Answer: 60°
Step-by-step explanation:
π/3
Since π is denoted as 180°, the question can be rewritten as:
π/3 .
To convert π/3 radians to the nearest degree will be:
π/3 = 180/3
= 60°
This shows that the value of π/3 rads is equal to 60°
Data;
[tex]\frac{\pi }{3}[/tex]radsConversion of radians to degreeThe formula of conversion from radians to degrees is given as
[tex]\pi rads = 180^0[/tex]
Let's convert our given radians to degrees.
[tex]\pi rads = 180^0\\\frac{\pi}{3} = ?\\[/tex]
This becomes
[tex]\frac{\pi }{3} * 180 = \pi \\\\\frac{\pi }{3} rads = \frac{180}{3} \\\frac{\pi }{3} rads = 60^0[/tex]
What we did was equate π rads to 180°, cross multiply the sides with π/3 and solve.
This shows that π/3 rads is equal to 60°
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Is it possible to make a triangle that has angles measuring 90 degrees, 30 degrees, and 100 degrees? If so, describe your drawing of an example. If not, explain your reasoning.
Answer: No, it's not possible as every triangle is 180 degrees. These angles add to 220 degrees which is more than 180.
Step-by-step explanation:
This is backed by the Triangle Sum Theorem which states that the three interior angles of any triangle add up to 180 degrees.
It's impossible to form a triangle with angles measuring 90, 30, and 100 degrees because the sum of those angles exceeds 180 degrees, which violates the rule that the sum of all angles in a triangle must equal 180 degrees.
Explanation:No, it is not possible to create a triangle with angle measures of 90 degrees, 30 degrees, and 100 degrees. This is because the sum of the angles in any triangle always equals 180 degrees. If you add up 90, 30, and 100, you get a sum of 220 degrees, which exceeds the 180-degree rule of triangles.
To understand this concept better, let's take a look at an example. In a right triangle, which is a triangle where one of the angles measures 90 degrees, the other two angles must add up to 90 degrees to satisfy the 180-degree rule. So, if we have a right triangle with one angle of 90 degrees and another angle of 30 degrees, the third angle would have to be 60 degrees (180 - 90 - 30), not 100 degrees.
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George’s parents are saving for his college fund. They put $5,000 into an interest bearing account with a compound interest rate of 5.5%. George’s parents want to determine what the balance of his college fund account will be after 15 years. Using the formula A = P (1 + r) Superscript t, which is the correct substitution for the formula?
Answer:
see below
Step-by-step explanation:
A = P (1 + r) ^t
A is the amount in the account
P is the principle or the amount invested
r is the interest rate
t is the time
A = 5000 (1 + .055)^15
5000(2.23247)
Rounding to 2 decimals since we round to the nearest penny
11162.38
Answer: A
Step-by-step explanation:
XD
Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118. If a recent test-taker is selected at random, what is the probability the student scored 691 or greater on the exam ?
Answer:
The probability is 0.06681
Step-by-step explanation:
To calculate this, we need to calculate the standard score or z-score
Mathematically, the standard score can be calculated using the formula;
z-score = (x - mean)/SD
from the question, the mean is 514 and the standard deviation is 118
The z-score is thus = (691-514)/118 = 177/118 = 1.5
The probability we are trying to calculate is thus;
P(x ≥ 691) or P(z ≥ 1.5)
Using standard score table or calculator,
Recall, P( x < 691) = 1 - P( x ≥ 691)
Hence, P( x ≥ 691) = 1 - P( x < 691)
P( x ≥ 691) = 1 - 0.93319
= 0.06681
Final answer:
To find the probability of scoring 691 or greater on the SAT Math section, you calculate the Z-score using the given mean and standard deviation, then use this to determine the percentage of students scoring below this score, with a Z-score of 1.5 corresponding to approximately 6.68% scoring higher.
Explanation:
To determine the probability that a student scored 691 or greater on the SAT Math section, given the distribution has a mean of 514 and a standard deviation of 118, we first calculate the Z-score. The Z-score formula is Z = (X - μ) / σ, where X is the score of interest, μ is the mean, and σ is the standard deviation.
