Answer:
2x + y = -10
Step-by-step explanation:
Simplify −2(x+7)
y−4=−2x−14
Move all terms containing variables to the left side of the equation.
2x+y−4= −14
Move all terms not containing a variable to the right side of the equation.
2x + y = −10
Hope this helps
Samantha has 5 granola bars. She wants to give 1/3 of a granola bar to each friend. Which expression can she use to find the number of friends to whom she can give granola bars?
Answer:
5/(1/3)
Step-by-step explanation:
She has 5 granola bars and gives 1/3 of one to each of her friends. To find how many friends she can give it to, divide 5 by 1/3. You would get a total of 15 friends that you can give granola bars to. The question is asking for an expression so the expression would be 5/(1/3) or 5*3
Answer:
1/3 x = 5
x=15
Step-by-step explanation:
You’re multiplying 1/3 times the number of friends (x), and then multiplying both sides by the reciprocal to solve for x
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Answer:
acute isosceles triangle
vertex angle, y = 44.0 degrees. (smallest angle)
Step-by-step explanation:
If the sides are in the ratio 4:4:3,
two of the sides have equal lengths, so it is an isosceles triangle.
Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.
To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.
The base angle x is given by the ratio
cos(x) = 1.5/4 = 3/8
Consequently the base angle is arccos(3/8) = 68.0 degrees.
The vertex angle equals twice the complement of 68.0
vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)
We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 175 had kids. Based on this, construct a 99% confidence interval for the proportion p of adult residents who are parents in this county. Express your answer in tri-inequality form. Give your answers as decimals, to three places.
Answer:
The 99% confidence interval is [tex]0.3003 < I < 0.3997[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 500[/tex]
The the number that are parents x = 175
The proportion of parents is mathematically represented as
[tex]\r p = \frac{x}{n}[/tex]
substituting values
[tex]\r p = \frac{175}{500}[/tex]
[tex]\r p = 0.35[/tex]
The level of confidence is given as 99% which implies that the level of significance is
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha =[/tex]1%
[tex]\alpha = 0.01[/tex]
The critical value for this level of significance is obtained from the table of critical value as
[tex]t_{x, \alpha } = t_{175, 0.05} = 2.33[/tex]
Generally the margin of error is mathematically evaluated as
[tex]M =\frac{ t_{175, 0.01 } * \sqrt{\r p (1-\r p)} }{\sqrt{n} }[/tex]
substituting values
[tex]M =\frac{ 2.33 * \sqrt{\r 0.35 (1-0.35)} }{\sqrt{500} }[/tex]
[tex]M = 0.0497[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]I = \r p \pm M[/tex]
[tex]\r p -M < I < \r p + M[/tex]
substituting values
[tex]0.35 -0.0497 < I < 0.35 + 0.0497[/tex]
[tex]0.3003 < I < 0.3997[/tex]
(very urgent) will gave 20 pts
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that
a) the bit string has exactly two 1s;
b) the bit string begins and ends with 0;
c) the bit string has the sum of its digits equal to seven;
d) the bit string has more 0s than 1s;
e) the bit string has exactly two 1s, given that the string begins with a 1.
Answer:
a. 45/1024
b. 1/4
c. 15/128
d. 193/512
e. 9/256
Step-by-step explanation:
Here, each position can be either a 0 or a 1.
So, total number of strings possible = 2^10 = 1024
a) For strings that have exactly two 1's,
it means there must also be exactly eight 0's.
Thus, total number of such strings possible
10!/2!8!=45
Thus, probability is
45/1024
b) Here, we have fixed the 1st and the last positions, and eight positions are available.
Each of these 8 positions can take either a 0 or a 1.
Thus, total number of such strings possible
=2^8=256
Thus, probability is
256/1024 = 1/4
c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string.
Also, it means there must also be exactly three 0's
Thus, total number of such strings possible
10!/7!3!=120
Thus, probability
120/1024 = 15/128
d) Following are the possibilities :
There are six 0's, four 1's :
So, number of strings
10!/6!4!=210
There are seven 0's, three 1's :
So, number of strings
10!/7!3!=120
There are eight 0's, two 1's :
So, number of strings
10!/8!2!=45
There are nine 0's, one 1's :
So, number of strings
10!/9!1!=10
There are ten 0's, zero 1's :
So, number of strings
10!/10!0!=1
Thus, total number of string possible
= 210 + 120 + 45 + 10 + 1
= 386
Thus, probability is
386/1024 = 193/512
e) Here, we have fixed the starting position, so 9 positions remain.
