Let's recall that If a set of 2 parallel lines, line m and line m, are crossed or cut by another line, line T, in our question, we say "a set of parallel lines are cut by a transversal.
Each of the parallel lines cut by the transversal has 4 angles surrounding the intersection.
These are matched in measure and position with a counterpart at the other parallel line.
At each of the parallel lines, there are two pairs of vertical angle. Each angle in the pair is congruent to the other angle in the pair.
In our question, the angle that measures 145 degrees is congruent with the opposites angles of angle x.
Let's recall that x and 145 degrees are adjacent supplementary angles. And these angles add up to 180 degrees. Then, for solve for x, we have:
x = 180 - 145
x = 35 degrees
simplify x⁹ divided by x^5
Answer:
[tex]x^{4}[/tex]
Step-by-step explanation:
Whenever it comes to the division of the same variable, we subtract their powers in order to get the correct answer:
[tex]x^{9}/x^{5}[/tex]
[tex]x^{9-5}[/tex]
[tex]x^{4}[/tex]
A company charges $7 dor a t-shirt and ships any order for $22 a school principal ordered a number of t-shirts for the school store the total cost of the order was 1,520 how many t-shirts did the principal buy
the equation is
[tex]7x+22=1520[/tex]then solve for x
[tex]\begin{gathered} 7x+22-22=1520-22 \\ 7x=1498 \\ \frac{7x}{7}=\frac{1498}{7} \\ x=214 \end{gathered}[/tex]answer: the principal bought 214 t-shirts
f(-9)=7x+6
what would the value of F(-9) be?
I need help with solving residential plots and correlation vs causation how do I solve a liner model from the data ?
The image shows point that have a value that is close to zero, so they are small values
In the question, they say that those points represent the residual plot, that means that they represent the error of the linear model
The error is very small, close to zero
So the residual plot shows a non-random pattern, becuase all the point are close to zero
And then the date can be represented by a linear model
So the answer for the left box is "non-random"
And for the right box is "linear"
On the left box:..... non-random
On the right box...... linear
Can I get help w this pleaseThe dimensions of a rectangular prism are quadrupled.if the original surface area was 225ft^2 was is the new surface area?
Answer:
Concept:
Doubling the dimensions of a prism will increase the new area by 4 times the original area
Tripling the the dimensions of the prism will increase the new area by 9 times the original area
Quadrupling will increase the new area by 16 times the original area
Given that the original area given is
[tex]=225ft^2[/tex]The new area therefore will be
[tex]\begin{gathered} 16\times225 \\ =3600ft^2 \end{gathered}[/tex]Hence,
The final answer will be
[tex]\rightarrow3600ft^2[/tex]TASK 2: Awards DinnerTran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family membersto sit around for dinner. Below is the floor plan that she drew for the event.StageCLUE Illuminate EducationIncSign out11US 01:09hp
According to the image each table has an amount of 8 seats, and there are
WhaGraph the piecewise-defined function. Use the graph to determine the domain and range of the function. x + 2 if x < -1F(x)={ - 2x + 3 if x ≥ - 1
The domain of the function is all possible x-values a function can have; therefore, we see here that the domain of the function is all real numbers (including -1).
The range of a function is all possible y values a function can take. We see from the graph above that can take only the values that are greater than or equal to 1; therefore, the range of the function is all real numbers greater than or equal to 1.
740In the table on the right there are grades that were earned by students on a midtermbusiness math exam What percent of the students earned a grade below 80?83977084986685687783958879648890859396The percent of students with grade below 80 is(Round to the nearest whole number as needed)
Notice that the number of students that got a grade below 80 is:
[tex]7,[/tex]and the total number of students is:
[tex]20.[/tex]Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:
[tex]\frac{x}{y}*100.[/tex]Finally, we get that 7 represents the
[tex]\frac{7}{20}*100=35\%,[/tex]of 20.
Answer:
[tex]35\%.[/tex]My answer is correct or no please check
Answer:
D) 5 minus a number M
hope this helps!
Answer:
Yep. You got it right. Good job!
Step-by-step explanation:
A population forms a normal distribution with a meanof μ = 85 and a standard deviation of o = 24. Foreach of the following samples, compute the z-score forthe sample mean.a. M=91 for n = 4 scoresb. M=91 for n = 9 scoresc. M=91 for n = 16 scoresd. M-91 for n = 36 scores
In this problem, we have a population with a normal distribution with:
• mean μ = 85,
,• standard deviation σ = 24.
