x + (x + 1) + (x + 2) = -54
x + x + 1 + x + 2 = -54
3x = -54 - 3
3x = -57
x = -57/3
x = -19
x + 1 = -19 + 1 = -18
x + 2 = -19 + 2 = -17
The numbers are = - 17, -18, -19
A data set has these values: 8, 10, 10, 12, 12, 12, 12, 14, 14, 16. The histogramof the distribution is shownWhich statement does not describe the data set?O A. It has a mode of 12.O B. It is symmetricO c. It has a range of 17OD. It has a mean of 12.
Given a data set has these values: 8, 10, 10, 12, 12, 12, 12, 14, 14, 16.
It is clear that the frequency of 12 is the greatest of all. So, the mode of the data is 12.
From the graph it is clear that, it is symmetric.
The range of the data is Max - Min = 16 - 8 = 8. Thus, range is 8.
The mean of a data is:
[tex]\text{Mean}=\frac{\text{ sum of all observation}}{\text{ total number of observation}}[/tex]For the given data:
[tex]\begin{gathered} \text{Mean}=\frac{8+10+10+12+12+12+12+14+14+16}{10} \\ =\frac{120}{10} \\ =12 \end{gathered}[/tex]Thus, the mean of the data is 12.
Thus, the statement that does not describe the data set is c.
3All 6 members of a family work. Their hourly wages (in dollars) are the following.26, 11, 12, 40, 21, 22Send data to calculatorAssuming that these wages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
Bearing in mind that the formula for the population standard deviation is
[tex]{\sigma={\sqrt{{\frac{1}{N}}\sum_{i=1}^{N}(x_{i}-\mu)^{2}}}}[/tex]Using the calculator and remembering that we are assuming that the information is about the whole population.
The standard deviation requested is equal to 10.60.
A lifeguard earns $320 per week for working 40 hours plus $12 per hour worked over 40 hours. A lifeguard can work a maximum of 60 hours per week. Which graph represents the lifeguard's weekly earnings in dollars for working h hours over 40?
For working h hours over 40, the lifeguard earns 12h dollars.
Then for h = 20 hours over 40, the lifegurad earns:
12(20) = 240
However, it is necessary to take into account that the life guard earns $320 per week for working 40 hours.
Then, the total amount of money he earns is:
320 + 240 = 560
The line that best represent the previous calculations is the graph G.
THere you can notice that for h=0 hours after 40 the earning are 320, and for h=20 hours the earning are 560.
Sam borrowed Php14,500.00 for 2 years and had to pay Php2320.00 simple interest at the end of that time. What rate of interest did he pay?
We will use the next formula
[tex]I=P\cdot r\cdot t[/tex]Where
P is the principal
r is the rate
t is the time
I is the interest
we have the next information
P=14,500
t=2
I=2320
we substitute in the formula
[tex]2320=14500(r)(2)[/tex]We isolate the rate
[tex]r=\frac{2320}{14500(2)}=0.08[/tex]The rate of interest is 8%
ANSWER
the rate of interest did he pay is 8%
This is Geometry so can you please help me out!
To map the purple figure onto the white figure we have to
• Translate ,10 units right side.
,• Translate, 8 units up.
Hence, both transformations are translations.
Determine the domain and range of the function using the graph below. Give your answer as an inequality using the appropriate variables.12345-1-2-3-4-51234567-1-2-3-4-5-6-7-8-9-10-11-12-13-14-15Domain: Range:
Remember that
The Domain is the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
The Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair).
in this problem
the domain is the interval (0,5]
[tex]0\text{ < x }\leq\text{ 5}[/tex]and the range is the interval [-3,6]
[tex]-3\leq\text{ y }\leq6[/tex]Express (7 - 3i) + (- 2 - 3i) in the form of a + ib.5 - 6i5 + 6i6 - 5i6 - 3i
SOLUTION:
Step 1:
In this question, we are given the following:
Express (7 - 3i) + (- 2 - 3i) in the form of a + ib.
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
[tex]5\text{ - 6i \lparen OPTION A \rparen}[/tex]Two circles have their centers at (2, 4) and (-14, 2) and they intersect at the point (-2, 7). What is the radius of each circle?
To determine the radius of each circle, find the distance of the intersection and the center of the circles.
Thus, the radius of the circle with center (2,4) is as follows:
[tex]\begin{gathered} r_1=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{(-2-2)^2+(7-4)^2} \\ =\sqrt[]{(-4)^2+(3)^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5 \end{gathered}[/tex]Thus, the radius of the circle with center (-14,2) is as follows:
[tex]\begin{gathered} r_2=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{\lbrack-2-(-14)\rbrack^2+(7-2)^2} \\ =\sqrt[]{(-2+14)^2+(7-2)^2} \\ =\sqrt[]{(12)^2+(5)^2} \\ =\sqrt[]{144+25} \\ =\sqrt[]{169} \\ =13 \end{gathered}[/tex]Thus, the radius of the circles with centers at (2,4) and (-14,2) passing through (-2,7) are 5 and 13, respectively.
All I need is the answer please and thank you
we have
the ordered pairs
(0,4)
(3,5)
(2,1)
(-1,0)
Plot the given points
see the attached figure
therefore
the answer is a parallelogramThe Kirkpatrick family placed a large back-to-school order online. The total cost of the clothing was $765.47, and the shipping weight was 29 lb. 12 oz. They live in the PostalZone 2 (shipping charges are $5.94 for 15 lb. or less; every additional lb. or fraction of a lb. above 15 lbs. is $0.12 per lb) and the sales tax rate is 9.0%. Find the total cost ofthe order$837.33$842.10$844.09$847.87None of these choices are correct.
Given:
The total cost of the clothing, C=$765.47.
The shipping weight, W=29 lb. 12 oz.
The sales tax rate, R=9.0%.
The shipping weight in lb is,
[tex]\begin{gathered} W=29\text{ lb+0.12 oz} \\ =29\text{ lb+0}.12\text{ oz}\times\frac{\frac{1}{16}\text{ lb}}{1\text{ oz}} \\ =29\text{ lb+0.0075 lb} \\ =29.0075\text{ lb} \end{gathered}[/tex]Given, shipping charges are $5.94 for 15 lb. For every additional lb. or fraction of a lb. above 15 lbs., the shipping charge is $0.12 per lb.
The shipping weight above 15 lb is,
[tex]\begin{gathered} w=W-15 \\ =29.0075-15 \\ =14.0075\text{ lb} \end{gathered}[/tex]Now, the total shipping charge for 29.0075 lb is,
[tex]\begin{gathered} S=5.94+0.12w \\ =5.94+0.12\times14.0075 \\ =5.94+1.6809 \\ =7.6209\text{ dollars} \end{gathered}[/tex]Now, the pre tax cost of the item is,
[tex]\begin{gathered} c=C+S \\ =765.47+7.6209 \\ =773.0909 \end{gathered}[/tex]Now, the sales tax of the item is,
[tex]\begin{gathered} ST=\frac{R}{100}\times c \\ =\frac{9}{100}\times773.0909 \\ =69.578 \end{gathered}[/tex]Now, the total cost of the order is,
[tex]\begin{gathered} T=C+ST \\ =773.0909+69.578 \\ =842.67 \end{gathered}[/tex]So, the total cost of the order can be $842.10.
7) On a cold, dark, and windy day in Witchita, the temperature was 3 degrees. That night the temperature dropped 24 degrees. What was the temperature that night?
3-24= -21
The temperature was -21 degrees because it dropped 24 degrees from 3 degrees. thats why we used the substraction below.
Categorize the following logical fallacy.We can go to the amusement park or the library. The amusement park is too expensive, so we must go to the library.The options are listed in the picture
False dilemma fallacy
The argument either misrepresents the consequences of choices that are available when making a decision, or else it fails to present all the choices available.
The given statement is:
We can go to the amusement park or the library. The amusement park is too expensive, so we must go to the library.
Therefore, the correct answer is the False dilemma.
Evaluate10y + x^2, if x is 6, and y is 4
Substitute the following values to their respective variables
[tex]\begin{gathered} 10y+x^2 \\ \Rightarrow10(4)+(6)^2 \\ \Rightarrow40+36 \\ \Rightarrow76\text{ (final answer)} \end{gathered}[/tex]Suppose sin(theta) = -3/7 and theta is in quadrant 4. Use a trig identity to find the value of cos(theta).
Since theta is in quadrant 4, the cosine of theta is positive.
Now, to solve this problem, we can use the following trigonometric identity:
[tex]\begin{gathered} \cos ^{2}\theta+\sin ^2\theta=1 \\ \\ \cos ^2\theta=1-\sin ^{2}\theta \\ \\ \cos \theta=\sqrt[]{1-\sin ^{2}\theta} \end{gathered}[/tex]Then, using
[tex]\sin \theta=-\frac{3}{7}[/tex]we obtain:
[tex]\begin{gathered} \cos \theta=\sqrt[]{1-\mleft(-\frac{3}{7}\mright)^2} \\ \\ \cos \theta=\sqrt[]{1-\frac{9}{49}} \\ \\ \cos \theta=\sqrt[]{\frac{49}{49}-\frac{9}{49}} \\ \\ \cos \theta=\sqrt[]{\frac{40}{49}} \\ \\ \cos \theta=\frac{2\sqrt[]{10}}{7} \end{gathered}[/tex]Therefore, the answer is
[tex]\cos \theta=\frac{2\sqrt[]{10}}{7}[/tex]10) Which statement is true about the following pentagon?Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the originas the center of dilation using the rule (x,y) → (n) to create pentagon M'N+PQR.NMPentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.Pentagon M'N'PQ'R' is smaller r than pentagon MNPQR, because the scale factor is less than 1.Pentagon M'N'PQ'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.
Since the scale factor is a fraction of 1, the scale factor less than one.
When the scale factor is less than one, the result of the dilation is smaller than the original figure.
So, the correct answer is:
Pentagon M'N'PQ'R' is smaller r than pentagon MNPQR, because the scale factor is less than 1.
I cannot find out EF for the life of me! Can someone help
Since the segments AE and EB are congruent and DF and FC are congruent, the trapezoid ABCD and EBCF are similar.
Therefore the proportion between the top bases of the trapezoids is the same as the bottom bases of the trapezoids.
So we have:
[tex]\begin{gathered} \frac{AD}{EF}=\frac{EF}{BC} \\ \\ \frac{5}{3x+7}=\frac{3x+7}{7x+6} \\ 5\cdot(7x+6)=(3x+7)^2 \\ 35x+30=9x^2+42x+49 \\ 9x^2+7x+19=0 \end{gathered}[/tex]Finding the roots using the quadratic formula, we have:
[tex]\begin{gathered} a=9,b=7,c=19 \\ \\ x_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a}=\frac{-7+\sqrt[]{49-4\cdot9\cdot19}}{18} \end{gathered}[/tex]Define an exponential function, f(x), which passes through the points (0,36) and(2,1). Enter your answer in the form a · b^xf(x) =
The general form of the exponential function is:
[tex]f(x)=a\cdot b^x[/tex]we will find the equation of the exponential function which passes through the points (0, 36) and (2, 1)
So,
when x = 0, f(0) = 36
[tex]\begin{gathered} 36=a\cdot b^0 \\ 36=a\cdot1 \\ a=36 \end{gathered}[/tex]and when x = 2, f(x) = 1
Using the substitution with a = 36
So,
[tex]\begin{gathered} 1=36\cdot b^2 \\ b^2=\frac{1}{36} \\ \\ b=\sqrt[]{\frac{1}{36}}=\frac{1}{6} \end{gathered}[/tex]So, the answer will be the equation of the function is:
[tex]f(x)=36\cdot(\frac{1}{6})^x[/tex]Evaluate the polynomial X^4 + 4x^3 – 2x² +9 when x=-1.
For x = -1, we have:
[tex]\begin{gathered} x^4+4x^3-2x^2+9 \\ \Rightarrow(-1)^4+4(-1)^3-2(-1)^2+9=1+4(-1)-2(1)+9 \\ =1-4-2+9=-3+7=4 \end{gathered}[/tex]Therefore, the polynomial evaluated in x=-1 results in 4
9) An observer standing on the top of a vertical cliff spots a house in the adjacent valley at an angle of depression of 17 degrees. The cliff is 65 m tall. How far is the house from the base of the cliff, to the nearest meter?
Answer:
213 meters.
Explanation:
Height of the cliff = 65 m
The angle of depression = 17 degrees.
A diagram representing this problem is attached below:
We solve for x in the diagram.
[tex]\begin{gathered} \tan \theta=\frac{Opposite}{\text{Adjacent}} \\ \tan 17^0=\frac{65}{x} \\ x\tan 17^0=65 \\ x=\frac{65}{\tan 17^0} \\ x=212.6m \\ x\approx213m \end{gathered}[/tex]The distance of the house from the base of the cliff, to the nearest meter, is 213 meters.
Calculate the volume of a regular pyramid if the area of the base and the altitude lenght are given.
Solution:
Given regular pyramids;
The volume, V, of a regular pyramid is;
[tex]\begin{gathered} V=\frac{1}{3}bh \\ \\ \text{ Where }b=area\text{ of base},h=height \end{gathered}[/tex](a)
[tex]\begin{gathered} S_{ABCD}=9cm^2,SO=5cm \\ \\ V=\frac{1}{3}(9)(5)cm^3 \\ \\ V=15cm^3 \end{gathered}[/tex](b)
[tex]\begin{gathered} S_{ABCDEF}=500mm^2,SO=3cm \\ \\ S_{ABCDEF}=50cm^2 \\ \\ V=\frac{1}{3}(50)(3)cm^3 \\ \\ V=50cm^3 \end{gathered}[/tex]One month Lucy rented 3 movies and 5 video games for a total of $39. The next month she rented 9 movies and 7 video games for a total of $63. Find the rental cost for each movie and each video game.Rental cost for each movie:Rental cost for each video game:Solve by using system of linear equations.
Given the word problem, we can deduce the following information:
1. One month Lucy rented 3 movies and 5 video games for a total of $39.
2. The next month she rented 9 movies and 7 video games for a total of $63.
To determine the rental cost for each movie and each video game, we first let:
m= Rental cost for each movie
v= Rental cost for each video game
Hence, the linear equations would be:
[tex]\begin{gathered} 3m+5v=39 \\ 9m+7v=63 \end{gathered}[/tex]We solve for m in 3m+5v=39:
[tex]\begin{gathered} 3m+5v=39 \\ Simplify\text{ and rearrange} \\ 3m=39-5v \\ m=\frac{39-5v}{3} \end{gathered}[/tex]Next, we plug in the value of m into 9m+7v=63:
[tex]\begin{gathered} 9m+7v=63 \\ 9(\frac{39-5v}{3})+7v=63 \\ Simplify\text{ and rearrange} \\ 3(39-5v)+7v=63 \\ 117-15v+7v=63 \\ 117-8v=63 \\ 8v=117-63 \\ 8v=54 \\ v=\frac{54}{8} \\ v=6.75 \end{gathered}[/tex]Then, we plug in v=6.75 into m=(39-5v)/3:
[tex]\begin{gathered} m=\frac{39-5v}{3} \\ m=\frac{39-5(6.75)}{3} \\ Simplify \\ m=1.75 \end{gathered}[/tex]Therefore,
Rental cost for each movie = $1.75
Rental cost for each video game= $6.75
The equation D=žn(n-3) gives the number of diagonals D for a polygon with n sides. Use this equation to find the number of diagonals for a palygon that has 6 sides.
1) Considering that the formula for the number of diagonals of a polygon is:
[tex]D=\frac{n(n-3)}{2}[/tex]2) And the question tells us that we need to find the number of diagonals for a polygon that has 6 sides, we can plug into that n=6 and solve it this way:
[tex]\begin{gathered} D=\frac{6(6-3)}{2} \\ D=\frac{6\left(3\right)}{2}=\frac{18}{2} \\ D=9 \end{gathered}[/tex]Given the point A (-8 , 1) and point B (-2 , 4), find the following.A. Find the slope of line ABB. Write the equation of a line in point-slope form for ABC. Write the equation of a line in slope-intercept form for AB
First, find the slope (m):
Apply the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Given the points:
(x1,y1) = (-8,1)
(x2,y2)= (-2.4)
m= 4-1 / -2-(-8) = 3 / 6 = 1/2
Slope intercept form:
y=mx+b
Where:
m= slope = 1/2
b= y-intercept
So far:
y = 1/2x + b
Replace (x,y) with any point , for example (-8,1), and solve for b
1 = 1/2 (-8) + b
1 = -4 + b
1+4= b
b= 5
Slope intercept form:
y= 1/2x + 5
point slope form:
y-y1 = m ( x- x1 )
y- 1 = m ( x + 8 )
If the sequence 2, 2, 4, 6, 10,... were to follow the same pattern as the Fibonacci sequence, what are the next three terms?A. 14,20,26B.14,22,30C.16,26,36D.16,26,42
Okay, here we have this:
Considerando que la sucesión fibonacci sigue el siguiente patrón:
[tex]f_n=f_{n-1}+f_{n-2}[/tex]So, we need to find the terms 6th, 7th, 8th; let's do it:
Term 6th:
[tex]\begin{gathered} f_6=f_5+f_4 \\ f_6=10+6=16 \end{gathered}[/tex]Term 7th:
[tex]\begin{gathered} f_7=f_6+f_5 \\ f_7=16+10=26 \end{gathered}[/tex]Term 8th:
[tex]f_8=f_7+f_6=26+16=42[/tex]Finally we obtain that the correct answer is the option D.
Solve for x and graph.|35-7x| less then or equal to 70And/Or
Solving for x
[tex]\begin{gathered} \text{Apply the absolute rule:} \\ \text{If }|u|\le a,a>0,\text{ then }-aCombine the two solutions, the solution for the inequality | 35 - 7x | ≤ 70 is[tex]-5\le x<15[/tex]Using this interval, draw a solid vertical line at x = -5, and x = 15, and shade the interval in between which gives us
drag each tile the correct box not all tiles will be used Consider the recurslvely defined function below f(1)=10f(n)=2.2. . f(n-1), for n =2,3,4create the five terms of the sequence defined by the given function20. 48.4. 10. 101.64. 234.256. 52.8127.776. 106.48. 22
We want to find the five terms of the sequence:
f (n) = 2.2 · f (n - 1)
where f (1) = 10
Replacing when n = 2:
f (n) = 2.2 · f (n - 1)
f (2) = 2.2 · f (2 - 1)
f (2) = 2.2 · f (1) [f(2- 1 )= f(1)]
f (2) = 2.2 · 10 [f (1) = 10]
f (2) = 22 [2.2 · 10 = 22]
f(2) = 22Replacing when n = 3:
f (n) = 2.2 · f (n - 1)
f (3) = 2.2 · f (3 - 1)
f (3) = 2.2 · f (2) [f(3- 1 )= f(2)]
f (3) = 2.2 · 22 [f (2) = 22]
f (3) = 48.4 [2.2 · 22 = 48.4]
f (3) = 48.4Replacing when n = 4:
f (n) = 2.2 · f (n - 1)
f (4) = 2.2 · f (4 - 1)
f (4) = 2.2 · f (3) [f(4- 1 )= f(3)]
f (4) = 2.2 · 48.4 [f (3) = 48.4]
f (4) = 106.48 [2.2 · 48.4 = 106.48]
f (4) = 106.48Replacing when n = 5:
f (n) = 2.2 · f (n - 1)
f (5) = 2.2 · f (5 - 1)
f (5) = 2.2 · f (4) [f(5- 1 )= f(4)]
f (5) = 2.2 · 106.48 [f (4) = 106.48]
f (5) = 234.256 [2.2 · 106.48 = 234.256]
f (5) = 234.256 Answer: the five first terms of the sequence are: 10, 22, 48.4, 106.48, 234.256Here are the scores of 13 students on a history test*Check Photo*
Answer
Minimum = 61
Lower quartile = 67
Median = 72
Upper quartile = 87
Maximum = 95
Interquartile range = 20
Explanation
61, 66, 67, 67, 69, 70, 72, 74, 82, 85, 89, 92, 95
Minimum
This is the least number in the distribution.
