Answer:
There were 300 students
Step-by-step explanation:
Original * 30 = increase
Add the increase to get the new number
original + increase = 308
original + original*30% = 390
Factor out original number
original ( 1+30%) = 390
Change to decimal form
original ( 1+.30) = 390
original ( 1.30) = 390
Divide by 1.3
original = 390/1.3
=300
Which of the following sequences is arithmetic? A 3, 9, 15, 21, 27, . . . B 3, 9, 17, 27, 39, . . . C 3, 9, 27, 81, 243, . . .
Answer:
A) 3, 9, 15, 21, 27, . . .
Step-by-step explanation:
EDGE 2020
Answer:
The second answer is 6.
Step-by-step explanation:
D=6
PLEASE HURRY! Circle B is shown. Line segments A B and C B are radii. The length of A B is 6. Sector A B C is shaded. The measure of central angle ABC is StartFraction pi Over 2 EndFraction radians. What is the area of the shaded sector? 6Pi units squared 9Pi units squared 18Pi units squared 36Pi units squared
Answer:
(B)[tex]9 \pi $ units squared[/tex]
Step-by-step explanation:
In circle B, AB is one of the radii; and
AB=6
Central Angle of ABC [tex]=\dfrac{\pi}{2}$ radians[/tex]
Now, Area of a Sector
[tex]\text{Area of a Sector}=\dfrac{\theta}{2\pi} \times \pi r^2 \\=\dfrac{\frac{\pi}{2}}{2\pi} \times \pi \times 6^2\\=\dfrac{\pi}{4\pi} \times \pi \times 6^2\\=\dfrac{36}{4} \times \pi \\= 9 \pi $ units squared[/tex]
Answer:
b
Step-by-step explanation:
Given the function f(x) = 2|x + 6|- 4, for what values of x is f(x) = 6?
x=-1, x = 11
x=-1, x=-11
x = 14, x=-26
x = 26. x=-14
Answer:
solution is [tex]\boxed{x=-1,x=-11}[/tex]
Step-by-step explanation:
f(x)=2|x+6|-4
either x+6 is positive and then |x+6|=x+6
or it is negative and |x+6| = -(x+6)=-x-6
case 1: x>=-6
f(x)= 2x+12-4=2x+8
f(x)=6 <=> 2x+8=6 <=> 2x = 6-8=-2 <=> x = -1
case 2: x<=-6
f(x)=-2x-12-4=-2x-16
f(x)=6 <=> -2x-16=6 <=> 2x=-16-6 = -22 <=> x = -11
so to recap, the solutions are x=-1 and x=-11
The value of x from the modulus value function is x = -1 and x = -11
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = 2 | x + 6 | - 4 be equation (1)
On simplifying , we get
when the value of f ( x ) = 6
Substituting the value of f ( x ) = 6 , we get
6 = 2 | x + 6 | - 4
Adding 4 on both sides , we get
2 | x + 6 | = 10
Divide by 2 on both sides , we get
| x + 6 | = 5
And , If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
So , the two values of x are given by
when x + 6 = -5 and x + 6 = 5
x = -1 and x = -11
Hence , the values of x of modulus function is x = -1 and x = -11
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What’s the correct answer for this question ?
Answer:
C
Step-by-step explanation:
It closely resembles to a sphere.
Solve 23 - Q >-3(2-6)
Answer:
q < 11
Step-by-step explanation:
Distribute the -3
23 - q > 12
Add q and subtract 12
q < 11
Step-by-step explanation:
the answer is
q<11
23-q>12
simplify 2x+x+x+2y times 3y times y
Answer:
12 x y² + 6 y³
Step-by-step explanation:
Step(i):-
Given ( 2 x + x + x + 2 y ) times 3 y times y
( 2 x + x + x + 2 y ) × 3 y × y = ( 4 x + 2 y) × 3 y × y = ( 4 x + 2 y) 3 y²
By applying Distributive property
( a + b ) c = a . c + b . c
= 4 x . 3 y² + 2 y . 3 y²
= 12 x y² + 6 y³
Final answer:-
( 2 x + x + x + 2 y ) times 3 y times y = 12 x y² + 6 y³
What is the approximate length of minor arc LM? Round to
the nearest tenth of a centimeter.
