Answer: An isosceles trapezoid is a trapezoid with two sides of equal length, and those are called legs.
Using the given information that the shorter base is 21, the longer base is 47 and the legs are 50, we can use the Law of Cosines to find the angle between the legs and the longer base.
The Law of Cosines states that for any triangle with sides of length a, b, and c and the angle opposite side c is denoted as C:
c^2 = a^2 + b^2 - 2ab * cos(C)
We will use the legs (a = b = 50) and the longer base (c = 47) as our sides and call the angle we are looking for angle x:
50^2 = 50^2 + 47^2 - 2(50)(47) * cos(x)
Solving for cos(x) will give us the angle x in terms of a cosine. To get the angle x in degrees, we will use the inverse cosine function, which gives the angle in degrees whose cosine is the input value.
cos(x) = (50^2 + 47^2 - 50^2) / (2(50)(47)) = 47/100
x = acos(47/100)
x = approx 126.6
So, the lower base angle in this isosceles trapezoid is approximately 126.6 degrees.
Step-by-step explanation:
Which function is the inverse of f(x) = 2/3 x³ + 1?
The inverse of f(x) = 2/3 x³ + 1 is f^-1(x) = (3/2)(x-1)^(1/3).
Which function is the inverse of f(x) = 2/3 x³ + 1?The inverse of a function f(x) is a function that reverses the operation of the original function.The inverse of a function f(x) = 2/3 x³ + 1 can be found by switching the x and y values and then solving for x.In other words, we can set y equal to the original equation and solve for x.
Let y = 2/3 x³ + 1
We can then subtract 1 from both sides to get y – 1 = 2/3 x³
We can then divide both sides by 2/3 to get (y – 1) • (3/2) = x³
Finally, we can take the cube root of both sides to get the inverse function:
x = (y – 1)¹/₃ • (3/2)¹/₃
Therefore, the inverse of f(x) = 2/3 x³ + 1 is x = (y – 1)¹/₃ • (3/2)¹/₃.
The inverse of f(x) = 2/3 x³ + 1 is denoted as f^-1(x). To find the inverse, we need to solve for x in terms of y, since the inverse of a function is a reflection of the function across the line y = x. To do this, we need to rearrange the equation, so that x is on the left side of the equation. We can start by subtracting 1 from both sides.This yields 2/3x³ = y - 1. We can then divide both sides by 2/3 to get x³ = (y - 1)/2/3. To solve for x, take the cube root of both sides. This yields x = cube root[(y - 1)/2/3]. Therefore, the inverse of f(x) = 2/3 x³ + 1 is f^-1(x) = cube root[(y - 1)/2/3].To learn more about the inverse of a function refer to:
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As the sample size gets larger; what happens to the size of the correlation that is needed for significance?
It gets smaller
It also gets larger
There no consistent relationship between sample size and the critical value for a significant correlation
It stays constant
The degree of correlation required for significance reduces as the sample size increases. As a result, the correlation size needed to determine significance will be smaller.
The size of our sample and the sample size has an impact on the significance of a sample link. For results to be relevant for high sample sizes, a minimal correlation is required. Fewer correlations and linkages are required for significance as the sample size increases.
Each sampling distribution's variability declines with the sample number and gradually moves toward leptokurtic behavior. The sample distribution's range is smaller than the range of the initial population.
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ou are tasked to perform a linear regression using the least-squares method on the following (x,v) data points: (6,7) (8,9) (13,17) From the list of answers, pick the point that will be part of the regression line Hint: Find the equation of the line (slope, intercept) as you did in the regression assignment: Then for a (X1, Y1) given below; replace the value of X in the equation with the value of X1, and find out if you get the value of Y1. If you do (meaning the equivalence is true), that point is part of the regression line: (0,01) (9.11) (6,7)
(8,9)
The point that will be part of the linear regression line is (6,7).
The least-squares method is used to perform a linear regression on the given data points (6,7), (8,9), and (13,17). This method finds the line of best fit through the set of data points by minimizing the sum of the squares of the differences between the observed values and the predicted values from the line. To check whether a point is part of the regression line or not, we can substitute the x value of the point into the equation of the line and see if it gives the corresponding y value.
In this case, point (6,7) is part of the regression line because it satisfies the equation of the line.
