Answer:
Step-by-step explanation:
Before you can answer you have to solve the equation for y.
Y = 9/7 x+8/7
Parallel lines have the same slope so would also be 9/7
Perpendicular lines have opposite reciprocal slope so would be -7/9
Answer:
y=-9/7x-8/7
Step-by-step explanation:
9x – 7y=-8
-9x -9x
-7y=-9x-8
then divide all sides by -7
y=-9/7x-8/7
Calculate the standard score of the given X value, X=28.3, where μ=26.3 and σ=28.1 and indicate on the curve where z will be located. Round the standard score to two decimal places.
Answer:
Standard score z=0.07
Step-by-step explanation:
The z-score, or standard score, represents an equivalent value for X but in the standard normal distribution, where μ=0 and σ=1.
For X=28.3 in a normal distribution with μ=26.3 and σ=28.1, the standard score can be calculated as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{28.3-26.3}{28.1}=\dfrac{2}{28.1}=0.07[/tex]
This value is 0.07 standard deviations right to the mean.
In the picture attached, we have located the z-score.
The numerator of a
fraction is 1 more than
twice its denominator. If 4
is added to both the
numerator and the
denominator, the fraction
pos
inve
reduces to 3. Find the
denominator.
Answer:
-7
Step-by-step explanation:
The numerator of a fraction is 1 more than twice its denominator.
Let the denominator=x
Therefore, the numerator=2x+1
The fraction is: [tex]\dfrac{2x+1}{x}[/tex]
If 4 is added to both the numerator and the denominator, the fraction reduces to 3.
Therefore:
[tex]\dfrac{2x+1+4}{x+4} =3[/tex]
First, we solve for x
[tex]\dfrac{2x+5}{x+4} =3[/tex]
Cross multiply
2x+5=3(x+4)
Open the bracket on the right-hand side
2x+5=3x+12
Collect like terms
3x-2x=5-12
x=-7
Therefore, the denominator of the fraction, x=-7
i got +2 is that the correct answer
Answer:
Option (1)
Step-by-step explanation:
Quadratic equation is given as,
2x² + 8 = 0
Let the function is,
f(x) = 2x² + 8
f(x) = 2(x - 0)² + 8
Now we will prepare the table for every input value,
x -2 -1 0 1 2
y 16 10 8 10 16
By plotting these points we get a parabola having vertex at (0, 8).
Graph of the given function doesn't touches or intersects the x-axis.
And we know if a graph has no x-intercept, function graphed will have no real solution.
Therefore, function f(x) will have no real solutions.
Option (1) will be the answer.
Error Analysis A math test asks the students to solve the inequality X-2<16, and then graph the
solutions. Mason said the solutions are x < 14 and graphed the solutions as shown below. Solve
the inequality and graph the solutions. What error might Mason have made?
What are the solutions?
Answer:
The solution is X<18
Step-by-step explanation:
When Mason was solving the inequality he subtracted two from the equation instead of adding two to solve for x.
X-2<16
X<18
Answer:
x < 18Step-by-step explanation:
x - 2 < 16
We eliminate 2 to isolate the variable, x by adding 2 to both sides. -2 + 2 = 0.
x < 18
We can test this because 17 is less than 18. Pretend x = 17
17 < 18✅
Mason subtracted 2, instead of adding 2.
In order to graph this, put an open circle at 18, and the arrow should point to the left.
Hope this helps ;D
If f(x)=2x squared + 1 and g(x)=x squared-7 find (f-g)(x)
Answer:
[tex]x^2+8[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2+1 \\\\g(x)=x^2-7 \\\\(f-g)(x)= (2x^2+1)-(x^2-7)=x^2+8[/tex]
Hope this helps!
What value of y satisfies the system of equations {9x+2y=24y=6x+19? Enter your answer as the correct value for y, like this: 42
Answer:
Step-by-step explanation:
9x + 2y = 24 (A)
y = 6x + 19 ------ > y - 6x = 19 * (-2) -------> -2y + 6x = -38 (B)
(A) + (B)
15x = -14
x = -14/15
y = 6 * (-14/15) + 19 = -28/5 + 19 = 67/5
Answer:
A. 9x + 2y = 24
What’s the surface area of this shape?
