Answer:
The answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Step-by-step explanation:
Given that pizza is divided into six unequal slices.
Largest slice has an angle of [tex]90^\circ[/tex].
He eats the pizza from largest to smallest.
Let the difference in angles in each slice = [tex]d^\circ[/tex]
1st angle = [tex]90^\circ[/tex]
2nd angle = 90-d
3rd angle = 90-d-d = 90 - 2d
4th angle = 90-2d-d = 90 - 3d
5th angle = 90-3d-d = 90 - 4d
6th angle = 90-4d -d = 90 - 5d
We know that the sum of all the angles will be equal to [tex]360^\circ[/tex] (The sum of all the angles subtended at the center).
i.e.
[tex]90+90-d+90-2d+90-3d+90-4d+90-5d=360\\\Rightarrow 540 - 15d = 360\\\Rightarrow 15d = 540 -360\\\Rightarrow 15d = 180\\\Rightarrow d = 12^\circ[/tex]
So, the angles will be:
1st angle = [tex]90^\circ[/tex]
2nd angle = 90- 12 = 78
3rd angle = 78-12 = 66
4th angle = 66-12 = 54
5th angle = 54-12 = 42
6th angle = 42 -12 = 30
So, the answer is 5th angle = [tex]\bold{42^\circ}[/tex]
Need Answers ASAP!!!!
Answer:
15.9degrees
Step-by-step explanation:
in photo above
Answer:
[tex]\boxed{15.95\°}[/tex]
Step-by-step explanation:
The angle can be found by using trigonometric functions.
tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]
tan (θ) = [tex]\frac{4}{14}[/tex]
θ = [tex]tan^{-1} \frac{4}{14}[/tex]
θ = 15.9453959
θ ≈ 15.95
plzzz helppppp. 4>n/-4
Answer:
-16 < n
Step-by-step explanation:
4>n/-4
Multiply each side by -4, remembering to flip the inequality
-4 *4 < n/-4 * -4
-16 < n
Answer:
[tex]n > -16[/tex]
Step-by-step explanation:
[tex]4 > n/-4[/tex]
Multiply each part by -4 (flip sign).
[tex]-4 *4 < n/-4 * -4[/tex]
[tex]-16 < n[/tex]
Switch sides.
[tex]n>-16[/tex]
A cylinder has a volume of 200 mm3 and a height of 17 mm.
a) The volume formula for a cylinder is v = pie r squareℎ. Isolate for the variable r in this formula.
b) Using the equation where you isolated for r in part a, find the radius of the cylinder. Round your answer to the nearest hundredth. (1 mark)
Answer:
The radius of the cylinder is 1.93mm.
Step-by-step explanation:
1) Formula to find the missing radius : V= pi r^2 (h)
( V= volume, pi=3.14 r=radius, h= height)
2) Plug all the give variables into the formula: 200=pi r^2 (17)
3) Multiply pi with 17 and then round it to the nearest hundredth which you get 53.401707511 -> 53.41, now your equation is: 200= 53.41 r^2
4) Next you want to isolate the r^2 by dividing both sides by 53.41
200/53.41= 53.41r^2/53.41 ( 3.74461711 round to the nearest hundredth --> 3.74) ---> 3.74=r^2
5) Now you have to square both sides to get rid of that exponent : squared 3.74 = squared r^2
6) Your equation would be 1.933907961 = r, round that whole decimal to the nearest hundredth and you will get 1.93 ( 19.3 = r)
7) So the radius of the cylinder given the volume is 200 mm^3 and a height of 17 mm is 1.93 mm.
less than 0 but greater than (−5)
Answer:
-5 < x < 0
Step-by-step explanation:
f(x) = x + 2
g(x) = x - 4
(fg)(x) =
Answer:
Step-by-step explanation:pleased to help u....
Simplify the expression.
Write your answer without negative exponents. NEED AN ANSWER ASAP
Answer:
[tex]\boxed{\frac{-3b^4 }{a^6 }}[/tex]
Step-by-step explanation:
[tex]\frac{-18a^{-8}b^{-3}}{6a^{-2}b^{-7}}[/tex]
[tex]\frac{-18}{6} \times \frac{a^{-8}}{a^{-2}} \times \frac{b^{-3}}{b^{-7}}[/tex]
[tex]-3 \times \frac{a^{-8}}{a^{-2}} \times \frac{b^{-3}}{b^{-7}}[/tex]
Apply the law of exponents, when dividing exponents with same base, we subtract the exponents.
