to round to the nearest thousand, we have to look at the hundreds place. In this case, there is a 2 in the hundreds place, which is less than 5. Then, the 3 in the thousands place must be kept. In conclusion, 3,204 rounded to the nearest thousand is 3,000
Answer:
3,000
Step-by-step explanation:
the thousands place is where the 3 is and we look at the number next to it if it is 5 or over we round up or if it’s under 5 we round down and since 2 is under 5 we round down to 3,000
The pentagonal prism below has a cross-sectional area of
27 cm² and a length of 3 cm.
Calculate the volume of the prism.
Give your answer in cm³.
Answer:
volume=27 multiply 3 =81
Check for the discontinuity of the function and tell if the discontinuity is removable or not
Which is an equation of a direct proportion? y=8x y=
12x+4 y=12x y=4x−4
The equation of a direct proportion is A. y=8x.
What is a direct proportion?It should be noted that a direct proportion is also a direct variation. It is one when the relation between the two quantities have a value that's constant.
In this case, it's illustrated as y = 8x.
Let's say x = 1 y will be = (8 × 1) = 8
When x = 2, y = (8 × 2) = 16
In this case, it should be noted that the constant of 8 is illustrated.
In conclusion, the correct option is A.
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Simplify the following expression.-5a - 10(-a - 10) + 1 - 2a
Step 1
break the parenthesis
[tex]\begin{gathered} -5a-10(-a-10)+1-2a \\ -5a+10a+100+1-2a \\ \end{gathered}[/tex]Add similar terms
[tex]\begin{gathered} -5a+10a+100+1-2a \\ 3a+101 \end{gathered}[/tex]so, the answer is 3a+101
What number belongs in the blank space in the recursive formula?
The recursive formula of the arithmetic sequence is
[tex]a_n=a_{n-1}+d[/tex]Where d is the common difference between each 2 consecutive terms
The explicit form of the arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
Since the given explicit form of the sequence is
[tex]a_n=13+(n-1)6[/tex]Then
a = 13
d = 6
The recursive form of the sequence should be
[tex]a_n=a_{n-1}+6[/tex]The missing number is 6
The answer is D
4(3x-6) + (x + 22) how do I simplify it?
Answer:
13x - 2
Step-by-step explanation:
First Were going to do the distributive property:
So, 4(3x) + 4(-6) = 12x + -24
Now we have :
12x - 24 + x + 22
Now we have to add like terms together:
So, 12x + x = 13x
and 22-24 = -2
So in the end we have 13x -2
What is 2/3 divided by -5/7
[tex] = \frac{2}{3} \div - \frac{5}{7} \\ = \frac{2}{3} \times - \frac{7}{5} \\ = - \frac{14}{15} [/tex]
ATTACHED IS THE SOLUTION.
NOTE WHEN WE ARE DIVIDING WE CHANGE THE DIVISION SIGN TO A MULTIPLICATION SIGN TO AND SWAP THE FOLLOWING FRACTION .
Answer:
-0.019047619
That’s the Answer Hope this helps:)
I quite do t understand will I be now to help mrunderstand
From the given inequality graph
6. The solution shown by the graph is
[tex]\begin{gathered} x<0,or,x\ge4 \\ x<0\cong0>x \\ So, \\ 0>x\ge4 \end{gathered}[/tex]7. The solution shown by the graph is
[tex]x<-6,or,x>-3[/tex][tex]\begin{gathered} x<-6\cong-6>x \\ So, \\ -6>x>-3 \end{gathered}[/tex]8.
The graph of k ≤ -1 is
The graph of k > 4 is
The graph of k ≤ -1, or, k > 4 is
The radius of a circle is 100 millimeters.
What is the diameter?
Answer:
200 millimeters
Step-by-step explanation:
The radius is the distance from the center outwards. The diameter goes straight across the circle through the center, and is therefore twice the radius.
Youngs rule to calculate a child medicine dosage is c=na/n+12 where c is the child's dosage in mL, n is the child's age and A is the adult's dosage in mLA nurse gave an 8-year-old child a dose of 6 mL of medicine. What would be the adult equivalent of this dosage
1) Given that rule, we can write out the following for this case:
[tex]\begin{gathered} C=\frac{nA}{n+12}= \\ \end{gathered}[/tex]2) So let's plug into that the data:
[tex]\begin{gathered} 6=\frac{8A}{8+12} \\ 8A=20\times6 \\ 8A=120 \\ \frac{8A}{8}=\frac{120}{8} \\ A=15 \end{gathered}[/tex]Note that we have cross multiplied and then divided both sides by 8. So the dosage of an adult, according to this rule would be 15 ml
A computer consultant charges $50 plus $40 for each hour she works. The consultant charged $650 for one job. This can be represented by the equation below, where h represents the number of hours worked. How many hours did the consultant work?
