(-2,0) and (3, 2)
m = (2 - 0)/(3 - (-2))
m = 2/5
Graph 4; Let us pick two coordinates;
(1, 1) and (4, 5)
m = (5 - 1)/(4 - 1)
m = 4/3
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Zach is 23 years old. Zach's age is 3 years older than twice Maya's age. Let m represent maya's age
Which equation can be used to solve for Maya's age?
A.) 23=m+3
B.) 23=2m
C.) 23=3m+2
D.) 23=2m+3
Why does the sum of -4 and 3 complain more than the sum of -3 and 5
Final answer:
The sum of -4 and 3 is -1, while the sum of -3 and 5 is 2. The sum of two numbers depends on their signs and the rules of adding negative and positive numbers.
Explanation:
The sum of -4 and 3 is -1, while the sum of -3 and 5 is 2. The reason why the sum of -4 and 3 is a smaller number than the sum of -3 and 5 is because of the rules of adding positive and negative numbers:
When two negative numbers add, the answer has a negative sign.When two positive numbers add, the answer has a positive sign.When two numbers with opposite signs add, the sign of the larger number is retained.In this case, -3 is larger than -4, so when adding 5 to -3, we retain the negative sign and get -1. However, when adding 3 to -4, we retain the negative sign and get -1, which is smaller than 2.
The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −7 0 −1 1 5 g(x) g(x) = 5x − 4 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
Suppose a kite has diagonals of 10 and 20. Find the perimeter of the quadrilateral formed
by joining the midpoints of the kite’s sides.
FREE POINTS!!!!!!!!!!!
2+3(8-2)= x
Answer:
30
Step-by-step explanation:
Abeer sat a French test and a Geramn test.
In the French test she scored 34 out of 50.
In the German test she scored 14 out of 20.
In which test did she do better?
You must show your working.
Final answer:
After converting Abeer's scores to percentages, it is clear that she did better in the German test with a score of 70%, as opposed to the French test where she scored 68%.
Explanation:
To find out in which test Abeer did better, we need to compare her test scores in percentages. For the French test, Abeer scored 34 out of 50, which we can convert to a percentage by dividing 34 by 50 and then multiplying by 100:
34 ÷ 50 = 0.68 × 100 = 68%
For the German test, she scored 14 out of 20, which we also convert to a percentage:
14 ÷ 20 = 0.70 × 100 = 70%
By comparing these percentages, we can see that Abeer did better in the German test where she scored 70% compared to the French test where she scored 68%.
What is the parents function of f(x)=3x-5
LINEAR PROGRAMMING help must answer both questions and explain ur answer for brainliest.
12. Find the surface area of each figure to the nearest tenth.Show your work.
e. What is a real-world example or use of surface area?
How many ways can first, second, and third place be assigned?At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
The total number of ways can first, second and third place can be assigned are:
6840
Step-by-step explanation:The total number of people that compete are: 20
Out of these 20 people we have to chose 3 people and also arrange them according to their ranks.
We know that when we have to choose and arrange r items out of total n items then we need to use the method of permutation.
Hence, the formula is given by:
[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]
Here we have:
n=20 and r=3
Hence, the number of ways first, second and third place can be assigned are:
[tex]{20}_P_3=\dfrac{20!}{(20-3)!}\\\\\\{20}_P_3=\dfrac{20!}{17!}\\\\\\{20}_P_3=\dfrac{20\times 19\times 18\times 17!}{17!}\\\\\\{20}_P_3=20\times 19\times 18\\\\\\{20}_P_3=6840[/tex]
Hence, the answer is:
6840
Answer:
The correct answer is
1. 6,840
2. 342
3. 18
At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
This should be simple but it’s Monday and my brain is fried T_T
what does “b” equal?
-10 = -b/4
to get b multiply both sides by 4
-10 *4 = -40
since b already has the negative sign the 40 would be positive
so b = 40
What are the vertices for the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ? i need x y and z
The operations on geometric shapes that involves moving, flipping, change of shape, reflection and new shape creation through operations on another shape is known as transformations
The coordinates of the vertices of the image ΔX'Y'Z' after the composite transformation T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180° are X'(-4, -1), Y'(-5, 2), and Z'(-6, 1)The reason the above values are correct is as follows:
The given transformation sequence is T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180°
Where;
T₍₋₂, ₄₎ = A translation two (2) units to the left and four (4) units upwards
R₀ 180° = A rotation of 180° about the origin
The image and preimage of a 180° rotation transformation about the origin is as follows;
Preimage (x, y) [tex]\underset \longrightarrow {R_o \ 180 ^{\circ} }[/tex]Image(-x, -y)
It is to be noted that the first transformation to be performed in a composite transformation is the transformation to the right
The composite transformation is therefore presented as follows;
Combined; (x, y) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-x - 2, -y + 4 )
The coordinates of the vertices points on triangle ΔXYZ are X(2, 5), Y(3, 2), Z(4, 3)
Therefore;
The coordinates of the vertices points on triangle ΔX'Y'Z' after the composite transformations are;
X(2, 5) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-2 - 2, -5 + 4 ) = X'(-4, -1)Y(3, 2) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-3 - 2, -2 + 4 ) = Y'(-5, 2)Z(4, 3) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] Z(-4 - 2, -3 + 4 ) = Z'(-6, 1)Which gives that the coordinates of the triangle ΔX'Y'Z' after the transformation, T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180° are;
X'(-4, -1), Y'(-5, 2), and Z'(-6, 1)
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What is the area of the region of the complex plane defined by $|z|<5$?
This will be the same area as that inside a circle with a radius of 5
So....the area will be ≈ pi * 5^2 ≈ 25 pi units^2
The area of the region of the complex plane defined by |z|<5 is 78.5 square units.
Explanation:The region of the complex plane defined by |z|<5 is the inside of the circle with radius 5 centered at the origin. To find the area of this region, we can use the formula for the area of a circle, which is A = πr². In this case, the radius is 5, so the area is A = 3.14 × 5² = 78.5 square units.
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