Answer:
d = 2r = 2(5 cm) = 10 cm (Answer D)
Step-by-step explanation:
The arc length formula is s = r·Ф, where r is the circle radius and Ф is the central angle in radians. Here we need to find r, and from r we need to find d.
If s = r·Ф, then s / Ф = r. In this particular case, r = (6 cm) / (1.2 rad) = 5 cm.
If r = 5 cm, then d = 2r = 2(5 cm) = 10 cm (Answer D)
The diameter of the circle is 10 cm
What is a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
Given that, A central angle of a circle measures 1.2 radians, and the length of the related intercepted arc measures 6 cm.
The arc length of a circle is given by = θ/360×2πr
Converting 1.2 rad into degrees
1.2 radians = 68.755°
Therefore, 68.755°/360×2πr = 6
r = 5
diameter = 5x2 = 10
Hence, The diameter of the circle is 10 cm
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A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (–3, 1), (1, 1), and (1, –2). What is the perimeter of the triangle?
Answer:
The perimeter of the triangle is [tex]12\ units[/tex]
Step-by-step explanation:
Let
[tex]A(-3,1),B(1,1),C(1,-2)[/tex]
we know that
The perimeter of triangle is equal to
[tex]P=AB+BC+AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(-3,1),B(1,1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(1-1)^{2}+(1+3)^{2}}[/tex]
[tex]AB=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]AB=4\ units[/tex]
step 2
Find the distance BC
[tex]B(1,1),C(1,-2)[/tex]
substitute in the formula
[tex]BC=\sqrt{(-2-1)^{2}+(1-1)^{2}}[/tex]
[tex]BC=\sqrt{(-3)^{2}+(0)^{2}}[/tex]
[tex]BC=3\ units[/tex]
step 3
Find the distance AC
[tex]A(-3,1),C(1,-2)[/tex]
substitute in the formula
[tex]AC=\sqrt{(-2-1)^{2}+(1+3)^{2}}[/tex]
[tex]AC=\sqrt{(-3)^{2}+(4)^{2}}[/tex]
[tex]AC=5\ units[/tex]
step 4
Find the perimeter
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=4+3+5=12\ units[/tex]
Please help with this !!
Answer:
A
Step-by-step explanation:
The graph of the parabola has no points of intersection with the real x- axis
and therefore has no real solutions
Complex roots occur in conjugate pairs so cannot be C
The solution would be 2 complex roots → A
Answer:
A
Step-by-step explanation:
The graph has no intersection with x-axis therefore has no real roots.
Please help me out please
Answer is A) Acute due to the lengths
Answer:
A
Step-by-step explanation:
The lines shown below are perpendicular. If the green line has a slope of -1/4 what is the slope of the red line
Answer:
4
Step-by-step explanation:
Since perpendicular lines have negative reciprocals, we have to find out the negative reciprocal of -1/4.
To get the negative reciprocal of -1/4, we have to switch the numbers in the numerator and denominator.
That becomes 4/-1, and then we have to remove the negative, which makes the final answer 4/1.
4/1 = 4
Therefore, the negative reciprocal of -1/4 is 4.
Hope this Helps!
The slope of the red perpendicular line is 4.
What is slope of a perpendicular line ?Slope of a straight line is defined as the inclination of the line with respect to the coordinate axis. The slope is also measure of the tangent of angle with which the line is inclined to the axis.
If the slope of a given straight line is m then the slope of its corresponding perpendicular line will be negative reciprocal of the given slope which is -(1/m).
How to find the slope of the given curve ?It is said that the lines shown below are perpendicular. Also it is mentioned that the green line has a slope of -1/4 .
As the red line is perpendicular to the green line, thus its slope is negative reciprocal of the given slope of green line.
Slope = -(-4) = 4 .
Therefore, the slope of the red perpendicular line is 4.
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Which second-degree polynomial function f (x) has a lead coefficient of 4 and roots 5 and 2?
