The length of major arc ACB with angle measure of 325° and diameter of 10 feet is (325/36)π
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
angle of arc ACB = 360° - 35° = 325°
The length of major arc ACB = (325/360) * π * 10 = (325/36)π
The length of major arc ACB with angle measure of 325° and diameter of 10 feet is (325/36)π
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What is the Domain and Range of the function f(x)[tex]\sqrt{x-7} +9[/tex]?
For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}
How to get the domain and range?
Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:
x - 7 ≥ 0.
Solving for x we get:
x ≥ 0 + 7
Then the domain is:
x ≥ 7
To get the range, we evaluate in the minimum of the domain:
f(7) = √(7 - 7) + 9 = 9
Then the range is the set of all values larger than 9, because the function is increasing.
So the range is R: y ≥ 9.
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_____ cups rice is equivalent to 1 pound
Answer:
2.5 cups is equal to 1 pound.
Step-by-step explanation:
___2.5__ cups rice is equivalent to 1 pound
Hope This Helped
Answer:
2.5 cups of rice
I hope this helps
Need Help with this..
Answer:
119 4/7
Step-by-step explanation:
Add up all the sides
Hi Student!
Looking at the picture that was provided, we see that the problem statement is asking for us to determine the perimeter of the shape is. Perimeter is the outer layer of the shape which would include the lengths of all the sides that are exposed to the outside.
In this case, we are given 7 different values which represent each of the different sides of the shape which we need to add together to get the perimeter.
Create an expression
[tex]\textsf{Perimeter = side_{1}}[/tex][tex]\textsf{Perimeter = side1 + side2 + side3 + side4 + side5 + side6 + side7}[/tex]Using the expression above, all we need to do is combine all of the values which will give us the outline on our shape. However, since some of the values have different denominators, we will first need to combine the whole numbers and then combine those with a common denominator and finally apply a common denominator to be able to add the rest.
Combine the whole numbers
[tex]\textsf{Perimeter = }35\frac{3}{7} + 10\frac{1}{7} + 10\frac{1}{7} + 12\frac{2}{7} + 12\frac{2}{7} + 15\frac{3}{14} + 24\frac{1}{14}[/tex][tex]\textsf{Perimeter = }(35 + 10 + 10+12+12+15+24)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex]Combine those with a common denominator
[tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7}) + (\frac{3}{14} + \frac{1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{3+1+1+2+2}{7}) + (\frac{3+1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{9}{7}) + (\frac{4}{14})[/tex]Covert to mixed fraction and simplify
[tex]\textsf{Perimeter = }(118)+(1\frac{2}{7}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{2}{7}) + (\frac{4}{14})[/tex]Find common denominator and combine
[tex]\textsf{Perimeter = }(119)+(\frac{2*2}{7*2}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{14}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{14}+\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4+4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{8}{14})[/tex]Simplify the expression
[tex]\textsf{Perimeter = }(119)+(\frac{8/2}{14/2})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{7})[/tex][tex]\textsf{Perimeter = }119\frac{4}{7}[/tex]Therefore, the final answer for the perimeter of the figure that was provided would be [tex]119\frac{4}{7}[/tex] units.
help heelp help help help
Which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)?
x squared over 4 plus y squared over 1 equals 1
x squared over 1 plus y squared over 2 equals 1
x squared over 1 minus y squared over 4 equals 1
x squared over 1 minus y squared over 2 equals 1
The answer will be x squared over 4 plus y squared over 8 equals 1.
What is an ellipse?An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.
The general equation of the ellipse is given as;
(x²/a²) + (y²/b²) = 1
The coordinates of a foci are: (±c, 0) where;
c² = b² - a²
However, we know that equation of directrix is; x = ±a/e
Now, Directrix is given ±4
Thus, a/e = 4
a = 4e
We also know that c = ae from ellipse foci coordinates.
Thus, ae = 2
since ae = 2, then (4e)e = 2
4e² = 2
e² = 2/4
e = 1/2
Thus;
a = 4 × 1/2
a = 2
Since c² = b² - a²;
2² = b² - 2²
4 = b² - 4
b² = 8
From (x²/a²) + (y²/b²) = 1, we can put our values to get;
x²/4 + y²/8 = 1
Hence the answer will be x squared over 4 plus y squared over 8 equals 1.
