Answer:
area: 144.5 cm^2
Step-by-step explanation:
Maybe you want the area of this figure.
The area of a trapezoid is given by the formula ...
A = (1/2)(b1 +b2)h
Using the given dimensions, the area is ...
A = (1/2)(9.7 cm +24.3 cm)(8.5 cm)
A = (1/2)(34 cm)(8.5 cm) = 144.5 cm^2
Work out the perimeter of a quarter- circle with radius 7cm.
Perimeter = radius + radius + 1/4 circumference
= 7 + 7 + (2 x 22/7 x 7)/4
= 7 + 7 + 44/4
= 7 + 7 + 11
= 25 cm
Answer: 5.5 cm
Step-by-step explanation:
The perimeter of a circle is referred to as the circumference
Circumference of a FULL circle = π·r
\(\text{Circumference of a quarter of a circle}= \dfrac{1}{4}\pi \cdot r\)
\(C=\dfrac{1}{4}\pi \cdot 7\\\\\\.\quad =\dfrac{7}{4}\pi\\\)
\(\text{Remember that}\ \pi=\dfrac{22}{7}\\\\\dfrac{7}{4}\times \dfrac{22}{7}\quad =\dfrac{22}{4}\quad \rightarrow \quad \dfrac{11}{2}\quad = \quad \large\boxed{5.5}\)
An environment engineer measures the amount ( by weight) of particulate pollution in air samples ( of a certain volume ) collected over the smokestack of a coal-operated power plant. Let X1 denote the amount of pollutant per sample when a certain cleaning device on the stack is not operating, and let X2 denote the amount of pollutant per sample when the cleaning device is operating under similar environmental conditions. It is observed that X1 is always greater than 2X2, and the relative frequency behavior of (X1, X2) can be modeled by
f(x,y)= k for 0 <= x <= 2, 0<=y <=1 , 2y<= x and 0 elsewhere
(X and Y are randomly distriibutied over the region inside the tricanle bounded by x=2, y=0 and 2y=x)
a. Find the value of k that makes this a probability desnsity function.
b. Find P >= 3y
Answer:
\(k = 1\)
\(P(x > 3y) = \frac{2}{3}\)
Step-by-step explanation:
Given
\(f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.\)
Solving (a):
Find k
To solve for k, we use the definition of joint probability function:
\(\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1\)
Where
\({ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }\)
Substitute values for the interval of x and y respectively
So, we have:
\(\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1\)
Isolate k
\(k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1\)
Integrate y, leave x:
\(k \int\limits^2_{0} y {dx} \, [0,x/2]= 1\)
Substitute 0 and x/2 for y
\(k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1\)
\(k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1\)
Integrate x
\(k * \frac{x^2}{2*2} [0,2]= 1\)
\(k * \frac{x^2}{4} [0,2]= 1\)
Substitute 0 and 2 for x
\(k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1\)
\(k *[ \frac{4}{4} - \frac{0}{4} ]= 1\)
\(k *[ 1-0 ]= 1\)
\(k *[ 1]= 1\)
\(k = 1\)
Solving (b): \(P(x > 3y)\)
We have:
\(f(x,y) = k\)
Where \(k = 1\)
\(f(x,y) = 1\)
To find \(P(x > 3y)\), we use:
\(\int\limits^a_b \int\limits^a_b {f(x,y)}\)
So, we have:
\(P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy\)
\(P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy\)
\(P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy\)
Integrate x leave y
\(P(x > 3y) = \int\limits^2_0 x [0,y/3]dy\)
Substitute 0 and y/3 for x
\(P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy\)
\(P(x > 3y) = \int\limits^2_0 y/3\ dy\)
Integrate
\(P(x > 3y) = \frac{y^2}{2*3} [0,2]\)
\(P(x > 3y) = \frac{y^2}{6} [0,2]\\\)
Substitute 0 and 2 for y
\(P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}\)
\(P(x > 3y) = \frac{4}{6} -\frac{0}{6}\)
\(P(x > 3y) = \frac{4}{6}\)
\(P(x > 3y) = \frac{2}{3}\)
Please tell me the answer and how to do it.