[tex]-3 \times a^{-8-(-2)} \times b^{-3- (-7)}[/tex]
[tex]-3 \times a^{-8+2} \times b^{-3+7}[/tex]
[tex]-3 \times a^{-6} \times b^{4}[/tex]
[tex]{-3a^{-6}b^{4}}[/tex]
The answer should be without negative exponents.
[tex]a^{-6}=\frac{1}{a^6 }[/tex]
[tex]\frac{-3b^4 }{a^6 }[/tex]
Answer:
[tex] - \frac{3 {b}^{4} }{ {a}^{6} } [/tex]Step-by-step explanation:
[tex] \frac{ - 18 {a}^{ - 8} {b}^{ - 3} }{6 {a}^{ - 2} {b}^{ - 7} } [/tex]
Reduce the fraction with 6
[tex] \frac{ - 3 {a}^{ - 8} {b}^{ - 3} }{ {a}^{ - 2} {b}^{ - 7} } [/tex]
Simplify the expression
[tex] \frac{ - 3 {b}^{4} }{ {a}^{6} } [/tex]
Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b \: } [/tex] to rewrite the fraction
[tex] - \frac{3 {b}^{4} }{ {a}^{6} } [/tex]
Hope this helps...
Best regards!!
In the diagram AB=AD and
Answer:
AC ≅ AE
Step-by-step explanation:
According to the SAS congruence theorem, if two triangles have 2 corresponding sides that are equal, and also have one included corresponding angle that are equal to each other in both triangles, both triangles are regarded as congruent.
Given ∆ABC and ∆ADC in the question above, we are told that segment AB ≅ AD, and also <BAC ≅ <DAC, the additional information that is necessary to prove that ∆ABC and ∆ADC are congruent, according to the SAS theorem, is segment AC ≅ segment AE.
This will satisfy the requirements of the SAS theorem for considering 2 triangles to be equal or congruent.
Determine if the survey question is biased. If the question is biased, suggest a better wording. How often do you eat fruit during an average week?
1. Is the question biased?
A. Yes, because it influences the respondent into thinking that eating fruit is good for you. A better question would be "Do you think that eating fruit is good for you?"
B. No, because it influences the respondent into thinking that eating fruit is good for you.
C. Yes, because it does not lead the respondent to any particular answer. A better question would be "Why is eating fruit good for you?"
D. No, because it does not lead the respondent to any particular answer.
2. Choose the best question below.
A. Do you think that eating fast food is good for you?
B. Do you think that eating fast food is bad for you?
C. Why is eating fast food bad for you?
D. The original question is not biased.
Answer:
The correct answers are:
1. No, because it does not lead the respondent to any particular answer (D)
2. The original question is not biased (D)
Step-by-step explanation:
In developing survey questions, response biases are tendencies for respondents to respond inaccurately or falsely to a particular question and this largely has to do with the way the questions are framed. Biased questions build preconceived thoughts in the mind of the respondent, increasing the tendency for them to lean towards a particular answer.
In this example, the question "How often do you eat fruit during an average week?" is not biased because it does not suggest to the respondent whether eating fruits is good or bad, it just directs the respondent to a particular number, hence the question is not biased.
Triangle ABC has vertices A(-5, -2), B(7, -5), and C(3, 1). Find the coordinates of the intersection of the three altitudes
Answer:
Orthocentre (intersection of altitudes) is at (37/10, 19/5)
Step-by-step explanation:
Given three vertices of a triangle
A(-5, -2)
B(7, -5)
C(3, 1)
Solution A by geometry
Slope AB = (yb-ya) / (xb-xa) = (-5-(-2)) / (7-(-5)) = -3/12 = -1/4
Slope of line normal to AB, nab = -1/(-1/4) = 4
Altitude of AB = line through C normal to AB
(y-yc) = nab(x-xc)
y-1 = (4)(x-3)
y = 4x-11 .........................(1)
Slope BC = (yc-yb) / (xc-yb) = (1-(-5) / (3-7)= 6 / (-4) = -3/2
Slope of line normal to BC, nbc = -1 / (-3/2) = 2/3
Altitude of BC
(y-ya) = nbc(x-xa)
y-(-2) = (2/3)(x-(-5)
y = 2x/3 + 10/3 - 2
y = (2/3)(x+2) ........................(2)
Orthocentre is at the intersection of (1) & (2)
Equate right-hand sides
4x-11 = (2/3)(x+2)
Cross multiply and simplify
12x-33 = 2x+4
10x = 37
x = 37/10 ...................(3)
substitute (3) in (2)
y = (2/3)(37/10+2)
y=(2/3)(57/10)
y = 19/5 ......................(4)
Therefore the orthocentre is at (37/10, 19/5)
Alternative Solution B using vectors
Let the position vectors of the vertices represented by
a = <-5, -2>
b = <7, -5>
c = <3, 1>
and the position vector of the orthocentre, to be found
d = <x,y>
the line perpendicular to BC through A
(a-d).(b-c) = 0 "." is the dot product
expanding
<-5-x,-2-y>.<4,-6> = 0
simplifying
6y-4x-8 = 0 ...................(5)
Similarly, line perpendicular to CA through B
<b-d>.<c-a> = 0
<7-x,-5-y>.<8,3> = 0
Expand and simplify
-3y-8x+41 = 0 ..............(6)
Solve for x, (5) + 2(6)
-20x + 74 = 0
x = 37/10 .............(7)
Substitute (7) in (6)
-3y - 8(37/10) + 41 =0
3y = 114/10
y = 19/5 .............(8)
So orthocentre is at (37/10, 19/5) as in part A.
