Answer:
-8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
3x + 10 = 4
2 + 5x
Step 2: Solve for x
Subtract 10 on both sides: 3x = -6Divide 3 on both sides: x = -2Step 3: Evaluate
Substitute in x: 2 + 5(-2)Multiply: 2 - 10Subtract: -8A randomized trial tested the effectiveness of diets on adults. Among 36 subjects using Diet 1, the mean weight loss after a year was 3.5 pounds with a standard deviation of 5.9 pounds. Among 36 subjects using Diet 2, the mean weight loss after a year was 0.6 pounds with a standard deviation of 4.4 pounds. Construct a 95% confidence interval estimate of the difference between the population means, assuming the population standard deviations are equal.
Answer:
The 95% confidence interval is
[tex] 0.45 < \mu_1 - \mu_2 < 5.35 [/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 36[/tex]
The first sample mean is [tex]\= x_1 = 3.5[/tex]
The first standard deviation is [tex]\sigma_1 = 5.9 \ pounds[/tex]
The second sample size is [tex]n_2 = 36[/tex]
The second sample mean is [tex]\= x_2 = 0.6[/tex]
The second standard deviation is [tex]\sigma = 4.4[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = \frac{ [ \frac{s_1^2 }{n_1 } + \frac{s_2^2 }{n_2} ]^2 }{ \frac{1}{(n_1 - 1 )} [ \frac{s_1^2}{n_1} ]^2 + \frac{1}{(n_2 - 1 )} [ \frac{s_2^2}{n_2} ]^2 }[/tex]
=> [tex]df = \frac{ [ \frac{5.9^2 }{34 } + \frac{4.4^2 }{34} ]^2 }{ \frac{1}{(34 - 1 )} [ \frac{5.9^2}{34} ]^2 + \frac{1}{(34- 1 )} [ \frac{4.4^2}{ 34} ]^2 }[/tex]
=> [tex]df =63[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{ \frac{s_1 ^2 }{n_1} + \frac{s_2^2 }{ n_2 } }[/tex]
=> [tex]SE = \sqrt{ \frac{ 5.9 ^2 }{ 36 } + \frac{ 4.4^2 }{36} }[/tex]
=> [tex]SE = 1.227[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\frac{\alpha }{2}, 63 } = 1.998 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2}, 63 } * SE[/tex]
=> [tex]E = 1.998 * 1.227[/tex]
=> [tex]E = 2.45[/tex]
Generally 95% confidence interval is mathematically represented as
[tex](\= x_1 - \x_2) -E < \mu <(\= x_1 - \x_2) + E[/tex]
=> [tex](3.5 - 0.6) - 2.45 < \mu_1 - \mu_2 < ( 3.5 - 0.6) + 2.45 [/tex]
=> [tex] 0.45 < \mu_1 - \mu_2 < 5.35 [/tex]
what’s the equation for this
Hope it work for u
Step-by-step explanation:We can make points from the given figure as ,
1 point =(x1, y1)=(-2, -3)
2nd point =(x2, y2)= (0, -6)
3rd point = (x3, y3)=(2 , -9)
Now the equation of line is,
Y=m X+ c where m is slope and c is constantnow two point formula of slope is ,
m = y2-y1/x2-x1putting points in it we get
m=(-6-(-3))/(0-(-2)
m=-3/2 is slope
Now to find C putt the value of m and 3rd point in equation of line we get
y3=m(x3)+c
-9=(-3/2)(2) +c
C= -9+3
C=-6 is value of c
Now at last putt the value of C and m in equation of line we get the required equation ,
Y=(-3/2)X-6 Ans.........................
Which is the correct answer?
Note: (if you give me a silly or absurd answer I will report you)
Answer:
D. None are true.
Step-by-step explanation:
f(x)=-2x-1
g(x)=-1/2x+1/2
perpendicular( inverse ) slope = -1
-2*-1/2 = 1, so not perpendicular.
III is wrong.
So, it can't be C.
Since they are not perpendicular, if you place x in one, the other will be wrong, same with the other, so not A or B.
The correct answer is D.