12.4 centimeters
15.7 centimeters
31.4 centimeters
36.7 centimeters
Answer:its 15.7
Step-by-step explanation:
Answer:
15.7
Step-by-step explanation:
For a particular disease, the probability of having the disease in a particular population is 0.04. If someone from the population has the disease, the probability that she/he tests positive of this disease is 0.95. If this person does not have the disease, the probability that she/he tests positive is 0.01. What is the probability that a randomly selected person from the population has a positive test result
Answer:
4.76% probability that a randomly selected person from the population has a positive test result
Step-by-step explanation:
We have these following probabilities:
4% probability of having the disease.
If a person has a disease, 95% probability of a positive test.
100-4 = 96% probability a person does not have the disease.
If a person does not have the disease, 1% probability of a positive test.
What is the probability that a randomly selected person from the population has a positive test result
95% of 4% and 1% of 96%. So
p = 0.95*0.04 + 0.01*0.96 = 0.0476
4.76% probability that a randomly selected person from the population has a positive test result
Please help. I’ll mark you as brainliest if correct!
Answer:
[tex]\sqrt{-6} \sqrt{-384}=\sqrt{(-6)(-384)}=\sqrt{2304}=48\\ a=48\\b=0[/tex]
or
[tex]a=-48\\b=0[/tex]
both solutions are correct because root square has two solutions, one positive and one negative.
Answer:
a= -48
b=0
Step-by-step explanation:
[tex]\sqrt[]{-6} = i\sqrt{6}[/tex]
[tex]\sqrt{-384} =i\sqrt{384}[/tex]
[tex](i\sqrt{6} )(i\sqrt{384} )[/tex]
[tex]i^{2} \sqrt{2304}[/tex]
(-1)(48) = -48
a + bi
a= -48
b= 0
Please help me HURRY!!!!!!
What is the solution? X/12+3< or = 7
Answer:
x <= 48
Step-by-step explanation:
Subtract 3 from both sides
x/12 <= 4
Multiply by 12
x <= 48
Given ∠E≅∠P, K is the midpoint of EP Prove EG≅MP
Answer:
∠E≅∠P || Given
∠EKG≅∠PKM || Vertical angles
EK≅KP || Midpoint Theorem
EKG≅PKM || AAS(Angle Angle Side)
EG≅MP || CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Step-by-step explanation:
Four men are to divide K500 equally among them. When the money was given, 20% was taken away.
How much each did the four men receive?
Answer: 20% of 500= 100
So 500-100 = 400
4x100= 400
Step-by-step explanation:
In order to solve for the variable in the equation 2 (x + 3) + 5 x = 3 (2 x minus 1), Jaleesa begins by applying the distributive property, then combines like terms. Which equation is the result of these steps?
Answer:
7x+6 = 6x-3
Step-by-step explanation:
2 (x + 3) + 5 x = 3 (2 x - 1)
Distribute
2x+6+5x = 6x-3
Combine like terms
7x+6 = 6x-3
Answer:
7x + 6 = 6x - 3 Option A
Step-by-step explanation:
Now Jalesa wants to simplify this equation.
Firstly applying the distributive property
Distribute the 2 over the parenthesis and distribute the over the parenthesis
that is,
2*x + 2*3 + 5x = 3*2x - 3*1
2x + 6 + 5x = 6x - 3
After that combine like terms
2x + 5x + 6 = 6x - 3
7x + 6 = 6x - 3
Result is:
7x + 6 = 6x - 3
That's the final answer.
Write the coordinates of the vertices of a triangle A'B'C' that results from a translation of triangle ABC two units to the right and four units down .
Answer:
A'(4,-6) , B'(0,1), C'(-2,-2)
Step-by-step explanation:
From the given graph the coordinates of ΔABC area A (2,-2), B(-2,5) and C(-4,2)
If a translation is applied on ΔABC two units to the right and four units down to create ΔA'B'C'.
Then to find the coordinates of ΔA'B'C' will be we need to apply the translation rule
[tex](x,y)\rightarrow(x+2,y-4)[/tex]
Now, [tex]A(2,-2)\rightarrow A'(2+2,-2-4)=A'(4,-6)[/tex]
[tex]B(-2,5)\rightarrow B'(-2+2,5-4)=B'(0,1)[/tex]
and [tex]C(-4,2)\rightarrow C'(-4+2,2-4)=C'(-2,-2)[/tex]
2y + 5x – z = 4y + 6x solve for y
(show work)
Answer:
y = -z/2 - x/2
Step-by-step explanation:
2y + 5x – z = 4y + 6x
-5x. -5x
2y - z = 4y + x
+z. +z
2y = 4y + z + x
-4y -4y
-2y = z + x
÷-2. ÷-2
y = -z/2 - x/2
The table represents a linear equation.