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What is the probability that the top-three finishers in the contest will all be seniors?
Type in the correct answer in each box. Use numerals instead of words. If necessary, round your answers to the nearest tenth.
There are __ different orders of top-three finishers that include all seniors.
The probability that the top-three finishers will all be seniors is __%.
CONTEXT: Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
Using the combination formula, it is found that:
There are 364 different orders of top-three finishers that include all seniors.
The probability that the top-three finishers will all be seniors is 15.38%.
The order in which the players are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In total, three students are taken from a set of 14, hence:
[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]
Including only seniors, it would be three students from a set of 8, hence:
[tex]C_{8,3} = \frac{8!}{3!5!} = 56[/tex]
Hence the probability is given by:
p = 56/364 = 0.1538 = 15.38%.
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Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 100 points
packs of collectible cards claim that 1 out of 3 packs contains a rare card. margie bought 7 packs and only received a rare card in 1 of the packs.
margie runs a simulation of 100 trials. in the simulation, she used a random number generator to select 7 digits from 1 to 3 with 1 representing a pack with a rare card and 2 and 3 representing a pack without a rare card. the frequency of the number of packs with rare cards in each trial of 7 samples in the simulation is represented by this table.
what is the best conclusion for margie to make based on the data?
the claim that 1 out of 3 packs contains a rare card is plausible because the simulation shows that only 1 pack with a rare card out of 7 is likely.
the claim that 1 out of 3 packs contains a rare card is plausible because the simulation shows that only 1 pack with a rare card out of 7 is unlikely.
the claim that 1 out of 3 packs contains a rare card is not plausible because the simulation shows that only 1 pack with a rare card out of 7 is likely.
the claim that 1 out of 3 packs contains a rare card is not plausible because the simulation shows that only 1 pack with a rare card out of 7 is unlikely.
Answer:
My guess would be b or d
Step-by-step explanation:
Is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
The distribution of the values obtained from a simple random sample of size n from the same population is incorrect.
What is sampling distribution?The sampling distribution of a statistic of size n is the distribution of the values obtained from a simple random sample of size n from the same population.
The sampling distribution is the process of getting a sample through simple random techniques from the sample population.
So, it is incorrect that the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
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Which of these values represents the strongest correlation?
O A -0.8
O B. -0.6
O C. -0.5
O D. -0.7
Answer:
A. -0.8
Step-by-step explanation:
The closer its absolute value to 1, the stronger the relationship is.
A. |-0.8| = 0.8
B. |-0.6| = 0.6
C. |-0.5| = 0.5
D. |-0.7| = 0.7
0.8 is closest to 1, therefore representing the strongest correlation.
Hope this helped :)
Which of the following expressions are equivalent to
4-3
?
4-8
U
ful foo
45
DONE
Answer: The correct answers are the first and the fourth one.
Step-by-step explanation:
Find the first 3 iterates of the function f(x) = 0.80x when x^0= 150
Based on the calculations, the first three (3) iterations of the given function are 120, 96 and 76.8.
How to find the first three iterations?In this exercise, you're required to find the first three (3) iterations of the given function. Thus, we would substitute the value of x₀ into the function and then evaluate as follows:
First iteration:
f(x) = 0.80x
f(x₀) = 0.80x₀
f(150) = 0.80 × 150
f(150) = 120.
Second iteration:
f(x) = 0.80x
f(x₁) = 0.80x₁
f(120) = 0.80 × 120
f(120) = 96.
Third iteration:
f(x) = 0.80x
f(x₂) = 0.80x₂
f(96) = 0.80 × 96
f(120) = 76.8.
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Work out the perimeter of the shaded shape.
4m
19m
14m
8m
The diagram is not drawn to scale.
Answer:
45m
Step-by-step explanation:
4m+19m+14m+8m=45m
I don't under stand what is wrong.
Answer:
In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.
The full correct process is:
(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15
= 4m - 6m + 9 + 15
= -2m + 24
Solve for x:
2x² - 2x+5=0
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
How to solve a quadratic function by the quadratic formula
Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] (1)
Where a, b, c are the coefficients of the quadratic function.