Hope this helps plz hit the crown :D
Solve for x if the horizontal lines below are parallel.
fo
Answer:
[tex]x=82^{\circ}[/tex]
Step-by-step explanation:
We can draw a perpendicular line through the two parallel lines to create a pentagon (there is an image attached in case you need to see where the line intersects the two parallel lines). Since the angle sum of a pentagon is [tex]540^{\circ}[/tex], we can solve for [tex]x[/tex].
[tex]x+140+138+90+90 = 540[/tex] (Angle sum of pentagon is [tex]540^{\circ}[/tex])
[tex]x+458=540[/tex] (collect like-terms)
[tex]x=82^{\circ}[/tex]
Hope this helps :)
Thanks in advance.............
Find the slope of the line.
(6, 10)
3
(a, 8)
(4, b)
(2, 2)
Answer:
2
Step-by-step explanation:
Slope of the line can be found using the two points, (2, 2) and (6, 10):
[tex] Slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (2, 2) = (x_1, y_1) [/tex]
[tex] (6, 10) = (x_2, y_2) [/tex]
[tex] slope (m) = \frac{10 - 2}{6 - 2} [/tex]
[tex] Slope (m) = \frac{8}{4} = 2 [/tex]
20 of the 80 coffee mugs at Carson's Pancake House are dirty. What percentage of the coffee mugs at the pancake house are dirty?
Answer:
25%
Step-by-step explanation:
20/80 in can be reduced to 1/4 and 1/4 equals 25%.
We have:
[tex]\dfrac{20}{80} = \dfrac{\%} {100}[/tex]
Solving for %:
[tex]\% = \dfrac{20\cdot 100}{80} = 25\%[/tex]
R/ 25% of coffee mugs are dirty.
A 60 minute television program consists of 6 commercials, each 2.5 minutes long, and four equal length entertainment segments. How long is each entertainment segment?
Answer:
5 minutes
Step-by-step explanation:
I need help please
Answer:
L = 25
Step-by-step explanation:
Let's call the Length x and width x - 15 since the width is 15 less than length
Eric needs 70 of fencing in total, the perimeter of a rectangle is calculated by adding all sides
x + x + (x - 15) + (x - 15) = 70 add like terms
4x - 30 = 70 add 30 to both sides
4x = 100 divide both sides by 4
x = 25
Answer :
Given :
The shape of the yard is rectangularWidth is 15 yards less than the lengthTotal fencing required is 70 feetTo find :
Appropriate equation DimensionsSolution :
We know that for fencing we need to find the perimeter ,
Perimeter of a rectangle => 2 ( length + breadth )Let us assume the value of length be x yards
Width = x - 15 yardsSolving the question we get ,
2 ( x + ( x - 15 ) ) = 702 ( x + x - 15 ) = 702 ( 2x - 15 ) = 704x - 30 = 704x = 100[tex]\sf\implies\:x\:=\:\dfrac{100}{4}[/tex]x = 25Length = 25 yards
Breadth = 25 - 4
21 yardsWhat is the solution to the inequality -6+12p+31 > 71
Step-by-step explanation:
-6 + 12p + 31 > 71
12p + 25 > 71
12p > 46
p > 23/6.
Answer:
Step-by-step explanation:
12p>71+6-31
12p>46
p>23/6
In a office building, 58 offices are currently being rented. This represents 40% of the total units. How many offices are there in a building?
Answer: 145
Step-by-step explanation:
Given:
58 = 40%(x)
Step 1: Turn 40% into a decimal and divide it to the other side
When turning a percentage into a decimal, the decimal point has to be moved two places to the left. This means that 40% will be turned into 0.4.
58 = 0.4(x)
Divide 0.4 over to the other side.
58/0.4 = 0.4/0.4(x)
0.4 is the same as 4/10. This means that 58/1 is divided by 4/10. When dividing a number by a fraction, you invert the fraction and multiply it by the number.
58/1 * 10/4 = 580/4 = 145
145 = x
This is your answer
HELP PLEASE ILL VENMO THE FIRST PERSON WHO ANSWERS
Answer:
y=2p+9 i really hope this helps and you dont have to venmo me anything but i had to hurry because i have a quiz and i have to go. bye. hope this helped
Step-by-step explanation:
Point G and point H are the same distance form point F. Which coordinates could be the location of point H?