Which equation correctly uses point (-2, -6) to write the
equation of this line in point-slope form?
х
-4
-2
6
10
y
-11
-6
14
24
y-6 = {(x - 2)
• y-6 = (x - 2)
y +6 = } (x + 2)
y+6= {(x + 2)
Answer:
see below
Step-by-step explanation:
Considering the last two table entries, we can find the slope of the line to be ...
Δy/Δx = (24 -14)/(10 -6) = 10/4 = 5/2
The point-slope form of the equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
For (h, k) = (-2, -6) and m = 5/2, this is ...
y -(-6) = 5/2(x -(-2))
y +6 = 5/2(x +2) . . . . . matches the last choice
Answer:
d is the right choice
Step-by-step explanation:
What is the circumference of the circle? Use 3.14 for Pi. A circle with diameter 33 centimeters.
Answer:
207.24cm
Step-by-step explanation:
Circumference=2pi*r
=2 (3.14)(33)
=207.24cm
The circumference of the circle is 103.62 cm².
Given that, a circle with diameter of 33 cm.
Radius=d/2=16.5 cm.
What is the formula to find the circumference of the circle?The formula to find the circumference of the circle is 2πr.
Now, 2×3.14×16.5=103.62 cm².
Therefore, the circumference of the circle is 103.62 cm².
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Could someone help me with this trigonometry question where you have find the x which is the adjacent. the reference angle is 39 degree and the opposide side is 30 cm.
Answer:
37.047
Step-by-step explanation:
Sin(39) = 30/hyp
Cos(39) = x/hyp
hyp = 30/Sin(39)
and hyp = x/Cos(39)
hyp = hyp
30/Sin(39) = x/Cos(39)
x = 30(Cos(39))/Sin(39)
x is approximately equal to 37.047
Concur Technologies Inc is a large expense-management company located in Redmond Washington. The wall street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city with an avg daily hotel room rate of $198 and an avg amount speny on entertainment, including group meals and tickets for shows sports and other events of $172 in comparison the U.S averages for these two categories were $89 for the room rate and $99 for entertainment the following table shows the average daily hotel room rate and the amount spent on the entertainment for a sample of 9 of the 25 most visited U.S cities Room Rate EntertainmentCity ($) ($)Boston 148 161Denver 96 105Nashville 91 101New orleans 110 142Phoenix 90 100San Diego 102 120San Francisco 136 167San Jose 90 140Tampa 82 98 develop a scatter diagram for these data with the room rate as the independent variablewhat does the scatter diagram developed in part (a.) indicate about the relationship between the two variablesdevelop the least squares estimated regression equationprovide an interpretation for the slope of the estimated regression equationthe avg room rate in Chicago is $128 considerably higher than the U.S avg predict the entertainment expense per day in Chicago
Answer:
Step-by-step explanation:
Hello!
Given the variables
X: daily hotel room rate
Y: amount spent on the entertainment
See second attachment for scatter plot.
The population regression equation is E(Yi)= α + βXi
To estimate the y-intercept and the slope of the regression equation you have to apply the following formulas:
[tex]b= \frac{sum XY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
a= Y[bar]-bX[bar]
n= 9; ∑X= 945; ∑X²= 103325; ∑Y= 1134 ∑Y²= 148804; ∑XY= 123307
X[bar]= ∑X/n= 945/9= 105
Y[bar]= ∑Y/n= 1134/9= 126
[tex]b= \frac{123307-\frac{945*1134}{9} }{103325-\frac{(945)^2}{9} }= 1.03[/tex]
a= 126 - 1.03*105= 17.49
^Y= 17.49 + 1.03Xi
Slope interpretation: The estimated average amount spent on entertainment increases 1.03 every time the daily hotel room rate increases one unit.
If the room rate for Chicago is $128 (X), to predict the mount spent in entertainment (Y) you have replace it in the estimated regression line:
^Y= 17.49 + 1.03Xi= 17.49 + 1.03*128= 149.33
The expected amount spent on entertainment for Chicago is $149.33
I hope this helps!
What are two possible measures of the angle below?
The smaller angle, inside the bold lines, is -90 degrees.
The larger angle, outside the bold lines, is 270 degrees.
Angles can be measured in increments between -90° and 630°.
What angles are created when two lines cross one other?Two straight lines are considered to be intersecting if they come together at the same point. The intersection of two lines is known as the junction point. When two lines intersect, four angles are produced. The sum of the four angles is always 360 degrees.