Answer:
The second degree polynomial is f(x) = 4x² - 28x + 40
Step-by-step explanation:
* Lets revise the general form of the second-degree polynomial
- The general form of the second degree polynomial is
f(x) = ax² + bx + c, where a , b , c are constant
- The highest power of the variable that occurs in the polynomial
is called the degree of a polynomial.
- The leading term is the term with the highest power, and its
coefficient is called the leading coefficient.
- The leading coefficient is the coefficient of x²
∴ a = 4
∴ f(x) = 4x² + bx + c
- The roots of a polynomial are also called its zeroes, because
the roots are the x values at which the function equals zero
∴ When f(x) = 0, the values of x are 5 and 2
* To find the value of b and c substitute the values of x in f(x) = 0
- At x = 5
∵ 4(5)² + b(5) + c = 0 ⇒ simplify it
∴ 100 + 5b + c = 0 ⇒ subtract 100 from both sides
∴ 5b + c = -100 ⇒ (1)
- At x = 2
∵ 4(2)² + b(2) + c = 0 ⇒ simplify it
∴ 16 + 2b + c = 0 ⇒ subtract 16 from both sides
∴ 2b + c = -16 ⇒ (2)
- Subtract (2) from (1)
∴ 3b = -84 ⇒ divide both sides by 3
∴ b = -28
- Substitute the value of b in (1) or (2) to find c
∵ 2(-28) + c = -16
∴ -56 + c = -16 ⇒ add 56 to both sides
∴ c = 40
∴ f(x) = 4x² - 28x + 40
* The second degree polynomial is f(x) = 4x² - 28x + 40
Answer:
d
Step-by-step explanation:
Determine whether the situation involves a permutation or a combination, and how many possibilities are there are?
A team of six students is chosen from a class of 36.
Answer:
This situation involves a combination as the team will be the same no matter what order the students are chosen in.
There are 1402410240 possibilities for the six student team
Step-by-step explanation:
Each time a student is chosen, they cannot be chosen again, so the number of available students decreases each time that one is chosen.
[tex]36*35*34*33*32*31=1402410240[/tex]
Look at the two circles below . They share a center point . The larger circle has a radius of 10 inches . The distance between the smaller circle and the larger circle is 2 inches . Which best represents the shaded area between the two circles
Answer:
π(10 in)² - π(8 in)²
Step-by-step explanation:
Area between the two circles=
Area of larger circle less area of smaller circle, or
π(10 in)² - π(8 in)² Since the difference in the radii of the
two circles is 2, that means the smaller
circle has radius 10 - 2, or 8 (inches)
Next time, please share the answer choices. Thank you.
To find the shaded area between the two circles, subtract the area of the smaller circle from the area of the larger circle. The area of a circle is calculated using the formula A = πr^2. By finding the radius of the smaller circle, we can calculate its area and subtract from the larger circle's area to find the shaded area.
Explanation:The shaded area between the two circles can be found by subtracting the area of the smaller circle from the area of the larger circle. The radius of the larger circle is given as 10 inches and the distance between the two circles is given as 2 inches. To find the area of the shaded region, we first need to find the radius of the smaller circle. Since the distance between the two circles is equal to the sum of their radii, the radius of the smaller circle is 10 inches - 2 inches = 8 inches.
The area of the larger circle is calculated using the formula A = πr^2, where r is the radius. Therefore, the area of the larger circle is A = π(10 inches)^2 = 100π square inches.
The area of the smaller circle is calculated in the same way, using the radius of 8 inches. Therefore, the area of the smaller circle is A = π(8 inches)^2 = 64π square inches.
To find the shaded area, we subtract the area of the smaller circle from the area of the larger circle: 100π square inches - 64π square inches = 36π square inches.
On Orca Beach, the high tide is 2 meters and only occurs at 12 a.m. and 12 p.m. The low tide is 0.8 meter and only occurs at 6 a.m. and 6 p.m. Which function models the height of the tide t hours after 12 a.m.?
