If [tex]D>0[/tex] then [tex]x_1,x_2\in\mathbb{R}[/tex].
If [tex]D=0[/tex] then [tex]x_1=x_2\wedge x_1,x_2\in\mathbb{R}[/tex].
If [tex]D<0[/tex] then [tex]x_1,x_2\in\mathbb{C}[/tex].
Hope this helps.
−p(51+z)=dz+84 solve for z
[tex]\text{Solve for z:}\\\\-p(51+z)=dz+84\\\\\text{Use the distributive property}\\\\-51p-pz=dz+84\\\\\text{Add 51p to both sides}\\\\-pz=51p+dz+84\\\\\text{Subtract dz from both sides}\\\\-pz-dz=51p+84\\\\\text{Factor out z}\\\\z(-d-p)=51p+84\\\\\text{Divide both sides by (-d - p)}\\\\z=\frac{51p+84}{(-d-p)}\\\\\text{The denominator shouldn't be zero, so we have to make it positive}\\\\\boxed{z=\frac{-51p-84}{d+p}\,\,or\,\,z=-\frac{51p+84}{d+p}}[/tex]
Answer:
[tex] \boxed{\sf z = \frac{ - 51p - 84}{ p + d} \ \ \ OR \ \ \ z = - \frac{51p + 84}{ p + d} } [/tex]
Step-by-step explanation:
[tex] \sf solve \: for \: z : \\ \sf \implies −p(51+z)=dz+84 \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \sf \implies - 51p - pz = dz + 84 \\ \\ \sf Subtract \: d z - 51 p \: from \: both \: sides: \\ \sf \implies - 51p - pz - (dz - 51p)= dz + 84 - (dz - 51p) \\ \\ \sf - (dz - 51p) = - dz + 51p : \\ \sf \implies - 51p - pz - dz + 51p= dz + 84 - dz + 51p \\ \\ \sf - 51p + 51p = 0 : \\ \sf \implies - pz - dz = dz + 84 - dz + 51p \\ \\ \sf dz - dz = 0 : \\ \sf \implies - pz - dz = 84 + 51p \\ \\ \sf \implies z( - p - d) = 84 + 51p \\ \\ \sf Divide \: both \: sides \: by \: - p - d: \\ \sf \implies z = \frac{51p + 84}{ - p - d} \\ \\ \sf \implies z = \frac{51p + 84}{ -( p + d)} \\ \\ \sf \implies z = \frac{ - (51p + 84)}{ p + d} \\ \\ \sf \implies z = \frac{ - 51p - 84}{ p + d} [/tex]
Liam works at a zoo. He was looking at some data showing the masses of their 5555 African elephants. The mean mass of the elephants was 3,800 kg3{,}800\,{\text{kg}}3,800kg3, comma, 800, start text, k, g, end text, and the median mass was 3,600 kg3{,}600\,{\text{kg}}3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed 2,700 kg2{,}700\,{\text{kg}}2,700kg2, comma, 700, start text, k, g, end text. Lola then got very sick and lost weight until her mass reached 1,800 kg1{,}800\,{\text{kg}}1,800kg1, comma, 800, start text, k, g, end text. How will Lola's mass decreasing affect the mean and median? Choose 1 answer: Choose 1 answer: (Choice A) A Both the mean and median will decrease. (Choice B) B The median will decrease, and the mean will stay the same. (Choice C) C The mean will decrease, and the median will stay the same. (Choice D) D The mean will decrease, and the median will increase.
Answer:
The mean will decrease, and the median will stay the same.
Step-by-step explanation:
Khan Academy
Answer:
C- The mean will decrease, and the median will stay the same
Step-by-step explanation:
I got it right in Khan. Have a great day!
3) BRAINLIEST & 10 + POINTS! :)
Answer:
33,175.21/radians/sec
Step-by-step explanation:
22 rev/sec x 60sec/1 min x 4ft x2 pi/1 rev
22 x 60 = 1320
1320 x 4 = 5280
2 x pi = 6.2831853072
5280 x 6.2831853072= 33,175.218421884
A surveyor is trying to find the height of a hill. He/she takes a ‘sight’ on the top of the hill and find that the angle of elevation is 40°. He/she move a distance of 150 metres on level ground directly away from the hill and takes a second ‘sight’. From this point, the angle of elevation is 22°. Find the height of the hill, correct to 1 d.p.
