Answer:
22.84, 5.83
Step-by-step explanation:
Pythagoras theorem states that: a^2+b^2=c^2
So, for red triangle, it will be: 9^2+21^2=b^2
81+441=b^2
522=b^2
square root of 522=b
22.84=b
For purple one,
3^2+5^2=a^2
9+25=a^2
34=a^2
square root of 34=a
5.83=a
The math dept is buying pizza for the students from either Papa Johns or
Cicis. The equation for Papa Johns can be represented as C=12p+15 which
includes a one time delivery charge. The equation for Cicis can be presented
as C=10p+12 which includes a one time delivery charge.
How much more does Papa Johns charge PER PIZZA than Cicis?
answer
Papa Johns charges 2 more per pizza plus 3 more for the delivery charge so 5 total
The cost to rent an rv is $150 per day plus $0.35 per mile. what is the maximum distance you can drive the rv in a day if your budget is $200?
Answer:
142.86 miles
Step-by-step explanation:
150 + .35m < 200
150 + .35m -150 < 200-150
.35m < 50
.35m/35 < 50/.35
m < 142.86
The maximum distance I can drive the rv in a day if my budget $200 is, approx. 142 miles
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
The cost to rent an rv is $150 per day + $0.35 per mile
The maximum distance in a day = ?
Budget is $200
So,
The maximum distance in a day ≤ 200
The maximum distance in a day = 150 + 0.35x
Now,
⇒ 150 + 0.35x ≤ 200
⇒ 0.35x ≤ 200 - 150
⇒ x ≤ 142.85
Hence, maximum distance in a day is approx. 142 miles
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Please Help!!! 10 Points! Brainliest Answer
Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria? (graph in photo)
no, the frequencies do not increase from the low frequency to a maximum frequency.
no, the distribution is not symmetric.
yes, all the requirements are met.
Answer: I think its C, yes, all the requirements are met.
Step-by-step explanation: I might be wrong, so check to make sure
Yes, all the requirements are met.
The correct option is (C)
What is normal distribution?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
A graph or table that displays the frequency of various outcomes is called a frequency distribution.
The bell-shaped normal distribution is the norm.
As, the frequency value is lower for scores 5.5000 to 5.5499,
and then it increases 5.5500- 5.7499, then decreases for scores 5.7500-5.7999.
So, the frequency distribution curve looks bell-shaped when plotted.
hence, it follow a normal distribution.
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on 10.
Which inequality represents the phrase below?
a number less than 44
A. x > 44
نه نه
x < 44
C. x < 45
D.
X = 44
Answer:
B
Step-by-step explanation:
We're looking for a number (x) that's less than 44
We can represent it by simply using the less sign, so x < 44
1. Solve for the unknown in each triangle. Round each answer to the nearest tenth.
The values of the missing sides are;
a. x = 35. 6 degrees
b. x = 15
c. x = 22. 7 ft
d. x = 31. 7 degrees
How to determine the valuesTo determine the values, we have;
a. Using the tangent identity;
tan x = 5/7
Divide the values
tan x = 0. 7143
x = 35. 6 degrees
b. Using the Pythagorean theorem
x² = 9² + 12²
find the square
x² = 225
x = 15
c. Using the sine identity
sin 29= 11/x
cross multiply the values
x = 11/0. 4848
x = 22. 7 ft
d. sin x = 3.1/5.9
sin x = 0. 5254
x = 31. 7 degrees
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At the instant shown, the shaft and plate rotates with an angular velocity of 19 rad/s and angular acceleration of 9 rad/s2 0.6 m 0.2 m 0.4m 0.3 m 0.3 m 0.4 m Part A eterminethe wocl a n D sea c Enter the ", y, and Z components of the velocity separated by commas vec m/s Submit Request Answer Part B Determine the acceleration of point D located on the corner of the plate at this instant. Enter the , y, and Z components of the velocity separated by commas vec m/s Submit Request Answer
The acceleration components of point D are, ax = 3.6 m/s², ay = 6.4 m/s², az = -1.14 m/s²
At the instant shown, the shaft and plate rotates with an angular velocity of 19 rad/s and angular acceleration of 9 rad/s2. The given diagram is shown below. Angular velocity (w) = 19 rad/sAngular acceleration (α) = 9 rad/s²Plate dimension AB = 0.6 m, BC = 0.2 m, CD = 0.4 m, DA = 0.3 m, AE = 0.3 m and EF = 0.4 m.