Answer:
there is no constant rate
Step-by-step explanation:
at first i thought it was 25 cents for each, but once i saw the last 3, it broke the rate.
A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?
31 students
40 students
41 students
66 students
Answer:
40 students
Step-by-step explanation:
I think it is 40 students because 60 + 40= 100 then 100 x 40 = 4,000
then the SCHOOL has to pay a $30 cleaning fee so that will add up to $4,030! I hope this helps everybody!
40 students will be going on the trip
How to calculate the number of students that will be going on the trip ?Each student will pay $60 for food and lodging
Each student will also pay $40 for the bus
Total amount of fee that will be paid by each student is
= 60 +40
= 100
The school will pay $30 cleaning fee for the bus, it's only the school that will be paying this fee, the students are not included. This will will be subtracted from the total cost which is $4,030 leaving us with $4,000
Therefore the number of students going on the trip can be calculated as follows
= 4,000/100
= 40
Hence 40 students will be going on the trip
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What’s the answer by chance
The sales tax rate of the cocktail table is 0.055
What is sales tax ?A sales tax is a consumption tax imposed by the government on the sale of goods and services
The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:
Sales tax = list price * sales tax rate
Therefore,
sale tax rate = sales tax / list price
sales tax = $13.75
list price = $250
sale tax rate = 13.75 / 250
sales tax rate = 0.055
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Find f(-1) given f(x) = –2x^3 + 3x^2 – 22
\(\\ \sf\longmapsto f(-1)\)
\(\\ \sf\longmapsto -2x^3+3x^2-22\)
\(\\ \sf\longmapsto -2(-1)^3+3(-1)^2-22\)
\(\\ \sf\longmapsto -2(-1)+3(1)-22\)
\(\\ \sf\longmapsto 2+3-22\)
\(\\ \sf\longmapsto 5-22\)
\(\\ \sf\longmapsto -17\)
In the group of ordered pairs shown, the x-values are inputs and the y-values are outputs. Which statements are true about the inputs and outputs? Select all that apply. (2, 4), (6, 3), (5, 4), (7, 3), (8, 2)
Answer:
I dont see the statements but this is a parabola. As you can see some of the ys repeat.
Step-by-step explanation:
three tenths of x is 15
Answer:
50
Step-by-step explanation:
3/10 of x is 15, which means that 1/10 of x must be 5 because 15/3 = 5.
Now we can multiply 5 x 10, which is 50, so we know that x is equal to fifty
Answer:
=15
Step-by-step explanation:
Furthermore, you can convert "three" to "3" and "tenths" to "10" and then the equation and answer is:
3/10 x 15 = 4.50
Two trains start from towns 540 mi apart and travel towards each other on parallel track. They pass each other 4.5 hr later. If one train travels 20 mph faster than the other, find the rate of each train
3×10 – 10 5×10 – 8 plsss help me im dying
Answer:
3×10 – 10 = 30 - 10 = 20
5×10 – 8 = 50 - 8 = 42
I need help can you help me please
Answer:
with i cant see the problem so i dont lnow
Question 1 of 10
On a timeline, a milestone 6 years in the future will be to the
of a
milestone 3 years in the future and to the
of a milestone 12 years
in the future.
O A. right; right
O B. left; left
C. right; left
D. left; right
Answer: right, left
Step-by-step explanation:
which expression is a cube root of -2i?
The cube root of -2i,
⇒ ∛2[ cos(π/6) + i sin(π/6) ]
We can represent -2i in polar form as,
r(cosθ + i sinθ)
by computing its magnitude and angle.
The magnitude of -2i is 2
Since the absolute value of any imaginary number is equal to its magnitude.
To find the angle θ,
We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case,
The opposite side is -2 and the adjacent side is 0.
Therefore, we have tanθ = -2/0, which is undefined.
However,
We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.
So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).
Now, we need to find the value of θ/3. Since θ is undefined,
we will represent it as π/2 + 2πn,
where n is any integer.
So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.
Therefore, the cube root of -2i is equal to
⇒ ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]
Now put n = 0
⇒ ∛2[ cos(π/6) + i sin(π/6) ]
This is the final form of the cube root of -2i in the required form.