Note: It seems, you missed to add the correct option. But, I am solving the question to clear your concept anways.
Answer:
The coordinates of H are:
(x₂, y₂) = (2, 0)Step-by-step explanation:
Given the points
F(3, 2)G(4, 4)Since Point G and point H are the same distance from point F, therefore the point F is the mid-point of G and H
using the mid-point formula
[tex]m\:=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
Since the point F is the mid-point of G and H, so
m = (3, 2)
as
(x₁, y₁) = (4, 4) = G (x₂, y₂) = H = ?Thus, substituting m = (3, 2), (x₁, y₁) = (4, 4) to determine coordinates of the point H (x₂, y₂)
[tex]m\:=\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(3,\:2\right)\:=\:\left(\frac{x_2+4}{2},\:\:\frac{y_2+4}{2}\right)[/tex]
so
[tex]\:\:3\:=\:\frac{x_2+4}{2}[/tex]
[tex]x_2+4=6[/tex]
subtract 4 from both sides
[tex]x_2+4-4=6-4[/tex]
[tex]x_2=2[/tex]
and
[tex]2=\:\frac{y_2+4}{2}[/tex]
[tex]\:y_2+4\:=\:4[/tex]
subtract 4 from both sides
[tex]y_2=0[/tex]
Thus, the coordinates of H are:
(x₂, y₂) = (2, 0)Note: It seems, you missed to add the correct option.
Help me please I neeed help heree
Answer: 1/12
i think maybe
Please answer this fast!!
Options:
- SSS
- SAS
- ASA
- AAS
- HL
- Not Possible
Answer:
SAS
Step-by-step explanation:
Only two sides are proven to be congruent and the angle in between the two is a corresponding angle, making them congruent.
If a normal distribution has a mean of 62 and a standard deviation of 12, what
is the z-score for a value of 74?
Step-by-step explanation:
N~(62, 12^2)
Use Z-score formula (can find in internet)
[tex] z = \frac{74 - 62}{12} \\ z = \frac{12}{12} \\ z = 1[/tex]
help me please !!!??!!?
Answer:
23358.1
Step-by-step explanation:
Answer:
216.2
Step-by-step explanation:
[tex]a^2+b^2=c^2\\\\c=3959+5.9\\\\b=3959\\\\a=x\\\\\\(x)^2+(3959)^2=(3964.9)^2\\\\x^2=(3964.9)^2-(3959)^2\\\\x^2=(3964.9-3959)(3964.9+3959)\\\\x^2=5.9(7923.9)\\\\x\approx 216.2[/tex]
X^2 + 6x + 16y - 23 = 0
What is the standard form of the equation?
Answer:
hard!
Step-by-step explanation:
Mathematics, 04.03.2020 23:32 jtoole5341 DIVISION OF PROFITS Tom 20% Ellen 30% Sarah 25% Joel 25% Tom, Joel, Sarah, and Ellen divided the profits of their after-school business as shown in the circle graph above. If Tom's share of the profits was $492, what was Ellen's share?
9514 1404 393
Answer:
$738
Step-by-step explanation:
The ratio of Ellen's share (e) to Tom's share is ...
30%/20% = e/492
Multiplying by 492, we have ...
e = 492(3/2) = 738
Ellen's share of the profits is $738.
Select the correct answer. What is the solution for x in the equation? 29 + 15x = -x − 3
First of all, move the terms so that all those who involve [tex]x[/tex] are on one side, and all the costants are on the other:
[tex]29 + 15x = -x - 3 \iff 15x+x=-29-3[/tex]
Sum like terms:
[tex]15x+x=-29-3 \iff 16x=-32[/tex]
Divide both sides by 16:
[tex]x=-2[/tex]
Melanie’s smartphone has 48 apps. This is 4 times the number of apps Priscilla and Cynthia have altogether on their phones. If Cynthia has 5 apps, how many apps does Priscilla have?
