Answer:
see below
Step-by-step explanation:
5 – 3(2x – 7) = 12 – 5(x – 2)
Substitute x=2
5 – 3(2*2 – 7) = 12 – 5(2 – 2)
5 – 3(-3) = 12 – 5(0)
5 - 3*(-3) = 12
5+9 = 12
14=12
This is false so it is not a solution
5 – 3(2x – 7) = 12 – 5(x – 2)
Substitute x=5
5 – 3(2*4 – 7) = 12 – 5(4 – 2)
5 – 3(8-7) = 12 – 5(2)
5 - 3*1 = 12-10
5-3 = 2
2=2
This is true so it is a solution
A tiling company completes two jobs. The first job has $1200 in labor expenses for 40 hours worked, while the second job has $1560 in labor expenses for 52 hours worked. The relationship between the labor expenses and the hours worked is linear. Which equation can be used to calculate the y-intercept of the linear equation?
Answer: 1560 = 30(52) + b
Step-by-step explanation:
Based on the information given in the question, the straight line passes through two points which are (40, 1200) and (52, 1560). Then, the equation if the straight line will be:
y - 1560 = (1200 - 1560)/(40 - 52) (x - 52)
y - 1560 = (-360)/(-12) (x - 52)
y - 1560 = 30(x - 52)
Lets put the value of x to be 0.
y - 1560 = 30(x - 52)
y - 1560 = 30(0 - 52)
y - 1560 = -30(52)
Therefore, 1560 = 30(52) + b
A survey of 35 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated. You're testing the claim that the mean difference is greater than 0.7. From the sample, the mean difference was 0.95, with a standard deviation of 0.44. Calculate the test statistic, rounded to two decimal place
Answer:
The test statistic is t = 3.36.
Step-by-step explanation:
You're testing the claim that the mean difference is greater than 0.7.
At the null hypothesis, we test if the mean difference is of 0.7 or less, that is:
[tex]H_0: \mu \leq 0.7[/tex]
At the alternate hypothesis, we test if the mean difference is greater than 0.7, that is:
[tex]H_1: \mu > 0.7[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that [tex]\mu = 0.7[/tex]
A survey of 35 people was conducted to compare their self-reported height to their actual height.
This means that [tex]n = 35[/tex]
From the sample, the mean difference was 0.95, with a standard deviation of 0.44.
This means that [tex]X = 0.95, s = 0.44[/tex]
Calculate the test statistic
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}[/tex]
[tex]t = 3.36[/tex]
The test statistic is t = 3.36.
A 36-foot-tall tree that is leaning toward the sun casts a 40-foot-long shadow when the sun is at a
41° angle of elevation. Approximately how many degrees does the tree lean?
a. 1°
c. 4°
b. 2°
d. 7°
Answer:
64degrees
Step-by-step explanation:
Give the following
Height of tree H = 36feet
length of the shadow L = 40feeet
Requires
Angle of eleation
Using the SOH CAH TOA identity
Sin theta = opposite/hypotenuse
Sin theta = H/L
Sin theta = 36/40
SIn theta = 0.9
theta = arcsin0.9
theta = 64.16
Hence the required angle is 64degrees
Which of the following shapes are polygons with more than 444 sides?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Hexagon
(Choice B)
B
Pentagon
(Choice C)
C
Triangle
(Choice D)
D
Rectangle
Answer:
It's the hexagon and pentagon.
Volume of Prisms and Cylinders
a. 339.12 cu. in.
b. 113.04 cu. in
c. 226.08 cu. in.
d. 1356.48 cu. in
Please select the best answer from choices provided
Answer:
A. 339.12 cu. in.
Step-by-step explanation:
I calculated it logically
Jeff and Eric roommates and enjoy talking about sports. They mainly discuss their favorite professional soccer teams. Jeff enjoys European soccer whereas Eric prefers American teams. Outside soccer they do not discuss much. Their lack of range of talking to it fall into which category?
0°
EXPLANATION:In each figure below find m∠1 and m∠2, if a||b. Show your work with statements.
====================================
If you have any questions feel free to ask me^^
Have a nice and great day!
Cayler#PilipinasAngBayanKo
0°
Sana Maka help ako tnx
Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48.3 ppm and a standard deviation of 8 ppm. The Environmental Protection Agency takes a random sample of 40 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 48.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate comp
Answer:
0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 48.3 ppm and a standard deviation of 8 ppm.
This means that [tex]\mu = 48.3, \sigma = 8[/tex]
Sample of 40:
This means that [tex]n = 40, s = \frac{8}{\sqrt{40}}[/tex]
Find the probability that the disposal of such capacitors will be regulated.
Sample mean above 48.5, which is 1 subtracted by the p-value of Z when X = 48.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48.5 - 48.3}{\frac{8}{\sqrt{40}}}[/tex]
[tex]Z = 0.16[/tex]
[tex]Z = 0.16[/tex] has a p-value of 0.5636.
1 - 0.5636 = 0.4364
0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.
On their way up the hill, Jack and Jill were stopped by their parents. It seems the two of them were trying to skip out on some chores. They were told to mow the lawn, clean the kitchen, and sweep the leaves off the deck. If Jack can complete all the chores in 3 hours by himself and Jill takes only 2.25 hours to get all of it done on her own, how many minutes will it take for the two of them to get the work done together
Answer:
77.14 minutes.
Step-by-step explanation:
Jack's time = 3 hours
Jill's time = 2.25 hours = 2 1/4 = 9/4 hours
Combined time = x
Rates :
Jack = 1/3 ; jill = 1 / 2.25 = 1 / 9/4 = 4 /9
Combined rate = 1/x
Setting up the equation :
1/3 + 4/9 = 1/x
Lcm of 3 and 9 = 9
(3 + 4) / 9 = 1/x
7/9 = 1/x
Cross multiply :
7x = 9
x = 9/7 hours
x = (9/7)* 60
x = 77.14 minutes
Combined time = 77.14 minutes.
An economist, an expert in the study of sales and production of goods and services, is interested in studying the average amount of money people spend, each month, on entertainment. For example, he wants to know how much people spend, each month, going to the movies, attending a concert, etc. His assistant conducted a poll of 500 randomly selected people across the country. He found a 95% confidence interval: $72 to $198. From this confidence interval the assistant concluded that people spend an average of $200 a month on entertainment. Is this a reasonable conclusion and why
Answer:
$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.
Step-by-step explanation:
95% confidence interval: $72 to $198.
This means that we are 95% sure that the true mean spending is between $72 and $198.
From this confidence interval the assistant concluded that people spend an average of $200 a month on entertainment. Is this a reasonable conclusion and why?
$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.
The vertices of JKL are J(4,3), K(-3,4), L(-1,-1). Graph the image of JKL after a reflection in the line y=-x.
y=-x
J(-4,3)
K(3,-4)
L(1,1)
5 -3 over 2 x > 1 over 3
Answer:
It's true because 5-3/2 is grater than 1/3
Based on a random sample of 1140 adults, the mean amount of sleep per night is 7.96 hours. Assuming the population standard deviation for the amount of sleep per night is 1.6 hours, construct 95% confidence interval for the mean amount of sleep per night.
a. (7.67, 8.05)
b. (7.87, 8.05)
c. (8.09, 9.12)
d. (7.87, 8.23)
Answer:
at 95% confidence interval, the mean amount of sleep per night is ( 7.87, 8.05 ).
Option b) (7.87, 8.05) is the correct answer.
Step-by-step explanation:
Given the data in the question;
sample size n = 1140
sample mean x" = 7.96
standard deviation σ = 1.6
At 95% confidence interval,
significance level ∝ = 1 - 95% = 1 - 0.95 = 0.05
∝/2 = 0.05 / 2 = 0.025
Z-Critical [tex]Z_{\alpha /2[/tex] = [tex]Z_{0.025[/tex] = 1.96
Top get the Margin of error E;
E = [tex]Z_{\alpha /2[/tex] × ( σ /√n )
we substitute
E = 1.96 × ( 1.6 /√1140 )
E = 0.09
So, At 95% confidence interval of the population mean is;
⇒ x" ± E
⇒ x" - E or x" + E
we substitute
⇒ 7.96 - 0.09, 7.96 + 0.09
⇒ 7.87, 8.05
Therefore, at 95% confidence interval, the mean amount of sleep per night is ( 7.87, 8.05 ).
Option b) (7.87, 8.05) is the correct answer.
Antonio is planning a birthday party for his daughter. SkateWorld charges a flat fee of $50 plus $3 per child. Roller Land charges $5 per child. If Antonio's daughter wants to invite 21 friends from school and five friends from her basketball team, which rink should Antonio use and how much would he save by doing so?
Answer:
skateworld
Step-by-step explanation:
26x3+50=128 aka skate worlds price
26x5=130 aka roller land price
Antionio should use skateworld and he would save 2$
Answer: SkateWorld. He saves $2
Step-by-step explanation:
SkateWorld:
21 *3 =63
5*3=15
63+15=78
78+50= 128
Roller Land:
21*5= 105
5*5=25
105+25=130
130-128= 2
What is the perimeter of rectangle J K L M
Step-by-step explanation:
you could count the squares around the shape or you could do it by points
For example point M is (2,3)
L is (6,3)
We want to find the length of this side so we subtract the x values
6 - 2 = 4 units
that gives use the length of that leg and since a rectangle is symmetrical, you can just measure 2 sides
Which algebraic expression represents the phrase "seven more than half of a number"?
Answer:
Step-by-step explanation:
½X+7
A bag contains 5 blue, 4 red, 7 black and 2 white marbles. What is the probability of selecting a marble that is NOT white?
Answer:
8/9 (simplified)
Step-by-step explanation:
Total marbles = 18
Total of marbles not white = 16
Numerator = 16 / Denominator = 18
= 16/18
= 8/9 (simplified)
Total number of marble=18
probability of getting white marble = 2/18 =1/9
Now,
probability of not getting white marble = 1 - 1/9 = 8 / 9
pls help quicklyyy i will give 10 points pls
Answer:
[tex]0.156[/tex]
Step-by-step explanation:
[tex]15.6 \div 100[/tex]
[tex]0.156[/tex]
Hope it is helpful...pls help im giving brainless. i need it Asap plss
find the value of x.
