The values of the variables are:
1.
a = 14.69
b = 20.22
2.
p = 11.28
q = 4.08
3.
x = 18.25
y = 17
4.
a = 9
b = 16.67
We have,
1.
Sin 36 = a / 25
0.59 = a/25
a = 0.59 x 25
a = 14.69
Cos 36 = b / 25
0.81 = b / 25
b = 0.81 x 25
b = 20.22
2.
Sin 20 = q / 12
0.34 = q / 12
q = 0.34 x 12
q = 4.08
Cos 20 = p / 12
0.94 = p / 12
p = 0.94 x 12
p = 11.28
3.
Sin 43 = y/25
0.68 = y / 25
y = 0.68 x 25
y = 17
Cos 43 = x/25
0.73 = x / 25
x = 0.73 x 25
x = 18.25
4.
Sin 57 = 14 / b
0.84 = 14 / b
b = 14 / 0.84
b = 16.67
Cos 57 = a / b
0.54 = a / 16.67
a = 0.54 x 16.67
a = 9
Thus,
The values of the variables are:
1.
a = 14.69
b = 20.22
2.
p = 11.28
q = 4.08
3.
x = 18.25
y = 17
4.
a = 9
b = 16.67
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Use the similar triangles to find the slope on the lines??? Hello plzzz
Answer:
the slope is 1/4 my friend
Answer:
We can use line segments QR and the points on it to find the slope.
The equation for slope is y2 - y1 / x2 - x1 where x1 is the x value of the first point you chose, y2 is the y value of the second point you chose and so on.
By using this eqution we can pick any 2 points on the line. I will pick q which is (1, 3) and R which is (5, 4)
y2 - y1 / x2 - x1
4 - 3 / 5 - 1
1/4 is the slope
Step-by-step explanation:
Given the equation startfraction 2 x 2 over y endfraction = 4 w 2 what is the value of x? x = y w y minus 1 x = 2 y w y minus 1 x = 2 y w y minus 2 x = 4 y w 2 y minus 2
The value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.
According to the given question.
We have an equation
2x + 2/y = 4w + 2
Since, we have to find the value of x for the given equation
2x + 2/y = 4w + 2
Thereofore,
2x + 2/y = 4w + 2
⇒ 2(x + 1)/y = 2(2w + 1) (taking 2 common from both the sides)
⇒ (x + 1)/y = 2w + 1
⇒ (x + 1) = y(2w + 1) (multiplying both the sides by y)
⇒ x + 1 = 2yw + y
⇒ x = 2yw + y - 1 ( subtracting 1 both the sides)
Hence, the value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.
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Try 1: (3 pts) Find the antiderivative ∫(12x 3
+2 x
+ x
3
+4e −0.5x
− x 3
4
)dx Try 2: (2 pts) The slope f ′
(x) at each point (x,y) on a curve y=f(x) is given along with a particular point (a,b) on the curve. Use this information to find f(x). f ′
(x)=3x 2
+6x−2;f(2)=6
Answer:
when X =2/3
Step-by-step explanation
y=2-9*2/3
2-6
-4
A quadratic function that is shifted 7 units up and 5 units to the right ( please explain the answer , how to answer it and how you got the answer )
f(x) = (x - 5)² + 7
Translations are transformations that change the position of the graph of a function. The general shape of the graph of a function translates up, down, to the right, or to the left.
Vertical translations:
Let k > 0:
To graph y = f (x) + k, shift the graph up k units.
To graph y = f (x) -k, shift the graph of k units down.
Horizontal translations:
Let w>0
To graph y = f (x-w), shift the graph w units to the right.
To graph y = f (x + w), shift the graph w units to the left.
Let:
f(x) = x²
Shift f(x) 7 units up:
f(x) = x² + 7
And shift f(x) 5 units to the right:
f(x) = (x - 5)² + 7
on a piece of paper graph y=-2x-3. then determine which answer matches the graph you drew
The line will cut the y-axis at y = -3
Equation of a lineThe standard equation of a line is expressed as y = mx + b
where:
m is the slopeb is the y-interceptGiven the equation y = -2x - 3, you can see that the slope is -2 and the y-intercept is -3.