Complete the steps below to solve for the number of apps on Priscilla’s smartphone.
A -Write a numerical expression to represent the number of apps Priscilla and Cynthia have combined. (Do not simplify the expression just yet.)
B -Cynthia has 5 apps. Write a numerical expression that represents the number of apps Priscilla has. Refer to the expression you wrote in part A.
C -Simplify the expression from part B to find the number of apps Priscilla has.
D -You just worked with numerical expressions. Now let's try an equation. Let p be Priscilla’s number of apps. Write an equation in terms of p to represent the problem.
E -Solve the equation you found in part D. What is the value of p? Show your work.
F -You solved the problem using two methods: numerical expressions and an equation with variable p. Did you use the same sequence of operations in both methods?
H -What does your answer to part F imply? Explain.
Rectangle LMNP was dilated using the rule DP,3. Which statements are true? Check all that apply. The length of line segment M'N' is 18 units. The length of segment M'N' is 14 units. The dilation is a reduction. The dilation is an enlargement. The scale factor is One-third. The scale factor is 3.
The given rule of the dilation indicates that the scale factor is 3 which is
larger than one, therefore, given an enlarged image.
The correct options are;
The length of line segment M'N' is 18 unitsThe dilation is an enlargementThe scale factor is 3Methods by which the scale factor is obtainedPlease find attached the possible diagram of rectangle LMNP obtained from a similar question posted online;
L'M' = 12
LM = 4
MN = 6
The rule of the dilation of rectangle LMNP = [tex]D_{p, \, 3}[/tex]
L'M' = 3 × LM
Therefore;
The image following the dilation of the preimage LMNP, which is rectangle L'M'N'P' is larger than LMNP
Therefore;
The dilation is an enlargementThe scale factor is the number with which the preimage dimension is multiplied to get the image, which is 3
The scale factor is 3M'N' = 3 × MN
Therefore;
The length of line segment M'N' = 3 × 6 units = 18 unitsLearn more about scale factor of a dilation here:
https://brainly.com/question/840682
Answer:
a. The length of line segment M'N' is 18 units.
d. The dilation is an enlargement.
f. The scale factor is 3.
Step-by-step explanation:
got it right on ed23
i need to know the slopes of these problems, they all the numbers are 1,2,3,4,5
Answer:
5 is 1
6 is 2/3
7 is 2/3
8 is 2
You and your best friend have decided to go out Friday night to spend the money you received from having a great report card. The amount of money each received is $25. You are deciding if you would like to go bowling at Splitsville or go to a movie at Paragon Village.
Question : Write an equation to determine the number of friends who can come to the movie (Paragon Village) with both of you if you and your best friend put your money together and only buy one large combo.
Paragon Village: Tickets are $5 per person and a large combo (Large Popcorn and Large Drink) is S7 together.
Splitsville: Games are $6.00 per person and shoe reantal is $2.
I need help, please try you're best and show you're work(if you want). I need a eqation. Hope you the best of luck.
Answer:
Step-by-step explanation: X=-4y+4
A number decreased by 5 is 14
Simplify the following fraction expressions. Show all of your work. a. 3/4+2/3 b. 7/8-1/4 c. 3/5.1/3 d. 4/7.2/3
Answer:
Step-by-step explanation:
a. 9/12 + 8/12 = 17/12= 1 5/12
b. 7/8 - 2/8 = 5/8
c. 3/5 x 1/3 = 3/15 = 1/5
d. 4/7 x 2/3 = 8/21
Please help I need it
how many times greater is 3.4 times 10^5 than 2 times 10^3
Answer:
170
Step-by-step explanation:
3.4*10^5= 34*10000=340000
But, 2* 10^3= 2*1000= 2000
finaly you do 340000/2000=170
So the final answer is 170.
Answer:
170
Step-by-step explanation:
Hope this helped have an amazing day!
I need help with this problem
Two vectors with magnitudes of 6 and 9 have a dot product equal to –27.
Find the angle between the vectors.
150°
120°
60°
30°
Answer: 120
B
Step-by-step explanation: got it right on edge
Answer:
B.) 120
Step-by-step explanation: