Answers
Related Questions
two angles of a triangle measure 30 and 45 degrees. if the side of the triangle opposite the 30-degree angle measures units, what is the sum of the lengths of the two remaining sides? express your answer as a decimal to the nearest tenth.
Answers
The length of the remaining sides of the traingle based on stated information is around 28.4 units.
Let angle A and angle B be 30 and 45 degrees. So, angle C will be -
A + B + C = 180
30 + 45 + C= 180
C = 180 - (30 + 45)
C = 180 - 75
C = 105 degrees
Using law of sines we get -
side a/sin A = side b/Sin B = side c/sin C (each side a, b and c will have opposite angle A, B and C)
Keep the values in formula to find the remaining ones.
6✓2/sin 30 = side b/Sin 45 = side c/sin 105
Solving for side b
side b = (sin 45 × 6✓2)/sin 30
side b = (1/✓2 × 6✓2)/(1/2)
side b = 12
Solving for side c
side c = sin 105 × 6✓2/sin 30
On solving we get side c = 16.4
Sum of sides = 12 + 16.4
Sum = 28.4 units
Hence, the remaining two sides are 28.4 units.
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Two angles of a triangle measure 30 and 45 degrees. If the side of the triangle opposite the 30-degree angle measures 6√2 units, what is the sum of the lengths of the two remaining sides? Express your answer as a decimal to the nearest tenth.
Could someone help me?
Answers
Answer:
a + b = 180
180 - a = b
Step-by-step explanation:
Angles ∠a and ∠b are on a line and are supplementary, which means their sum is equal to 180°.
So the options which represent the relationship between the measures of angles are:
a + b = 180 and
180 - a = b
lewis read 35 pages of a novel in 25 minutes. at this rate, determine how many pages he can read in a hour
Answers
Answer:
84 pages per hour.
Step-by-step explanation:
We know that 60 minutes is an hour.
So, what you need to do is divide 60 by 25. (this equals 2.4)
then, all you have to do is multiply 2.4 with 35.
2.4×35=84
so, he'll read 84 pages in an hour.
What is the measure of RCD in the figure below?
P
11
D
350
11
C
R
A. 350
B. 55°
C. 11°
D. 60°
E. 700
F. Cannot be determined
Answers
HELP!
The net of a cylinder with a radius of 5cm and a height of 8cm is drawn below. Work out the surface area of the cylinder.
Answers
Answer:
408.41 cm²
is the answer
Suppose you are an engineer trying to recreate an experiment involving a weight on the end of a spring. This simulation will give you an idea of what the experiment will look like. For more information, you can visit this simple harmonic motion website. You are given the equation y(t)=2 sin 4 pi t + 5 cos 4pi t, which models the position of the weight, with respect to time. You need to find the amplitude of the oscillation, the angular frequency, and the initial conditions of the motion. You will also be required to find the time(s) at which the weight is at a particular position. To find this information, you need to convert the equation to the first form, y(t) = A sin (wt+0).
Answers
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
How to find the canonical form of the equation for simple harmonic motion
Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.
The amplitude of the canonical function is determined by the Pythagorean theorem:
A' = √(2² + 5²)
A' = √ 29
The angular frequency C is the constant within the trigonometric functions from the non-canonical formula:
C = 4π
Then, we find the initial position of the weight in time: (t = 0)
y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)
y(0) = 5
And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)
5 = √ 29 · sin (4π · 0 + D)
5 / √ 29 = sin D
D ≈ 0.379π rad
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
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A roller coaster train with 6 passenger cars and the front decoration has a mass of 3,500kg. when the train has the front decoration and only 4 passenger cars, it has a mass of 2,400kg.
what is the mass of the decoration and of each passenger car?
Answers
The mass of the decoration is 200 kg and for each passenger car is 550 kg
How to determine the mass of the decoration and of each passenger car?From the question, we have the following parameters that can be used in our computation:
6 passenger cars and the front decoration = 3,500kg4 passenger cars and the front decoration = 2,400kgThese can be represented as
(6, 3500) and (4, 2400)
The slope of the above points represent the mass of each passenger car
This is calculated as
Slope = Difference in mass/Difference in number of cars
So, we have
Slope = (3500 - 2400)/(6 - 4)
Evaluate
Slope = 550
When there are no passenger cars in the train, we have
(0, Mass of decoration)
Using the slope formula, we have
Slope = (Mass of decoration - 3500)/(0 - 6)
So, we have
Slope = (Mass of decoration - 3500)/(-6)
This gives
(Mass of decoration - 3500)/(-6) = 550
Cross multiply
Mass of decoration - 3500 = -3300
Add 3500 to both sides
Mass of decoration = 200
Hence, the mass of decoration is 200 kg
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Charles has four songs on a playlist. Each song is by a different artist. The artists are Cardi B, Post Malone, Taylor Swift, and BTS. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Cardi B and the second song is by Taylor Swift
Answers
The probability that the first song is by Cardi B and the second song is by Taylor Swift is 1/24.