Answer:
210 in²
Step-by-step explanation:
6*2.5+6*6*2+(8+6)*2.5+10*2.5+1/2*6*8*2+6*2.5= 210 in²
The percentage charged each month on purchases charged to the credit card
account is called the__?
A) periodic rate
B) new balance
C) unpaid balance
D) minimum payment
Answer:
A) periodic rate
Step-by-step explanation:
Because a percentage that is charged or added to the credit card we assume that it is an interest rate, they also tell us that it is charged every month, that is, it has a known collection frequency, which means that it is Newspaper.
therefore, the answer in this case is A) periodic rate since it complies with the premise of the statement
A standard deck has 52 cards consisting of 26 black and 26 red cards. Three cards are dealt from a shuffled deck without replacement. Let A=first card red and B=second card red. Are A and B independent? Explain why or why not.
They aren't independent since the probability uses all the cards in the deck
So at the first deal we have the chance of 26/52 of getting a red card, at the second deal we have the chance of a 25/51 of getting another red card, so they aren't independent
Awnser in the lowest terms 5 years 6 months + 8 years 9 months
Answer:
14 years 3 months.
Step-by-step explanation:
5 + 8 = 13 years
6 + 9 = 15 months = 1 year 3 months.
Total = 14 years 3 months.
A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below. Firework B is launched 0.25 s before Firework A. How many seconds after Firework B launches will both fireworks
explode?
Firework A
360 ft/s
Firework B
340 ft/s
Answer:
both fireworks will explode 4.5 seconds after Firework B launches
Step-by-step explanation:
Given;
speed of firework A, [tex]V_A[/tex]= 360 ft/s
speed of firework B, [tex]V_B[/tex] = 340 ft/s
If the two fireworks explodes at the same height, then the height attained by the two fireworks are equal.
let the distance traveled by each firework before explosion = d
Distance = speed x time
Distance A = Distance B
speed A x time = speed B x time
let the time both fireworks explodes after Firework B launches = t
([tex]V_A[/tex]) t = ([tex]V_B[/tex] ) t
360t = 340t
if firework B is launched 0.25 s before Firework A, for the time of the two fireworks to be equal since we are considering time (t) after 0.25 seconds, we will have;
360(t-0.25) = 340t
360t - 90 = 340t
360 t - 340 t = 90
20 t = 90
t = 90/20
t = 4.5 seconds
Therefore, both fireworks will explode 4.5 seconds after Firework B launches
What makes things concurrent?
Answer:
When the are intercepted by other lines (math)
Existing, happening at the same time (definition)
N. Section 2.2
Find the difference. Write the difference in lowest terms.
8 1/3 - 5=
Answer:
3 1/3
Step-by-step explanation:
8-5=3=3 1/3.
hope u understand
A retail store had sales of $45000 in April and $56000 in May. The store employs eight full time workers who work 40 hours per week. In April the store also had seven part time workers at 10 hours per week, and in may the store had 9 part time workers at 15 hours per week. Using sales dollars as the measure for output, what is the percentage of change in productivity from April to May?
The percentage of change in productivity from April to May is found to be 6.66%.
Productivity ChangeWhat is meant by change in productivity?A change in labour productivity reflects an output change that cannot be accounted for by a change in the number of hours worked. The development of technology over time might lead to an increase in output per hour enhanced employee skills.
Step by step solutionStep 1: Productivity for month of AprilWe must first determine the number of man hours worked in April in order to compute the percentage change in productivity:
8 employs worked for 40 hours along with 7 employs worked for 10 hours in a week( total 4 weeks in April).
Input of April is,
= 8×40 + 7×10×4
= 1560 hours
To determine the productivity in April, divide the total sales by the number of man hours:
= 45000/1560
= 28.846
Step 2: Productivity for month of May8 employs worked for 40 hours along with 9 employs worked for 15 hours in a week( total 4 weeks in April).