Answer:
The height of the hill is 116.9 meters.
Step-by-step explanation:
The diagram depicting this problem is drawn and attached below.
From Triangle ABC
[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]
From Triangle XBC
[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]
Therefore:
[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]
Therefore, the height of the hill
[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]
The height of the hill is 116.9 meters.
what is the the square route of 98985947875875847688748687587865758 add 9547589777778747 to the answer.
Answer:
800090908988
Step-by-step explanation:
the vertices of ABC are A(-2, 2), (6,2), and (0,8). Its area is _ square units.
Answer:
T = 24 so it would be 24x24=576 square units
Step-by-step explanation:
How did we calculate this triangle?
The calculation of the triangle progress in two phases. The first phase is such that we try to calculate all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase is the calculation of other characteristics of the triangle, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).
Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.
Answer:
m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)
Step-by-step explanation:
Use sin to solve m∠A
sin x = 12/42 Simplify
sin x = 0.2857 Use the negative sin to solve for x
sin^-1 x = 17 degrees
Add together all of the angle measures to solve for m∠B
17 + 90 + x = 180 Add
107 + x = 180
-107 -107
x = 73 degrees
Use Pythagorean Theorem to solve for b
12^2 + x^2 = 42^2 Simplify
144 + x^2 = 1764
-144 -144
x^2 = 1620 Take the square root of both sides
x = 40
How many ways can 8 people stand in a line if Alice and Bob refuse to stand next to each other?
====================================================
Explanation:
We have 8 people to start with. If we remove Alice and Bob, and replace them with Charlie (who will be a stand in for both people), then we have 8-2+1 = 7 people in this line. There are 7! = 7*6*5*4*3*2*1 = 5040 different permutations or line orderings for these seven people.
For any given permutation, replace Charlie with Alice and Bob. There are two ways to do this for any ordering. We could have Alice in front of Bob, or Bob in front of Alice. So there are 2 times as many permutations compared to 5040. In other words, there are 2*5040 = 10,080 different permutations where Alice and Bob are standing together.
This is out of 8! = 8*7*6*5*4*3*2*1 = 40,320 different permutations overall of arranging 8 people in a line.
This means there are 40,320 - 10,080 = 30,240 different ways to arrange 8 people such that Alice and Bob are not standing together.
In summary, the idea is to find out how many ways there are to have Alice and Bob together. Then we subtract that result from the total number of ways to arrange 8 people to get our final answer.
Answer:
30240 got it from a teacher :>
Step-by-step explanation:
RSM XD
Find the values of a and b in the rhombus. Solve for the value of c, if c=a+b.
Answer:
a = 5
b = 1.3
c = 6.3
Step-by-step explanation:
To find the values of a, b and C respectively, let's find a first by recalling that the diagonals of a rhombus are perpendicular to each other.
Therefore, the angle given as (14a + 20) = 90°
Solve for a
14a + 20 = 90
14a = 90 - 20
14a = 70
a = 70/14
a = 5
==>To find b, also recall that all sides of a rhombus are equal.
Therefore 3b + 4 = 13b - 9
Solve for b
4 + 9 = 13b - 3b
13 = 10b
13/10 = b
b = 1.3
==>Find value of c
c = a + b
c = 5 + 1.3
c = 6.3
What are the angle measurements of 1,2,3 & 4 for #3 & the measurements for 1 &2 on #4?