This shows that the line will cut the y-axis at y = -3
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3. . 4. The mileage of returned leased vehicles at a local dealership is normally distributed with a mean of 36,400 and a standard deviation of 3200. What percent of the vehicles are returned with fewer than 30,000 miles? (A) 5% (C) 84.9% (B) 2.5% (D) 92.5% A survey is conducted to determine how students will vote for the student council candidacy. The result of the 220 students surveyed showed that 38% will vote for Candidate B. Find the margin of error. (A) +0.5% (B) +2.6% (C) 23.8% (D) 26.7%
The first question asks for the percentage of vehicles returned with fewer than 30,000 miles. The second question asks for the margin of error represents the maximum amount by which the survey estimate may differ from the true population proportion.
Explanation: For the first question, we can calculate the z-score as follows:
z = (30,000 - 36,400) / 3200
z = -2.00
Looking up the area to the left of z = -2.00 in the standard normal distribution table, we find that the area is approximately 0.0228 or 2.28%. Therefore, the percentage of vehicles returned with fewer than 30,000 miles is approximately 2.28%. The correct answer is (B) 2.5%.
For the second question, the margin of error can be calculated using the formula:
Margin of Error = Critical Value * Standard Error
Since the sample proportion is 38% or 0.38, and the survey is based on 220 students, the standard error can be calculated as:
Standard Error = sqrt((0.38 * (1 - 0.38)) / 220)
Using a confidence level of 95%, the critical value corresponds to approximately 1.96. Multiplying the critical value by the standard error, we can find the margin of error. Without specific calculations, we cannot determine the exact margin of error from the given options. However, based on the options provided, the closest answer is (D) 26.7%.
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the diagram shows a triangle. work out the area of the triangle.
Answer:
30cm^2
Step-by-step explanation:
area of triangle = bxh/2
12x5=60/2=30cm^2
Answer:
My answer is 30.
Step-by-step explanation:
Area of a triangle is 1/2×b×h or b×h/2.
The base in the diagram is 12 and the height is 5. then 12×5=60 then 60÷2=30....Thank you for the question....
Determine the amplitude of the function y = negative one-half cosine x. On a coordinate plane, a function curves up from (0, negative 0.5) through (1.5, 0) to (3, 0.5). a. -1 c. One-half b. -Negative one-half d. 2
Step-by-step explanation:
The amplitude is the value that the cosine is being multiplied by.
The general equation of a sinusoid is
\( a \cos(b(x + c) ) + d\)
where a is the amplitude
\( \frac{2\pi}{ |b| } \)
is the period
-c is the phase shift
d is the midline(vertical shift)
Here the amplitude is -1/2 so b is the correct answer.
Answer:
the amplitude of the function that is y= -1/2 cos x, is 1/2.
Step-by-step explanation:
Which expressions are solutions to the equation 3/4x=15? Select all that apply.
a. 15/3
b. 15/4
c. 4/3 x 15
d. 3/4 x 15
e. 15 ÷ 3/4
Answer:
c and e
x=20
Step-by-step explanation:
a=5
b= 3 \(\frac{3}{4}\)(or) 3.75
c=20
d= \(\frac{45}{4}\)(or) 11 \(\frac{1}{4}\)(or) 11.25
e=20
Julio is doing an experiment in science class where he tests how high a ball bounces when it is dropped from 1 meter.
He tests several balls made of different materials and records the results. The results are shown below.
85 cm, 83 cm, 57 cm, 89 cm, 62 cm, 68 cm, 91 cm, 22 cm, 28 cm, 58 cm, 37 cm, 41 cm, 36 cm, 59 cm, 88 cm, 54 cm, 76 cm, 90 cm
Use the drop-down menus to explain how to choose the intervals for a frequency table to represent the data.
The data values have a spread of centimeters. Intervals with a range of centimeters are reasonable.
Gets THE BRANLIeST QUICKLY ANSWER AND I WILL GIVE YOU ALL MY POINTS!!!!!!!!!!!!!!!!ASAP
Answer: The data values have a range of 70 centimeters. Intervals with a range of 10-20 centimeters should be reasonable.