Determine the wocl and Dsea of Enter the ", y, and Z components of the velocity separated by commas vec m/sThe velocity components for point D can be calculated using the following formula.Vd = R x wWhere R is the position vector of D relative to the origin.
According to the given diagram, the position vector of point D relative to the origin is, R = 0.2i + 0.4j + 0.3kThe velocity of point D can be calculated as follows.Vd = R x w = 0.2i + 0.4j + 0.3k x 19The cross product of R and w can be calculated as follows.i j k 0.2 0.4 0.3 0 19 0 = [(0.4 × 0) - (0.3 × 19)] i - [(0.2 × 0) - (0.3 × 0)] j + [(0.2 × 19) - (0.4 × 0)] kVd = -5.7i + 6.8kThus, the velocity components of point D are, Vx = -5.7 m/s, Vy = 0 m/s, Vz = 6.8 m/s
Determine the acceleration of point D located on the corner of the plate at this instant. Enter the, y, and Z components of the velocity separated by commas vec m/sThe acceleration components of point D can be calculated using the following formula.aD = R x α + w x (w x R)Where R is the position vector of D relative to the origin.
According to the given diagram, the position vector of point D relative to the origin is, R = 0.2i + 0.4j + 0.3kThe acceleration of point D can be calculated as follows.aD = R x α + w x (w x R) = (0.2i + 0.4j + 0.3k) x 9 + 19 x (19 x (0.2i + 0.4j + 0.3k)) = (0.4k - 0.3j) x 9 + 19 x (0.4 x (0.4j - 0.3k))aD = 3.6i + 6.4j - 1.14k.
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Work out the size of angle x.
Answer:
x = 46°
Step-by-step explanation:
Angles on a straight line sum to 180°.
Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:
⇒ 180° - 130° = 50°
The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:
⇒ 180° - 96° = 84°
The interior angles of a triangle sum to 180°. Therefore:
⇒ 50° + 84° + x = 180°
⇒ 134° + x = 180°
⇒ 134° + x - 134° = 180° - 134°
⇒ x = 46°
Therefore, the size of angle x is 46°.
The sum of the first 25 multiples of 4 is: 4 + 8 + 12 ... 100. the sum of the first 25 multiples of 3 is: 3 + 6 + 9. + 75. what number is equal to the difference of the two sums?
The number that is equal to the difference of sum of both the sum is 325.
The multiples of 4 are 4,8,12,16,20...
The multiples of 3 are 3,6,9,12,15,...
Both the sequences are forming an Arithmetic progression(AP),
The sum of n terms of an AP is,
Sₙ = n/2(2a + (n-1)d)
Where,
n is the number of terms,
a is the first term,
d is the common difference.
So, For multiples of 3,
a = 3
d = 3
n = 25
So, putting values in the formula,
S₂₅ = 25/2(6+24x3)
S₂₅ = 975
For the multiples of 4,
a = 4
d = 4
n = 25
Putting values in the formula,
S'₂₅ = 25/2(8+24x4)
S'₂₅ = 1300
The difference in both the sums,
S'₂₅ - S₂₅ = 1300-975
S'₂₅ - S₂₅ = 325
The difference of the sum is 325.
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Product Rule states: keep the base the same and do this to the exponents. Your
A). answer
B). multiply
C). subtract
Answer: B multiply
Step-by-step explanation:
Let n be the largest integer for which 14n has exactly 100 digits. Counting from right to left, find the 68th digit of n
Counting from right to left, find the 68th digit of n is 10.
An integer, is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
The largest integer with exactly 100 digits is the integer that consists of 100 copies of the digit 9.
This integer is equal to 10100 = 10
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Find the vector equation that represents the curve of intersection of the paraboloid z = surface y = e. Write the equation so that one of the functions is simply t. x(t) = y(t) z(t) - = = 4x² + y² and the
The vector equation of the curve of intersection of the paraboloid z = 4x² + y² and the plane y = e is given by r(t) = ti + ej + (4t² + e²)k, where -∞ < t < ∞.
The curve of intersection of two surfaces is the set of points that lie on both surfaces. In this case, we are interested in finding the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y² and the plane y = e.
To find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y² and the plane y = e, we need to substitute y = e into the equation of the paraboloid and solve for x and z.
This will give us the x and z coordinates of the curve at any given point on the plane y = e.
Substituting y = e into the equation of the paraboloid, we get
z = 4x² + e²
Let's solve for x in terms of z.
4x² = z - e²x² = (z - e²)/4x
= ±√((z - e²)/4)
= ±√(z/4 - e²/4)
= ±√(z - e²)/2
Note that x can take either the positive or negative square root of (z - e²)/4 because we want the curve on both sides of the yz plane.
Similarly, we can solve for z in terms of x.
z = 4x² + e²
Let's write the vector equation of the curve in terms of the parameter t such that x = t and y = e.
x(t) = t
y(t) = e z(t) = 4t² + e²
The vector equation of the curve of intersection of the paraboloid z = 4x² + y² and the plane y = e is given by:
r(t) = ti + ej + (4t² + e²)k, where -∞ < t < ∞.
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Partial Derivative Applications, Vectors and Matrices
If z = F(u, v, w) where u = r 2 , v = −2s 2 , and w = lnr + lns,
find ∂z/∂r and ∂z/∂s.
The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.
To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.
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Pls help me. It due ASAP...
Answer:
b
Step-by-step explanation:
-7y-8=6y+18 i need help with this urgent!
Answer:
Y= -2
Step-by-step explanation:
Define and distinguish among mean, median, and mode. Choose the correct description of the mean below. O A. The mean is the most common value in a data set. It can be strongly affected by outliers. O B. The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers. O C. The mean is the most common value in a data set. It is not affected by outliers. O D. The mean is the sum of all the values divided by the number of values. It is not affected by outliers. O E. The mean is the middle value in a data set. It can be strongly affected by outliers O F. The mean is the middle value in a data set. It is not affected by outliers.
Answer:
As far as I know
Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.
The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Help please rn please
Answer:
c
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
T = temperature
-52 < T < 108
Temperatures fall between the values of -52 and 108. D is the number line that shows this.
Find the value of h(-67) for the function below.
h(x) = -49x − 125
A.
-3,408
B.
3,158
C.
3,283
D.
-1.18
Answer:
B. 3,158
Step-by-step explanation:
h(x) = -49x − 125
Let x = -67
h(-67) = -49(-67) − 125
=3283-125
= 3158
Answer:
Answer B
Step-by-step explanation:
To find the value of h(-67) for the function h(x) = -49x - 125,
we substitute -67 for x in the function and evaluate it.
h ( - 67 ) = - 49 ( - 67 ) - 125
Now we can simplify the expression:
h ( -67 ) = 3283 - 125
h ( -67 ) = 3158
Problem Page Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.
Note: Consider we need to find the possible number of ways to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.
Given:
Number of letters = 4
Number of letters selected without replacement = 2
To find:
The total possible number of ways.
Solution:
We have 4 letters A, B, C and D.
So, the number of ways to select first letter is 4.
After selecting a letter the number of remaining letters is 3.
So, the number of ways to select second letter is 3.
Now, the total number of ways to select 2 letters, without replacement, from the 4 letters A, B, C, and D is:
\(4\times 3=12\)
Therefore, the required number of ways is 12.
the perimeter of a square box is 12x+32.Complete an equivalent expression that shows the perimeter as four times the Side length of the box
To prove that the perimeter of a square box is equal to four times the side length of the box.
Given that, the perimeter of a square box = 12x + 32
So, we have to prove that perimeter = 4 x Side
Let's assume Side = S
Therefore, Perimeter = 4 x S
or 12x + 32 = 4 x S
We know that the perimeter of a square is equal to the sum of all of its four sides.
Therefore, P square = S + S + S + S
So, we can write it as P square = 4S ....... (1)
Also, the perimeter of a square box is also given which is equal to 12x + 32.
=> P square = 12x + 32 ....... (2)
Taking 4 as common on the right-hand side,
=> P square = 4 x (3x + 8)
From equation (1) putting the value of P square = 4S
=> 4S = 4 x (3x + 8)
=> S = 3x + 8
Putting this value of S in equation (1), we get
P square = 4 x (3x + 8)
P square = 4 x Side length(S)
Hence, we can say that the perimeter of the square is four times the side length of the box.
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The Johnson twins were born eight years after their older sister.
This year, the product of the three siblings' ages is exactly
1422 more than the sum of their ages. How old are the twins?
The age of the twins is 9 if the Johnson twins were born eight years after their older sister.
What are ages?When a ratio, such as p:q, is used to express age, qx and px are taken into account. The current age will be (xn) years if you assume the current age to be x. If you're assuming that x is the age you are now, then 1/n of your age will be equivalent to (x/n) years.
What are known as age problems are one use for linear equations. The ages of two separate persons (or objects), both present and future (or past), are typically compared for solving age-related problems. These issues typically seek to determine the current age of each subject.
Let the age of twins be x
The age of older sister be x+8
x(x)(x+8) = x + x + (x+8)+1422
x²(x+8) = 3x+1430
x³+8x² = 3x+1430
x³+8x²- 3x-1430=0
x=9.2045≈9
Therefore, the age of the twins is 9
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we classify events into four types or categories, which vary in scale, with corresponding variations in their impacts. which scale does the masters' golf tournament belong to?
The Masters golf tournament belongs to a large scale event category, given the corresponding variations in its impacts such as attracting thousands of visitors and generating significant economic activity in the host city.
The Masters Golf Tournament belongs to a large-scale event category. Large-scale events typically have significant impacts, including attracting international attention, generating substantial economic benefits, and requiring considerable planning and resources.
In the case of the Masters Golf Tournament, it is an annual event held at Augusta National Golf Club in Georgia, USA, and it attracts professional golfers from around the world, as well as a global audience, creating corresponding variations in economic, social, and environmental impacts.
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which of the following corresponds to the predictor variable in simple linear regression?
In simple linear regression, the predictor variable is the independent variable, which is used to predict the value of the dependent variable. It is also referred to as the explanatory variable, as it is used to explain the variability in the response variable.
For example, in a study that examines the relationship between the hours studied and exam scores, the predictor variable is the number of hours studied, and the dependent variable is the exam score.
The predictor variable is plotted on the x-axis, while the dependent variable is plotted on the y-axis in a scatter plot. The relationship between the predictor and the dependent variable is represented by a straight line, which is determined by the regression equation.
The slope of the line represents the change in the dependent variable for each unit change in the predictor variable.
In summary, the predictor variable is the variable that is used to predict or explain the changes in the dependent variable in simple linear regression.
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The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 40 to 85 minutes. What is the probability that the cycle time exceeds 75 minutes if it is known that the cycle time exceeds 45 minutes
The probability that the cycle time exceeds 75 minutes, given that it already exceeds 45 minutes, is 25%.
Given the information provided, we know the following:
1. The cycle time for trucks hauling concrete is uniformly distributed over the interval 40 to 85 minutes.
2. We need to find the probability that the cycle time exceeds 75 minutes, given that it already exceeds 45 minutes.
Step 1: Determine the length of the original interval.
The original interval is from 40 to 85 minutes, so the length is 85 - 40 = 45 minutes.
Step 2: Determine the length of the conditional interval.
Since we know that the cycle time already exceeds 45 minutes, our new interval starts at 45 minutes and ends at 85 minutes. The length of this interval is 85 - 45 = 40 minutes.
Step 3: Determine the length of the interval for cycle times exceeding 75 minutes.
The interval for cycle times exceeding 75 minutes starts at 75 and ends at 85, so the length of this interval is 85 - 75 = 10 minutes.
Step 4: Calculate the probability.
Since the cycle time is uniformly distributed, the probability is equal to the ratio of the lengths of the intervals:
Probability = (Length of interval for cycle times exceeding 75 minutes) / (Length of conditional interval)
Probability = 10 minutes / 40 minutes = 0.25 or 25%
So, the probability that the cycle time exceeds 75 minutes, given that it already exceeds 45 minutes, is 25%.
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One week Grace spent 16% of her
weekly wage on a new bookshelf
that cost $184. What is her weekly
wage?
Answer:
$1150 will be the weekly wage
Step-by-step explanation:
184 = 16%*x
184 = 0.16*x
184/0.16 = x
x = $1150
Here, "x" is her weekly wage.
Find the coordinates of the image of the point (-5,5) under translation
(3, 0) I Hope this helps But If you had an image could you show it? Because its hard to do this without the image.
May I Have Brainliest? <3
what is an equation equivalent to 5x-25
25-25=0
Assuming that x is five then this would work.
Answer:
x-5
Step-by-step explanation:
divide both sides by 5
5x-25
/5 /5
_____
x - 5
given sin (-∅) = -1/4 and tan∅ = √15/15.
What is the value of cos∅?
Find the area of the entire region round two decimal places
SOLUTION.
The area of the entire region will be to find the area of the isosceles triangle and the semi-circle.
\(\begin{gathered} \text{Area of the triangle is } \\ =\frac{1}{2}\times a\times b\times\sin \theta \\ \text{Where } \\ \text{where a and b are two sides and }\theta=angle\text{ betwe}en\text{ the two sides } \end{gathered}\)Then
\(\begin{gathered} =\frac{1}{2}\times8\times8\times\sin 72.6 \\ =32\sin 72.6 \\ =30.54\text{unit}^2 \end{gathered}\)The area of the isosceles triangle is 30.354 square units
We need to obtain the diameter of the semi-circle using the cosine rule
We need to obtain the value of x,
\(\begin{gathered} x^2=8^2+8^2-2(8)(8)\cos 72,6 \\ x^2=128-128\cos 72.6 \\ x^2=128-38.27 \\ x^2=89.72 \end{gathered}\)Take square root of both sides, we have
\(x=\sqrt[]{89.72}=9.74\)Hence, the diameter is 9.74
Then the radius will be
\(r=\frac{9.74}{2}=4.87\)The area of the semi-circle is
\(\begin{gathered} =\frac{1}{2}\pi r^2 \\ =\frac{1}{2}\times3.14\times4.87^2 \\ =37.24\text{unit}^2 \end{gathered}\)The area of the semi circle is 37.42 square units
Therefore the area of the region will be
\(\begin{gathered} =\text{Area ot triangle + Area of semi circle } \\ =30.54+37.42 \\ =67.96uniits^2 \end{gathered}\)Thus
The area of the region is 67.96 units²
A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass-spring system is disturbed from its rest state by the force F(t) = 100cos(8t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.
Determine the spring constant k.
k = ? Newtons / meter
Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y,y′,y′′,t.)
Differential equation: ?
Initial conditions: y(0) = ? and y′(0) = ?
Solve the initial value problem for y(t).
y(t) = ?
Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 ≤ t < [infinity]. If there is no such maximum, enter NONE.
maximum excursion = ? meters
Using Hooke's law the maximum value of |cos(8t)| is 1, so the maximum excursion is 1/6 meters.
To find the spring constant k, we use Hooke's law:
F = -ky
where F is the weight of the object, and y is the distance it is stretched from its rest position. At equilibrium, F = mg = 10 × 9.81 = 98.1 N. Thus,
98.1 = -k × 0.098
k = -1000 N/m
The equation of motion for the system is given by:
my'' + ky = F(t)
Substituting the given values, we get:
10y'' + (-1000)y = 100cos(8t)
y'' - 100y = 10cos(8t)
with initial conditions y(0) = 0 and y'(0) = 0.
The characteristic equation is r² - 100 = 0, with roots r = ±10i. The complementary solution is therefore y_c(t) = c1cos(10t) + c2sin(10t).
For the particular solution, we assume a form of yp(t) = Acos(8t) + Bsin(8t), and substitute it in the differential equation to get:
-64Acos(8t) - 64Bsin(8t) - 100(Acos(8t) + Bsin(8t)) = 10cos(8t)
Solving for A and B, we get A = -1/6 and B = 0. Thus, the particular solution is yp(t) = (-1/6) × cos(8t).
The general solution is therefore y(t) = c1cos(10t) + c2sin(10t) - (1/6)*cos(8t). Applying the initial conditions, we get c1 = 0 and c2 = 0, so the particular solution is simply y(t) = (-1/6) × cos(8t).
The maximum excursion from equilibrium can be found by taking the absolute value of y(t) and finding its maximum value. We have:
|y(t)| = (1/6) × |cos(8t)|
The maximum value of |cos(8t)| is 1, so the maximum excursion is 1/6 meters.
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