Answer:
15
Step-by-step explanation:
from the equation 50+40h=650
solving for h which is the number of hours worked.
40h=650-50
40h=600
h=600÷40
h=15
Select all of the expressions that are less than 10 2/3.A.10 2/3×9/10B.1×10 2/3C.10 2/3×2 1/3D.1/8×10 2/3E.10 2/3×3/5
Given:
[tex]10\frac{2}{3}[/tex]To Determine: All expressions that are less than 10 2/3
Verify for each of the options
OPTION A
[tex]\begin{gathered} 10\frac{2}{3}\times\frac{9}{10} \\ =\frac{32}{3}\times\frac{9}{10} \\ =\frac{96}{10}=9\frac{6}{10} \end{gathered}[/tex]OPTION B
[tex]1\times10\frac{2}{3}=10\frac{2}{3}[/tex]OPTION C
[tex]undefined[/tex]Students (ages 10–18) were surveyed to choose a favorite free-time activity.
Playing Sports Watching Movies/TV Total
Middle School 16 21
High School 11
Total 19
Which category has the greatest marginal frequency?
High school students who chose playing sports
Middle school students who chose watching movie/TV
Students who chose playing sports
Students that are in middle school
Answer:
students that are in middle school
Step-by-step explanation:
i took the test and got it correct.
The category with the greatest marginal frequency is students who chose playing sports. The correct option is C.
What's the frequency?There are 16 students who chose playing sports in middle school and 11 students who chose playing sports in high school, for a total of 27 students who chose playing sports. This is the greatest marginal frequency of all the categories.
The marginal frequency for high school students who chose playing sports is 11.
The marginal frequency for middle school students who chose watching movies/TV is 21.
The marginal frequency for students who chose playing sports is 27.
The marginal frequency for students that are in middle school is 21.
Therefore, the answer is (C) Students who chose playing sports.
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I really need help with this I have been stuck on this for a while. Thank you, Laniyah Hill.
As given by the question
There are given that the graph of line.
Now,
For find the slope, first select point from the graph of line.
So,
The point is:
[tex](1,\text{ -3) and (3, -1)}[/tex]Then,
From the formula of slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1_{}+3_{}}{3_{}-1_{}} \\ m=\frac{2}{2} \\ m=1 \end{gathered}[/tex]Hence, the slope of the line is 1.
Which model(s) below could represent the solution to the problem 45 X 15?
Circle the letter for all that apply.
675 is product by using multiplication's commutative property.
What does multiplication's commutative property mean ?
According to the multiplication's commutative property, you can multiply numbers in any sequence, and the result will always be the same. The amount of seeds is the same even though your gardens differ in appearance (one is longer and one is taller). Whether you multiply 3 by 8 or 8 by 3 is irrelevant.Examples of Commutative Multiplication Property
1 × 2 = 2 × 1 = 2.
3 × 8 = 8 × 3 = 24.
12 × 5 = 5 × 12 = 60.
45 X 15
= 675
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1. Create a box plot using this data: A large school summarizes the number of
teachers at 51 schools in the area. Here is some of the information:
25 25 30 35 40 44 47 52 56
60
64
70
71
75 82 95 110
20
58
H 10
0
20
Explain.
110
40
60
teachers per school
80 100 120
Hint use a straight edge for box
What measure of center would you use to describe the typical value for this data?
me
hotween 2 do
Answer:Display data graphically and interpret graphs: stemplots, histograms, and box plots.
Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.
Box plots (also called box-and-whisker plots or box-whisker plots) give a good graphical image of the concentration of the data. They also show how far the extreme values are from most of the data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them.
To construct a box plot, use a horizontal or vertical number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks one end of the box and the third quartile marks the other end of the box. Approximately the middle
50
percent of the data fall inside the box. The “whiskers” extend from the ends of the box to the smallest and largest data values. The median or second quartile can be between the first and third quartiles, or it can be one, or the other, or both. The box plot gives a good, quick picture of the data.
NOTE
You may encounter box-and-whisker plots that have dots marking outlier values. In those cases, the whiskers are not extending to the minimum and maximum values.