Input of May is,
= 8×40 + 9×15×4
= 1820 hours
To determine the productivity in April, divide the total sales by the number of man hours:
= 56000/1820
= 30.769
Step 3: Calculate the total productivityFinding the difference between productivity in each month and dividing by April's productivity percentage yields the percent change in productivity:
= [tex]\frac{30769-28.846}{28.846}[/tex]×[tex]100[/tex]
= 6.66 %
Therefore, the productivity from April to May increased by 6.66%.
To know more about how to find percentage change, here
https://brainly.com/question/809966
#SPJ2
Recent survey data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. Their parents must have a basement! A random sample of 125 young adults in this age group was selected. What is the probability that between 13 and 17 of these young adults lived with their parents? Hint: use 14.2% to determine the standard error and the p-bar would be the 13/125 and the 17/125.
Answer:
38.76% probability that between 13 and 17 of these young adults lived with their parents
Step-by-step explanation:
I am going to use the normal approxiation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]p = 0.142, n = 125[/tex]
So
[tex]\mu = E(X) = np = 125*0.142 = 17.75[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.142*0.858} = 3.9025[/tex]
What is the probability that between 13 and 17 of these young adults lived with their parents?
Using continuity correction, this is [tex]P(13 - 0.5 \leq X \leq 17 + 0.5) = P(12.5 \leq 17.5)[/tex], which is the pvalue of Z when X = 17.5 subtracted by the pvalue of Z when X = 12.5. So
X = 17.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 17.75}{3.9025}[/tex]
[tex]Z = -0.06[/tex]
[tex]Z = -0.06[/tex] has a pvalue of 0.4761
X = 12.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.5 - 17.75}{3.9025}[/tex]
[tex]Z = -1.35[/tex]
[tex]Z = -1.35[/tex] has a pvalue of 0.0885
0.4761 - 0.0885 = 0.3876
38.76% probability that between 13 and 17 of these young adults lived with their parents
evaluate the limit of tan 4x/ 4tan3x
Answer:
1/3
Step-by-step explanation:
The ratio is undefined at x=0, so we presume that's where we're interested in the limit. Both numerator and denominator are zero at x=0, so L'Hôpital's rule applies. According to that rule, we replace numerator and denominator with their respective derivatives.
[tex]\displaystyle\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\lim\limits_{x\to 0}\dfrac{\tan'{(4x)}}{4\tan'{(3x)}}=\lim\limits_{x\to 0}\dfrac{4\sec{(4x)^2}}{12\sec{(3x)^2}}=\dfrac{4}{12}\\\\\boxed{\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\dfrac{1}{3}}[/tex]
What is the factored form of the polynomial?
x2 + 9x +20
A. (x - 4)(x - 5)
B.(x-2)(x - 10)
C.(x + 4)(x+5)
D.(x + 2)(x + 10)
Answer:
C. (x + 4)(x + 5).
Step-by-step explanation:
We need 2 numbers whose product is + 20 and whose sum is + 9.
They are + 5 and + 4 , so
x2 + 9x +20
= (x + 4)(x + 5).
On moving day, Jorge needs to rent a truck. The length of the cargo space is 12 ft, and the height is 1 ft less than the width. The brochure indicates that the truck can hold 504 ft3. What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid.
Answer:
12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft
Step-by-step explanation:
Given that truck can hold = 504 [tex]ft^{3}[/tex] i.e.
Volume, V = 504 [tex]ft^{3}[/tex]
Length of cargo space = 12 ft
Let width of cargo space = w ft
As per question statement:
Let height of cargo space = (w-1) ft
To find: The Dimensions of Cargo Space
Formula for Volume of Cargo Space:
V = Length [tex]\times[/tex] Width [tex]\times[/tex] Height
Putting the given values and conditions:
504 = 12 [tex]\times[/tex] [tex]w \times (w-1)[/tex]
[tex]\Rightarrow w(w-1) = \dfrac{504}{12}\\\Rightarrow w^{2} -w = 42\\\Rightarrow w^{2} -w - 42=0\\\Rightarrow w^{2} -7w +6w -42 =0\\\Rightarrow w(w -7) +6(w -7) =0\\\Rightarrow (w -7)(w+6) = 0\\\Rightarrow w =7, -6[/tex]
Dimensions can not be negative, so width, w = 7 ft
Height = (w-1) = 7-1 = 6 ft
So, the dimensions are 12ft [tex]\times[/tex]7ft [tex]\times[/tex]6ft.