Step-by-step explanation:
iii=90
41+i=90(opposite angle)
i=90-41
i=49
26+ii+49+41=180(straight line angle)
116+ii=180
ii=180-116
ii=64
50+25+iv=26+64(opposite angle)
75+iv=90
iv=90-75
iv=15
55+i+55=180(straight line angle)
110+i=180
i=180-110
i=70
ii=55(alternative angle)
Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01? Recent 78 91 89 78 58 99 62 87 70 89 82 84 56 81 75 101 61 Past 90 87 93 94 65 86 84 92 88 91 91 91
Answer:
p value = 0.039
t = - 2.169
Step-by-step explanation:
Applying the null and alternate hypothesis
[tex]H_{0} : U1 = U2[/tex]
[tex]H_{\alpha } : U1 \neq U2[/tex]
using excel worksheet to calculate for ( t and p )
t = -2.169
p = 0.039
from the results obtained
The conclusion is affected by the significance level because : 0.1 < p > 0.01
so when the significance level is = 0.1 the Null hypothesis is rejected and we can say the mean time interval will change while
if the significance level = 0.01 the Null hypothesis is accepted and we can not say the mean time interval has changed because the p -value is greater than 0.01
attached is the excel solution
The data shows that the conclusion is affected by whether the significance level because 0.1 < p > 0.01.
What is a significance level?A significance level simply means the probability that the event could have taken place due to chance.
In this case, it should be noted that from the Excel worksheet, the value of t is -2.169 and the value of p is 0.039.
In this case, the conclusion is affected by the significance level because 0.1 is less than p which is greater than 0.01. Therefore, the null hypothesis is rejected.
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El perímetro de un rectángulo es 28cm, uno de los lados es 6cm más que el otro lado. Hallar el mayor lado del rectángulo.
Answer: El mayor lado del rectangulo tiene 10cm
Step-by-step explanation:
El perímetro de un rectángulo puede escribirse como:
P = 2*L + 2*A
Donde L es el largo y A es el ancho.
Sabemos que uno de los lados es 6cm mas largo que el otro, entonces podemos escribir:
L = A + 6cm.
P = 28cm = 2*L + 2*A
podemos reemplazar la primera ecuación en la segunda:
28cm = 2*(A + 6cm) + 2*A
28cm = 12cm + 4*A
28cm - 12cm = 4*A
16cm/4 = A
4cm = A.
Entonces el ancho es 4 cm, y el largo es L = 4cm + 6cm = 10cm
Un rectángulo es una figura geométrica que tiene 4 lados. Un rectángulo también se puede llamar cuadrilátero. En un rectángulo, un lado es más largo que el otro.
El lado más largo de un rectángulo se llama largo, mientras que el lado más corto se llama ancho.
El lado más largo del rectángulo (longitud) mide 10 cm.
La fórmula para el perímetro de un rectángulo se da como:
2L + 2W = P
Dónde:
P = 28cm
L = longitud
W = ancho
La pregunta dice que un lado mide 6 cm más que el otro. Esto significa que la longitud es 6 cm más que la anchura. Por lo tanto, podemos representar matemáticamente la declaración anterior:
L = W + 6
Sustituimos W + 6 por L en la fórmula
2 (W + 6) + 2W = 28
2W + 12 + 2W = 28
Recopilar términos semejantes
2 W + 2 W = 28 - 12
4W = 16
Dividir ambos lados entre 4
4W / 4 = 16/4
Ancho = 4 cm
El ancho del rectángulo es de 4 cm.
Debemos encontrar el lado más largo que es la longitud. Por eso:
L = W + 6
L = 4 + 6
L = 10 cm.
Por lo tanto, el lado más largo del rectángulo (Longitud) es de 10 cm.
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Help me with this please I will give you Brainliest
3. A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles. (20 points)
a. What is the plane's speed in miles per hour?
b. At this rate, how many miles can it travel in 10 hours?
Answer:
a. The plane's speed in mph is 560
b. At this rate, the plane can travel 5,600 miles in 10 hours.
Step-by-step explanation:
In order to find the planes speed in mph, some simple arithmetic must be done and you should divide 3,360 by 6. Now that you have determined that 3,360/6 equals 560, you know that in order to figure out how many miles the plane can travel in 10 hours, all you must do is multiply 560 by 10 which equals 5,600.
Answer:
A. 560B. 5,600Step-by-step explanation:
A. = 3,360 / 6 = 560B. = 560 x 10 = 5,600[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!
Answer:
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
Step-by-step explanation:
[tex]\frac{5x-11}{2x^2+x-6}[/tex]
Factor the denominator.