Consider, again, this dataset.
1
,
1
,
2
,
2
,
4
,
6
,
6.8
,
7.2
,
8
,
8.3
,
9
,
10
,
10
,
11.5
The first quartile is two, the median is seven, and the third quartile is nine. The smallest value is one, and the largest value is
11.5
. The following image shows the constructed box plot.
NOTE
See the calculator instructions on the TI web site.
Horizontal boxplot's first whisker extends from the smallest value, 1, to the first quartile, 2, the box begins at the first quartile and extends to the third quartile, 9, a vertical dashed line is drawn at the median, 7, and the second whisker extends from the third quartile to the largest value of 11.5.
The two whiskers extend from the first quartile to the smallest value and from the third quartile to the largest value. The median is shown with a dashed line.
NOTE
It is important to start a box plot with a scaled number line. Otherwise the box plot may not be useful.
EXAMPLE
The following data are the heights of
40
students in a statistics class.
59
;
60
;
61
;
62
;
62
;
63
;
63
;
64
;
64
;
64
;
65
;
65
;
65
;
65
;
65
;
65
;
65
;
65
;
65
;
66
;
66
;
67
;
67
;
68
;
68
;
69
;
70
;
70
;
70
;
70
;
70
;
71
;
71
;
72
;
72
;
73
;
74
;
74
;
75
;
77
Construct a box plot with the following properties; the calculator instructions for the minimum and maximum values as well as the quartiles follow the example.
Minimum value =
59
Maximum value =
77
Q1: First quartile =
64.5
Q2: Second quartile or median=
66
Q3: Third quartile =
70
Horizontal boxplot with first whisker extending from smallest value, 59, to Q1, 64.5, box beginning from Q1 to Q3, 70, median dashed line at Q2, 66, and second whisker extending from Q3 to largest value, 77.
Each quarter has approximately
25
% of the data.
The spreads of the four quarters are
64.5
–
59
=
5.5
(first quarter),
66
–
64.5
=
1.5
(second quarter),
70
–
66
=
4
(third quarter), and
77
–
70
=
7
(fourth quarter). So, the second quarter has the smallest spread and the fourth quarter has the largest spread.
Range = maximum value – the minimum value = 77 – 59 = 18
Interquartile Range:
I
Q
R
=
Q
3
–
Q
1
=
70
–
64.5
=
5.5
.
The interval
59
–
65
has more than
25
% of the data so it has more data in it than the interval
66
through
70
which has
25
% of the data.
The middle
50
% (middle half) of the data has a range of
5.5
inches.
USING THE TI-83, 83+, 84, 84+ CALCULATOR
To find the minimum, maximum, and quartiles:
Enter data into the list editor (Pres STAT 1:EDIT). If you need to clear the list, arrow up to the name L1, press CLEAR, and then arrow down.
Put the data values into the list L1.
Press STAT and arrow to CALC. Press 1:1-VarStats. Enter L1.
Press ENTER.
Use the down and up arrow keys to scroll.
Smallest value =
59
.
Largest value =
77
.
Q
1
: First quartile =
64.5
.
Q
2
: Second quartile or median =
66
.
Q
3
: Third quartile =
70
.
To construct the box plot:
Press 4:Plotsoff. Press ENTER.
Arrow down and then use the right arrow key to go to the fifth picture, which is the box plot. Press ENTER.
Arrow down to Xlist: Press 2nd 1 for L1
Arrow down to Freq: Press ALPHA. Press 1.
Press Zoom. Press 9: ZoomStat.
Press TRACE, and use the arrow keys to examine the box plot.
Step-by-step explanation:
y=-cos(x+pi/4)amplitude period phase shift
Given the equation of the function:
[tex]y=-\cos (x+\frac{\pi}{4})[/tex]The graph of the function will be as shown in the following picture:
As shown in the figure:
The amplitude = 1
The period = 2π
The phase shift = π/4
Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 59 and in a separate drawing you must also select the correct single number between 1 and 30 find the probability of winning the jackpot
Winning the jackpot in a certain lottery requires you to pick two correct numbers between 1 and 59, and in a separate drawing, you also have a 7.32397915e-8 chance of winning when you also pick one correct number between 1 and 30.
A number of ways to select r items from n, nCr = n!/(r! x (n - r)!)
Number of possible methods to choose 4 winning numbers from 59 = 59C4
= 59!/(55! x 4!)