What type of angels are <1 and <4?
The six faces of a cube are painted black. The cube is then cut into [tex]5^3 = 125[/tex] smaller cubes, all the same size. One of the small cubes is chosen at random and rolled. What is the probability that when it lands, the face on the top is black?
Answer:
The probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.
Step-by-step explanation:
We have a cube, with the faces painted black, that each side is divided in 5, so we end up with 125 cubes.
We have to calculate the probability that a randomly selected cube is rolled and the face on the top is black.
This probability is equal to the proportion of black area in the total area of the cube.
We can define the side of the original cube as A=5a, being a the side of the small cubes.
The area that is painted black is equal to the sum of 6 squares of side A. In terms of a, that is:
[tex]S_b=6\cdot A^2=6\cdot(5a)^2=6\cdot25a^2=150a^2[/tex]
The total area of the 125 small cubes is:
[tex]S=125(6a^2)=750a^2[/tex]
Then, the ratio of black surface to the total surface is:
[tex]s_b/s=(150a^2)/(750a^2)=0.2[/tex]
Then, we can conclude that the probability that a randomly selected small cube is rolled and the face on the top is black is P=0.2.
Kim and Dan sold 160 homes together. Kim sold 4 times more than Dan. How many homes did Kim sell?
The equation for the trend line for the scatterplot shown below is y = 5x + 24. What does the slope mean in the context of this problem?
A). The total amount of dollars earned is about $64
B). If no hours are worked, $24 is made
C). For each hour worked the dollars earned increases by $5
D). A total of $80 was earned
Please help
Answer:
C) For each hour worked the dollars earned increases by $5
Step-by-step explanation:
I don't have the context of the problem.
However, we do know that in math, when we have an equation of the form [tex]y=mx+b[/tex], the slope m represents the rate of change. This means, how much one quantity changes in regards to other quantity (from the options I can assume that we are talking about amount earned and hours worked).
Thus, in this case we have [tex]m=5[/tex] and this tells us how much the payment increase in terms of hours worked. Thus, we can say that for each work we work the payment increases by $5.
Thus, the correct answer is c) For each hour worked the dollars earned increases by $5
There are 454 grams in a pound. Convert 330 grams to ounces.
Answer:
11.62 ounces
Step-by-step explanation:
Tamera and Adelina are throwing a birthday party for their friend.
Tamera invited 5 fewer friends than Adelina. Together they invited 47 guests.
How many guests did each girl invite?
Answer: Tamera invited 21 guests while Adelina invited 26 guest.
Step-by-step explanation:
x + (x-5) = 47
x + x -5 = 47
2x -5 =47
+5 +5
2x= 52
x= 26
26 -5 = 21
Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are mound-shaped and symmetric for these two regions.
Region I: ; 438 1013 1127 737 491 840 306 402 1155 1075 500 340
Region II: ; 778 464 563 610 827 894 476 394 824 387 816 767 479 710 389 826
Required:
Find a 90% confidence interval.
Answer:
The 90% confidence interval for the difference between means is (-161.18, 205.18).
Step-by-step explanation:
Sample mean and standard deviation for Region I:
[tex]M=\dfrac{1}{12}\sum_{i=1}^{12}(438+1013+1127+737+...+1075+500+340)\\\\\\ M=\dfrac{8424}{12}=702[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{12}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}\cdot [(438-(702))^2+(1013-(702))^2+...+(500-(702))^2+(340-(702))^2]}\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{11}\cdot [(69696)+(96721)+...+(131044)]}\\\\\\s=\sqrt{\dfrac{1174834}{11}}=\sqrt{106803.1}\\\\\\s=326.8[/tex]
Sample mean and standard deviation for Region II:
[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(778+464+563+...+479+710+389+826)\\\\\\ M=\dfrac{10204}{15}=680[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(778-(680))^2+(464-(680))^2+...+(389-(680))^2+(826-(680))^2]}\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{14}\cdot [(9551.804)+(46771.271)+...+(84836.27)+(21238.2)]}\\\\\\ s=\sqrt{\dfrac{545975.7}{14}}=\sqrt{38998}\\\\\\s=197.5[/tex]
Now, we have to calculate a 90% confidence level for the difference of means.