In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.
Thus, total number of such strings possible
9!/2!7!=36
Thus, probability is
36/1024 = 9/256
What is the equation of the line whose y-intercept is 3 and slope is 1? A.y = x + 3 B.y = 3x + 1 C.y = x - 3
Answer:
The answer is option A
Step-by-step explanation:
Equation of a line is y = mx + b
where
m is the slope
b is the y intercept
From the question
b / y intercept = 3
m / slope = 1
Substitute these values into the below equation
y = mx + b
We have the answer as
y = x + 3
Hope this helps you
Answer: A. Y= x+3
Step-by-step explanation: since the value of the slope is 1 it would go next to the x but x is also equal to 1x. And you add 3 since the y intercept is 3 and the format of the equation is y equals slope plus the y intercept hope this helps
Use multiplication or division of power series to find the first three nonzero terms in the maclaurin series for the given function. (Enter your answers as a comma-separated list.)
y=(e^-x^2)cosx
Answer:
1 , - ( 3x^2/2), + (25x^4/24).
Step-by-step explanation:
We are given the following information:
y = (e^-x^2)cosx.
STEP ONE: Write out the power series out(either by deriving it or otherwise).
If you check the power series table, you will get the power series for the two functions that is cos x and e^-x^2.
e^-x^2 = 1 - (x^2) + ( x^4/2! ) - (x^6/3!) +...
Cos x = 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...
STEP TWO: Multiply both the power series of e^-x^2 and Cos x together because we are to determine or find the first three nonzero terms in the maclaurin series for the given function.
1 - (x^2) + ( x^4/2! ) - (x^6/3!) +... - 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...
= 1 - ( 3x^2/2) + (25x^4/24).
= 1, - ( 3x^2/2) , + (25x^4/24) => comma- separated list.
[tex]3\sqrt{2} - 5 \sqrt{18}[/tex] Help is appreciated!! Thank you so much! :D ❤❤
Given: (in picture as I cannot type it like that.) Name the postulate or theorem you can use to prove: (also in the picture) A. HL Theorem B. AAS Theorem C. SAS Postulate D. ASA Postulate
Answer:
You need to use the AAS (angle angle side) congruency theorem
Step-by-step explanation:
youre welcome!!!
Answer:
The Angle-Angle-Side Postulate (AAS)
Step-by-step explanation:
It is given that angle 1 and 2 are equivalent so that is angle #1
It is given that angle 3 and 4 are also equivalent so that is angle #2
And finally, it is given that side TS and side TR are equivalent giving you that last side you need to prove the type of Postulate it is
If this helped, please consider giving me brainliest, it will help me a lot
Have a good day! :)
144 + h^2 = 225 WHAT THE HECK DOES ^ MEAN!???
Answer:
h^2 means h²
(h squared)
Step-by-step explanation:
Step 1: Write equation
144 + h² = 225
Step 2: Subtract 144 on both sides
h² = 81
Step 3: Take square root
√h² = √81
h = 9
What is the range of y=log2(x-6)
Answer:
6<y<∞
Step-by-step explanation:
Logarithmic curves can never go left to 0 and go on forever to the right.
x=6 would make the function 0, so 6 is the lower limit and infinity would be the upper limit.
In a sequence, the 40th term is 70, the 41st term is 72 and the 42nd term is 74.
a) State the term-to-term rule
b) Work out the first term
c) Work out the 80th term
Answer:
term to term rule is +2
The first term is -8
80th term is 150
Step-by-step explanation:
70 to 72 is adding 2
72 to 74 is adding 2
term to term rule is +2
The equation for a sequence like this is
xn = a + d(n−1)
where n is the term number a is the first term and d is the term to term rule
Using the 40th term is 70
70 = a + 2( 40-1)
70 = a + 2( 39)
70 = a + 78
Subtract 78 from each side
-8 = a
The first term is -8
80th term
xn = a + d(n−1)
x80 = -8 +2 (80-1)
= -8+2(79)
= -8+158
= 150
What is the missing side lenght in the triangle below?
Answer:
45
Step-by-step explanation:
Let's call the missing side x
This is a right triangle and in right triangles the square length of hypotenuse is equal to sum of square length of base and side lengths
53^2 = 28^2 + x^2
x = 45
Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .
Answer:
2
Step-by-step explanation:
We are given that a graph which represents f(x).