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What is the value of the function y = 2x - 3 when x = -5?
A.-5
B.-13
C.2
D.3
what is 58.008-9.438
and 7 x 65
Answer:
The first one is 48.57 and the second one is 455
Step-by-step explanation:
Mofor has homework assignments in five subjects. He only has time to do two of
them.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.
If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:
1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.
2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.
3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.
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Use the Pythagorean Theorem to find the
length of the hypotenuse in the triangle shown
below.
52
39
Answer:
\(um \: where \: the \: \\ triangles \: are ???\)
The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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In triangle ABC, AB = 6, BC = 8, and angle ABC = 90 degrees. Find the area of triangle ABC.
Answer:
24
Step-by-step explanation:
The formula for area of any triangle is (length * width) * 1/2. This makes the angle of 90 degrees irrelevant.
6 x 8 = 48
48 / 2 = 24
A woman weighing 130 lbs drinks 2 mixed drinks (2 oz of liquor mixed with soda) with
dinner between 7-8 pm. At 10 pm she had a glass of wine.What was her BAC at 8 pm?
Answer:
Step-by-step explanation:
The BAC (Blood Alcohol Concentration) of a person depends on several factors, such as the amount of alcohol consumed, the time over which the alcohol was consumed, and the weight and gender of the person. For this problem, we will assume that the woman has a normal metabolism and that the alcohol is completely absorbed into her bloodstream.
To calculate the BAC at 8 pm, we need to know the amount of alcohol that the woman consumed and the time over which she consumed it. We are given that she had 2 mixed drinks between 7-8 pm, which contained a total of 2 ounces of liquor. We are also given that she had a glass of wine at 10 pm, but we don't need to consider this for the BAC at 8 pm.
Using the Widmark formula, we can calculate the BAC at 8 pm:
BAC = (Alcohol consumed / (Body weight x r)) - (0.015 x Hours since first drink)
where r is the gender constant (0.55 for females) and 0.015 is the rate at which the liver metabolizes alcohol.
Plugging in the values we know, we get:
BAC = (2 oz / (130 lbs x 0.55)) - (0.015 x 1 hour)
BAC = 0.0208 - 0.015
BAC = 0.0058
Therefore, the woman's BAC at 8 pm was approximately 0.0058, which is below the legal limit for driving in most states in the US.
Which graph was created using a table of values calculated from the equation y=(2/5)^x+1
Usually, an important point to verify the graph is the point:
\((0,f(0))\)It's when the function touches the y-graph, then, let's evaluate the function at x = 0
\(\begin{gathered} y=\left(\frac{2}{5}\right)^{x+1}\text{ , \lparen x =0\rparen} \\ \\ y=\left(\frac{2}{5}\right)^{0+1} \\ \\ y=\left(\frac{2}{5}\right)^1 \\ \\ y=\frac{2}{5}=0.4 \end{gathered}\)Therefore the point should be
\((0,0.4)\)Therefore any graph that does not include that point is not correct!
We can also eliminate all graph that shows a crescent curve, but, in fact, only the point we calculated can eliminate all graphs and gives us the correct answer:
A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°. What is the angle between the ground and steepest slope on the real rollercoaster?
The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.
A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?
To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.
The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.
The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.
That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)
The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.
That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,
the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°
The negative sign indicates that the angle is measured below the horizontal line.
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Let f be a continuous function on the interval [a, b]. Determine if the following statement is true or false. The expression lim f(xi") ax may lead to different limits if we choose the x * to be the left endpoints instead of midpoints. ni=1 Choose the correct answer below. O A. The statement is true. Each sum will be smaller when picking a left endpoint, so the limit will be smaller. OB. The statement is false. Any sample point can be chosen within the interval without affecting the limit. O C. The statement is true. The value of the function at the left endpoint is not the same as the value at the midpoint of the interval D. The statement is false. The value of the function at the left endpoint is the same as the value at the midpoint of the interval. w Click to select your answer
Answer:
The correct answer is B.
Step-by-step explanation:
We have the expression:
\(\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}f(x_i\, ^\star)\Delta x\)
In this case, B is the correct answer.