another pls! lolllllll
Answer:
P = 126; A = 927
Step-by-step explanation:
Enlarging by a scale factor means multiplying each number by the given. 6 x 4.5 = 27; 8 x 4.5 = 36. 2(27) + 2(36) = 126; 27 x 36 = 927.
Answer:
Hey there!
Original Width: 6
New Width: 27
Original Length: 8
New Length: 36
Perimeter: 36+36+27+27, or 126
Area: 36(27), or 972.
Hope this helps :)
Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
Answer: y > 2x + 1
Step-by-step explanation:
In the graph first, we can see two things:
The line is not solid (so the values in the line are not included), and the shaded part is above, so we will be using the symbol:
y > f(x)
Now, in the line we can see that when x = 0, y = 1.
So the linear equation must be something like:
f(x) = a*x + 1
The only one that has an y-intercept equal to 1 is y > 2x + 1
Answer:
C or y>2x +1
Step-by-step explanation:
edge
what is the surface area of a cylinder height is 4 cm and diameter is 5 cm
Answer:
20cm it's is the answers
Step-by-step explanation:
5*4=20
At what point does the line
Y = -1/2 X + 2 intercept the Y-axis?
A. - 1
B. -1/2
C. 1
D. 2
E. -2
Answer:
D. 2
Step-by-step explanation:
The y-intercept is when the graph crosses the y-axis when x = 0. In that case, simply plug in x as 0:
y = -1/2(0) + 2
y = 2
Therefore, the graph crosses the y-axis at 2.
Answer:
D
Step-by-step explanation:
our equation is y= [tex]\frac{-1}{2}[/tex] x +2
-1/2 is the slope 2 is the y-interceptso the answer is 2
if we want to verify our answer we can follow these steps
the y-intercept is given by calculating the image of 0
y= -1/2*0+2 = 2so it's right
x=7 what would match this soulotion
Answer:
x = 7
Step-by-step explanation:
7 = 7
It's given
4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7
Answer:
[tex]1 \frac{1}{4} [/tex]Step-by-step explanation:
[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]
To divide by a fraction, multiply the reciprocal of that fraction
[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]
Reduce the number with the G.C.F 7
[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]
Reduce the numbers with the G.C.F 17
[tex] \frac{5}{6} \times \frac{3}{2} [/tex]
Reduce the numbers with the G.C.F 3
[tex] \frac{5}{2} \times \frac{1}{2} [/tex]
Multiply the fraction
[tex] \frac{5}{4} [/tex]
In mixed fraction:
[tex]1 \frac{1}{4} [/tex]
Hope this helps..
Good luck on your assignment...
A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 9-digit e
A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 9-digit entry code if they know that no digits repeat?
Answer:
the probability of a person correctly guessing a 9-digit entry code if they know that no digits repeat is 0.1
Step-by-step explanation:
We know that probability= number of required outcomes /number of all possible outcome.
From the given information;
the number of required outcome is guessing a 9-digit = 1 outcome
the number of all possible outcome = ¹⁰C₉ since there are 10 numbers and 9 number are to be selected.
Since there are only 9-digit that opens the lock;
the probability of a person correctly guessing a 9-digit entry code is
[tex]P =\dfrac{1}{^{10}C_9}[/tex]
[tex]P =\dfrac{1}{\dfrac{10!}{9!1!}}[/tex]
[tex]P =\dfrac{1}{10}[/tex]
P = 0.1
Calculate: 1/(1×3) + 1/(3×5) + ... + 1/(47×49) . Please give explanation
Answer:
4611/11515
Step-by-step explanation:
1/(1×3)- 1 times 3 simply equals 3. so the answer would be 1/3.