Choices:
1. h(t)=2cos(πt/3)+0.8
2. h(t)=0.6cos (πt/6) + 1.4
3. 0.6sin(πt/6) + 1.4
4. 1.4sin (πt/3) + 2
Answer:
2. h(t)=0.6cos (πt/6) + 1.4
Step-by-step explanation:
The average water level is (2 +0.8)/2 = 1.4, so this is the offset that is added to the sine or cosine function. That eliminates choices 1 and 4.
The high tide occurs when t=0 (at 12 AM), so eliminating choice 3.
The function that models the height of the tide t hours after 12 AM is ...
h(t)=0.6cos (πt/6) + 1.4
Final answer:
The height of the tide t hours after 12 a.m. at Orca Beach can be modeled by the function h(t)=0.6cos(πt/6)+1.4, which is choice 2 among the given options. This function correctly represents the amplitude and timing of the high and low tides with the period of 12 hours between each high tide.
Explanation:
The question is asking to find a function that models the height of the tide at Orca Beach t hours after 12 a.m. Given that the high tide of 2 meters occurs at 12 a.m. and 12 p.m., and the low tide of 0.8 meter occurs at 6 a.m. and 6 p.m., we're looking for a trigonometric function with a period that corresponds to the tidal cycle of 12 hours. The amplitude of the tide would be half the difference between the high and low tides, and the vertical shift would position the midline of the oscillation at the average of the high and low tides.
First, we calculate the amplitude (A) as half the difference between the high and low tide heights:
A = (2 - 0.8) / 2 = 0.6 meters
Next, we calculate the vertical shift (D) as the average of the high and low tide heights:
D = (2 + 0.8) / 2 = 1.4 meters
Now, knowing that the period (T) of the tide is 12 hours, we can use the cosine function, as it starts at the maximum value at t=0, corresponding to the high tide at 12 a.m. The function representing the tide's height h(t) can be modeled as:
h(t)=Acos(Bt)+D
Where B is the frequency, calculated as B = 2π / T.
Since the tide has a 12-hour period, we plug T = 12 into B:
B = 2π / 12 = π / 6
So the function that models the height of the tide t hours after 12 a.m. with the correct amplitude, frequency, and vertical shift is:
h(t)=0.6cos(πt/6)+1.4
Therefore, the correct choice from the options provided is:
Choice 2: h(t)=0.6cos (πt/6) + 1.4
Please select the best answer from the choices provided
A is the correct answer but I did do it in my head so fair warning
Troy is making a flag shaped like a square. Each side measures 12 inches. He wants to add ribbon along the edges. He has 36 inches of ribbon. Does he have enough ribbon?
Answer:
no he needs 12 more
Step-by-step explanation:
The double number line shows that 444 pounds of almonds cost \$34$34dollar sign, 34. Based on the ratio shown in the double number line, what is the cost for 555 pounds of almonds?
Answer:
$42.5
Step-by-step explanation:
Answer:
42.5
Step-by-step explanation:
Are data at the nominal level of measurement quantitative or qualitative?
a. both qualitative and quantitative
b. qualitative
c. quantitative
d. neither qualitative nor quantitative
Answer:
B. qualitative
Step-by-step explanation:
How do I expand (x-2)^6
The expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
How to expand the algebraic expression
From the question, we have the following parameters that can be used in our computation:
(x - 2)⁶
This is a binomial expression that can be expanded using Pascal triangle
The power of the expression is 6
At n = 6, we have the following coefficients
1 6 16 20 16 6 1
So, we have
(x - 2)⁶ = 1 * x⁶ + 6 * x⁵ * (-2) + 16 * x⁴ * (-2)² + 20 * x³ * (-2)³ + 16 * x² * (-2)⁴ + 6 * x * (-2)⁵ + 1 * (-2)⁶
Expand the exponents
(x - 2)⁶ = x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
Hence, the expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64
Each edge of a wooden cube is 4 centimeters long. The cube has a density of 0.59 g/cm3 . What is the mass of the wooden cube?