To calculate the probability of the first song being by Cardi B and the second song being by Taylor Swift, we need to consider the total number of possible outcomes and the number of favorable outcomes.
There are four songs in total, and we want to determine the probability that the first song is by Cardi B and the second song is by Taylor Swift. Since the order matters (the first song and then the second song), we can use the concept of permutations.
The total number of possible outcomes is the number of ways to arrange four songs, which is 4!.
The number of favorable outcomes is the number of ways to arrange the songs such that the first song is by Cardi B and the second song is by Taylor Swift. Since each song can only be played once, there are 1 way to choose Cardi B as the first song and 1 way to choose Taylor Swift as the second song.
The probability can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 4!
Simplifying:
4! = 4 x 3 x 2 x 1 = 24
Probability = 1 / 24
The probability that the first song is by Cardi B and the second song is by Taylor Swift is 1/24.
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Madeline drives 15 miles in 12 minutes. If she drove three hours in total at the same rate, how far did she go?
Before you try that problem, answer the question below.
How many minutes did Madeline drive in total?
Answers
Answer:
225 miles in total
Step-by-step explanation:
Justin’s doctor said that the expression StartFraction x + y + 5 over 2 EndFraction, where x and y are his parents’ current heights in inches, gives an estimate of how tall Justin will be as an adult. Justin’s work evaluating the formula is shown below.
Mom’s height = 54 inches
Dad’s height = 71 inches
StartFraction 71 + 54 + 5 over 2 EndFraction = 71 + 27 + 5 = 103 inches
What error did Justin make?
He should have made x equal 54 and y equal 71.
He should have added the values in the numerator before dividing by 2.
He should have divided the 71 by 2 instead of the 27.
He should have made the numerator 76 + 59.
Mark this and return
Answers
The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".
The correct answer choice is option B
What error did Justin make?(x + y + 5) / 2
Where,
x and y are his parents’ current heights in inches,
Mom’s height = 54 inches
Dad’s height = 71 inches
Substitute into the expression
(71 + 54 + 5) / 2
= 130/2
= 65 inches
Justin's work:
( 71 + 54 + 5 ) / 2
= 71 + 27 + 5
= 103 inches
Therefore, Justin should have added the numerators before dividing by 2.
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Am I a function? Asking for a friend
Answers
Answer: No.
Step-by-step explanation:
This is not a function because it fails the vertical line test.
What is the vertical line test?
The vertical line test is a test used to check if a graph is a function. If we place a vertical line on the graph, we should be able to shift it left and right without intersecting the graph in two places at once. Since this is a circle, it fails this test and is not a function.
-8p +6y -3p+10 what are the like terms?
Answers
HELP ME PLS LOV U HUYS ,333<33445
Answers
Answer:
141.6 cm cubed
Step-by-step explanation:
Modern commercial airliners are fargely made of aluminum, a tight and strong metal. But the fact that aluminum is cheap enough that airplanes can be made out of it is a bit of historical luck. Before the discovery of the Hall-Heroult process in 1886, aluminum was as rare and expensive as gold: What would happen if airplanes had to be made of steel? The fuselage of the Boeing 777 , which can carry 305 passengers, is approximately a hollow aluminum eylinder without ends, 64.0 m long, 6.2 m wide, and 2.5 mm thick (see sketch at right). Suppose this fuselape was made of steel (densty 7.87 g/cm ^3
) instead of aluminum (density 2.70 g/cm ), and lets tay the average passenger has a mass of 79 kg. We'll also assume the engines can't lift any greater mass than they already do. Calculate the number of passengers that the Boeing 777 could carry if its fuselage was made of steel.
Answers
If the fuselage of the Boeing 777 were made of steel instead of aluminum, the number of passengers it could carry would decrease.