1/(3×5)- 3 times 5 simply equals 15. so the answer would be 1/15.
1/(47×49)- 47 times 49 is 2303. so the answer would be 1/2303.
after all this you find the common deonomator. The common denominator is 34545. 34545 divided by 3 equals to 11515 so you muliplty that number by 1/3. 34545 divided by 15 equals to 2303 so you muliplty that number by 1/15.
34545 divided by 2303 equals to 15 so you multiply that number by 1/2303. After adding all that together you get 13833/34545. However after you simplify that number you get 4611/11515
NEED HELP ASAP!!
What is the equation of the line that is parallel to the
given line and has an x-intercept of -3?
O y = x + 3
O y = ?X + 2
Oy=-3x + 3
y=-3x+2
Answer:
B
Step-by-step explanation:
The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have a graph.
So, slope of line in graph is
= (-1-1)/ (0.-3)
= -2/ (-3)
= 2/3
and, we know that two parallel line have same slope.
so, the slope of parallel line is 2/3 and the x intercept is -3.
So, the Equation line is y= 2/3 x + b
0 = 2/3 (-3) +b
b= 2
Thus, the required equation is y= 2/3x + 2.
Learn more about Slope here:
https://brainly.com/question/2863474
#SPJ5
Classify the triangle with angles measuring 1130, 47°, and 20°.
A. Straight
B. Right
C. Acute
D. Obtuse
Answer:
D. Obtuse
Step-by-step explanation:
Answer:
You typed that incorrectly. That first angle should be 113 degrees.
It would be an obtuse triangle.
Step-by-step explanation:
−11b+7=40 b= pls help
Answer:
[tex]\boxed{b = -3}[/tex]
Step-by-step explanation:
[tex]\sf -11b+7 = 40\\Subtracting\ 7\ to\ both\ sides\\-11b = 40-7\\-11b = 33\\Dividing\ both\ sides \ by \ -11\\ b = 33/-11\\b = -3[/tex]
URGENT!!!!!! A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame? REPLY IN COMMENTS PLEASE IM GLITCHING AND CANT SEE ANSWERS
Answer:
the perimeter of the square is just "(5+2x)(2)+(7+2x)(2)
Step-by-step explanation:
Answer:
2 × 10 + 2 × 14
Step-by-step explanation:
The frame is given to have measurements 2 times that of the photograph's measurements. We also know that the photograph is given by dimensions being 5 inch by 7 inch. Therefore the measurements of the frame should be 5 [tex]*[/tex] 2, which = 10 inches, by 7 [tex]*[/tex] 2 = 14 inches.
So the dimensions of the frame are 10 inch × 14 inch. As the frame is present as a rectangle, the perimeter is given by two times both dimensions together. That would be represented by the expression " 2 × 10 inch + 2 × 14 inch. " In other words you can say that the expression is 2 × 10 + 2 × 14 - the expression that represents the perimeter of the frame.
a variable with an exponent is a perfect square if the exponent is divisible by____
Answer: 3
Step-by-step explanation:
According to genetic theory, there is a very close to even chance that both children in a two child family will be of the same gender. Here are two possibilities.
(i). 24 couples have two children. In 16 or more of these families, it will turn out that both children are of the same gender.
(ii). 12 couples have two children. In 8 or more of these families, it will turn out that both children are of the same gender. Which possibility is more likely and why?
Answer:
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Step-by-step explanation:
(i) probability with 16 success out of 24 = 16/24 = 2/3
(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3
Since the two experiments have the same probability, the observed probabilities are the same.
HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.
Using the binomial distribution,
(i)
p = 1/2
N = 24
x = 16 (number of successes)
P(16,24) = C(24,16) p^16* (1-p)^8
= 735471* (1/65536)*(1/256)
= 0.0438
(ii)
p = 1/2
N = 12
x = 8 (number of successes)
P(8,12) = C(12,8) p^8* (1-p)^4
= 495*1/256*1/16
= 0.1208
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Note: It would help to mention the topic you're on so answers will correspond to what is expected. Here we cover probability and binomial distribution.