= 455,126
The number of possible ways to choose a single accurate number from 30 = 30.
The odds of winning the jackpot are 1/(probability) (Number of ways in which 4 winning numbers can be selected from 59 x Number of ways in which the correct single number can be selected from 30)
= 1/(455,126 x 30)
= 1/13653780
= [tex]7.32397915^{8}[/tex]
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Double quantity more than 5
Answer:
Any answer greater than 10 seems to work.
Step-by-step explanation:
This question is not that specific, but 5*2 is 10, so anything more than 10 would be more than double the quantity.
2. $24 shirt; 6% tax
Answer: $25.44
Step-by-step explanation:
Multiply 24 by 0.06.
You get 1.44
Add 1.44 + 24 = 25.44
5. You go out to eat with your friends. You get 2 orders of bacon and eggs, an order of pancakes, and 3 glasses of milk. What is the cost of your total bill? You split the bill evenly between you and your 2 friends. What does each person pay?
2 orders of bacon and eggs cost: 2*$3.99 = $7.98
an order of pancakes cost: $2.55
3 glasses of milk cost: 3*$0.95 = $2.85
Total bill: $7.98 + $2.55 + $2.85 = $13.38
Each person pays $13.38/3 = $4.46
Given F(x) = x2 + 4x − 9, evaluate. F(−4)
Customers return 14% of their gifts during the holiday season. How many gifts were returned during the holiday season if 500 gifts were purchased?
Given:
Customers return 14% of their gifts during the holiday season.
The total number of gifts = 500
So, the returned gifts = 14% of 500 = 0.14 x 500 = 70 gifts
So, the number of gifts were returned during the holiday season = 70 gifts
-5-What is the intercept of function gif 9(r) = -4/(r) + 127
The parent function is given to be:
[tex]f(x)=10^x[/tex]The new function is given to be:
[tex]g(x)=-4f(x)+12[/tex]Therefore, the function will be:
[tex]g(x)=-4(10)^x+12[/tex]The y-intercept is the value of y when x = 0. Therefore, we have:
[tex]\begin{gathered} y=-4(10)^0+12 \\ y=-4+12 \\ y=8 \end{gathered}[/tex]Therefore, the y-intercept is:
[tex]\mathrm{Y\:Intercepts}:\:\left(0,\:8\right)[/tex]Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in slope-intercept form, if possible.(-1,3); y = 1
we have that
The equation of the given line is
y=1
this equation represents a horizontal line
so
the slope is zero (m=0)
Remember that, if two lines are parallel, then their slopes are equal
that means
the slope of the parallel line is m=0 too
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=0
point (-1,3)
the equation is
y=3Which of the statements below is true for the following set of numbers?20, 15, 50, 85, 75, 60a) The range is 85 and the midrange is 55.b) The range is 70 and the midrange is 35.c) The range and the midrange are equal.d) The range is 70 and the midrange is 50.
RANGE
The range of a given data is the difference between the largest and smallest numbers.
Steps for solving range:
Step 1: Arrange the data values in ascending order
[tex]\Rightarrow15,20,50,60,75,85[/tex]Step 2: Identify the largest and smallest numbers
[tex]\begin{gathered} Largest=85 \\ Smallest=15 \end{gathered}[/tex]Step 3: Calculate the difference between the numbers.
[tex]\begin{gathered} Range=Largest-Smallest \\ \therefore \\ Range=85-15=70 \end{gathered}[/tex]The range is 70.
MIDRANGE
The midrange of a given set of data is the average of the largest and smallest number.
Steps for solving midrange:
Step 1: Arrange the data values in ascending order
[tex]\Rightarrow15,20,50,60,75,85[/tex]Step 2: Identify the largest and smallest numbers
[tex]\begin{gathered} Largest=85 \\ Smallest=15 \end{gathered}[/tex]Step 3: Calculate the average of the numbers.
[tex]\begin{gathered} Midrange=\frac{Largest-Smallest}{2} \\ \therefore \\ Midrange=\frac{85-15}{2} \\ Midrange=\frac{70}{2} \\ Midrange=35 \end{gathered}[/tex]The midrange is 35.
ANSWER:
The correct option is OPTION B.
The connective "⇒ " in logic is a…
The binary connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B). It can be read « A implies B », « A is a sufficient condition for B », or « B is a necessary condition for A ».
What is connective?
Connective is function, or the symbol representing a function, which corresponds to English conjunctions such as "and," "or," "not," etc. that takes one or more truth values as input and returns a single truth value as output.