Answer:
it might be
69
10-20
If EF = 4x-15, FG=3x-7, and EG =20, find the value of x, EF and FG. The drawing is not to scale.
Step-by-step explanation:
EF = 4x - 15
FG = 3x - 7
EG = EF + FG = 20
so,
4x - 15 + 3x - 7 = 20
7x - 22 = 20
7x = 42
x = 6
EF = 4×6 - 15 = 9
FG = 3×6 - 7 = 11
Allysa’s new employer offered her health insurance coverage for $96.00/month. She was also offered a "family plan" for herself, husband and young daughter for $250.00/month. How much more a month would she pay if she chose the family plan?
Answer: The difference in cost between Allysa's individual plan and the family plan is:
$250.00/month - $96.00/month = $154.00/month
Therefore, Allysa would pay $154.00 more per month if she chose the family plan.
Solve -2(2x + 5) - 3 = -3(x - 1)
Answer:
x = -16
Step-by-step explanation:
Answer: X = -16
Step-by-step explanation:
1. -2(2x + 5) - 3 = -3(x - 1)
2. -4x-10-3=-3x+3
3. -13=x+3
4. x=-16
check: -2(-16*2+5)-3=-3(-16-1)
51=51
find the distance of the point (2,6,−4)(2,6,−4) from the line r(t)=⟨1 3t,1 4t,3−2t⟩.
The distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector.
To find the distance between the point P(2, 6, -4) and the line defined by the parametric equations r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩, we can use the formula for the distance between a point and a line in three-dimensional space.
The formula for the distance between a point and a line is given by:
d = ||PQ||/||v||
where PQ is the vector connecting the point P to any point Q on the line, v is the direction vector of the line, and || || represents the magnitude of a vector.
Let's first find the direction vector of the line. By examining the parametric equations, we can see that the direction vector of the line is v = ⟨1, 4, -2⟩.
Now, we need to find the vector PQ connecting the point P(2, 6, -4) to any point Q on the line. We can represent PQ as the difference between the coordinates of P and Q:
PQ = ⟨2 - 1, 6 - 3t, -4 - 1, 4t, -4 - 3, -2t⟩ = ⟨1, 6 - 3t, -5, 4t, -7, -2t⟩
Next, we calculate the magnitude of PQ:
||PQ|| = √(1^2 + (6 - 3t)^2 + (-5)^2 + (4t)^2 + (-7)^2 + (-2t)^2)
= √(1 + 36 - 36t + 9t^2 + 25 + 16t^2 + 49 + 4t^2)
= √(29t^2 - 36t + 111)
Finally, we calculate the magnitude of the direction vector v:
||v|| = √(1^2 + 4^2 + (-2)^2) = √(1 + 16 + 4) = √21
Now we can substitute these values into the formula for the distance:
d = ||PQ||/||v|| = (√(29t^2 - 36t + 111))/√21
To find the minimum distance between the point P and the line, we need to minimize the function d with respect to t. We can accomplish this by finding the critical points of the function and determining the value of t that gives the minimum distance.
Taking the derivative of d with respect to t and setting it equal to zero, we have:
d' = (29t - 18)/(√21(√(29t^2 - 36t + 111))) = 0
Solving for t, we get:
29t - 18 = 0
29t = 18
t = 18/29
By substituting this value of t into the formula for d, we can find the minimum distance between the point P and the line.
d = (√(29(18/29)^2 - 36(18/29) + 111))/√21
Simplifying this expression will give us the final value of the distance.
In summary, the distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector
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show that every infinite turing-recognizable language has an infinite decidable subset
The set of all strings accepted by M is an infinite decidable subset of L.
Every infinite Turing-recognizable language has an infinite decidable subset.
Let's prove this theorem.
We must know the properties of the Turing recognizable language before the proof. A language is considered Turing recognizable if a Turing machine M accepts all strings in the language, and either rejects or loops forever on all strings not in the language. We can define that any language is infinite if it contains infinite strings.
Similarly, the set of all strings in the language is infinite if the language is infinite.
Let us suppose that L is an infinite Turing-recognizable language over the alphabet Σ. It implies that there exists a Turing machine M that accepts all the strings in L. We need to consider the following facts to prove that every infinite Turing-recognizable language has an infinite decidable subset:
If a Turing machine accepts an infinite number of strings in a language L, then it accepts at least one infinite subset of the language.
Suppose that a Turing machine accepts a language L, then the set of all strings accepted by the Turing machine is decidable.
Now, let's construct a new Turing machine M′ that works in the following manner:
In the first step, M' simulates M on the input w.
In this step, M' generates the strings of Σ* in some order.
In this step, for each string generated in step 2, M' runs M on that string. If M accepts that string, then M' outputs the string.
Suppose that there are only finite strings of L that are accepted by M. It implies that M has an infinite loop on all other strings not in L.
since M′ generates the strings of Σ* in some order, M′ will eventually simulate M on the string w for which M has an infinite loop.
Therefore, M′ will be in an infinite loop and will never halt.
So, the set of all strings accepted by M is infinite. We can say that the set of all strings accepted by M is an infinite decidable subset of L.
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the national health and nutrition examination survey (nhanes) reported that in a recent year, the mean serum cholesterol level for u.s. adults was 202, with a standard deviation of 41 (the units are milligrams per deciliter). a random sample of 100 adults is chosen. what is the probability that the sample mean cholesterol level is less than 190?
Therefore, the probability that the sample mean cholesterol level is less than 190 is approximately 0.23%.
We can use the central limit theorem to approximate the distribution of the sample mean cholesterol level as normal with a mean of 202 and a standard deviation of 41/sqrt(100) = 4.1.
To find the probability that the sample mean cholesterol level is less than 190, we can standardize the sample mean using the formula:
z = (x - mu) / (sigma / sqrt(n))
where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (190 - 202) / (4.1) = -2.93
Now we can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -2.93. The probability is approximately 0.0023 or 0.23%.
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h(t) = t² − 2; Find h(1)
Answer:
-1
Step-by-step explanation:
1^2-2=1-2=-1
A node or event with duration of 0 days is a(n) ______________.
a. error
b. milestone
c. short term activity (less than 1 day)
d. zero sum game
A node or event with a duration of 0 days is a b. milestone
A milestone refers to an important event in a project that has a duration of zero days. It signifies the completion of a significant phase or task within the project. Milestones are numbers placed on roads, such as roads, railroads, canals, or borders. They can show distances to cities, towns, and other places or regions; or they can set their work on track with respect to a reference point.
They are found on the road, often by the roadside or in a warehouse area. They are also called mile markers (sometimes abbreviated MM), milestones, or mileposts (sometimes abbreviated MP). "mile point" is the term used for the medical field where distance is usually measured in kilometers rather than miles. "Distance marking" is a general term that has nothing to do with units.
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When palpating the abdomen, you should note whether the liver is enlarged in the:a. left lower quadrant.b. midepigastric region.c. periumbilical area.d. right upper quadrant.
When palpating the abdomen, you should note whether the liver is enlarged in the right upper quadrant, option d.
The liver is the largest internal organ located in the upper right portion of the abdomen. When assessing for liver enlargement through palpation, healthcare professionals typically focus on the right upper quadrant of the abdomen.
Anatomical Location: The liver is positioned primarily in the right upper quadrant of the abdomen. It is situated beneath the right rib cage, extending from the midline to the right side of the abdomen. The liver does not extend into the left lower quadrant (a), mid-epigastric region (b), or periumbilical area (c).Liver Enlargement: Palpation is a technique used to assess the size, consistency, and tenderness of organs or structures within the abdomen. When examining for liver enlargement, the right upper quadrant is the most appropriate location to focus on. Enlargement of the liver, known as hepatomegaly, may occur due to various conditions such as liver disease, hepatitis, cirrhosis, or tumors.By concentrating on the right upper quadrant during palpation, healthcare professionals can gather information about the size, tenderness, or abnormalities of the liver. This specific region provides the best access and proximity to assess the liver and detect any potential enlargement or abnormalities.
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Which table shows the correct values of time and earnings for a student earning $6.50 per hour working in a library?
Answer:
A)
Step-by-step explanation:
first one
Answer:
A
Because 2×6.5= 13
And 4×6.5= 26
And 8×6.5=52
please help im taking a test i need helppp please
The linear equation or equation of line will be 3x-4y-13=0 and graph is in image.