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One cube has edge length 2 cm. A larger cube has edge length 5 cm. What is the ratio of the surface area of the smaller cube to the surface area of the larger cube in simplest form?
i think i onestly i think maybe 7 cm.
A hotel manager is adding a tile border around the rectangular pool. Let represent the width of the pool in feet. The length is
feet more than
times the width, as shown. Write two expressions that represent the perimeter of the pool.
LOADING... Click the icon for a diagram of the pool.
Question content area bottom
Part 1
Which expressions will give the perimeter of the pool? Select all that apply.
Substituting into the formula for the perimeter of a rectangle, the perimeter is [tex]2\left(n+3 \frac{1}{2} n +4 \frac{1}{2} \right)=2n+7n+9=\boxed{9n+9}=\boxed{9(n+1)}[/tex]
Solve for C. Explain your steps for brainliest
Answer:
[tex]\sf \frac{2A-hb}{h}=c[/tex]
Step-by-step explanation:
[tex]\sf A=\frac{1}{2}h(b+c)[/tex]
First, multiply both sides by 2.
[tex]\sf 2A=h(b+c)[/tex]
Solve the brackets.
[tex]\sf 2A=hb+hc[/tex]
Subtract h b from both sides.
[tex]\sf 2A-hb=hc[/tex]
Divide both sides by h.
[tex]\sf \frac{2A-hb}{h}=c[/tex]
Rollins read books create expression
When Rollins read books it is a expression in which the number of books he has completed is, N = P/( a × b )
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
In given problem,
we have to make relationship between number of books he has completed, how many pages he can read per minute and daily how many minutes he reads book.
suppose,
the number of books he has completed = N
pages he can read per minute = a
time spent on reading per day = b
Total page in a book = P
N = P/( a × b )
Hence, The expression is N = P/( a × b )
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Can somebody please tell me how do we solve this? Thank you.
Convert:
63 decimeters 58 millimeters
= millimeters
Please help I don’t understand this
Answer:
6358 mm
Step-by-step explanation: multiply the value of decimeters by 100,
we get 6300 mm and then we add the 58 mm in 6300 mm.
Solve: e^(2x+5) = 4
mc001-1 .j pg
mc001-2 .j pg
mc001-3 .j pg
The Answer Is C, x=((ln4)-5)/(2)
The value of the logarithm equation is given by x = [ ln ( 4 ) - 5 ] / 4
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithm equation be represented as A
Now , the value of A is
e⁽ ²ˣ ⁺ ⁵ ⁾ = 4 be equation (1)
On simplifying the equation , we get
Taking logarithm on both sides of the equation , we get
2x + 5 = ln ( 4 )
On simplifying the equation , we get
ln ( 4 ) = 2x + 5
Subtracting 5 on both sides of the equation , we get
2x = ln ( 4 ) - 5
Divide by 2 on both sides of the equation , we get
x = [ ln ( 4 ) - 5 ] / 4
Hence , the equation is x = [ ln ( 4 ) - 5 ] / 4
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Complete the following statements with the correct words Note: Correct spelling is important. func a. If s(t) is a distance (or height or position) function, then s'(t) would be a velocity b. If c(x) is a cost function, then c'(x) would be called the cost x c. If y(t) is a velocity function, then v'(t) would be a acceleration function
Velocity, marginal cost, and acceleration are derivatives of displacement, cost, and velocity functions.
The velocity of an object or particle describes how far it has moved or displaced over time. If the function s(t) determines the position of an object, then the velocity is its first derivative. And, this is written as s'(t). The initial blank is therefore filled with velocity.
The cost difference between producing one more product or serving one more customer is known as the marginal cost. As a result, it can be calculated by dividing the change in overall costs by the change in energy output. So, the cost function's derivative is the marginal cost. If the cost function is c(x), then its derivative c'(x) is the marginal cost. The second blank is filled with marginal cost.
Acceleration is the time-dependent derivative of velocity. If v(t) is the velocity, then the acceleration is v'(t). The third blank is filled with acceleration.
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Three specimens of Alloys A, B, C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in the alloy A?
Answer:
X=10%
Y=30%
Step-by-step explanation:
The required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Percentage of copper in A = 1/2 [percentage of copper in ingot]
= 1/2 × 20% = 10%
Percentage of zinc in A = 1/3 [percentage of zincin ingot]
= 1/3 × 40% = 13.34%
Thus, the required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.