Two straight lines that cross one other and produce right angles are called perpendicular lines. There are four right angles created when two perpendicular lines cross.
There are two types of angle connections produced when lines intersect:
Congruent opposite angles
Nearby angles are helpful
The information is
Let O (0, 0) be the origin, where the y and x axes must connect.
Thus, the angles on the four quadrants of the axis are produced.
The fourth quadrant's crossing lines create an angle that is given by For, the anticlockwise measure, A = -90°.
B = 360n - 180° for the clockwise measure, and n = 3 in this case.
Hence, when we simplify, we obtain
The second angle has a length of = 630°.
As a result, the angles are 90° and 630°.
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Let:T : ℝ3→ℝ3 be the transformation that projects each vector x=(x1,x2,x3)onto the plane
x2=0,
so
T(x)=(x1 ,0 ,x3). Show that T is a linear transformation.
The first property for T to be linear is
T(0) =_________________________________________________
Check if this property is satisfied for T.T(x1, x2, x3) =(x1, 0,x3)
T(0,0,0) = ( _____ ,_____, _,_______) ,
So, is the first property satisfied?
Yes 0r No
The second property for T to be linear is T(cu+dv)=______(see choices below)___________________________________________for all vectors(u and v)i n the domain of T and all scalars c, d
cT(u)+dT(v)
dT(u)+cT(v)dT(u)−cT(v)
cT(u)−dT(v)
for all vectors
u,
v in the domain of T and all scalars c, d.
Check if this property is satisfied for T. Let u=(u1, u2, u3) and v =(v1, v2, v3).
T(cu+dv)=(cu1+dv1, 0, cu3+dv3) =(cu1, _______, _________) +(dv1, ________, _________)
Factor out the scalar in each ordered triple.
T(cu+dv) = ____(u1, 0, u3) + ______(v1, 0,v3)
Further simplify the previous equation.
T(cu+dv) = c
▼
(choices pick one)
T(v)
T(u)+d
▼
(choices for the arrow above pick one)
T(v)
T(u)
So, is the second property satisfied?
Yes
No
Thus, T ▼
is
is not
linear.
Answer:
Step-by-step explanation:
A linear transformation must satisfy the following properties.
- T(0) = 0.
- For vector a,b then T(a+b) = T(a) + T(b).
- For a vector a and a scalar r, it must happen that T(ra) = rT(a)
In this case we have that T(a,b,c) = (a,0,c).
Note that T(0) = T(0,0,0) = (0,0,0) = 0. So, the first property holds.
Let [tex] a=(a_1,a_2,a_3), b=(b_1,b_2,b_3) [/tex]. Then
[tex]T(a+b) = T((a_1+b_1,a_2+b_2,a_3+b_3)) = (a_1+b_1,0,a_3+b_3) = (a_1,0,a_3)+(b_1,0,b_3) = T(a) + T(b)[/tex]
So the second property holds.
Finally, let r be a scalar and let [tex] a=(a_1,a_2,a_3)[/tex]. Then
[tex] T(ra) = T((ra_1,ra_2,ra_3)) = (ra_1,0,ra_3) = r(a_1,0,a_3)= rT(a)[/tex]
So, the three properties hold, and therefore, T is a linear transformation.
It is true that T represents a linear transformation
How to determine if T is a linear transformationA linear transformation is such that have the following properties
T(0) = 0.If u and v are vectors, then T(u+v) = T(u) + T(v).If u is a vector and r is a scalar, then T(ru) = rT(u)For the first property, we have:
T(x1,x2,x3) = (x1,0,x3)
The above property becomes
T(0) = T(0,0,0)
T(0) = (0,0,0)
T(0)= 0.
So, we can conclude that the first property of the linear transformation is satisfied
For the second property, we make use of the following:
u = (u1, u2, u3) and b = (v1,v2,v3)
The above property becomes
T(u + v) = T(u1 + v1, u2 + v2, u3 + v3)
Expand
T(u + v) = T(u1 + v1, 0, u3 + v3)
Expand
T(u + v) = (u1,0,u3) + (v1, 0, v3)
Simplify
T(u + v) = T(u) + T(v)
The above means that the second property is also satisfied
Recall that:
u = (u1, u2, u3)
So, we have:
T(ru) = (ru1, ru2, ru3)
Where r is a scalar
Expand
T(ru) = (ru1, 0, ru3)
Further, expand
T(ru) = r(u1, 0, u3)
So, we have:
T(ru) = rT(u)
The above means that, the third property is also satisfied
Hence, T represents a linear transformation
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Lesson 10 congruent triangles unit test
Answer:
Step-by-step explanation:
Wheres the question??