Interval:[-4,-1]
We have to find the average rate of change of the function f(x).
From the graph we can see that
f(-4)=-3
f(-1)=3
We know that the average rate of change of the function
Average rate =[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using the formula
Average rate of change of f=[tex]\frac{3-(-3)}{-1-(-4)}[/tex]
Average rate of change of f=[tex]\frac{6}{3}=2[/tex]
A smartphone company found in a survey that 6% of people did not own a smartphone, 15% owned a smartphone only, 26% owned a smartphone and only a tablet, 32% owned a smartphone and only a computer, and 21% owned all three. If a person were selected at random, what is the probability that the person would own a smartphone only or a smartphone and computer
Answer:
47%
Step-by-step explanation:
we are required to find the probability to randomly select from the union of those who own a smartphone only and those who own a smartphone and computer.
an addition of the subsets cover the entire set.
6 + 15 + 26 + 32 + 21 = 100%
let
p(A)= probability of smartphone only
p(B) = probability of smartphone and computer
p(A U B) = P(A) + P(B)
= 15% + 32%
= 47%
In the equation, the value of a is:
Answer:
Please check if the answer is a = 4 or not
What is the quotient in polynomial form?
Answer:
Step-by-step explanation:
We are given the polynomial [tex]x^3+2^2-2x+3[/tex] and we are dividing by (x+3). So by performing one step of synthetic division we get
1 2 -2 3|-3
-3 3 -3
1 -1 1 0
So the quotient in polynomial form is [tex]x^2-x+1[/tex]
Hommie Delicacies produces two products (Orapine and Banango) from a joint process. The joint cost of production is GH¢80,000. Five thousand units of Orapine can be sold at split-off for GH¢20 per unit or processed further at an additional cost of GH¢20,000 and sold for GH¢25 per unit. Ten thousand units of Banango can be sold at split-off for GH¢15 per unit or processed further at an additional cost of GH¢20,000 and sold for GH¢16 per unit. Advise Hommie on further processing each of the products?
Answer:
Orapine: do additional processingBanango: no additional processingStep-by-step explanation:
The processing cost of split-off Orapine units is ...
GH¢20,000/(5000 units) = GH¢4/unit
The increase in revenue from the further processing is ...
GH¢25 -GH¢20 = GH¢5
The increased processing cost is less than the increased revenue, so there is additional profit from further processing 5000 units.
__
The processing cost of split-off Banango units is ...
GH¢20,000/(10000 units) = GH¢2/unit
The increase in revenue from the further processing is ...
GH¢16 -GH¢15 = GH¢1
The increased processing cost is more than the increased revenue, so the company takes a loss from further processing 10000 units. No additional processing of Banango units should be undertaken.
Amber says that the data set is left-skewed because the box is farther to the left on the number line. (A) Is Amber correct? (B) Explain your reasoning.
Line segment TS is tangent to circle O at point N.
Circle O is shown. Line segment Q N goes from one side of the circle to the other side. Tangent T S intersects the circle at point N. Point P is on the circle between points Q and N. Point R is on the circle between points Q and N. Angle Q N T is 74 degrees.
If the measure of Angle Q N T is 74°, what is the measure of Arc Q P N?
37°
74°
148°
212°\
Answer:
148°
Step-by-step explanation:
The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.
arc QN = 2(74°) = 148°
_____
Comment on the question and answer
Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.
__
We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.
Answer:
148
Step-by-step explanation:
Edge 2020
A circular garden has a diameter of 12 feet. About how much trim is needed to surround the garden by placing trim on the garden's circumference?
Trim = circumference
= 2[tex]\pi r[/tex]
= 2 x 3.14 x 6
= 37.68 feet
need help thanksssssssss
Answer:
Volume: 112 m³.
Surface area: 172 m².
Step-by-step explanation:
The volume is the base times height times length. So, the volume will be 2 * 8 * 7 = 16 * 7 = 112 m³.
The surface area is 2lw + 2lh + 2wh. l = 8; w = 7; h = 2.
2(8)(7) + 2(8)(2) + 2(7)(2) = 2 * 56 + 2 * 16 + 2 * 14 = 112 + 32 + 28 = 112 + 60 = 172 m².
Hope this helps!
write the statement for 6x-3=9
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The statement for [tex]6x - 3 = 9[/tex] is :
[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = 18x
B.
y = 9x
C.
y = -9x
D.
y = - x
E.
y = -18x
F.
y = x
Answer:
y=9x
Step-by-step explanation:
rise over run the rise is the y=9 and run is x=1.