Given that the fuselage of the Boeing 777 is a hollow aluminum cylinder, we can calculate its volume using the dimensions provided: length = 64.0 m, width = 6.2 m, and thickness = 2.5 mm. Using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height, we can determine the volume of the aluminum fuselage. Since the cylinder has no ends, the height is the same as the length of the fuselage. The radius can be calculated by dividing the width by 2. By substituting these values into the formula, we can find the volume of the aluminum fuselage. Once we have the volume, we can multiply it by the density of aluminum to find the mass of the aluminum fuselage. Dividing the mass by the average passenger mass of 79 kg will give us the approximate number of passengers the Boeing 777 could carry if its fuselage were made of steel. However, we need the specific maximum total mass or engine's lifting capacity to provide an exact answer.
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How many and of which kind of roots does the equation f(x) = x³ - x² - x + 1 have?
A. 1 real; 2 complex
B. 2 real; 1 complex
C. 3 real
D. 3 complex
Answers
The number and the kind of roots of the equation, f(x) = x³ - x² - x + 1, is: D. 3 complex roots.
How to Find the Kind of Roots of an Equation?To determine the number and kind of roots of the equation f(x) = x³ - x² - x + 1, we can analyze the discriminant of the equation.
The discriminant, denoted as Δ, is given by:
Δ = b² - 4ac
In this case, the equation is in the form ax³ + bx² + cx + d = 0, where a = 1, b = -1, c = -1, and d = 1.
Calculating the discriminant:
Δ = (-1)² - 4(1)(-1)(-1) = 1 - 4(1)(1) = 1 - 4 = -3
The discriminant is negative (Δ < 0). This means that there are no real roots for the equation f(x) = x³ - x² - x + 1.
Therefore, the answer is:
D. 3 complex roots
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How will you describe the roots of the quadratic equation x² + 3 = 5 when solved using quadratic formula?
help pleasee
A. Equal
B. Irrational
C. Rational
D. Non - real
Answers
Answer:
I will answer you
Step-by-step explanation:
D is correct
1. Subtract 5 from both sides. x^2+3-5=5-5
2. New equation. x^2-2=0
3. To make it easier I am going to add 2 to the other side and take the square root of 2. x^2-2+2=0+2, x^2=2, sqrt(x^2)= sqrt(2).
4. You will get plus or minus radical 2 because when you take the square root you will always have a positive root and a negative root of any quadratic equation. x= plus and minus sqrt(2).
5. So the answer is that it’s irrational because plus and minus radical 2 is not an integer, and secondly it isn’t a perfect root which means that plus and minus radical 2 is an irrational set roots for this quadratic equation.
Drag the labels into place in the figure for a market leaving, and then returning to, equilibrium as firms exit after a decrease in demand. original short-run supply* final short-run demand* original short-run demand* long-run supply* final short-run supply* Drag each item above to its appropriate location in the image. Note that every item may not have a match, while some items may have more than one match. Price P2 +--- Q3 Q2 Q2 Market quantity (Q)
Answers
The original short-run supply curve shifts left, causing the market price to decrease to P2 and the quantity to decrease to Q2.
As a result, some firms exit the market, causing the short-run supply to shift back to the right and the market to return to equilibrium at a lower quantity, Q3, and the same price, P2.
When demand decreases, the original short-run supply curve shifts leftward as firms reduce production to meet the lower demand. This causes the market price to decrease to P2 and the quantity to decrease to Q2.
At this lower price, some firms may exit the market if they are unable to cover their costs, causing the short-run supply curve to shift back to the right.
As a result, the market quantity decreases further to Q3, and the market returns to equilibrium at the same price, P2. In the long run, the supply curve may shift further to accommodate the lower demand, resulting in a new equilibrium price and quantity.
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Is this a function?
{(2, 9),(5, 8),(19, 9)}
Answers
Answer:
Yes
Step-by-step explanation:
As long as no x values repeat it is considered a function
In the given set no x values repeat therefore it is a function
Answer:
Yes.
Step-by-step explanation:
Each input has exactly one output. Therefore, this is indeed a function.
Let p, q, and r be primes other than 3. Show that 3 divides p2 + q2 + r2.
Answers
Given that p, q, and r are primes other than 3, we can show that 3 divides \(p^2 + q^2 + r^2\).
To prove that 3 divides \(p^2 + q^2 + r^2\), we need to consider the possible remainders of primes when divided by 3. Since p, q, and r are primes other than 3, they can only leave remainders of 1 or 2 when divided by 3.