In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:
[tex]x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{1} = \frac{2 + \sqrt{4-40}}{4}[/tex]
x₁ = 0.5 + i 1.5
[tex]x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{2} = \frac{2 - \sqrt{4-40}}{4}[/tex]
x₂ = 0.5 - i 1.5
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
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Given lines l, m,n are parallel and cut by two transversal lines, find the value of x. Round your answer to the nearest tenth if necessary.
Answer: 50.5
Step-by-step explanation:
[tex]\frac{30}{22}=\frac{x}{37}\\x=(30/22)(37) \approx \boxed{50.5}[/tex]
How many modes does the following data set have?
2, 2, 3, 3, 3, 4, 4, 4, 4, 11, 11, 11, 25, 25, 25, 25, 26, 26, 26
A. 2
B. 6
C. 4
D. 1
SUBT
Write the slope-intercept form of the equation of the line through the given points.
through: (0, 2) and (-1,-5)
Answer:
y = 7x +2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 1, - 5 )
m = [tex]\frac{-5-2}{-1-0}[/tex] = [tex]\frac{-7}{-1}[/tex] = 7
the line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = 7x + 2 ← equation of line
Simplify the following expressions
2x-2y+5z-2x-y+3z
Answer:
-3y+8z
Step-by-step explanation:
2x-2y+5z-2x-y+3z
you don't need to change their signs just place them accordingly
2x-2x-2y-y+5z+3z
-3y+8z
According to the Centers for Disease Control and Prevention (CDC) , 47% of adults in the United States have hypertension. In a random sample of 500 U.S adults, find the probability that sample the proportion of adults with hypertension is greater than 0.5.
The probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090
How to determine the probability?The given parameters are:
p = 47%
Sample size, n =500
The standard deviation is calculated as:
[tex]\sigma = \sqrt{np(1 - p)[/tex]
So, we have:
[tex]\sigma = \sqrt{500 * 47\%(1 - 47\%)[/tex]
Evaluate
σ = 11.16
The number of adults with hypertension is calculated as:
x = 500 * 0.5 = 250
And the mean is:
μ = 500 * 0.47 = 235
Start by calculating the z-score
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{250 - 235}{11.16}[/tex]
Evaluate
z = 1.34
The probability is then calculated as:
P(z >1.34) = ??
From z table of probabilities, we have:
P(z >1.34) = 0.090
Hence, the probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090
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-2h - 8 = 4h - 3(2h + 12)
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
(32)4
3-3
3243 2-1
(34)²
3-3 2-3 63 24 35
(40)2
(23)
1
112122
2
23.3
The simplified value is shown below:
What is exponents and powers?Exponent refers to the number of times a number is used in a multiplication. Power can be defined as a number being multiplied by itself a specific number of times.
First,
3²*4³*[tex]2^{-1}[/tex]/(3*4)²
=9*64/144*2
= 576/288
=2
Second,
(3*2)^4 *[tex]3^{-3}[/tex]/2³*3
=1296/8*81
=1296/648
=2
Third,
[tex]3^{-3} *2^{-3} *6^{3} /(4^{0} )^{2}[/tex]
= [tex]6^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]
= [tex]2^{3}* 3^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]
=1
Fourth,
[tex]2^{4}* 3^{5} /(2*3)^{5}\\=2^{4}* 3^{5} /2^{5}*3^{5}[/tex]
= 1/2
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Rotate the triangle 180° about the cross.
A triangle is a three-edged polygon with three vertices. If the triangle is rotated 180° about the cross then it will be done as shown below.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to b
If the triangle is rotated 180° about the cross then it will be done as shown below. This is because the triangle is 2 units away from the cross(dot) therefore, after rotation it will be at the same distance from the point.
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In order to meet ada requirements, a wheelchair ramp must have an angle of elevation of no more than $4.8\degree$. a builder needs to install a ramp to reach a door that is 1.5 feet off the ground. what angle of elevation will this ramp have ?
