The direction of the resulting force upon the piling is approximately 298.85 degrees
We can use vector addition to find the direction of the resulting force. Let's call the force exerted by the first bulldozer F1, and the force exerted by the second bulldozer F2. We can represent each force as a vector with a magnitude and direction.
F1 has a magnitude of 1850 pounds and points in a westerly direction. We can represent it as a vector (-1850, 0).
F2 has a magnitude of 3250 pounds and points in a northerly direction. We can represent it as a vector (0, 3250).
To find the resulting force, we need to add these two vectors. We can do this by adding the x-components and the y-components separately.
The x-component of the resulting force is -1850 (from F1) plus 0 (from F2), which is -1850.
The y-component of the resulting force is 0 (from F1) plus 3250 (from F2), which is 3250.
So the resulting force is a vector with components (-1850, 3250). We can find the direction of this vector by taking the inverse tangent of the ratio of the y-component to the x-component.
tan(theta) = (3250) / (-1850)
theta = -61.15 degrees
The negative sign indicates that the resulting force points to the southwest. To get the angle in the range of 0 to 360 degrees, we can add 360 degrees to the angle if it is negative.
theta = 360 - 61.15
theta = 298.85 degrees
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Please Help!! Find the exact value of the last 5 remaining trig functions. I believe theta lands in the first quadrant but correct me if I'm wrong. Please write out the steps since I am a visual learner. THANK YOU SO MUCH!! 25. cscθ= 3 and [0, π /2 ]
:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3
Answer:Given, csc θ = 3 and θ lies in [0, π/2]We need to find the values of the remaining 5 trigonometric functions.Here is how we can find them:We know that csc θ = 3. csc θ = 1/sin θ. Hence, we can say sin θ = 1/csc θ = 1/3.In the first quadrant, sin θ is positive (All are positive except tan θ and cot θ). Hence, sin θ = 1/3, and cos θ = √(1 - sin²θ) = √(1 - 1/9) = √8/3 = (2/3)√2.The remaining trigonometric functions are:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3
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Thuli wants to buy TV R8 500 A bank offers to loan her the money at an interest of 5 percent she decide to pay her TV off 3 years. Calculate the simpled interest she will have to pay also calculate the total she will pay
The simple interest she will have to pay equals R 1275, and the total she will pay equals R 9775 for her TV over the past 3 years.
Thuli wants to buy TV, and a bank offers to loan her the money at an interest rate.
Principal, P = R 8,500
Interest Rate, R = 5%
Time, t = 3 year
Simple interest is defined as an interest charge that borrowers pay their lenders for a loan. It is calculated using the principal only. Formula for SI is written as SI = (P×T×R)/100
Here, SI = Simple interest
P = Principal (sum of money borrowed)
R = Rate of interest p.a
T = Time (in years)
We have to calculate simpled interest she will have to pay also calculate the total she will pay.
So, Simple interest = (8500×3×5)/100
= 85× 15 = R 1275
Now, total she will have to pay = Principle + SI
= 8500 + 1275
= R 9775
Hence, required total she will pay is R9775.
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Please answer with formula and how to find it
Radius is the distance in a straight line from the centre of the circle to its circumference. The diameter is twice the radius. Therefore, radius and diameter of the circle are 7 and 14 yards respectively.
How to find area of a circle?The above figure is a circle. The area of the circle is given as 49π yard squared. The question want us to find the radius and diameter of the circle.
Hence,
area of a circle = πr²
where
r = radius of a squareTherefore,
area of the circle = 49π
Hence,
49π = π × r²
divide both sides by π
r² = 49
square root both sides
r = √49
r = 7 yards
The diameter of a circle is twice the radius.