Historically, the proportion of students entering a university who finished in 4 years or less was 63%. To test whether this proportion has decreased, 114 students were examined and 51% had finished in 4 years or less. To determine whether the proportion of students who finish in 4 year or less has statistically significantly decreased (at the 5% level of signficance), what is the critical value
Answer:
z(c) = - 1,64
We reject the null hypothesis
Step-by-step explanation:
We need to solve a proportion test ( one tail-test ) left test
Normal distribution
p₀ = 63 %
proportion size p = 51 %
sample size n = 114
At 5% level of significance α = 0,05, and with this value we find in z- table z score of z(c) = 1,64 ( critical value )
Test of proportion:
H₀ Null Hypothesis p = p₀
Hₐ Alternate Hypothesis p < p₀
We now compute z(s) as:
z(s) = ( p - p₀ ) / √ p₀q₀/n
z(s) =( 0,51 - 0,63) / √0,63*0,37/114
z(s) = - 0,12 / 0,045
z(s) = - 2,66
We compare z(s) and z(c)
z(s) < z(c) - 2,66 < -1,64
Therefore as z(s) < z(c) z(s) is in the rejection zone we reject the null hypothesis
Which of the following is a point-slope equation of a line that passes through
the points (5,2) and (-1,-6)?
A. y-2-(X-5)
B. y-2-(X-5)
C. y-2 =(x-5
D. V-2--0-5)
Please, check the options of the question. The point-slope equation needs the slope, m, in the equation.
Answer:
The point-slope equation of the points (5,2) and (-1,-6) is
[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex] or,
[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]
which are the same as
[tex] \\ 3y-4x+14 = 0[/tex] , (which is not a point-slope equation, though)
Step-by-step explanation:
The point-slope equation is given by:
[tex] \\ y - y_{1} = m(x - x_{1})[/tex]
Where m is the slope of the line:
[tex] \\ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
Having the points (5,2) and (-1,-6), then
[tex] \\ m = \frac{-6 - 2}{-1 -5}[/tex]
[tex] \\ m = \frac{-8}{-6}[/tex]
[tex] \\ m = \frac{4}{3}[/tex]
Then, the point-slope equation of the points (5,2) and (-1,-6) is
[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex] or
[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]
The below graph represents both lines (they are the same line).
in the diagram ,a and 46° are complementary angles. It is given that a and b are supplementary angles and the angle conjugate to c is 283°. Calculate the values of a,b,c and d. pleaseeeee answer soonn
Answer:
[tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Step-by-step explanation:
It is given that a and 46° are complementary angles.
[tex]a+46^{\circ}=90^{\circ}[/tex]
[tex]a=90^{\circ}-46^{\circ}[/tex]
[tex]a=44^{\circ}[/tex]
It is given that a and b are supplementary angles.
[tex]a+b=180^{\circ}[/tex]
[tex]44^{\circ}+b=180^{\circ}[/tex]
[tex]b=180^{\circ}-44^{\circ}[/tex]
[tex]b=136^{\circ}[/tex]
Angle conjugate to c is 283°.
[tex]c+283^{\circ}=360^{\circ}[/tex]
[tex]c=360^{\circ}-283^{\circ}[/tex]
[tex]c=77^{\circ}[/tex]
Sum of all angles at a point is 360 degrees.
[tex]a+b+c+d+46^{\circ}=360^{\circ}[/tex]
[tex]44^{\circ}+136^{\circ}+77^{\circ}+d+46^{\circ}=360^{\circ}[/tex]
[tex]d+303^{\circ}=360^{\circ}[/tex]
[tex]d=360^{\circ}-303^{\circ}[/tex]
[tex]d=57^{\circ}[/tex]
Therefore, [tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Determine whether the value given below is from a discrete or continuous data set. In a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. Choose the correct answer below. A. The data set is neither continuous nor discrete. B. A continuous data set because there are infinitely many possible values and those values can be counted C. A continuous data set because there are infinitely many possible values and those values cannot be counted D. A discrete data set because there are a finite number of possible values
Answer:
D. A discrete data set because there are a finite number of possible values.
Step-by-step explanation:
Assuming in a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. The value given is from a discrete data set because there are a finite number of possible values.
In Mathematics, a discrete data is a data set in which the number of possible values are either finite or countable.
On the other hand, a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable.
Hence, if 725 couples used the XSORT method and 368 of them had baby girls; this is a discrete data because the values (725 and 368) are finite and can be counted.
[PLEASE HELPP] write an equation that represents the area Bruce covered (y) in terms of the number of tiles he used, x?
Answer:
y=(x/6)
Step-by-step explanation
divide every input by 6 to get the output
find the locus of a point which moves such that it is equidistant from (a,b) and (b,a)
Answer:
the line y = x
Step-by-step explanation:
(a, b ) and (b, a ) are reflections of each other in the line y = x.
They are therefore both equidistant from the line y = x
What is the equation of the line with a slope of 4 and a y-intercept of -5?
Answer:
y = 4x -5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x -5