Case 1: If any of p, q, or r leaves a remainder of 1 when divided by 3, then its square, denoted as \(x^2\), will also leave a remainder of 1 when divided by 3 (since \((1^2) % 3 = 1)\)% 3 = 1). In this case, \(p^2 + q^2 + r^2\) will be a sum of three numbers that each leave a remainder of 1 when divided by 3. Hence, \(p^2 + q^2 + r^2\) will leave a remainder of 3 when divided by 3, and thus, it is divisible by 3.
Case 2: If p, q, and r each leave a remainder of 2 when divided by 3, then their squares, denoted as \(x^2\), will also leave a remainder of 1 when divided by 3 (since (\(2^2\)) % 3 = 1). Similar to Case 1, \(p^2 + q^2 + r^2\) will be a sum of three numbers that each leave a remainder of 1 when divided by 3. Hence, \(p^2 + q^2 + r^2\) will leave a remainder of 3 when divided by 3, and it is divisible by 3.
In both cases, we see that \(p^2 + q^2 + r^2\) is divisible by 3. Therefore, we have shown that if p, q, and r are primes other than 3, then 3 divides \(p^2 + q^2 + r^2\).
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The starting numbers for the patterns for x and y are shown in the table below.
The blanks in the table represent the next four terms for each of the patterns.
• The rule for the x-values is add 3.
•The rule for the y-values is add 6.
X
y
0
0
Which graph represents the ordered pairs of the first five terms of the patterns
from the table?
Answers
The graph that represents the ordered pairs of the first five terms of the patterns from the table is the line graph.
The graph that represents the ordered pairs of the first five terms of the patterns from the table is the **line graph**.
The x-values in the table are increasing by 3 each time, while the y-values are increasing by 6 each time. This means that the ordered pairs are forming a straight line. The line graph is the only graph that shows a straight line.
The other graphs are either curves or not straight lines. The **scatter plot** shows a cloud of points that are not evenly distributed. The **bar graph** shows a series of vertical bars that are not evenly spaced. The **histogram** shows a series of horizontal bars that are not evenly spaced.
Here is a table of the first five terms of the patterns from the table, along with the corresponding ordered pairs:
X | Y | Ordered Pair
-- | -- | --
0 | 0 | (0, 0)
3 | 6 | (3, 6)
6 | 12 | (6, 12)
9 | 18 | (9, 18)
12 | 24 | (12, 24)
As you can see, the ordered pairs form a straight line.
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Each ordered pair is from an inverse variation. Find the constant of variation. (0.9,4)
Answers
The constant of variation is 3.6
What is Inverse variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means, we can say that if one values will increase then other will automatically decrease and vice versa.
Let say if x and y are two values and k is a constant value, then
According to inverse variation
k = xy or y = k/x
In the given question,
Take the order pair (0.9,4)
As it is an inverse variation, we can substitute it
y=k/x
Now find the constant of variation
4=k/0.9
K=3.6
Therefore, constant of variation is 3.6
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Draw a 30-60-90 triangle of any size. Using the ratios that you know, write expressions for sin(30) and
cos (60) . What do you notice? Write a sentence or two justifying what you notice.
Answers
Answer:
sin(30)=cos(60)
Step-by-step explanation:
sapling a quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. of the bags inspected, 3 had too much salt. which of the conditions for calculating a confidence interval for the population proportion
Answers
The condition that is not met is that the sample size must be large enough to assume that the sample proportions are normally distributed.
What is number?Number is a mathematical object used to count, measure, and label. It is one of the fundamental building blocks of mathematics and is essential for any kind of calculation or measurement. Number is an abstract concept that is used in many different ways, from counting objects to expressing complex mathematical systems. Numbers can be used to represent anything from a single item to the entire universe. Numbers are also used to represent abstract ideas such as time, money, and probability.
With a sample size of only 25, it is not possible to assume that the sample proportions follow a normal distribution. As such, calculating a confidence interval for the population proportion of bags with too much salt is not possible.
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Complete questions as follows-
sapling a quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. of the bags inspected, 3 had too much salt. which of the conditions for calculating a confidence interval for the population proportion of bags with too much salt is not met?
on a circle of radius 4 and center (0, 0), find the x and y coordinates at angle 180 degrees (or π in radian measure).
Answers
On a circle with a radius of 4 and center at (0, 0), to find the x and y coordinates at an angle of 180 degrees (or π in radian measure), we can use the trigonometric functions.