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
The fraction cannot be simplified further.
Answer:
[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]solution,
[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]
Hope this helps..
A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?
Answer:
41°, 56°, 83°
Step-by-step explanation:
We can find the largest angle from the law of cosines:
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab))
C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°
Then the second-largest angle can be found the same way:
B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°
Of course the third angle is the difference between the sum of these and 180°:
A = 180° -82.8192° -55.7711° = 41.4096°
Rounded to the nearest degree, ...
the angles of the triangle are 41°, 56°, 83°.
1) Which statement contains an exact number? A) A gross of paper contains 144 sheets. B) One sheet of paper is 0.0042 inches thick. C) One sheet of paper measures 8.5 x 11 inches. D) A ream of medium weight paper weighs 20 pounds. Answer: A
Answer:
B) One sheet of paper is 0.0042 inches thick
Step-by-step explanation:
All the other values are not give from just a sheet of paper, and/or they are either a cumulative value, or values that will be used to calculate another value
Only option B defines a value for a unit of paper, and the value is definite.
Option A indicates the number in a group (gross)
Option C shows two values that can be used to calculate one value; the area.
Option D indicates an accumulated value of weight.
Hurry plz!!!!
Which linear inequality is represented by the graph?
O y> 2x + 3
O y < 2x + 3
Oy> -2x + 3
O y < -2x + 3
Option 4 is the correct choice.
We have a graph that represents a inequality.
We have to determine which of the following given inequalities is plotted in the graph
What is an Inequality?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
The straight line is not uniform but dashed. Hence, the type of inequality will be strict (either < or > ).
The y - intercept of the line is at : + 3.
The slope of the line will be = [tex]\frac{3 -0}{0-1.5} = -2[/tex]
Now, it is clear from the above discussion that the we are left with two possible options - option C and D. Consider a point (0, 0) and check both the inequalities mentioned in option C and D.
For y > -2x + 3 at (0,0)
0 > 0 + 3
0 > 3
which is false.
For y < -2x + 3 at (0,0)
0 < 0 + 3
0 < 3
Which is true.
Hence, the inequality represented by the graph is : y < - 2x + 3
Therefore, Option 4 is the correct choice.
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A caterer receives an order for 25 sandwiches, 1 gallon of soup and 3 dozen cookies.
His food cost equals 28% and his labor and miscellaneous costs is 32%. What
percentage is his profit margin? a. 17%
b. 40%
c. 33%
d. 51%
Answer:
b. 40%
Step-by-step explanation:
The price he sells at is 100%.
His costs are 28% and 32%.
Total costs = 28% + 32% = 60%
His profit is
100% - 60% = 40%
Answer: b. 40%
Help me plzzzzz!!!!
Answer:124
Step-by-step explanation:
2x + 8 + x - 2 = 180
Add like terms
3x + 6 = 180
Subtract the 6 from both sides
3x + 6 - 6 = 180 - 6
3x = 174
Divide by 3
x = 58
Now we have to find the measure of angle ACD
2(58) + 8 = 124
What is the answer? ABCD ~ EFGH
Answer:
x = 3.6
Step-by-step explanation:
In similar polygons, corresponding sides are in same ratio
[tex]\frac{AB}{EF}=\frac{AD}{EH}\\\\\frac{3}{2}=\frac{x}{2.4}\\\\\frac{3}{2}*2.4=x\\[/tex]
3 * 1.2 = x
x = 3.6
Do class limits and class marks make sense for qualitative data classes? Explain
your answer.
NEED QUICKLY
Answer: NO, class limits and class marks are not meaningful to qualitative data.
Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.
Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.
help me please for the love of god what is the answer
Answer:
150 Degrees
Step-by-step explanation:
The angle next to the 30 deg. is the same angle as x because the lines are parallel.
So we do 180 - 30 = 150
So x = 150
Answer:
B. 150
Step-by-step explanation:
Opposite angles are equal so 180-30=150. Points A X D and C add up to 180 degrees.