We must compute the z-score for different samples.
The standard deviation of a sample with mean M and size n is:
[tex]σ_M=\frac{σ}{\sqrt{n}}.[/tex]The z-score of the sample is given by:
[tex]z(M,n)=\frac{M-\mu}{\sigma_M}=\sqrt{n}\cdot(\frac{M-\mu}{\sigma})[/tex]Using these formulas, we compute the z-score of each sample:
(a) M = 91, n = 4
[tex]z(91,4)=\sqrt{4}\cdot(\frac{91-85}{24})=0.5.[/tex](b) M = 91, n = 9
[tex]z(91,9)=\sqrt{9}\cdot(\frac{91-85}{24})=0.75.[/tex](c) M = 91, n = 16
[tex]z(91,16)=\sqrt{16}\cdot(\frac{91-85}{24})=1.[/tex](d) M = 91, n = 36
[tex]z(91,9)=\sqrt{36}\cdot(\frac{91-85}{24})=1.5.[/tex]Answera. z = 0.5
b. z = 0.75
c. z = 1
d. z = 1.5
Graph the line y=1/4x+3 then name the slope and y-intercept by looking at the graph. How do I graph this what are my points and what is m= as well as what is b=?
Make graph line using the slope and the y-intercept or the point.
m=1/4 and b=3
What is graph ?
graph is a mathematical representation of a networks and it describes that the relationship between lines and points. A graph consists of some points and lines are between them. The length of the lines and position of the points do not matter.
Sol-as per the given question y=1/4x+3
The slope-intercept form y=mx+b where m is the slope and b is the y intercept
y=mx+b
Reorder terms
y=1/4x +3
Use the slope-intercept form to find the slope and y-intercept
Slope=1/4
y-intercept :(0,3)
Any line can be graphed using two points is Select two x
values, and plug them into the equation to find the corresponding Y values.
In record terms -y=1/4 x+3
The table of x and y values are-
X-0,4
Y-3,4
graph the line using the slope and the y-intercept, or the points.
Slope -1/4
y-intercept (0,3)
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rectangle rstw has diagonals RT and SW that intersect at Z. If RZ= 5x+8 and SW= 11x-3 find the value of x.
Answer:
19
Explanation:
We know that the diagonals of a rectangle are always equal, therefore RT = SW.
So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;
[tex]\begin{gathered} 2(5x+8)=11x-3 \\ 10x+16=11x-3 \\ 16+3=11x-10x \\ 19=x \\ \therefore x=19 \end{gathered}[/tex]in a recent year the annual salary of the governor of New York was 1790000 during the same year the annual salary of the governor of Tennessee was 940000 less write and solve an equation to find the annual salary of the government of Tennessee in that year
Step 1 : Let's review the information given to us to answer the problem correctly:
• Annual salary of the governor of New York = $ 1,790,000
,• Annual salary of the governor of Tennessee = $ 940,000
Step 2: Let x to represent the annual salary of the governor of New York
and let's find the ratio of the salary of the governor of Tennessee, as follows:
940,000/1,790,000 = 0.525
Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:
• 0.525x = Annual salary of the governor of Tennessee
,•
Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:
0.525x = 0.525 * 2,000,000 = 1,050,000
The annual salary of the governor of Tennessee woudl be 1,050,000
Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
we have that
F=m*a
we have
m=30 kg
F=60 N
substitute in the formula
60=30*a
solve for a
a=60/30
a=2 m/s^2
therefore
the answer is 2 meters per second squaredMike is shopping for new clothes. He has a coupon for 20% off of his total purchase. His purchase price before the discount is $68. Let T represent the total cost after the discount. Which equation can be written to model this scenario? Select all that apply.68-0.2(68) = T68 - .20 =T68-20 = T0.8(68) = T0.2(68) =T
ANSWER
68 - 0.2(68) = T
0.8(68) = T
EXPLANATION
The coupon allows for 20% off of his total purchase.
His purchase price before the discount is $68.
To find the price after the discount, we can use two methods:
=> Find 20% of $68 and then subtract from $68 to get T.
That is:
[tex]\begin{gathered} 68\text{ - (}\frac{20}{100}\cdot\text{ 68) = T} \\ \Rightarrow\text{ 68 - 0.2(68) = T} \end{gathered}[/tex]=> Subract 20% from a total of 100% and then multiply by $68 to get T.
That is:
[tex]\begin{gathered} (100\text{ - 20)\% }\cdot\text{ 68 = T} \\ \Rightarrow\text{ 80\% }\cdot\text{ 68 = T} \\ \Rightarrow\text{ 0.8(68) = T} \end{gathered}[/tex]Those are the two answers.
what is 0.024 ÷ 0.231
Answer:
0.10389610389
Step-by-step explanation:
Hi!
I plugged it into a calculator:
0.024 ÷ 0.231 = 0.10389610389
Have a great day! :)
For the rotation 707°, find the coterminal angle from 0° ≤ 0 < 360°, thequadrant and the reference angle
Explanation
We are required to determine the coterminal, quadrant and reference angle of 707°.
This can be achieved as:
Therefore, the reference angle can be gotten as:
[tex]720\degree-707\degree=13\degree[/tex]Hence, the reference angle is 13°.
The angle lies in the fourth quadrant.
The cotermi
A company has developed a new deluxe AAA battery that is supposed to last longer than its regular AAA battery. However these new batteries are more expensive to produce. So the company would like to be convinced that they really do last longer. Based on years of experience, the company knows that its regular AAA batteries last lor 45 hours of continuous use. On average. The company selects an SRS Of 50 new batteries and uses them continuously until they are completely drained. The Sample mean lifetime is X =46.9 hours with a Standard deviation of S=4.6 hours A) Check for the conditions for the situation B) Calculate the test statistic for this situation C) What is the P value for this situation? D) What conclusion do you draw with 5% significance level? why? E) What type of error could you possibly make here? I
1 sample t-test
[tex]\mu=the\text{ true mean lifetime of new AAA batteries}[/tex][tex]\begin{gathered} H_0\colon\mu=45\text{ hours} \\ H_a\colon\mu>45\text{ hours} \end{gathered}[/tex][tex]n=50[/tex]B)
Calculating t test statistic
[tex]\begin{gathered} t=\frac{statistic-parameter}{s\tan dard\text{ deviation of statistic}} \\ t=\frac{\bar{x}-\mu_0}{\frac{s_x}{\sqrt[]{n}}} \end{gathered}[/tex]Plugging in the values, we have:
[tex]\begin{gathered} t=\frac{\bar{x}-\mu_0}{\frac{s_x}{\sqrt[]{n}}} \\ t=\frac{46.9-45}{\frac{4.6}{\sqrt[]{50}}} \\ t=\frac{1.9}{0.6505} \\ t=2.9207 \end{gathered}[/tex]C)t test statistic = 2.9207
degrees of freedom = n - 1 = 50 - 1 = 49
Using a calculator, we can calculate the p-value.
[tex]p-\text{value}=0.002633[/tex]D)Since p value is less than significance level (p value < alpha), then we will reject H_0 and take the alternate hypothesis.
Thus the test suggests that the new batteries do last more than 45 hours.
E)
We could've done Type I error here.
Type I error or α: Reject the null when it’s true.
Find the coordinates of the vertex of the graph of y=4-x^2 indentify the vertex as a maximum or minimum point A.(2,9);maximumB.(0,4);minimumC.(0,4);maximum D.(2,0);minimum
Let's begin by identifying key information given to us:
[tex]\begin{gathered} y=4-x^2 \\ y=-x^2+4 \\ a=-1,b=0,c=4 \\ x_v=-\frac{b}{2a}=-\frac{0}{2(-1)}=0 \\ y_v=-\frac{b^2-4ac}{4a}=-\frac{0^2-4(-1)(4)}{4(-1)} \\ y_v=-\frac{0+16}{-4}=\frac{-16}{-4}=4 \\ y_v=4 \\ \\ \therefore The\text{ vertex of the equation is }(0,4) \end{gathered}[/tex]To know if the vertex is the maximum or minimum point, we will follow this below:
[tex]\begin{gathered} y_v=4 \\ \Rightarrow This\text{ is a minimum point} \end{gathered}[/tex]Hence, the answer is B.(0,4); minimum
A local band was interested in the average song time for rock bands in the 1990s. They sampled eight different rock bands and found that the average time was 3.19 minutes with a standard deviation of 0.77 minutes.