In football seasons, a team gets 3 points for a win, 1 point for a draw and 0 points for a
loss. In a particular season, a team played 34 games and lost 6 games. If the team had a
total of 70 points at the end of the season, what is the difference between games won and lost
Answer:
The difference between the games won and lost = 21 - 6 =15
Step-by-step explanation:
According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.
A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.
The team played a total of 34 games.
Total games played = 34
Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,
34 - 6 = 28 games was won or draw
Let
the number of games won = x
the number of game drew = y
3x + y = 70.............(i)
x + y = 28................(ii)
x = 28 - y
insert the value of x in equation(i)
3(28 - y) + y = 70
84 - 3y + y = 70
84 - 70 = 3y -y
14 = 2y
divide both sides by 2
y = 14/2
y = 7
insert the value of y in equation(ii)
x + y = 28
x = 28 - 7
x = 21
The team won 21 games , drew 7 games and lost 6 games.
The difference between the games won and lost = 21 - 6 =15
What is the difference?
х
4
x2-2x-15 x² + 2x-35
x2 + 3x+12
(x-3)(x-5)(x+7)
x(x+3-12)
(x+3)(x-5)(x+7)
x2 + 3x+12
(x+3)(x-5)(x+7)
x2 + 3x-12
(x+3)(x-5)(x+7)
The difference of the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the first equation be P = x / ( x² - 2x - 15 )
Let the second equation be Q = 4 / x² + 2x - 35 )
Now , A = P - Q
On simplifying , we get
A = x / ( x² - 2x - 15 ) - 4 / x² + 2x - 35 )
Taking the LCM , we get
A = x ( x + 7 ) - 4 ( x + 3 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = x² + 7x - 4x + 12 / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Therefore , the value of A is ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Hence , the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
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Gary buys a 3 1/2 pound bag of dog food every 3 weeks. Gary feeds his dog the same amount of food each day. Which expression can Gary use to determine the number of pounds of dog food his dog eats each year?
Answer:
7/2 x 52/3
Step-by-step explanation:
Steps:
Since 1 year = 52 weeks
52*7/2*3= 7/2*52/3
Since 1 year equal 52 weeks meaning we have to times 52 by 7/2 then times by 3 the weeks. The answer is below.
Answer: 7/2 x 52/3
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Hope this helps.
A random sample pulled 43 catfish from a large lake. They were marked and released. A second sample pulled out 88 catfish. Seventeen had been marked. Calculate the estimated population
Answer: 114
Step-by-step explanation: You have 43 new catfish then you catch 88 but 17 of them have already been marked so you do not want to count those in the estimated population again because they have already been counted so you take 88 minus 17 and you get 71 new fish. So then you add the first new sample of fish 43 and then you add the second new sample of fish 71 and then you get 114
42,000 as a multipul of a power of 10
Answer:
[tex] 4.2 \times {10}^{4} [/tex]
Step-by-step explanation:
[tex]42000 = 4.2000 \times \times {10}^{4} \\ = 4.2 \times {10}^{4} [/tex]
A researcher conducts two studies on the effectiveness of a peer mentoring program. Self-evaluation ratings among participants before, during, and after the program were measured in both studies. In Study 1, 12 participants were observed, and in Study 2, 16 participants were observed. If Fobt = 3.42 in both studies, then in which study will the decision be to reject the null hypothesis at α= 0.05 level of significance?
Answer:
Study 2
Step-by-step explanation:
Okay, so in this question we are given the data or parameters or information Below;
=>" two studies were conducted on the effectiveness of a peer mentoring program."
=> "Self-evaluation ratings among participants before, during, and after the program were measured in both studies."
=> In Study 1, 12 participants were observed"
=> "Study 2, 16 participants were observed."
=> " If Fobt = 3.42 in both studies"
Say Vo = study 2 and V1 = study 1.
Hence, Vo: not effective.
V1 = effective.
The study in which the decision will be to reject the null hypothesis at α= 0.05 level of significance is the STUDY 2.
This is because the value of F > f-critical.
how do you add 9 in 1 6 + 2 1/12
Step-by-step explanation:
9 + 1/6 + 2 1/12
9 + 2.25
11.25