What is a linear equation?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Given that line has slope 3/4 and passes through (-1,-4).
As general form of equation of line is y=mx+c where m=slope
then c=-4+3/4=-13/4
Therefore equation of line will be y=3/4x-13/4
or 3x-4y-13=0. and graph is in image.
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find the exact length of the curve. x = et − t, y = 4et/2, 0 ≤ t ≤ 2
Length of the curve is e² - 1 .
What is function?
In arithmetic, a function from a group X to a group Y assigns to every part of X precisely one part of Y. The set X is termed the domain of the function and therefore the set Y is termed the codomain of the function
Main body:
A parametric curve is a function expressed in components form, such that
x=f(t) , y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral :
L = \(\int\limits^a_b {\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt} )^2} } \, dt\)
Let's begin by getting the first derivative of the components of the function with respect to the variable t.
x = e^t - t
dx / dt = e^t−1
y = 4 e^t/2
dy /dt = 2 e^t/2
Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval
[a,b]=[0,2].
L =\(\int\limits^a_b {\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt} )^2} } \, dt\)
L= \(\int\limits^2_0 {\sqrt{(e^{t}-1 )^2 + (2e^{t/2} } )^2} } \, dt\)
L =\(\int\limits^2_0 {e^{t} -1} \, dt\)
Evaluate the solution at the limits of integration to get the length.
L = (e² - 1 )- (e⁰ - 1)
L = e² - 1 - 1 + 1
L= e² - 1
Hence , length of the curve is e² - 1 .
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I'll give brainliest i swear
Answer:
See below for answer.
Step-by-step explanation:
Absolute value represents the number of units that a value is from zero taken in account that there is a negative side and a positive side. Therefore in solving an absolute value equation, we must solve for the positive side and also the negative side.
Step-by-step explanation:
The absolute value is a means of measuring the distance of a number from the origin along the number line. Regardless of the position (positive or negative) of a number on the number line, its distance from the origin will be positive. Thus, the absolute value will always be positive, or 0 if if solving for the absolute value of 0).
Suppose that we're tasked to find the ansolute value of 8. As per the definition of absolute value of numbers, we know that -8 and 8 are both 8 units away from zero on the number line.
These same rules apply when solving absolute value equations, for which we have to set up the equations as positive and negative equations:
If a is positive, and |x| = a, then:
x = a or x = -a
how much would a 10th dog have to weigh for the average weight to be 50 pounds? 7,8,26,28,50,65,65,70,90
^ other dogs weight
Answer:
91
I hope this helped you out!
So how do you do ratios and rates and portions im failing in math and i dont know what to do can you help?
Answer:
The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6." Finally, we could write this ratio using a colon between the two numbers, 3:6. Be sure you understand that these are all ways to write the same number.
A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. The first term of the ratio is measured in cents; the second term in ounces. You can write this rate as 69¢/12 ounces or 69¢:12 ounces.
Can someone plz help me with this one problem plz!!!
Answer:
alam nyo BA ANG sagot dito?
Step-by-step explanation:
haha sino may alam?
Please help im bad at this pls dont just steal my points =(
Answer:
the slope is a positive and the point is (-1,-2) the equation is 3=(×1,2)
Step-by-step explanation:
if im wrong im so sorry
calculate the area of a rectangle in cm2 with a width of 7.6 cm and height of 3.3 cm. be sure to include the proper number of significant figures.
The width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm²
To calculate the area of a rectangle, we need to multiply its width by its height.
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover the surface in a single coat.
Area = width x height
Substituting the given values, we get:
Area = 7.6 cm x 3.3 cm
Area = 25.08 cm²
Since the width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm² (rounded to one decimal place).
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complete this please, i really need your help ")
Answer:
²,2.5,2.5+10,25.0
may it help you
The track team is trying to reduce their time for a relay race. Firstthey reduce their time by 2.1minutes. Then they are able to reduce that time by. If their final time is 3.96 minutes, what was their beginning time?
Answer:
8.16 or 6.06
Step-by-step explanation:
final is 3.96
they reduced their time twice by 2.1min
3.96+2.1+2. 1=8.16