Calculate the 95% confidence interval (in minutes) for the population mean.
The 95% confidence interval (in minutes) for the population mean is of:
(2.55, 3.83).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are described as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The distribution is used when the standard deviation of the population is not known, only for the sample.
In the context of this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 3.19, s = 0.77, n = 8[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 63 df, is t = 2.3646.
Then the lower bound of the confidence interval is calculated as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3.19 - 2.3646\frac{0.77}{\sqrt{8}} = 2.55[/tex]
The upper bound is calculated as follows:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3.19 + 2.3646\frac{0.77}{\sqrt{8}} = 3.83[/tex]
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Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
The derivative of the function f(x) = -5x²+3x-2 is -10x+3.
Given the function is f(x) = -5x²+3x-2
Differentiate with respect to x.
d/dx -5x²+3x-2 = d/dx (-5x²) + d/dx(3x) - d/dx(2)
using the power rule d/dx [xⁿ] = nxⁿ⁻¹
⇒ d/dx -5x²+3x-2 = -5(2)x²⁻¹ + 3(1) - 0
⇒ d/dx -5x²+3x-2 = -10x+3
The power rule states that the derivative of xn is nx(n-1) for every x if n is a positive integer, regardless of whether you are thinking of derivatives at a point (numbers) or derivatives on an interval (functions).
Hence we get the derivative as -10x+3.
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I just need to answer the question number one NOT two .I just need a brief explanation with the answer
The bedroom of the apartment has 4 walls.
2 of them have the following dimensions: 16ft x 8ft.
2 of them have the following dimensions: 10ft x 8ft.
Find the area of each wall and then add them to find the total area:
[tex]\begin{gathered} Aw1=16ft\cdot8ft=128ft^2 \\ Aw2=10ft\cdot8ft=80ft^2 \end{gathered}[/tex][tex]\begin{gathered} TA=2\cdot Aw1+2\cdot Aw2 \\ TA=2\cdot128ft^2+2\cdot80ft^2 \\ TA=256ft^2+160ft^2 \\ TA=416ft^2 \end{gathered}[/tex]It means that the total area to be covered is 416ft^2.
Now, divide this area by the area that can be covered by one roll of wallpaper to find the number of rolls needed:
[tex]n=\frac{416ft^2}{50ft^2}=8.32[/tex]It means that 8.32 rolls are needed to cover the bedroom. You will have to buy 9 rolls.
2/(x - 1) - 1/(x + 1) - 3/(x ^ 2 - 1)
The first step to solve this problem is to solve the substraction between the first two fractions:
[tex]undefined[/tex]At one time, it was reported that 27.9% of physicians are women. In a survey of physicians employed by a large health system, 45 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians in the system exceeds 27.9%?Solve this hypothesis testing problem by finishing the five steps below.
SOLUTION
STEP 1
The hull hypothesis can written as
[tex]H_0\colon p=0.279[/tex]The alternative hypothesis is written as
[tex]H_1\colon p>0.279[/tex]STEP 2
The value of p will be
[tex]\begin{gathered} \hat{p}=\frac{X}{n} \\ \hat{p}=\frac{45}{120}=0.375 \\ \text{where n=120, x=}45 \end{gathered}[/tex]STEP3
From the calculations, we have
[tex]\begin{gathered} Z_{\text{cal}}=2.34 \\ \text{Z}_{\text{los}}=0.05 \end{gathered}[/tex]We obtained the p-value has
[tex]\begin{gathered} p-\text{value}=0.0095 \\ \text{level of significance =0.05} \end{gathered}[/tex]STEP4
Since the p-value is less than the level of significance, we Reject the null hypothesis
STEP 5
Conclusion: There is no enought evidence to support the claim
The volume of a right circular cylinder with a radius of 4 in. and a height of 12 in. is ___ π in^3.