What is logical connective?
A Logical Connective is a symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.
Generally there are five connectives which are −
OR (∨)
AND (∧)
Negation/ NOT (¬)
Implication / if-then (→)
If and only if (⇔).
connective of implication ⇒ is defined as (A ⇒ B) ⇔ ((¬ A) ∨ B).
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This is geometry I need helppppp
m∠C = (16x - 7 )° because ∠A ≅ ∠C
What exactly are complementary and additional angles?When two angles add up to 180 degrees, they are referred to as supplementary angles because they combine to make a linear angle. The opposite is true if the total of two angles is 90 degrees; in this case, they are considered to be complementary angles and together they create a right angle.
Which two supplementary angles come to mind?When two angles sum up to 180 degrees, they are referred to as supplementary angles in geometry. A and B are referred to as supplementary angles, for instance, if A + B = 180°. When supplementary angles are combined, they always create a straight angle (180 degrees).
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Solve for c: c-7≥-3O c≥ 4O c≥ 10O c≥ 10-Oc≥ 44
The inequality is c-7≥-30. The c value we get has inequality c≥-23.
Given that,
The inequality is c-7≥-30.
We have to solve the inequality c.
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. When two values are not equal, we typically use the "not equal symbol (≠)". However, a number of inequalities are used to compare the numbers and determine whether one is greater than the other.
When the symbols “>”, “<”, “≥”, “≤” are used to connect two real numbers or algebraic expressions, the relationship is referred to as an inequality.
Take the inequality,
c-7≥-30
c≥-30+7
c≥-23
Therefore, The c value we get has c≥-23.
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The Chandlers are moving across the countryMr. Chandler leaves 5 hours before Mrs. Chandlerhe averages 40 mph and she averages 80 mphhow many hours will it take Mrs. Chandler to catch up to Mr. Chandler?
From the information provided, we know that Mr Chandler travels at a speed of 40 miles per hour (40mph). He also left 5 hours before Mrs Chandler.
Therefore, we can tell that for 5 hours he has travelled
[tex]\begin{gathered} Dis\tan ce=speed\cdot time \\ \text{Distance}=40\times5 \\ \text{Distance}=200 \end{gathered}[/tex]We shall now label the total distance covered as d, and the number of hours taken (time) as t.
We now have for Mr Chandler;
[tex]d=40t+200---(1)[/tex]For Mrs Chandler, we would have;
[tex]d=80t---(2)[/tex]We would now solve the system of equations as follows;
[tex]\begin{gathered} d=40t+200---(1) \\ d=80t---(2) \\ \text{Substitute for the value of d into equation (1)} \\ We\text{ now have;} \\ 80t=40t+200 \\ \text{Collect all like terms;} \\ 80t-40t=200 \\ 40t=200 \\ \text{Divide both sides by 40} \\ t=5 \end{gathered}[/tex]This result shows that, travelling at the speed given for both Mr and Mrs Chandler, it would take her 5 hours to catch up with him.
ANSWER:
5 hours
PART B
If Mr Reeds leaves 3.5 hours ahead of Mrs Reeds and he travels at the speed of 55 miles per hour (55 mph), then his distance would be;
[tex]\begin{gathered} \text{Distance}=\text{spee}d\times\text{time} \\ \text{Distance}=55\times3.5 \\ \text{Distance}=192.5 \end{gathered}[/tex]If the total distance covered is given as d, then for Mr Reeds the total distance would be;
[tex]d=55t+192.5---(1)[/tex]For Mrs Reeds, we would have;
[tex]d=90t---(2)[/tex]Note that d represents the total distance covered and t represents the time taken (in hours).
We shall now solve the system of equations, as follows;
[tex]\begin{gathered} d=55t+192.5---(1) \\ d=90t---(2) \end{gathered}[/tex]We shall substitute for the value of d into equation two. Note that d = d, which means equation (1) equals equation (2). We now have;
[tex]\begin{gathered} 55t+192.5=90t \\ \text{Collect all like terms;} \\ 192.5=90t-55t \\ 192.5=35t \\ \text{Divide both sides by 35} \\ \frac{192.5}{35}=\frac{35t}{35} \\ 5.5=t \end{gathered}[/tex]The calculations here shows that travelling at the speeds given for both of them, it would take Mrs Reeds 5.5 hours to catch up with Mr Reeds.
ANSWER:
5.5 hours