At 180 degrees, the x-coordinate will be 0, as it lies on the y-axis. The y-coordinate can be found by using the sine function. Using the equation y = r * sin(θ), where r is the radius and θ is the angle in radians, we can substitute the values. In this case, r is 4 and θ is π (since 180 degrees equals π radians).
Therefore, the x-coordinate is 0 and the y-coordinate is 4 * sin(π) = 0. So, the x-coordinate is 0 and the y-coordinate is also 0.
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PLEASE HELP
7x-3= -24 what is x and how do you find it?
Answers
Answer:
x = -3
Step-by-step explanation:
7x - 3 = -24 (Given)
7x - 3 + 3 = -24 + 3 (Added 3 on both sides by using the addition property of equality)
7x = -21 (Simplified)
7x/7 = -21/7 (Divided 7 on both sides by using the division property of equality)
x = -3 (Simplified)
Therefore, x = -3.
Answer:
x= -3
Step-by-step explanation:
You do the opposite.
So,
-24 +3
= -21
-21/ 7
= -3
Therefore, the answer is -3
If six coins are flipped, what is the probability of obtaining at least one tail?
P(obtaining at least one tail) = (Type an integer or a simplified fraction.)
Answers
Answer:
Step-by-step explanation:
Probability of occurring at least one tail=1−641=6463
Study the patterns in the equations. Use your observations to solve the equation for a. Express your answer in terms of x. I've included the equations in the photo. Thank you!
Answers
Observing the given pattern in the equations :Equation 1: `a + x = 6`Equation 2: `2a + x = 8`Equation 3: `3a + x = 10`We notice that the constant term is incremented by 2 as we move from equation 1 to equation 2 and from equation 2 to equation .
Since the coefficient of `x` is constant in all equations, this implies that the value of `a` increases by `1` from equation 1 to equation 2 and increases by another `1` from equation 2 to equation 3.Hence, we can conclude that `a` increases by `1` for every increment of `2` in the constant term .Using this pattern, we can solve the equation for `a` as follows:To get from Equation 1 to Equation 2, the constant term increases by 2, and a increases by 1.So, we can express equation 2 in terms of equation 1 as follows :Equation 2 - Equation 1: `(2a + x) - (a + x) = 8 - 6`Simplifying the left-hand side of the equation: `2a - a + x - x = 2`Simplifying the equation further.
`a = 2`To get from Equation 2 to Equation 3, the constant term increases by 2, and a increases by 1.So, we can express equation 3 in terms of equation 2 as follows :Equation 3 - Equation 2: `(3a + x) - (2a + x) = 10 - 8`Simplifying the left-hand side of the equation: `3a - 2a + x - x = 2`Simplifying the equation further: `a = 2`Therefore, the solution of the equation for `a` is `a = 2`.
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there are two glass 1 of them with salt solution and one with sugar solution
NOW, if I took 1 spoon of salt solution and put it into the second one and stir it well
what would the ratio of sugar solution and salt solution ?
please help me
Answers
Answer:
how long question i did not found any answer
Gio sells gelato and collected sales data for the past few days. gio wants to use the naive method to forecast. calculate the naive forecast for day 6. day 1 2 3 4 5 sales 90 97 92 95 93
Answers
The naive forecast for day 6 is 94.
What is a naive forecast?A method of estimation that uses the last period's actuals as the forecast for a current period without making any adjustments or attempting to identify the causes. It is solely used to compare forecasts using more advanced (better) approaches.The calculation of an angle histogram using the naive assumption that the accumulation of points corresponding to the directions of interest will produce peaks that may be seen.There are three fundamental categories: causal models, time series analysis and projection, and qualitative approaches.The main four quantitative budget forecasting techniques—straight line, moving average, simple linear regression, and multiple linear regression—are covered in this article despite the fact that there are many other regularly used quantitative budget forecasting tools.
The naive forecast for the nth period is calculated as follows.
Forecast period Yn=Yn−1
Period Sales Naive Forecasts
1 90 -
2 97 90
3 92 97
4 90 92
5 94 90
6 94
Hence, the naive forecast for day 6 is 94.
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One week, Connor earned $322.00 at his job when he worked for 20 hours. If he is paid the same hourly wage, how much would he make the next week if he worked 18 hours?
Answers
Answer:
$289.8 in 18 hours hourly wage for him is $16.1
Step-by-step explanation:
322/20=16.1- $16.1
16.1x18=$289.8