"In order to meet ADA requirements, a wheelchair ramp must have an angle of elevation of no more than" the angle of elevation is mathematically given as
∅=3.434
What angle of elevation will this ramp have?Generally, the equation for the angle is mathematically given as
[tex]\theta=\frac{opp}{adj}\\\\Therefore\\\\tan\theta=\frac{1.5}{25}\\\\tan\theta=\frac{1.5}{25}\\\\\theta=tan^{-1}\frac{1.5}{25}\\\\[/tex]
∅=3.434
In conclusion, the angle of elevation
∅=3.434
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This table shows some values of an exponential function.
What is the function?
The exponential function of the table is y = 0.75(2)^x
How to determine the exponential function?From the table, we have the following points
(x,y) = (0,0.75) and (1,1.5)
An exponential function is represented as:
y = ab^x
At (0,0.75), we have:
0.75 = ab^0
a = 0.75
Substitute a = 0.75 in y = ab^x
y = 0.75b^x
At (1,1.5), we have:
1.5 = 0.75b^1
Evaluate
1.5 = 0.75b
Divide both sides by 0.75
b =2
Substitute b =2 in y = 0.75b^x
y = 0.75(2)^x
Hence, the exponential function is y = 0.75(2)^x
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Molly's jump rope is 6 1/3 feet long. Gail's jump rope is 4 2/3 feet long. How much longer is Molly's jump rope? NOT MUTLIPLE CHOICE IM SO SORRY PLS FORGIVE ME
Answer:
Molly's jump rope is 1 2/3 feet longer than Gail's jump rope.
Step-by-step explanation:
To get this answer, you would have to subtract 6 1/3 - 4 2/3 to find the difference between the two lengths.
To solve this subtraction problem: Start by doing 6 - 4 to get 2, because when the fraction parts are like that, start with whole numbers. Then, solve the fraction parts. 1/3 - 2/3 is -1/3 (you can go to negatives)! Lastly, combine the whole number and fraction parts. 2 - 1/3, because the negative symbol changes to a minus symbol, which will get you 1 2/3.
Hope this helped!
A rocket is launched from a height of 3m with an initial velocity of 15 m/s at what time will the rocket be 13m from the ground? first person to answer gets brainliest
Victoria is putting down fertilizer in her garden. For every 25 square feet of garden, she needs one pound of fertilizer.
Let p represent the number of pounds of fertilizer.
Let g represent the area, in square feet, of garden she covers.
Which correctly names the independent and dependent variables?
independent variable: number of pounds of fertilizer; dependent variable: number of square feet of garden covered
independent variable: brand of fertilizer; dependent variable: number of pounds of fertilizer
independent variable: number of square feet of garden; dependent variable: number of pounds of fertilizer
independent variable: number of square feet of garden; dependent variable: number of people it takes to fertilize the garden
The independent variable: number of pounds of fertilizer; and dependent variable: number of square feet of garden covered.
Let
p = number of pounds of fertilizer.g = area, in square feet, of garden she coversWhat is dependent and independent variable?Dependent variable are variables which takes its value based on other values in an equation.
Independent variable are variables which takes its value outside an equation.
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[100 POINTS] What is the measure of the arc from A to B that does not pass through C?
(Fill in the blanks)
Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.
What is the Inscribed Angle Theorem?Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).
m∠BAC = 40 degrees.
Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]
Corresponding arc BC = 80 degrees.
Arc AC through point B = 180 degrees [half circle]
Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.
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In the triangle below, which of the following best describes AD?
B
D
O A. Median
OB. Altitude
OC. Perpendicular bisector
A
38
38
Answer:
A. median
explain i just aced the test rn
Answer:
Angle bisector
Step-by-step explanation:
The line AD bisects both sides of the triangle. Both angles are congruent to each other since both sides are congruent to each other.
5^(9x)=25^(4x+2) SHOW STEPSSSS
Answer:
x = 4
Step-by-step explanation:
[tex]5^{9x} =25^{4x+2}[/tex]
First you need to get a common base as your number.
[tex]5^{9x} =5^{2(4x+2)}[/tex]
The second number changed because 5 squared is 25. Changing it to this form gives us the same base number of 5. Now we use the distributive property in the exponent.
[tex]5^{9x} =5^{8x+4}[/tex]
Now we can use this statement:
[tex]A^{m} =A^{n}[/tex] if [tex]m=n[/tex]
Using this we solve:
9x = 8x+4
-8x -8x
x = 4
Hope it helps!