9/1=9x
A researcher studying public opinion of proposed Social Security changes and asks a random sample of adult Americans whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many adult Americans does the researcher need to sample in the following cases
(a) if 37% of all adult Americans support the changes?
(b) 25% of all adults Americans support the changes?
Complete question is;
A researcher studying public opinion of proposed Social Security changes and asks a random sample of 30 adult Americans whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many adult Americans does the researcher need to sample in the following cases
(a) if 37% of all adult Americans support the changes?
(b) 25% of all adults Americans support the changes?
Answer:
A) 13 adults
B) 23 adults
Step-by-step explanation:
A) We are given;
p = 37% = 0.37
Since we are told that this is an approximately normal distribution, we will use the formula;
np(1 - p) ≥ 10
Thus;
0.37n(1 - 0.37) ≥ 10
n ≥ 10/(0.63 × 0.37)
n ≥ 42.9
We need a whole number, thus n = 43
From the question, we have already 30 adults , so the required number of adults are; 43 - 30 = 13 adults
B) We are given;
p = 25% = 0.25
Since we are told that this is an approximately normal distribution, we will use the formula;
np(1 - p) ≥ 10
Thus;
0.25n(1 - 0.25) ≥ 10
n ≥ 10/(0.75 × 0.25)
n ≥ 53.33
n ≈ 53
From the question, we have already 30 adults , so the required number of adults are; 53 - 30 = 23 adults
Each week, Rosario drives to an ice-skating rink that is 60 miles away. The round-trip takes 2.75 hours. If he averages 55 miles per hour on his way to the rink, which equation can be used to find x, the number of miles per hour he averages on his way home?
Answer:
The answer to your question is x = 4d/t - S1
Step-by-step explanation:
Data
total time = t = 2.75 hours
Initial speed = S1 = 55 mi/h
Final speed = x
distance = d = 60 mi
Formula
speed = distance / time
Average speed = (Initial speed + final speed)/2 or
= (S1 + x)/2
Substitution
(S1 + x)/2 = 2(d) / t
Solve for x
x = (2d/t)2 - S1
Simplification and result
x = 4d/t - S1
A fair die is rolled. What is the probability of rolling a 3 or a 4?
Answer:
2/6 which when simplified, is equal to 1/3
Answer:
1/3
Step-by-step explanation:
1. Manuel quiere fabricar banderitas chilenas para venderlas en los partidos de la selección nacional. Si se demora 1 hora en hacer 45 banderitas y trabaja 5 horas diarias. ¿Cuántos días se demorará en fabricar 1800 banderitas?
Answer:
[tex]\large \boxed{\text{Eight days}}[/tex]
Step-by-step explanation:
1. Calculate the hours
[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]
2. Calculate the days
[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]
WILL MAKE BRAINLIST----- Describe both rotational symmetry and reflection symmetry. Find four examples of symmetry in your classroom.
Answer:
When an obect has rotational symmetry, that means the object will look the same after a certain amount of rotating. When an object has reflection symmetry, it means the object mirrors itself at the midpoint.
Step-by-step explanation:
Determine the amount of paint required to cover a wall that is 11feet high and 15feet wide, if the wall has two rectangular windows (which are not to be painted), each measuring 3feet by 7feet.
Answer:
123 Square Feet. Of Paint. Probably gonna take a little more than a sample-size quart, let me know how it turns out.
Step-by-step explanation:
You would need 11*15=165 square feet of paint. BUT
You need 42 less square feet, because there are 2, 7*3=21 square-foot windows.
165-42
For a given function ƒ(x) = x5, a translation in the positive y-direction of two units is represented by which of the following?
Question 5 options:
A)
ƒ(x + 2) = ( x – 2)5
B)
ƒ(x + 2) = (x + 2)5
C)
ƒ(x) – 2 = x5 – 2
D)
ƒ(x) + 2 = x5 + 2
Answer:
D) ƒ(x) + 2 = x5 + 2
Step-by-step explanation:
You have the following function:
[tex]f(x)=x^5[/tex] (1)
In the case of a vertical translation of the function on the coordinate system, you have that a translation of a units upward is obtained with the function f(x)+a. In the same way, a translation downward is obtined with f(x)-a.
Thus, a translation in the positive y direction of 2 units (a=2) is given by the following function.
D) ƒ(x) + 2 = x5 + 2