The degrees of freedom are:
[tex]df=n1+n2-2=12+15-2=25[/tex]
The critical value for 25 degrees of freedom and a confidence level of 90% is t=1.708
The difference between sample means is Md=22.
[tex]M_d=M_1-M_2=702-680=22[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{326.8^2}{12}+\dfrac{197.5^2}{15}}\\\\\\s_{M_d}=\sqrt{8899.853+2600.417}=\sqrt{11500.27}=107.24[/tex]
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.708 \cdot 107.24=183.18[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 22-183.18=-161.18\\\\UL=M_d+t \cdot s_{M_d} = 22+183.18=205.18[/tex]
The 90% confidence interval for the difference between means is (-161.18, 205.18).
Which expression(s) are greater than 0? Select all that apply.
Answer:
1234567891011121314151617181920
Find the value of x and y in the parallelogram below.
Answer:
x = 18°
y = 6
Step-by-step explanation:
in a parallelogram:
Any two opposite sides are congruent
and any two opposites angles are congruent:
then
y + 4 = 10
and 3x = 54
then
y = 6
and x = 54/3 = 18
Answer:
x= 18 , y = 6
Step-by-step explanation:
A parallelogram has two opposite sides equal and parallel hence;
y + 4 = 10
y = 10 -4 = 6
Similarly
54 = 3x( opposite angle of a parallelogram are the same because it's congruent)
3x = 54
x = 54/ 3 = 18°
To be congruent means to have the same shape, size and form but can be flipped.
Calculate the slope between the two points: (7, –4), (7, 8)
Answer:
undefined
Step-by-step explanation:
We can find the slope by using the formula
m = (y2-y1)/(x2-x1)
m = (8 - -4)/97-7)
= (8+4)/(7-7)
= 12/0
We cannot divide by 0 so the slope is undefined
The study ran for several weeks during the semester. About a week after it started, the university announced that they would be holding training sessions for faculty and staff about how to handle situations involving a gunman on campus. This shut down the study for several days as the university needed the lab building for training. The study then resumed according to script after the training. The researchers found that those in the experimental group did not differ in their memories regarding the presence of a gun compared to those in the control condition. That is, the mean score that a gun was present was similar for the experimental group (M = 65%, SD = 11.4%) and the control group (M = 63%, SD = 13.26%). a. Maturation b. Regression to the mean c. Selection d. Mortality e. Instrumentation f. Testing g. History h. Interactions i. Diffusion j. No Threa
Answer: option (g)
Step-by-step explanation:
So the question says :
The study ran for several weeks during the semester. About a week after it started, the university announced that they would be holding training sessions for faculty and staff about how to handle situations involving a gunman on campus. This shut down the study for several days as the university needed the lab building for training. The study then resumed according to script after the training. The researchers found that those in the experimental group did not differ in their memories regarding the presence of a gun compared to those in the control condition. That is, the mean score that a gun was present was similar for the experimental group (M = 65%, SD = 11.4%) and the control group (M = 63%, SD = 13.26%). a. Maturation b. Regression to the mean c. Selection d. Mortality e. Instrumentation f. Testing g. History h. Interactions i. Diffusion j. No Threat
ANS ⇒ The correct answer to this question is option G.
We can confirm here that History is the biggest threat to internal validity in the study as a significant period of time was allowed to pass between the testing conditions.
cheers i hope this helped !!!
what is the center of the circle with a diameter having endpoints
Answer:
(0.5, 2)
Step-by-step explanation:
Since the y coordinates are the same, the distance is between the x values
4 - -3
4+3 = 7
The distance is 7
1/2 the distance would be the center
7/2 = 3.5
Add this to the left coordinate
The x coordinate of the center is -3 + 3.5 = .5
The y coordinate is 2