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The question seems to be incomplete,
Complete question.
Three specimens of Alloys A, B, and C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in alloy A when copper is half of the copper in the ingot and zinc is 1/3 of the zinc in the ingot?
Which of the following choices is equivalent to 2 - x > 5(x - 4)?
A. 2- x > 5x + 20
B. 2- x > 5x - 4
C. 2- x > 5x - 20
D. 2- x > x - 20
Answer:
Step-by-step explanation:43
Answer: C
Because 5(x - 4) is equal to 5 times x and 5 times -4, which is 5x - 20
graph the line with slope 3 passing through the point (-4,-4)
The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the line with slope 3 passing through the point (-4, -4)
The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as follows. We can write -
y = 3x + c
For the point ( -4, -4), we can write -
- 4 = 3 x - 4 + c
c = - 4 + 12
c = 8
Therefore, the equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.
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B) Find the 95% confidence interval for the mean Sales on days that have 12 employees working.
C) Find the 95% prediction interval for Sales on a day with 12 employees working.
To find the 95% confidence interval for the mean Sales on days that have 12 employees working, we would need to know the population standard deviation and the sample size. The formula for a 95% confidence interval for the mean is:
(sample mean) ± (critical value) x (standard deviation / sqrt(sample size))
Without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% confidence interval for the mean Sales on days that have 12 employees working.
Similarly, to find the 95% prediction interval for Sales on a day with 12 employees working, we would need to know the population standard deviation, sample size, and the sample mean. The formula for a 95% prediction interval for a single observation is:
(sample mean) ± (critical value) x (standard deviation of the mean) x sqrt(1 + (1/sample size))
Again, without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% prediction interval for Sales on a day with 12 employees working.
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Please help I’m struggling
Answer: it's C because 4% of 2170 is 86.8 and times 18 years is 1562.4 and 2170 minus 1562.4 equals 607.8. And C is the closest answer to that answer I gave.
Write a sine function that has an amplitude of 2, a midline of 4 and a period of 2/3
A sine function that has an amplitude of 2, a midline of 4 and a period of 2/3 is write as:
y = 2 sin 3πx + 4How to write the sine functionThe sine function is written considering the general formula in the form
sine function, y = A sin wx + b
where
A = amplitude
w = 2π / period
b = midline
In the problem the values available are
A = 2
b = 4
period = 2/3
substituting the known values
sine function, y = A sin wx + b
sine function, y = 2 sin (2π / 2/3) x + 4
sine function, y = 2 sin (3π) x + 4
sine function, y = 2 sin 3πx + 4
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A repair man charges an inspection fee plus $20 dollars per hour. A customer with a coupon for 40% off the inspection fee pays $110 for a 4-hour repair. How many hours are worked when a customer pays $90 without a coupon?
Without a coupon and paying $90 the customer was attended for 2 hours
How to find the number of hours the customer paid forWhen a customer with a coupon for 40% off the inspection fee pays $110 for a 4-hour repair the inspection fee is calculated
customer's pay = (inspection fee * 40% off the inspection fee) + charge per hour * number of hours
40% off means the customer paid 60% of the fees
let the inspection fee be x
110 = (x * 0.60) + 20 * 4
110 = 0.6x + 80
110 - 80 = 4x
0.6x = 30
x = 50
a customer without a coupon
let the number of hours be y
customer's pay = inspection fee + charge per hour * number of hours
90 = 50 + 20 * y
90 = 50 + 20y
20y = 90 - 50
20y = 40
y = 2
the customer spent 2 hours
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Select the correct answer. What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? A. x2 + y2 − 4x + 2y + 1 = 0 B. x2 + y2 + 4x − 2y + 1 = 0 C. x2 + y2 + 4x − 2y + 9 = 0 D. x2 − y2 + 2x + y + 1 = 0
Answer:
I think it's b. when you have a negative and a negative it becomes a positive
100 POINTS ANSWER RIGHT!11
Find the slope of the line.