Hence,
diameter of the circle = 7 × 2 = 14 yards
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What would be the best way to display the data below to see specific data but still see the shape of the data? line plot bar graph line graph stem-and-leaf graph
Whats the distance between (-1,-2) and (3,4)
Answer:
the answer is 7,21
Step-by-step explanation:
Distance formula is d=√(x1-x2)²+(y1-y2)²√(-1-3)²+(-2-4)²√(-4)²+(-6)²√16+36√527.21Lisa’s job pays $8 per hour, but if she works more than 35 hours per week she is paid 11 times her regular salary for the overtime hours. How much is she paid if she works hours 42 hours in one week?
Total pay = Regular pay + Overtime pay = $280 + $616 = $896. Therefore, if Lisa works 42 hours in one week, she would be paid $896
The first step is to calculate Lisa's regular pay for the week. We know that her regular hourly rate is $8 per hour. If she works 35 hours or less in a week, then her pay is simply her hourly rate times the number of hours worked. Therefore, her regular pay for a week where she works 35 hours or less would be:
Regular pay = $8/hour * 35 hours = $280
However, we know that Lisa worked 42 hours in one week, which is more than 35 hours. This means she also worked 7 overtime hours. According to the problem, Lisa is paid 11 times her regular salary for any overtime hours worked. This means her overtime pay for the 7 overtime hours would be:
Overtime pay = $8/hour * 11 * 7 hours = $616
To get Lisa's total pay for the week, we simply add her regular pay and overtime pay together:
Total pay = Regular pay + Overtime pay = $280 + $616 = $896
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Find the area of the triangle. A drawing of a triangle with base of 12 and a half feet and height of 4 feet.
Answer:
[tex]\large\boxed{ \sf Area = 25\ ft .^2}[/tex]
Step-by-step explanation:
We need to find out the area of the triangle which has a base of 12.5ft and s height of 4ft.
We know that the formula for calculating the area of the triangle is ,
[tex]\sf:\implies \pink{Area_{\triangle}=\dfrac{1}{2}\times (b)\times (h)}\\[/tex]
where,
b is the base .h is the height .F I G U R E : -
[tex] \setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){$\large\bf 4\ ft $}\put(2.8,.3){$\large\bf 12.5\ ft$}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\end{picture}[/tex]
Now on substituting the respective values, we have;
[tex]\sf:\implies Area = \dfrac{1}{2}\times (12.5) \times (4) \ ft.^2 \\[/tex]
Simplify,
[tex]\sf:\implies \underline{\underline{\boxed{\sf Area = \frak{25\ ft.^2} }}} \\[/tex]
Hence the area of the triangle is 25ft.²
f:g → 10 - g. Find f-1: g
pls i need this
The inverse function is [tex]f^{-1} (g) = 10 - g[/tex]
What is the Composition function?Composition function is a type of function that is formed by combining two or more functions, where the output of one function becomes the input of another function. Composition function shown by the symbol "∘".
The composition function is a mathematical operation that combines two functions to produce a new function. Specifically, given two functions f and g, the composition function (also called function composition) creates a new function h(x) = f(g(x)) that applies the function g to an input x, and then applies the function f to the output of g(x).
We can start by finding the inverse function of f(g), which is [tex]f^{-1} (g)[/tex]. To do so, we need to solve the equation:
[tex]f(g) = x = 10 - g[/tex]
for g, in terms of x:
x = 10 - g
g = 10 - x
This gives us the inverse function:
[tex]f^{-1} (x) = 10 - x[/tex]
Now we can find f^-1(g) by replacing x with g in the above equation:
[tex]f^{-1} (g) = 10 - g[/tex]
Therefore, the function [tex]f^{-1} (g)[/tex] is given by:
[tex]f^{-1} (g) = 10 - g[/tex]
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Complete question is: f:g → 10 - g. Find f-1: g.
A study of the amount of time it takes a specialist to repair a mobile MRI shows that the mean is 8. 4 hours and the standard deviation is 1. 8 hours. If 40 broken mobile MRIs are randomly selected, find the probability that their mean repair time is less than 8. 9 hours
Using the normal distribution, it is found that there is a 0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
[tex]Z=\frac{x-u}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s=\frac{\sigma}{\sqrt n}[/tex]
u=8.4, sigma=1.8 n=32 s=0.3182
The probability that their mean repair time is less than 8.9 hours is the p-value of Z when X = 8.9, hence:
Z=1.57
Z = 1.57 has a p-value of 0.9418.