For the given right cylinder:
Radius = r = 4 in
Height = h = 12 in
The volume of the cylinder =
[tex]\pi\cdot r^2\cdot h=\pi\cdot4^2\cdot12=192\pi[/tex]So, the answer will be the volume is 192π in^3
The state of California charges homeowners approximately $1,200 per year in property taxes for every $100,000 a person's home is worth. If Mr. Cohen's home in Studio City, CA is worth $1,600,000, how much does he have to pay in property taxes per year? Set up a pair of equivalent ratios and then use your knowledge of cross products to solve. You may use calculator.
We have the next information
1,200 ----- 100,000
x ----- 1,600,000
x is the missing quantity
x can be calculated in this way
[tex]x=\frac{1,600,000\cdot1200}{100,000}=19200[/tex]Mr. Cohen has to pay per year $19,200 taxes per year
help me please if you can A.(0, 3)B. (-1, 5)C.(1, 1.5)
Answer:
A. (0, 3)
C. (1, 1.5)
Explanation:
A point is a solution to the system if it satisfies both inequalities.
So for each option, we get:
Replacing (x, y) = (0, 3)
y ≥ -2x + 3
3 ≥ -2(0) + 3
3 ≥ 3
y ≤ -x² - x + 4
3 ≤ -0² - 0 + 4
3 ≤ 4
Since both inequalities are satisfied, (0, 3) is a solution.
For (x, y) = (-1, 5)
y ≥ -2x + 3
5 ≥ -2(-1) + 3
5 ≥ 2 + 3
5 ≥ 5
y ≤ -x² - x + 4
5 ≤ -(-1)² - (-1) + 4
5 ≤ -1 + 1 + 4
5 ≤ 4
Since 5 is not lower than 4, (-1, 5) is not a solution
For (x, y) = (1, 1.5)
y ≥ -2x + 3
1.5 ≥ -2(1) + 3
1.5 ≥ -2 + 3
1.5 ≥ 1
y ≤ -x² - x + 4
1.5 ≤ -(1)² - (1) + 4
1.5 ≤ -1 - 1 + 4
1.5 ≤ 2
Since both inequalities are satisfied, (1, 1.5) is a solution.
Therefore, the answers are
A. (0, 3)
C. (1, 1.5)
For these problems, please show your algebraic work using logarithms. 1. Determine the doubling time for each situation listed below. a. A population is growing according to P = P_0e^0.2t b. A bank account is growing by 2.7% each year compounded annually.
Answer: We need to find the doubling time for population growth:
Population growth is given by
[tex]P=P_oe^{(0.2)t}[/tex]Where:
[tex]\begin{gathered} P\rightarrow\text{final} \\ P_o\rightarrow I\text{nitial} \end{gathered}[/tex]For the population to double, it implies that:
[tex]P=2P_o[/tex]Therefore:
[tex]\frac{P}{P_o}=\frac{2P_o}{P_o}=2=e^{(0.2)t}[/tex]Solving for time "t" gives:
[tex]2=e^{(0.2)t}\rightarrow\ln (2)=(0.2)t\rightarrow t=\frac{\ln (2)}{(0.2)}=3.46u[/tex]Solve the following system of equations graphically on the set of axes below. Plot two or more dotes on the graphy = 2x - 8 y = -x + 4
Given:-
[tex]y=2x-8,y=-x+4[/tex]To find the graphical representation.
So the graph of y=2x-8 is,
Also the graph of y=-x+4 is,
Combining we get the graph
So the point is (4,0).
The table shows the amount of water used daily to water the fairways at Fairlawn Golf Course. To the nearest tenth,determine the mean absolute deviation of the data. A. 2.3 B. 7.7 C. 10 D. 12.3
Answer:
2.3
Explanation:
The formula for calulating mean deviation is expressed as:
[tex]\frac{1}{n}\sum ^n_{i\mathop=1}|x_i-m|[/tex]where;
m is the mean of the data set
Xi are individual values
n is the total sample space
Get the mean;
n = 7
mean = (10+12+11+15+9+8+5)/7
mean = 70/7
mean = 10
Get the mean deviation:
Mean deviation = (10-10)+(12-10)+(11-10)+(15-10)+(9-10)+(8-10)+(5-10)/7
Since the values is in modulus |xi - m| will give a positive value, hence;
Mean deviation = (0+2+1+5+1+2+5)/7
Mean deviation = 16/7
Mean deviation = 2.28
Mean deviation = 2.3 (to the nearest tenth)