What is the prime factorization of 24? 2 x 6 3 x 8 22 x 4 23 x 3
Its pair factors are (1, 24), (2, 12), (3, 8), and (4, 6). The prime factorization of 24 gives 2 x 2 x 2 x 3 = 23 x 3, where 2 and 3 are the prime factors of 24. The sum of factors of 24 is 60. The correct answer is 24 = 2³×3
More prime factorization of 24:So, the prime factorization of 24 are 2 × 2 × 2 × 3 or 23 × 3, where 2 and 3 are the prime numbers. Learn more about factors and prime factors here with us in BYJU’S and also download BYJU’S – The Learning App for a better experience. What are the factors of 24? Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
There are many ways to factorization 24 but we have to pick one:
There is a picture of what the solution is to factorization of 24.
Therefore, the correct answer is 24 = 2³×3
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When full, a car's petrol tank holds k litres. After using 15 litres, the remaining petrol is enough for the car to travel 344 km. if a car travels 8km litre find the value of k
Answer:
k = 58
Step-by-step explanation:
k = 15 litres + remaining petrol
Remaining petrol:
The car travels 8 km/litre.
344 km / (8 km/litre) = 43 litre
The car uses 43 litres to travel 344 km.
k = 15 + 43
k = 58
pls help I need to get a good grade
Answer:
3 1/2 cups of oats = 28 grams of fiber
Step-by-step explanation:
1 whole cup equals 8 grams (add halves for this)
8 x 3 = 24
24 + additional 4 from the remaining half makes 28 grams of fiber total.
R varies directly with S and inversely with T. When s=5 and T=100, R=45. find the exact value of R when S= 13 and T=63
The value of R when S = 13 and T = 63 is 4361.5
What is Variation?A variation is a relation between a set of values of one variable and a set of values of other variables.
If R varies directly with S and inversely with T . This statement is represented in the form:
R = KS/T.
K is called proportionality constant
When R = 45 ,S = 13 and T = 100, then K=
K = RT/S
K = 45×100/5
K = 4500/5= 900
When S = 13and T = 63, then
R = KT/S
R = 900× 63/13
R= 56700/13
R = 4361.5
Therefore when S = 13 and T = 63, the value of R is 4361.5
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Graph two lines whose solution is (1, 4) .
The lines y = x + 3 and y = 2 · x + 2 pass through point (1, 4) on Cartesian plane.
How to graph two lines that pass through a given point on Cartesian plane
In this problem we must graph two lines that pass through point (x, y) = (1, 4). Lines can be represented by equations of following form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptWe must choose two slope-intercept combinations to generate two different lines: (x, y) = (1, 4)
Line 1
4 = m · 1 + b
4 = m + b
m = 1
4 = 1 + b
b = 3
y = x + 3
Line 2
4 = m · 1 + b
4 = m + b
m = 2
4 = 2 + b
b = 2
y = 2 · x + 2
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the straight line l has equation x-y =3
the curve c has equation 3x^2 -y^2+xy=9
l and c intersect at the points p and q
find the coordinates of the midpoint of pq
Answer: The Midpoint of P and Q are (-0.5, -3.5)
Step-by-step explanation: To find the coordinates of the intersection points of the line and the curve, we can substitute the equation of the line into the equation of the curve and solve for x and y.
From the equation of the line: x - y = 3, we can see that y = x - 3
Substituting this into the equation of the curve:
3x^2 - (x-3)^2 + x(x-3) = 9
Now we can simplify and group
3x^2 - x^2 + 6x - 9 + x^2 - 3x = 9
3x^2 + 3x - 9 = 9
3x^2 + 3x = 18
3x(x+1) = 18
x(x+1) = 6
We can see that x = 2 and x = -3 are the solutions.
Substituting the x value back into the original equation of the line to find the y coordinate:
x = 2 => y = 2 - 3 => y = -1
x = -3 => y = -3 - 3 => y = -6
So the intersection points are (2,-1) and (-3,-6)
To find the midpoint of these two points, we take the average of their x and y coordinates:
x = (2 + -3) / 2 = -0.5
y = (-1 + -6) / 2 = -3.5
so the midpoint of the two intersection points is (-0.5, -3.5)
Answer:
Point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].
Step-by-step explanation:
Given the equations [tex]x-y=3[/tex] and [tex]3x^{2} -y^{2} +xy=9[/tex] . Find where they intersect and find the midpoint, [tex](p,q)[/tex], of the two intersection points. To find find points of intersection, you can either set up these equations as a system and solve algebraically or you can use a graphing calculator to graph the functions and see where they cross.