Hope this helps!!
Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?
Answer:
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Uniform distribution from 0 to 4.8 seconds.
This means that [tex]a = 0, b = 4.8[/tex]
61% of the time a person will wait at least how long before the wave crashes in?
This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]
[tex]x = 4.8*0.39[/tex]
[tex]x = 1.872[/tex]
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Han and Clare are stuffing envelopes. Han can stuff 20 envelopes in one minute, and
Clare can stuff 10 envelopes in one minute. They start working together on a pile of
1,000 envelopes. How long does it take them to finish the pile?
Answer:
33 1/2 min
Step-by-step explanation:
Billy takes out a $2400 discounted loan using a simple interest rate of 8% for a period of 18 months. What is the effective interest rate?
Answer:
9.1
Step-by-step explanation:
To calculate the total interest payable, we use the formula
I=P0rt,
and substituting our values yields
I=$2,400×0.08×1812=$288.
Therefore the total amount he receives at loan drawdown is $2,400−$288=$2,112. To calculate the effective interest rate, we use to formula
A=P0(1+ret).
In this instance we have A=$2,400,P0=$2,112 (redefined from the value above) and t=1.5. We substitute into the formula to get
$2,400=$2,112(1+1.5re).
Solve for re.
24002112=1+1.5re
24002112−1=1.5re
24002112−11.5=re
This gives re=0.0909⋯=9.0909…%, which is 9.1%
The surface area of a sphere is 3000 m2. What is the volume of the sphere
Answer:
The answer is
15448 cm³Step-by-step explanation:
Volume of a sphere is
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]
where r is the radius
From the question in order to find the volume of the sphere we must first find the radius of the sphere using it's surface area
Surface area of sphere = 4πr²
3000 = 4πr²
Divide both sides by 4π
r² = 750/π
r = 15. 45 cm
Now the volume of the sphere is
[tex]V = \frac{4}{3} \pi( {15 .45})^{3} [/tex]
[tex] = 15448.06[/tex]= 15448 cm³ to the nearest whole numberHope this helps you
Answer:
[tex]= 15450.96 {m}^{3} [/tex]
Step-by-step explanation:
[tex]v = \frac{ {area}^{ \frac{2}{3} } }{6 \sqrt{\pi} } \\ = \frac{ {3000}^{ \frac{2}{3} } }{6 \sqrt{\pi} } \\ = 15450.96 {m}^{3} [/tex]
There is no overlap between the graphs of y< x+ 2 and y> x-2.
True or False
Someone help please
Answer:I think it's TRUE not sure
Step-by-step explanation:
Find the pattern and fill in the missing numbers: 1, 1, 2, 3, 5, 8, __, __, 34, 55
Answer:
5+8=13, and 13+8=21, 13+21=34
Step-by-step explanation:
fibonacci sequence...
1+1=2
1+2=3
2+3=5, etc...
sooo,
5+8=13, and 13+8=21, 13+21=34
The missing numbers in the pattern is 13 and 21.
What is pattern of numbers?A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
The given sequence is 1, 1, 2, 3, 5, 8, __, __, 34, 55.
Here,
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
13+21=34
21+34=55
Therefore, the missing numbers in the pattern is 13 and 21.
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A sample of 1600 computer chips revealed that 43% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 41% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.
Answer: The value of the test statistic is z= 1.63 .
Step-by-step explanation:
Test statistic for proportion :
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
, where p =population proportion.
[tex]\hat{p}[/tex] = sample proportion
n= sample size.
Let p be the proportion of chips do not fail in the first 1000 hours of their use.
As per given, we have
[tex]p=0.41\\ n= 1600\\\hat{p}=0.43[/tex]
Then, required test statistic would be
[tex]z=\dfrac{0.43-0.41}{\sqrt{\dfrac{0.41(1-0.41)}{1600}}}\\\\=\dfrac{0.02}{\sqrt{0.0001511875}}\\\\\approx\dfrac{0.02}{0.0123}\approx1.63[/tex]
Hence, the value of the test statistic is z= 1.63 .