Answer:
37.76
Step-by-step explanation:
(What we know)
V = 4*4*4 = 64
Density = 0.59
___________________
Density = Mass/Volume
Mass = (Density)(Volume)
So
Mass = (0.59)(64)
or
Mass = .59 * 64
Mass = 37.76
_____________________________
So the answer would be 37.76
Hope this helps, if you see an error please correct me.
Please help me please !!!!!
Answer:
215.6 m²
Step-by-step explanation:
The area (A) of the polygon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
perimeter = 7 × 7.7 = 53.9 m, so
A = 0.5 × 53.9 × 8 = 215.6
The area of regular polygon with 7 sides is 215.6 m².
What is Polygon?Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
Here, the area (A) of the polygon is
A = 1/2 × perimeter × apothem
perimeter = length X width
= 7 × 7.7
= 53.9 m,
so, A = 0.5 × 53.9 × 8
= 215.6 m²
Thus, the area of regular polygon with 7 sides is 215.6 m².
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Chance has hired a construction crew to renovate his kitchen. They charge $3.92 per square foot for materials and $124.26 per day of labor. Chance spent $3,233.54 on the renovation. If the number of square feet is 269 more than the number of days it took for the renovation, how long did the renovation take?
A. 20 days
B. 17 days
C. 3 days
D. 15 days
Please show your work so I can understand how you got the answer. :)
Answer:
B. 17 days
Step-by-step explanation:
We want to know how many days it took, so it is convenient to define the variable x as the number of days. Then the number of square feet is (x+269) and the total cost is ...
124.26x +3.92(x+269) = 3233.54
128.18x + 1054.48 = 3233.54 . . . . . . . . simplify
128.18x = 2179.06 . . . . . . . . . . . . . . . . . . subtract 1054.48
2179.06/128.18 = x = 17 . . . . . . . . . . . . . divide by the coefficient of x
The renovation took 17 days.
For solving the problem, we first divide the question into two equations, and then substitute and solve the equations. The renovation took around 17 days that is option B)
Explanation:This is a system of equations problems in Mathematics. Let's denote the number of days as 'd' and the square footage as 'f'. According to the problem, we know that:
1. Costs of materials + Costs of labor = Total spent
$3.92f + $124.26d = $3233.542. The square footage is 269 more than the number of days. So:
'f = d + 269'We can replace 'f' from the second equation with the first one: $3.92(d + 269) + $124.26d = $3233.54. Simplifying this, we get $1052.48 + $4.93d = $3233.54, and solving for 'd', we get 'd' approximately equal to 17 days, so the answer is (B).
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Matt paid $55 at a restaurant. That amount included a 10% tip. What was the check amount before the tip? A. $40 B. $43 C. $45 D. $50 E. $52
Answer:
D $50
Step-by-step explanation:
50x.10=5
5+50=55
For this case we propose a rule of three:
$ 50 -------------> 100%
x -----------------> 10%
Where the variable "x" represents the amount of the tip.
[tex]x = \frac {10 * 50} {100}\\x = 5[/tex]
So, the tip was 5 dollars.
If we subtract that amount to what Matt paid at the restaurant we will have the amount of the check before the tip.[tex]55-5 = 50[/tex]
ANswer:
Option D
Please please help me
Answer:
31%
Step-by-step explanation:
Of the 6101 students on financial aid, 1879 are graduates. This fraction is ...
1879/6101 × 100% ≈ 30.798% ≈ 31%
question 70 true or false
Answer:
true
Step-by-step explanation:
For this case we have that by definition:
[tex]Sin (90) = 1\\Cos (90) = 0[/tex]
Now, the tangent of 90 is given by:
[tex]tg (90) = \frac {Sin (90)} {Cos {90}} = \frac {1} {0}[/tex]
Thus, it is observed that the tangent of 90 degrees is not defined. Is obtained ∞.
Similarly:
[tex]Sin (-90) = - 1\\Cos (-90) = 0[/tex]
Now, the tangent of -90 is given by:
[tex]tg (-90) = \frac {Sin (-90)} {Cos {-90}} = \frac {-1} {0}[/tex]
Thus, it is observed that the tangent of -90 degrees is not defined.
Answer:
False
A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter. 1
if it has a diameter of 8 units, then its radius is half that, or 4.
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=20 \end{cases}\implies V=\pi (4)^2(20)\implies V=320\pi \\\\\\ V\approx 1005.309649148733\implies \stackrel{\textit{rounded up}}{V=1005}[/tex]
To calculate the volume of a cylindrical cardboard tube, the formula V = πr²h is used with a given diameter of 8 cm (radius of 4 cm) and a height of 20 cm. After computation, the approximate volume is 1005 cm³, rounded to the nearest whole number.
Explanation:To find the volume of the cylindrical cardboard tube, we need to first understand the volume formula for a cylinder, which is V = πr²h. The radius is half of the diameter, so for this tube, the radius (r) is 4 centimeters (8 cm diameter / 2). The height (h) of the cylinder is given as 20 centimeters.
Now, we can plug in these values to find the volume:
V = π × (4 cm)² × 20 cmV = π × 16 cm² × 20 cmV = π × 320 cm³V = 3.142 × 320 cm³V ≈ 1005 cm³ (rounded to the nearest whole number)Therefore, the approximate volume of the tube is 1005 cubic centimeters when rounded to the nearest whole cubic centimeter.
The graph of which equation below is a horizontal line?
Answer:
2
Step-by-step explanation:
The equation of a horizontal line is y = c
where c is the value of the y- coordinates the line passes through
Thus y = 3 ← is the equation of a horizontal line
The area of a square is A = s?, where s is the length of one side of the square. What is the side length s for each square?
Answer:
s = +√A
Step-by-step explanation:
Start with the area formula, A = s². Solve this for the side length, s, as follows:
s = +√A
In words, if you're given the area of a square, find the square root of this area to determine the side length.
Solve the system of equations. y = -6x + 9 y = -3x + 3 a. ( 3, -2) c. ( 2, -3) b. ( -2, -3) d. No solution
For this case we have the following system of equations:
[tex]y = -6x + 9\\y = -3x + 3[/tex]
Equating the equations we have:
[tex]-6x + 9 = -3x + 3[/tex]
Adding 3x to both sides of the equation:
[tex]-6x + 3x + 9 = 3\\-3x + 9 = 3[/tex]
Subtracting 9 from both sides of the equation:
[tex]-3x = 3-9\\-3x = -6[/tex]
Dividing between -3 on both sides of the equation:
[tex]x = \frac {-6} {- 3}\\x = 2[/tex]
We look for the value of "and":
[tex]y = -3 (2) +3\\y = -6 + 3\\y = -3[/tex]
Thus, the solution of the system is (2, -3)
Answer:
(2, -3)
Find an equation equivalent to r=5/1+cos0 in rectangular coordinates
A. x^2=25-10y
B. X^2=10y-25
C.y^2=10x-25
C. Y^2= 25-10x
[tex]r=\dfrac5{1+\cos\theta}\implies r(1+\cos\theta)=5\implies r+r\cos\theta=5[/tex]
In converting between polar and rectangular coordinates, we take
[tex]x^2+y^2=r^2\implies r=\sqrt{x^2+y^2}[/tex]
[tex]x=r\cos\theta[/tex]
so that the equation becomes
[tex]\sqrt{x^2+y^2}+x=5[/tex]
which we can rewrite as
[tex]\sqrt{x^2+y^2}=5-x[/tex]
[tex]x^2+y^2=(5-x)^2[/tex]
[tex]x^2+y^2=25-10x+x^2[/tex]
[tex]\implies\boxed{y^2=25-10x}[/tex]
so the answer is C.
what is the approximate value of tan B?