I will set up these equations as a system of equations,
[tex]\left \{ {{x-y=3} \atop {3x^{2} -y^{2} +xy=9}} \right.[/tex]
I will solve the top equation for [tex]x[/tex], and substitute it into the bottom.
[tex]x-y=3 = > x=3+y[/tex]
Now substitute [tex]x=3+y[/tex] for x into the bottom equation. Solve for y,
=> [tex]3x^{2} -y^{2} +xy=9[/tex]
=>[tex]3(3+y)^{2} -y^{2} +(3+y)y=9[/tex]
=> [tex]3(y^{2}+6y+9) -y^{2} +y^{2}+3y =9[/tex]
=>[tex]3y^{2}+18y+27 -y^{2} +y^{2}+3y =9[/tex]
=> [tex]3y^{2}+18y+27+3y =9[/tex]
=> [tex]3y^{2}+21y+27 =9[/tex]
=>[tex]\frac{3y^{2}+21y+27 =9}{3}[/tex]
=>[tex]y^{2}+7y+9 =3[/tex]
=>[tex]y^{2}+7y+6 =0[/tex]
=> [tex](y+1)(y+6)=0[/tex]
=>[tex]y=-1[/tex] or [tex]y=-6[/tex]
Now plug these values for [tex]y[/tex] into [tex]x=3+y[/tex].
When y=-1:
[tex]x=3+(-1)[/tex]
=> [tex]x=2[/tex]
When y=-6:
[tex]x=3+(-6)[/tex]
=> [tex]x=-3[/tex]
The solution to the system (points of intersection) is [tex](-3,-6)[/tex] and [tex](2,-1)[/tex]. I also attached a graph of the intersection points.
Now to find the midpoint of the two intersection points, [tex]midpoint=(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]
[tex](x_{1},y_{1}) = > (-3,-6)[/tex]
[tex](x_{2},y_{2}) = > (2,-1)[/tex]
=>[tex]midpoint=(\frac{-3+2}{2} ,\frac{-6+(-1)}{2} )[/tex]
=>[tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex]
Thus, the point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].
12 is added to 25% of a number the result is 30 what is the number
Answer:
72
Step-by-step explanation:
30 minus 12 is 18 and 18 is 25% of 72
when you combine all the baking soda recipes from the recipes that use exactly 1 1/4 teaspoons how much baking soda will you have in all
Answer:
When you combine all the baking soda recipes from the recipes that use exactly 1 1/4 teaspoons, you will have the same amount of baking soda that was used in all the recipes.
Step-by-step explanation:
In other words, if you have X number of recipes that each use 1 1/4 teaspoons of baking soda, you will have X*1.25 teaspoons of baking soda in total.
It is important to notice that the question is asking about the amount of baking soda used in those exact recipes that calls for 1 1/4 teaspoons and not about the total amount of baking soda you would end up with after making all the recipes. Therefore, the total amount of baking soda you would have after making all the recipes would depend on how much was used in each recipe and how many were made .
Write an equation of the line that passes through (2, −4) and (0, −4).
Answer: x⁰⁄₂ + 0 = y or x⁰⁄₂ = y
Step-by-step explanation:
Equation of a line is mx+b=y
m=slope
The slope is ʸ⁄ₓ or in this case ⁰⁄₂
b=where the line cross the y-axis which is 0, when it is 0 there is no use in write +0 after the equation, as there is no difference, but it is your choice
Which two statements comparing stock and bond investments are true?
0 Bonds typically offer higher returns than stocks.
0
Stocks have higher risk than bonds.
0
A bond offers fixed interest income, while a stock may offer dividends to investors.
130
Investors pay a brokerage fee for buying and selling bonds, while they pay an advisory fee for
buying and selling stocks.
Bonds are traded on an equity-based exchange, while stocks are purchased directly from a
corporation.
Correct option is B and C, Stocks have higher risk than bonds. A bond offers fixed interest income, while a stock may offer dividends to investors.
In general, stocks are riskier than bonds simply because they do not provide investors with guaranteed returns, as opposed to bonds, which do so through coupon payments. Bondholders, who are a company's creditors, get priority in being paid back in the case of a business bankruptcy, making stocks intrinsically more volatile than bonds. Owners of common stock, on the other hand, are last in line and risk losing everything if the business fails.
Bonds would be a preferable choice for risk-averse investors who want to safely invest their money and feel secure with more standardized payout schedules.
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