B states that any sample point can be chosen without affecting the limit.
This is a true statement. Regardless of which point we choose for our sample point, since n approaches infinity, we will have infinite partitions.
Hence, this will not affect the sum of our expression.
A and C are false because we have infinite partitions, so the statements cannot be true. D is not true simply because the left-hand values do not have to be the same as the midpoint-values depending on the behavior of the function for [a, b].
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ACDE=AOPQ?
Check all that apply.
AA
E
A. LL
B. AAS
C. SAS
D. LA
E. HL
F. ASA
Answer is ADEF
Given that, two right tringle = R + ΔHEL , R +ΔPME
Hypotenuse equal , A set of corresponding right angles are equal.{HL};
LL=LE
So ∠E(M tringle HEL)∠LM (M tringle PME)
∠H=∠P 90°
∠L=∠E ⇒AAS
HE PM or LE =EM
∠E = ∠M
EL = ME ⇒ASA
∠L = ∠E
HF = PM
∠E = ∠M ⇒SAS
EL = ME
Hence choose A.D.E.F
{Determination of congruence of right tringle }
explanation of Determination of congruence of right tringle
A plane figure bounded by three finite line segments to form a closed figure is known as a triangle. A right-angled triangle is a special case of the triangle. In a right-angled triangle, one of the interior angles measures 90°. Two right triangles are said to be congruent if they are of the same shape and size. In other words, two right triangles are said to be conger
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What is a8 for the geometric sequence 6,561;−2,187;729;−243;….
Answer:
In geometric sequence you divide the terms. As I will show you the calculations step by step. Hopefully this becomes clear and helpful to you
Step-by-step explanation:
-2187÷6561
= -0.3333...
a8=a1 r^8-1
=(4374)(-0.3)^8-1
=(4374)(-0.3)^7
=(4374)(-4.572473708×10^-4)
=-2
Therefore a8= -2
2x + y = 7
x + y = 1
The solution to the system of equations is x = 6 and y = -5, which is the same as we obtained using the elimination method.
What is the system of equations?A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:
2x + y = 7 ---(1)
x + y = 1 ---(2)
To solve this system, we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.
Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:
-2(x + y) = -2(1) --
Multiplying equation
(2) by -2-2x - 2y = -2
Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:
2x + y = 7(-2x - 2y = -2)0x - y = 5
We now have a new equation in which y is isolated.
To solve for y, we can multiply both sides by -1:
-1(-y) = -1(5)y = -5
Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6
Therefore, the solution to the system of equations is (x,y) = (6,-5).
Method 2: Substitution
In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.
From equation (2), we can solve for y in terms of x:y = 1 - x
We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6
Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5
Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.
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How do you solve for x if x/5 = 7/3
We get that, the value of x is 11.67 when the equation is x / 5 = 7 / 3.
An equation is a combination of two expressions connected by an equal sign.
We are given an equation:
x / 5 = 7 / 3
We need to find the value of x.
Multiply both sides by 5
x / 5 × 5 = 7 / 3 × 5
x = 35 / 3
Now, we will divide 35 by 3 and round off the result to two decimal places:
x = 11.67
Therefore, we get that, the value of x is 11.67 when the equation is x / 5 = 7 / 3.
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The surface area of the United States is 3.797 million square miles. The state of Alaska, our largest state in terms of area, occupies 655,400 square miles. Using ratios, determine what percentage of the surface area of the United States is occupied by Alaska, rounded to the nearest whole number.
Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%
We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%
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Marcos talks to his grandfather in Alabama for about 95 minutes per month. About how long does he talk each day? (Hint: Use 1 month = 30 days).
Answer:
Divide 95 by 30
Step-by-step explanation:
Answer:
0.315
Step-by-step explanation:
divide talking time by number of days in month
a student skipped a step when he tried to convert 1020 seconds into hours and got the following incorrect result
1020seconds (1hours/60mins)=17hours
what conversion ratio did he skip in this multiple-step conversion
Answer:That student has forgot to convert it into minutes and then convert it to hours
Step-by-step explanation:
1020/7=17 minutes and
17/60=0.283hours