So,
Minimum = 61
Lower quartile
The lower quartile is given as the variable in the position of
¼ (N + 1)
N = 13
¼ (N + 1) = ¼ (13 + 1) = ¼ (14) = 3.5
The lower quartile is in between the 3rd and 4th
3rd variable = 67
4th variable = 67
Lower quartile = (67 + 67)/2 = (134/2) = 67
Median
The median is the number in the middle of the distribution when the variables are arranged in increasing or decreasing order.
For this distribution,
Median = 7th variable = 72
Upper quartile
The upper quartile is given as the variable in the position of
(3/4) (N + 1)
N = 13
(3/4) (N + 1) = (3/4) (13 + 1) = (3/4) (14) = 10.5
The upper quartile is in between the 10th and 11th variables
Upper quartile = (85 + 89)/2 = (174/2) = 87
Maximum
This is the number with the greatest value in the distribution.
Maximum = 95
Interquartile range
This is the difference between the upper and lower quartiles.
Interquartile range = (Upper quartile) - (Lower quartile)
Interquartile range = 87 - 67
Interquartile range = 20
Hope this Helps!!!
find the value of x and round to the whole degree
Using trigonometric ratio
[tex]\begin{gathered} \cos x^{\circ}=\frac{adjacent}{\text{hypotenuse}} \\ \text{cosx}=\frac{5}{8} \\ \cos x=0.625 \\ x=\cos ^{-1}0.625 \\ x=51.3178125465 \\ x=51^{\circ} \end{gathered}[/tex]Certain ball bearings are packed in boxes that hold 500. 25 boxes of ball bearings are then packed each crate for shipping. To make sure that theball bearings being prepared for shipping were being produced with the correct measurements, asupervisor decided to conduct asample for quality-control purposes.He randomly picked one crate,opened it up, and then randomlychose two boxes of ball bearingsfrom that crate. He measured all ofthe ball bearings from the two boxes.This is an example of a:Answer Choices:convenience sample.systematic sample.cluster samplestratified random sample.
Given:
Number of balls packed in a box = 500
Number of boxes packed for shipping = 25
Given that the supervisor randomly picked one crate, opened it up, then randomly chose two boxes from the crate.
He then measures all of the ball bearings from the two boxes.
Let's determine the type of sampling method used here.
Here, we can see that the balls were packed in boxes, then into crates.
Since the manger then chooses one crate out of all crates, then picks only two boxes and sampled all balls in the tow boxes, the type of sampling technique used here can be said to be the cluster sampling technique.
Cluster sampling involves a sampling method where by the population is divided into clusters(small groups), then they randomly select select among these clusters to form a sample.
The cluster sampling is used mostly when the population is large.
ANSWER:
Cluster sampling.
During the summer, Martin estimates that he must earn between $600 and 1000 inorder to pay for his car insurance. If he earns $8 an hour, how many hours must hework? Variable Represents:Inequality:Solve:Sentence:
Answer:
75≤h≤125
Explanation:
Let the variable = h
Variable h represents: the number of hours which he must work
If he works for h hours and earns $8 an hour, his income = $8h.
Since he must earn between $600 and 1000 in order to pay for his car insurance, we have the inequality
[tex]600\leq8h\leq1000[/tex]Next, we solve for h.
[tex]\begin{gathered} \frac{600}{8}\leq\frac{8h}{8}\leq\frac{1000}{8} \\ 75\leq h\leq125 \end{gathered}[/tex]Martin must work between 75 to 125 hours in order to be able to pay for his car insurance.