For this case we have that by definition of trigonometric relations of rectangular triangles, that the tangent of an angle is given by the opposite leg to the angle on the leg adjacent to the angle. So:
[tex]tg (B) = \frac {16} {7}\\tg (B) = 2.2857[/tex]
Rounding the value we have 2.29
Answer:
Option D
ANSWER
D 2.29
EXPLANATION
The tangent ratio, is the ratio of the opposite side to the adjacent side.
The side adjacent to angle B is 7 units.
The side opposite to angle B is 16 units.
This implies that:
[tex] \tan(B) = \frac{16}{7} [/tex]
[tex]\tan(B) =2.29[/tex]
The correct answer is D.
The profit a company earns every month depends of the amount of the product sold, p, for $855 each and the amount spent in rent,utilities and other expenses, which always totals to $6,780. The CEO of the company earns 15% of this profit. How much does the CEO earn if the company sells 250 products in a given month?
Answer:
$31,045.50
Step-by-step explanation:
Revenue from sales = ($855/item)p
Expenses: $6,780
Revenue if p = 250 is R(250) = ($855/item)(250 items) = $213,750
Subtracting expenses, we get a profit of $206,970.
The CEO of the company earns 15% of this profit, or:
0.15($206,970) = $31,045.50
In the game Yahtzee, players roll five dice. There are 13 rounds per game. In each round, each player can roll the dice up to three times. In a player's first roll of each round, he or she rolls all five dice. The second and third rolls, the player can choose to roll any subset of the dice again (any or all the dice). Yahtzee is a bit like poker with dice. An especially valuable roll is 5 of a kind (all 5 dice show the same number of spots), called a Yahtzee. The next two questions are about Yahtzee. Problem 3 The chance of rolling a Yahtzee (5 of a kind) on the first roll of a turn is closest to
Answer: 13
Step-by-step explanation: because I have the whole bookanswer duh
It costs 9.95 for 1 ticket to the movies. If 3 people go, how much would the total price of 3 tickets be?
It would be $9.95 x 3
An office building has a cement block under its dumpster. The pad has an area of 108 square feet. The dumpster is 9 ft long and 8 ft wide. What is the most likely perimeter of the cement pad
Answer:
Most likely Perimeter of the pad is 42 ft.
Step-by-step explanation:
Area of the Cement pad = 108 feet²
Length of the dumpster = 9 ft
Width of the dumpster = 8 ft
Cement pad surface is greater than dumpster to hold it.
Area of pad = 108 ft²
length × width = 108
we choose length and width such that they are greater than length and width of the dumpster.
So, length of the pad = 12 ft
Width of the pad = 9 ft
Thus, Perimeter = 2 × (length + width) = 2 × ( 12 + 9 ) = 2 × 21 = 42 ft
Therefore, Most likely Perimeter of the pad is 42 ft.
Develop a 95% confidence interval for the expected value of y when x = 8. estimate the standard deviation of an individual value of y when x = 8.
Final answer:
To create a 95% confidence interval for y when x=8, we need the sample mean and the standard deviation to calculate the Error Bound for the Mean (EBM). The CI is the sample mean ± EBM. Estimating the standard deviation of y involves using the sample standard deviation as an estimate or the known population standard deviation.
Explanation:
To develop a 95% confidence interval for the expected value of y when x = 8, we first need to know the sample mean (μ) and the standard deviation of the population or an estimate from the sample (known as σ or s, respectively). When we have these statistics, we can use the normal distribution to calculate the error bound for the mean (EBM), which is the margin of error. The confidence interval (CI) is then constructed as (sample mean - EBM, sample mean + EBM).
To estimate the standard deviation of an individual value of y when x = 8, which is essentially the standard deviation of the population (σ), you need to use the sample standard deviation (s) as an estimate unless the population standard deviation is known.
Remember, the EBM for the confidence interval depends on the chosen confidence level, the standard deviation, and the size of the sample. With a higher confidence level, you get a wider interval. In practice, the confidence interval gives us a range where we expect the true population parameter lies with a certain level of confidence, acknowledging there's still a small chance the true value lies outside of this range.