For a score of 691, the Z-score is:
Z = (691 - 514) / 118 = 177 / 118 ≈ 1.5
After calculating the Z-score, we look up this value in a standard normal distribution table or use a calculator with statistical functionalities to find the probability to the right of this Z-score. This gives us the probability of a student scoring 691 or higher on the SAT Math section.
However, without a Z-table or calculator at hand, we can approximate that a Z-score of 1.5 generally corresponds to being higher than approximately 93.32% of the distribution. Therefore, the probability of scoring 691 or greater is about 6.68% (100% - 93.32%).
A cylinder was enlarged by a scale factor of 4. The new volume is 2,240 cubic units. What was the volume of the original cylinder
We have been given that a cylinder was enlarged by a scale factor of 4. The new volume is 2,240 cubic units. We are asked to find the volume of original cylinder.
We know that a cylinder is a three dimensional object. Since scale factor is 4, so each side of new cylinder will be 4 times the side of original side of cylinder.
Due to 3 dimensions, the volume of new cylinder is [tex]4^3[/tex] times the volume of original cylinder.
[tex]\text{Volume of original cylinder}\times 4^3=\text{Volume of new cylinder}[/tex]
[tex]\text{Volume of original cylinder}\times 64=2240[/tex]
[tex]\frac{\text{Volume of original cylinder}\times 64}{64}=\frac{2240}{64}[/tex]
[tex]\text{Volume of original cylinder}=35[/tex]
Therefore, the volume of the original cylinder is 35 cubic units.
What two numbers multiply to 60, but add to -16?
Answer:
-6 and -10.
Step-by-step explanation:
Added together you get -16, multiplied together results in 60.
The value of two numbers gives multiplied by 60, but added to -16 are - 10 and - 6.
Given that,
The multiplication of two numbers is 60
And, the addition of two numbers is - 16.
Let us assume that the two numbers are x and y.
Hence we get;
[tex]x y = 60[/tex] ... (i)
And, [tex]x + y = - 16[/tex] .. (ii)
From equation (ii);
[tex]y = - 16 - x[/tex]
Substitute the above values in (i);
[tex]x (- 16 - x) = 60[/tex]
[tex]- 16x - x^2 = 60[/tex]
[tex]x^2 + 16x + 60 = 0[/tex]
[tex]x^2 + (10 + 6)x + 60 = 0[/tex]
[tex]x^2 + 10x + 6x + 60 = 0[/tex]
[tex]x(x + 10) + 6 (x + 10) = 0[/tex]
[tex](x + 10) (x + 6) =0[/tex]
This gives two solutions,
[tex]x = - 10[/tex]
[tex]x = - 6[/tex]
Substitute x = - 10 in (ii);
[tex]x + y = - 16[/tex]
[tex]- 10 + y = - 16\\y = - 16 + 10\\y = - 6[/tex]
Substitute x = - 6 in (ii);
[tex]x + y = - 16[/tex]
[tex]-6 + y = - 16\\y = - 16 + 6\\y = - 10[/tex]
Therefore, both the numbers are - 10 and - 6.
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what is the slope of the equation y+3x=-2
Answer:
The slope is -3 and the y intercept is -2
Step-by-step explanation:
y +3x = -2
We want this in slope intercept form
y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
y +3x-3x = -3x-2
y = -3x-2
The slope is -3 and the y intercept is -2
Answer:
the slope is -3 and the y intercept is -2
Step-by-step explanation:
y+3x=-2
you want to transform the equation into slope intercept form: y= mx+b
subtract 3x from both sides
y= -3x-2
hope this helps :)
What function is graphed y=3cot(x)+2 y=3cot(x+3) y=3tan(x)+2 y=3tan(x+2)
Answer: y=3tan(x)+2
Step-by-step explanation:
Answer:
y=3 tan(x)+2
Step-by-step explanation:
just did it on ed
Greg borrows $1975 at a simple interest rate of 5% for 3 years. Linda borrows $1975 at a simple interest rate of 4.5% for years. Who pays more interest at the end of their loan? How much more
Answer:
Greg pays more interest than Linda
He pays $17.45 more
Step-by-step explanation:
Greg
P=$1975
R=5%=0.05
T=3 years
Simple interest=P×R×T
=$1975×0.05×3
=$296.25
Linda
P=$1975
r=4.5%=0.045
n=1
t=3
Linda's Interest is compounded once per period, so we this formula
Compound Interest =P(1+r)^t
=$1975(1+0.045)^3
=$1975(1.045)^3
=$1975(1.141166125)
=$2,253.80
Interest paid=$2,253.80-$1975
=$278.8
Just help me please i really need it
Answer:
2.4 hours
Step-by-step explanation:
Identify the conic that is formed by the intersection of the plane described and the double-napped cone.