1 - 0.9418 = 0.0582.
0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
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Renting a roller rink for your birthday costs $ 150 plus $6 per person. The total charge for your party was $282 Translate this information into an equation using x to represent the number of guests at your party.
The equation to represent the number of guests at your party is 150 + 6x = 282 where, the number of guests at the party, x is 22.
How to write and solve equation?Let
Cost of renting a roller rink = $150
Cost per person = $6
Total charge of the party = $282
Number of persons at the birthday party = x
The equation:
150 + 6x = 282
subtract 150 from both sides
6x = 282 - 150
6x = 132
divide both sides by 6
x = 132/6
x = 22
Therefore, there are 22 guests at the birthday party.
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The sum of all of the exterior angles of an octagon is:
180°.
360°.
1080°.
36⁰.
Answer:
360°
Step-by-step explanation:
If you travel around the outside of any polygon, the angels will add to 360
Helping in the name of Jesus.
A number has three prime factors. Two of its prime factors are 3 and 5. The other prime factor is even
what is the number?
The other prime factor is even, the number is 30, and its prime factors are 2, 3, and 5.
To find the third prime factor and ultimately the number, we can use the fact that any integer greater than 1 can be expressed as a unique product of prime factors. We know that the number has three prime factors, and two of them are 3 and 5. So, we need to find the third prime factor.
Since the other prime factor is even, it must be 2 (the only even prime number). Therefore, the number can be calculated as:
Number = 3 x 5 x 2 = 30
So, the number is 30, and its prime factors are 2, 3, and 5.
Prime factors are the prime numbers that divide a given number exactly without leaving any remainder. For example, the prime factors of 12 are 2, 2, and 3, because 2 x 2 x 3 = 12 and these are the only prime numbers that divide 12 exactly. To factorize a number into its prime factors, we can use a method called prime factorization. We start by dividing the number by the smallest prime number that divides it exactly. We keep dividing the quotient by the smallest prime number that divides it exactly until we obtain only prime numbers. The prime factors are then the product of these prime numbers
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The football booster club raised $750 to take a group of students to a football game. The booster club will pay for the bus to transport the students to the game, the admission tickets to the game, and a meal at the concession stand for each student. The bus to transport the students to the game costs $200. Each admission ticket to the game costs $6.50.If the booster club pays for a medium sandwich, drink, and popcorn for each student, how many more students can go to the game than if the booster club pays for a large sandwich, drink, and popcorn for each student?
Let's first find the total cost of transportation and admission tickets:
$200 (transportation) + $6.50 (admission ticket) x n (number of students) = $750
$6.50n = $550
n = 84.62
So, the maximum number of students that can go to the game is 84.62. However, we cannot have a fractional number of students, so we can round down to 84 students.
Now, let's find the cost of the meal for each student:
$2.50 (medium sandwich) + $2.00 (drink) + $1.50 (popcorn) = $6.00
If the booster club pays for a large sandwich, drink, and popcorn for each student, the cost will be:
$3.00 (large sandwich) + $2.50 (drink) + $2.00 (popcorn) = $7.50
The difference in cost between the two options is $1.50 per student.
To find how many more students can go to the game with the cheaper meal option, we can divide the total amount of money available ($750) by the difference in cost per student ($1.50):
$750 ÷ $1.50 = 500
So, with the cheaper meal option, the booster club can take 500/6 students = 83 students.
Therefore, the booster club can take 1 more student to the game if they pay for a medium sandwich, drink, and popcorn for each student.
PLEASE HELP WITH THE PROBLEM !!
Answer:
the answer is 18
Step-by-step explanation:
volume of triangular prism =l×w×h
9×2×1=18
Luna's soccer team always starts practice
with a 12 minute warm-up. Then, the team
spends 6 minutes practicing each drill.
Write an equation in slope-intercent form
to represent this linear function.
If tomorrow’s practice is 60 minutes long, how many drills can Lunas team practice?
a) An equation in slope-intercept form representing the linear function is y = 12 + 6x.
b) If tomorrow’s practice is 60 minutes long, based on the slope-intercept equation above, the number of drills that Luna's team practice is 8.
What is the slope-intercept equation?The slope-intercept equation is a linear equation in slope-intercept form.
The slope-intercept equation is given as y = mx + b, where:
y = y-coordinatem = slopex = x-coordinateb = y-intercept.The number of minutes spent for warm-up practice = 12 minutes
The number of minutes spent per drill = 6 minutes
Let the number of drills per practice = x
Let the total number of minutes spent by the soccer team (length) per practice = y
Equation:y = 12 + 6x
The length for tomorrow's practice = 60 minutes
60 = 12 + 6x
60 - 12 = 6x
48 = 6x
x = 8
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Use the technique of linear regression to find the line of best fit for the given points. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
(1,10), (2,5), (3,4), (4,9),(5,4), (6,2), (7,3)
Answer y=
The line of best fit for the given points is y = -1.35x + 9.62, where x is the independent variable and y is the dependent variable. This line represents the linear relationship between the two variables that best fits the given data.
To find the line of best fit for the given points, we can use linear regression. Using a calculator or statistical software, we obtain the following results:
Slope (m) = -1.35
Y-intercept (b) = 9.62
Therefore, the equation of the line of best fit is:
y = -1.35x + 9.62
Rounding to two decimal places, we get:
y = -1.35x + 9.62
The line of best fit for the given points is y = -1.35x + 9.62, which represents the linear relationship between the variables.
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60% of all Americans live in cities with population greater than 100,000 people. If 34 Americans are randomly selected, find the probability that
a. Exactly 23 of them live in cities with population greater than 100,000 people.
b. At most 23 of them live in cities with population greater than 100,000 people.
c. At least 22 of them live in cities with population greater than 100,000 people.
d. Between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people.
a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is 0.095.
b. The probability that at most 23 of them live in cities with population greater than 100,000 people is 0.0332.
c. The probability that at least 22 of them live in cities with population greater than 100,000 people is 0.9876.
d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is 0.8782.
What is the probability of selecting the required numbers?Let X be the number of Americans out of 34 who live in cities with population greater than 100,000 people.
Then X follows a binomial distribution with n = 34 and p = 0.6.
a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is:
P(X = 23) = (34C₂₃) x (0.6)²³ x (0.4)¹¹ = 0.095
b. The probability that at most 23 of them live in cities with population greater than 100,000 people is:
P(X <= 23) = P(X = 0) + P(X = 1) + ... + P(X = 23)
= ∑(34Ci) x (0.6)^i x (0.4)^(34-i), i = 0 to 23
= 0.0332
c. The probability that at least 22 of them live in cities with population greater than 100,000 people is:
P(X >= 22) = 1 - P(X < 22) = 1 - P(X <= 21)
= 1 - ∑(34Ci) * (0.6)^i x (0.4)^(34-i), i = 0 to 21
= 0.9876
d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is:
P(18 <= X <= 24) = P(X <= 24) - P(X < 18)
= ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 24
- ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 17
= 0.8782
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A copy machine makes 28 copies per minute. How long does it take to make 126 copies?
A solid has volume 4 cubic units. The equation k = 3^ square root* v/4 represents the scale factor of k by which the solid must be dilated to obtain an image with volume V cubic units. List 2 points which are on the graph representing this
equation. (Lesson 5-7)
The volume of the solid is the amount of space value is k = 32.
What is volume in maths?.
Volume in mathematics refers to the quantity of space within a certain 3D object. A fish tank, for example, has measurements of 3 feet long by 1 foot wide and 2 feet high. If you increase the length, breadth, and height by 3x1x2, which is equal to six, you can calculate the volume.