Find the surface area of the cylinder. Round your answer to the nearest tenth.
Answer:
282.74
Step-by-step explanation:
what type of information is used to obtain information on how scores are spread from the center of a distribution
Answer:
You need variability
Step-by-step explanation:
Variability measures the degree to which the scores are spread out or clustered together in a distribution.
Hope this helps:)
Which fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)?
Answer:
Step-by-step explanation:
slope=y2-y1/x2-x1
here x1=2 , y1=-4 , x2=-6 , y2=1
=1-(-4)/2-(-6)
=1+4/2+6
=5/8
-5/8 fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
the slope formula for the line containing (2, -4) and (-6, 1) we calculate by plugging the values to the slope formula.
m=1-(-4)/-6-2
m=1+4/-8
m=-5/8
Hence, -5/8 fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)
To learn more on slope of line click:
https://brainly.com/question/14511992
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Expand 20 - 3 (5w+2) - 4w
14 - 19w
26 - 11w
23 + 9w
Which one ?
1 point
A water tank in the form of a rectangular prism is 80 meters long and 50 meters wide. What is the volume of the water in the tank,
if the water is 40 meters deep?
Answer:
160000m³
Step-by-step explanation:
Volume of a rectangular prism= A x h
V= l x b x h
V= 80x 50 x 40
V= 160000m³
Simplify each expression using Order of Operations.
a. 2(3 + 4) + 3 to the 3rd power
b. 5 + (3 to the 2nd power - 2 to the 2nd power)
Answer:
a) 4,913
b) 10
Step-by-step explanation:
a) [2(3 + 4) + 3]³
= [2(7) + 3]³
= (14 + 3)³
= 17³
= 4913
b) 5 + (3² - 2²)
= 5 + (9 - 4)
= 5 + 5
= 10
please help thx 7th grade
Answer:
All of them except a trapezoid
Step-by-step explanation:
The playground has two pairs of sides that are congruent to each other (70 = 70, 50 = 50), but a trapezoid only has ONE pair of sides that are congruent to each other; the other two are not the same. Therefore, this playground can be any shape besides a trapezoid.
Two numbers are in the ratio 5:6. If the smaller one is decreased by 5 and
the other is increased by 3, the new ratio is 2:3. Find the number.
Answer:
Smallest Number = 35
Other Number = 42
Step-by-step explanation:
Let the smaller number be x.
Let the other number be y.
Given:
x : y = 5 : 6
That is,
[tex]\frac{x}{y} = \frac{5}{6}[/tex]
[tex]=> 5y = 6x\\\\=>x = \frac{5y}{6}[/tex]
Next: Let the smaller number be reduced by 5, x - 5
Let the other number be increased by 3, y + 3
Given : (x - 5) : (y + 3) = 2 : 3
That is,
[tex]\frac{x-5}{y+3} = \frac{2}{3}\\[/tex]
[tex](x-5) \times 3 = (y+3)\times 2\\\\substitute \ x = \frac{5y}{6}\\\\3(\frac{5y}{6} -5) = 2y + 6\\\\\frac{5y}{2} - 15 = 2y + 6\\\\\frac{5y}{2} - 2y = 6 + 15\\\\\frac{5y-4y}{2} = 21\\\\y = 21 \times 2 = 42\\\\Substitute \ y \ in \ x = \frac{5y}{6} \\\\x = \frac{5 \times 42}{6} = 35[/tex]
What is the GCF of xy3 and x3y?
Answer:
xy
Step-by-step explanation:
xy³ and x³y
GCF is xy
Answer:
I think it's xy
Step-by-step explanation:
just find the prime factors of each term
Can somebody help me with this question
Answer:
[tex]\text{a) }1,080^{\circ}, \\\text{b) }360^{\circ}, \\\text{c) }135^{\circ}, \\\text{d) }45^{\circ}[/tex]
Step-by-step explanation:
a) The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, substitute in [tex]n=8[/tex]:
[tex](6-2)180=\boxed{1,080^{\circ}}[/tex]
b) The sum of the exterior angles for any polygon is equal to [tex]360^{\circ}[/tex].
c) By definition, all regular shapes have equal angles and sides. Since we've found the total sum of the interior angles of an octagon in part a, each interior angle of a regular octagon must be [tex]\frac{1080}{8}=\boxed{135^{\circ}}[/tex]
d) Similar to part c, all regular shapes must have equal angles and sides. From part b, we know the sum of the exterior angles of a octagon is [tex]360^{\circ}[/tex], thus we have [tex]\frac{360}{8}=\boxed{45^{\circ}}[/tex]
What percent of 15 is 45?
Answer:
Step-by-step explanation:
let the number be x %
according to the question the equation is
x% of 15=45
x/100*15=45
15x=45*100
x=4500/15
x=300
therefore x=300%