The plane intersects one nappe and is parallel to n.
What is the conic section formed?
A. ellipse
B. hyperbola
C. parabola
Answer:
B
Step-by-step explanation:
because a hyperbola is a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone. and if you view the picture its the same thing
Answer:
c
Step-by-step explanation:
The plane only intersects one cone and is parallel to n.
So it has to be a parabola.
please help its in math
Answer:
4044
Step-by-step explanation:
14 × (pi × d)
14 × 3.14 × 92
4044.32 feet
tan(-216°) = _____.
tan 36°
-tan 144°
tan 144°
-tan 36°
Answer:
Tan 144
Step-by-step explanation:
Because they have the same answer when typed in a calculator
Answer:
It is -tan(36
Step-by-step explanation:
What is 16.4 divide by .72
Answer:
22.7777777778
Step-by-step explanation:
Answer:
22.7777777778
Step-by-step explanation:
What is the value of x in the equation 5x+3 = 4x?
A. -3
B. -1/3
C. 1/3
D. 3
Answer: A
Step-by-step explanation:
[tex]5x+3=4x[/tex]
Subtract 5x from both sides to isolate x's on one side and independent values on the other
[tex]-5x+5x+3=4x-5x[/tex]
[tex]3=-x[/tex]
Multiply by -1 to make x positive
[tex]-3=x[/tex]
I need help bad only with the first 2
Answer:
C =75.36 m
A =452.16 m^2
Step-by-step explanation:
The circumference is found by where r is the radius and pi = 3.14
C = 2 * pi *r
C = 2 * 3.14 * 12
C =75.36 m
The area is found by
A = pi r^2
A = 3.14 * 12^2
A =452.16 m^2
Answer:
Circumference: 12.56 m
Area: 452.16 m²
Step-by-step explanation:
Circumference:
2 × 3.14 × 12
12.56 m
Area:
3.14 × 12²
452.16 m²
Please Help!
The point (4, π/6) can also be represented by which of the following polar coordinates?
a. (-4, 7π/6)
b.(4, 5π/6)
c. (4, -π/6)
d. (-4, 13π/6)
The point (4, π/6) can also be represented by the polar coordinates (-4, 7π/6).
We have given that,
a. (-4, 7π/6)
b.(4, 5π/6)
c. (4, -π/6)
d. (-4, 13π/6)
We have to determine the point (4, π/6) that can also be represented by which of the following polar coordinates.
What is the polar coordinate?
The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point is called the pole, and the ray from the pole in the reference direction is the polar axis.
The point (4, π/6) can also be represented by the polar coordinates (-4, 7π/6).
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Final answer:
The point (4, π/6) can also be represented by (-4, 7π/6), utilizing the polar coordinate system's symmetry by extending the radius to the negative side and adding π to the angle.
Explanation:
The point (4, π/6) in Cartesian coordinates corresponds to a point in the first quadrant since the radius is positive and the angle is positive, which is less than π/2. When we want to find an equivalent set of polar coordinates, we can utilize the symmetry of the polar coordinate system.
The point can also be represented by the coordinates (-4, 7π/6) because if you extend the radius to the negative side (so it becomes -4) and add π radians (180 degrees) to the angle, the point ends up in the same location, albeit in the third quadrant. Therefore, the correct answer is a. (-4, 7π/6).
Betsy has $468 in a personal bank account, and then withdraws $9 per week. Carlos has $18 in a personal bank account, and then deposits $66 earned from yard work each week. After how many weeks will they have the same amount of money in the bank?
Answer: 9 weeks
Step-by-step explanation:
First, we would have to set up an equation.
468 - 9w = 18 + 66w
The variable w stands for weeks.
We need to figure out when their bank account will become equal.
So, we need to solve for w.
First, let’s combine like terms. I will move 9w to the other side.
468 = 18 + 66w + 9w
Then simplify:
464 = 18 + 55w
Then, do the same as you did before, just move the 18 to the other side. Keep in mind that when a number switches sides, it’s switches signs (from negative to positive or positive to negative)
464 + 18 = 55w
482 = 55w
To isolate the variable, you would have to divided 55w by 55. Keep in mind, what you do to one side of an equation you must do to the other.
482/55 = 55w/55
8.76 = w
When you round to the nearest whole number, it will be 9 weeks.
Therefore, it will take 9 weeks for them to have the same amount of money in the bank.
A diameter of a circle has endpoints.
A) center: (-3, 2)
B) radius: √65
C) equation: (x +3)² +(y -2)² = 65
evaluate the expression when c= -4 and y= 3 c-5y
Answer:
-19
Step-by-step explanation:
If c = -4 and y = 3, replace c and y with their corresponding values in the expression, so that the expression will look like this: (-4) - (5 * 3).
Since multiplication comes before subtraction in PEMDAS, you would multiply 5 by 3, which gets you 15.
Now the expression is (-4) - (15). Then, you do the subtraction. -4 - 15 is equal to -19.
Does that help?
Final answer:
The expression c-5y evaluates to -19 when substituting c = -4 and y = 3.
Explanation:
To evaluate the expression c-5y when c = -4 and y = 3, we replace c with -4 and y with 3 in the expression. The value of the expression is -19, which is obtained by performing the arithmetic: (-4) - 5(3) = -4 - 15 = -19. Therefore, when c is -4 and y is 3, the expression c-5y yields -19.
This problem belongs to the topic of algebraic expressions, and this question demonstrates the importance of substitution to find the value of algebraic expression. This property is used has many applications in science and daily life.
A large rectangular area is to be fenced off ( a large rectangle divided into 2 smaller rectangles). The fence used to divide the space cost $10 per foot and the fence used for the perimeter costs$15 per foot. If the total budget for the project is $60000 what are the dimensions that yield the largest area
Answer:
Length of area is 857.14 ft
Width of area is 857.14 ft
Length of dividing fence is 857.14 ft
Step-by-step explanation:
Here we have
Area of rectangle = Length × Width
The dimension, of the rectangle with the largest area is the dimension of a square, hence we have;
Length of rectangle = Width of rectangle = x
Hence, the perimeter of the area = 4·x, while the width of the dividing fence = x
Therefore, since the we have;
Cost of the perimeter fence = $15/foot
Cost of the dividing fence = $10/foot
Then;
4·x × 15 + x × 10 = 60000
60·x + 10·x = 60000
x = 60000/70 = 857.14 ft
Which gives the following dimensions;
Length of area = 857.14 ft
Width of area = 857.14 ft
Length of dividing fence = 857.14 ft.
Alice makes a batch of cookies for her mom’s
birthday. She adds 2 3/4
cups of fl our and
1 1/2
cups of sugar to a bowl. How many cups of
dry ingredients does Alice add to the bowl?
9TH GRADE FUNCTIONS PLEASE HELP
Answer: g(x) is -x² -3
Step-by-step explanation:
First, you know that the parabola is facing downwards, so the x must be negative.
Next, it is 3 units down from the parent graph, which adds that -3.
All of these add up to get your final equation:
g(x) is -x² -3
The average waist size for teenage males is 29 inches with astandard deviation of 2 inches. If waist sizes are normallydistributed, determine the z-score of a teenage male with a33 inch waist.
Answer:
The z-score of a teenage with waist size 33 inch is 2
Step-by-step explanation:
Mathematically, the z-score can be calculated using the formula;
z-score = (x- mean)/SD
where mean = 29 inches , SD = 2 inches and x = 33 inch
Plugging these values, we have
z-score = (33-29)/2 = 4/2 = 2
The z-score of a teenage male with a33 inch waist is 2.
Given that,
The average waist size for teenage males is 29 inches with a standard deviation of 2 inches.Based on the above information, the calculation is as follows:
[tex]= (33-29)\div 2 \\\\= 4\div 2[/tex]
= 2
Therefore we can conclude that The z-score of a teenage male with a33 inch waist is 2.
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work out the circumference of this circle take pie to be 3.142and give your number to 1 decimal place and the radius is 11.2cm
The required circumference of circle up to 1 decimal place is 70.4.
Radius = 11.2 cm
π = 3.142
The circumference of the circle is to be determined.
The circumference of object is its boundary measure.
Here, Circumference of circle = [tex]2\pi r[/tex]
= 2 x 3.142 x 11.2
= 70.4
Thus, the required circumference up to 1 decimal place is 70.4.
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Números que multiplicados den 5 y sumados 7
Answer: No hay
Step-by-step explanation:
5 es producto de 5*1 y 1*5 solamente por lo tanto no hay número que sumado de 7
A rectangular aquarium is 1.5 ft wide, 6ft long, and 2 ft tall. If 1 ft^3 = 7.5 gallons, how much water can the aquarium hold?
Answer:
The aquarium is 1.5 * 6 * 2 = 18 cubic feet
Water measures 7.5 gallons per cubic foot, then the aquarium can hold
(7.5 * 18) = 135 gallons
**************************
By the way, there are 7.48052 gallons per cubic foot to be EXTREMELY accurate.
Step-by-step explanation:
A prime die uses the first six prime numbers on its faces, one prime per face. When two prime dice are rolled randomly, there is a 1/36 probability that the product of the two numbers will be equal to 4. What is the probability that the product has a units digit of one
Answer: [tex]\frac{5}{36}[/tex]
Step-by-step explanation:
Given
dice with Prime number is rolled
The number on the face of dice are 2,3,5,7,11 and 13
Probability of getting a product of 4 is [tex]\frac{1}{36}[/tex]
Now probability of getting product has a unit digit one is possible when outcome is
[tex](3,7),(7,3),(13,7),(7,13),(11,11)[/tex]
i.e. there are 5 favorable outcomes
So probability is [tex]\frac{5}{36}[/tex]
What type of slope is produced from the equation y=6?
Answer:
Slope = 0
Step-by-step explanation:
The slope is zero because it is a straight horizontal line. If it is a straight vertical line, the slope is undefined.
hope this helps :)
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
-5
-3
-2
-1
1
2
3
O
4
5
+
+
4
-3
-2
-1
0
1
2
4
5
+
w+ W0
+
at at at
+
fr
-3
-2
-1
o
1
2
3
4
5
+
-3
-2
-1
ó
1
2 3
4
5
Answer:
3 < x
Step-by-step explanation:
3(8 - 4x) < 6(x - 5)?
Distribute
24 -12x< 6x -30
Add 12x to each side
24-12x+12x < 6x+12x-30
24 < 18x-30
Add 30 to each side
24+30 < 18x-30+30
54 < 18x
Divide each side by 18
54/18 < 18x/18
3 < x
area formula of a kite
Answer:
(pq)/2
Step-by-step explanation:
p and q are the diagonals of the kite
Answer:
Area = (1/2) * (Diagonal_1)*(Diagonal_2)
where Diagonal_1 is one diagonal in the kite
and Diagonal_2 is 2nd diagonal in the kite
Step-by-step explanation:
The diagonals of a kite intersect at right angles and one diagonal bisects the other.
so you get two triangles, with a base length of (Diagonal 1)
the height_1 = a , height_2 = b
a + b = Diagonal_2
area of one triangle in Kite = (1/2)(Diagonal_1)*a
area of second triangle in Kite = (1/2)(Diagonal_1)*b
area of kite = area of triangle_1 + area of triangle_2
area of kite = (1/2)(Diagonal_1)*a + (1/2)(Diagonal_1)*b
area of kite = (1/2)*(Diagonal_1)*(a + b)
Area of kite = (1/2) * (Diagonal 1)*(Diagonal2)