The volume of the solid is represents in cubic units. Thus
k = ∛v/4
k³ = v/4
v = 4k³ ( k≥0)
when k = 1, v = 4
k = z, v = 4.z³ = 32
∴ points (1,1) , (7,32) are on the graph.
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What is the equation of parabola with focus (4,5) and a directrix y =-1
The equation of the parabola with focus (4,5) and directrix y=-1 is
[tex](y-5)^2=4(x-4) or (y+1)^2=4(x-4).[/tex]
The equation of a parabola is defined by its focus and directrix. The focus is the point on the parabola that is used to determine its shape, while the directrix is the line used to determine its orientation. The equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex]. This equation can be expressed in terms of the focus and directrix by substituting the x and y values of the focus and directrix into the equation. Substituting the x value of the focus (4) into the equation gives us[tex](y-5)^2=4(4-4)[/tex], which simplifies to[tex](y-5)^2=0[/tex]. This equation can be rearranged to give us y=5, which is the y value of the focus. Substituting the y value of the directrix (-1) into the equation gives us [tex](y+1)^2=4(x-4)[/tex]. This equation can also be rearranged to give us y=-1, which is the y value of the directrix. Therefore, the equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex] or[tex](y+1)^2=4(x-4)[/tex].
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SOMEBODY PLEASE HELP ME I'M DROWNING IN THIS WORK
The surface area of the triangular prism is 156.5 inches².
How to find the surface area of a prism?The surface area of a triangular prism can be found as follows:
Therefore, the prism is a triangular prism. The prism has two triangular base with side length 5 inches each. The height of the triangular bases are 4.3 inches each.
The height of the triangular prism is 9 inches. The surface area of the triangular prism is the sum of the whole individual area of each surface of the prism.
Hence,
surface area of the prism = bh + l(s₁ + s₂ + s₃)
Therefore,
surface area of the prism = 4.3 × 5 + 9(5 + 5 + 5)
surface area of the prism = 21.5 + 9(15)
surface area of the prism = 21.5 + 135
surface area of the prism = 156.5 inches²
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Compare the performance of Medstar Washington to other DC based hospitals (excluding Medstar Georgetown) on overall satisfaction in Hospital Compare data using data from 2014 through today. What advice you have for the hospital administrator on where improvements are needed. Find the data in Hospital Compare site. One purpose of this assignment is to make sure that you can find the data online on your own. Download and analyze the data.
To compare the performance of MedStar Washington to other DC-based hospitals on overall satisfaction, we can use the (HCAHPS) survey data available on the Hospital Compare website.
What does this survey do?The HCAHPS survey measures patients' perspectives of hospital care, including topics such as communication with doctors and nurses, the responsiveness of hospital staff, cleanliness and quietness of hospital environment, pain management, and medication communication.
To obtain the data for Medstar Washington and other DC-based hospitals (excluding Medstar Georgetown), you can follow these steps:
1) Go to the Hospital Compare website:
2) Click on "Find a Hospital."
3) Enter the city and state of the hospital you want to compare (e.g., Washington, DC) and click "Search."
4) Select "Patient Experience (HCAHPS) Survey" from the "Select a topic" drop-down menu.
5) Click on "Overall Hospital Rating" under the "Survey Summary Star Ratings" section.
6) Select the hospitals you want to compare and click "Compare."
7) You can view the survey results for each hospital on various dimensions of patient experience, such as communication with nurses, communication with doctors, the responsiveness of hospital staff, pain management, cleanliness and quietness, and overall hospital rating.
Based on the data, the administrator of MedStar Washington can identify areas of improvement and take necessary steps to enhance patient satisfaction.
For example, if the hospital is performing poorly in communication with nurses, the administrator can develop programs or training for nurses to improve their communication skills. If the hospital is struggling with pain management, the administrator can work with physicians and nurses to implement best practices and improve pain control.
It's worth noting that Hospital Compare data is based on self-reported patient experience, and other factors such as patient demographics, the severity of illness, and socioeconomic status can influence the scores.
Therefore, the data should be interpreted with caution, and administrators should use multiple sources of information to evaluate the quality of care in their hospitals
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Rachel, Sam and Thomas applied for a common position at the company. Only one of them will be hired for the position. The probabilities that each of them is hired for the role are given by 1 out of 7, 2 out of 7, and 4 out of 7 respectively.
The probabilities that Rachel, Sam and Thomas can help boost the company’s revenue are given by 4 out of 5, 1 out of 2, and 3 out of 10 respectively if they are hired.
(a) Find the probability that Thomas is selected for the position given that the company’s revenue did not improve.
(b) Find the probability, p, that the company’s revenue will generally improve.
Rachel, Sam and Thomas interviewed at another company for another position. The probabilities that each of them is hired for the role are now given by x, 2x and 4x respectively.
It can be assumed that the hiring process for each individual candidate are independent of one another.
(c) Suppose there is no limit to the number of hires the company can make (i.e. the company can hire any one of them, any two of them, all three of them or no one at all). Find an inequality that must satisfied by x.
7x ≤ 1, or x ≤ 1/7
(a) The probability that Thomas is selected for the position given that the company’s revenue did not improve is 4 out of 7.
(b) The probability that the company’s revenue will generally improve is the sum of the probabilities that Rachel, Sam and Thomas are hired multiplied by the probability that the company’s revenue will improve given that each individual is hired. This probability is given by (1/7)*(4/5) + (2/7)*(1/2) + (4/7)*(3/10) = 0.5.
(c) For the probabilities given for the second hiring process to be valid, the inequality x + 2x + 4x ≤ 1 must be satisfied. This inequality can be written as 7x ≤ 1, or x ≤ 1/7.
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mathematics homework
The angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.
Describe 16- notch socket?The 16-notch socket has a cylindrical shape with 16 notches or recesses machined into the interior of the socket. Each notch corresponds to a flat side of a 16-sided nut or bolt head. The notches are evenly spaced around the socket, providing a secure grip on the nut or bolt head and allowing for easy application of torque using a ratchet or wrench.
16-notch sockets are commonly used in automotive and industrial applications, particularly in heavy machinery where large bolts and nuts with 16-sided heads are often used. They are available in a range of sizes to fit different nut and bolt sizes and are typically made of durable materials such as chrome vanadium steel or high-grade aluminum.
Premise 1: Deondra is designing a 16-notch socket wrench.
Premise 2: The notches will be the same size.
Conclusion: Therefore, Deondra needs to know the angle measure for each notch.
To determine the angle measure for each notch, we can use the formula for the interior angle of a regular polygon, which is:
Interior angle = (n-2) x 180 / n
where n is the number of sides (or notches) in the polygon.
Applying this formula to a 16-sided polygon (or hexadecagon), we get:
Interior angle = (16-2) x 180 / 16
Interior angle = 1680 / 16
Interior angle = 105 degrees
Therefore, the angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.
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Amore scored 15 out of 20 in a test.Write as a percentage
Answer:
75%
Step-by-step explanation:
write it as a fraction first, so 15/20.
make the bottom number 100 to get the mark out of 100.
to do this, multiply the bottom by 5 (20x5=100) and then do the same to the top.
you get 75/100. this equals 75%
Answer:
75%
Step-by-step explanation:
In this question, 20 is the highest score you can get on the test so 20 is 100%. We will now want to divide 100 by 20.
100 ÷ 20 = 5
Each score Amore got on the test was worth 5% of the test.
We know he scored 15 on the text, so now we want to multiply 15 with 5.
15 × 5 = 75
Amore scored 75% on his test.
In rectangle QRST , QS=30-2x and RT=9+x . Find the lengths of the diagonals of QRST
Answer:
Each of the diagonals is 16
Step-by-step explanation:
The diagonals of a rectangular are equal
The two diagonals are QS and RT
QS = RT
→ 30 - 2x = 9 + x
Subtract 30 both sides:
30 - 30 - 2x = 9 - 30 + x
- 2x = -21 + x
Subtract x both sides
-2x - x = -21 + x - x
-3x = -21
x = -21/-3 = 7
So the diagonal RT = 9 + 7 =16
should be the same as diagonal QS
Qs = 30 - 2(7) = 30 - 14 = 16
Using a calculator, work out
(4.57 × 10-¹0) – (3.78 × 10−¹¹)
Give your answer in standard form.
Finally, we can express the answer in standard form by moving the decimal point one place to the left, and adjusting the exponent of 10 accordingly: 0.4192 × 10⁻⁹ = 4.192 × 10⁻¹⁰.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
To subtract the given values in standard form, we need to make sure that the exponents of 10 are the same.
We can rewrite 4.57 × 10⁻¹⁰ as 0.457 × 10⁻⁹ (by moving the decimal point one place to the right) and rewrite 3.78 × 10⁻¹¹ as 0.0378 × 10⁻⁹ (by moving the decimal point one place to the right).
Now we can subtract the values:
(4.57 × 10⁻¹⁰) – (3.78 × 10⁻¹¹) = (0.457 × 10⁻⁹) – (0.0378 × 10⁻⁹)
= 0.4192 × 10⁻⁹
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ANSWER FAST!!!
find the missing y value in the table
x y
4 2.5
11 9.5
15 13.5
21 y
The missing y value in the table can be found to be 19. 5.
How to find the missing value in the table?To find the missing value, you need to find the relationship that x and y have with each other on the table.
We find that when 4 increases to 11, 2. 5 as y, increases to 9. 5. The difference in both is:
= 11 - 4 = 9. 5 - 2.5
= 7 = 7
We see this common difference again with 15 and 11 being 4 and the difference between the y - values of 13. 5 and 9. 5 being 4 as well.
The y value corresponding to 21 as x would be:
= ( 21 - 15 ) + 13. 5
= 19. 5
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the iron bank offers a range of financial services and investment opportunities. of its customers, 36% invest in stocks, 22% invest in futures, and 15% invest in both stocks and futures. use this information and the rules of probability to answer the following:Part A: What proportion of Iron Bank customers invest in neither Stocks nor Futures? Part B: Of the Iron Bank customers who invest in Futures, what percentage invest in Stocks? Part C: What is the probability that a randomly selected Iron Bank customer invests in Stocks aud does not invest in Futures?
Part A: The proportion of Iron Bank customers who invest in neither stocks nor futures is 27%.
Part B: Of the Iron Bank customers who invest in futures, 61.54% also invest in stocks.
Part C: The probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%.
Part A: This can be calculated by subtracting the combined proportion of those who invest in stocks (36%) and those who invest in futures (22%) from 100%.
Part B: This can be calculated by dividing the proportion of those who invest in both stocks and futures (15%) by the proportion of those who invest in futures (22%).
Part C: This can be calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).
Given, that 36% of the customers are investing in stocks and 15% of those customers are also investing in futures.
So, 21% of the customers invest in stocks and not futures, while 79% of the customers either invest in futures, or in neither stocks nor futures.
Therefore, the probability is 21/100, or 18.18%.
In conclusion, the probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%. This is calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).
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If Manny sailed 500 nautical miles in 42 hours, what was his average speed in knots? (1 knot = 1 nautical mile per hour)
Manny's average speed in knots was approximately 11.9 knots. We simply used speed, distance and time formula.
To calculate the average speed in knots, we need to divide the distance sailed in nautical miles by the time taken in hours. So,
Average speed in knots = Distance / Time
Here, the distance is given as 500 nautical miles and the time is given as 42 hours.
Average speed in knots = 500 / 42
= 11.9 (rounded to one decimal place)
Therefore, Manny's average speed in knots was approximately 11.9 knots.
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