The equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4
Equation of a straight lineFrom the question, we are to determine the equation of the line that has a slope of 3 and that passes through the point (5,19)
Using the point-slope form of an equation of a line
y - y₁ = m(x - x₁)
Where m is the slope
and (x₁, y₁) is a point on the line
From the given information
m = 3
x₁ = 5
y₁ = 19
Putting the parameters into the equation, we get
y - 19 = 3(x - 5)
y - 19 = 3x - 15
y = 3x -15 + 19
y = 3x +4
Hence, the equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4
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How many ways can seven finalists for a job be selected from eleven interviewees?
i will mark brainlyist
The following are the distances (in miles) to the nearest airport for 12 families. 6, 7, 8, 8, 16, 19, 23, 24, 26, 27, 34, 35 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:
Minimum: 6Lower quartile: 8Median: 21.Upper quartile: 27Maximum: 35Interquartile range: 19What are the median and the quartiles of a data-set? How to find the interquartile range using it?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:
Me = (19 + 23)/2 = 21.
The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.
The first quartile is the median of the first half, composed by 6, 7, 8, 8, 16, which is the third element of 8.
The third quartile is the median of the second half, composed by 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.
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The population of a bacteria culture are tripling. after 6 days, the population has quadrupled. what is the tripling time? find the answer to the nearest thousandth. b) how long did it take for the population to double in size?
The tripling time of population is 6 days and the population will be doubled in 3.5 days.
Given that the population of a bacteria is tripling in 6 days.
We have to find the tripling time of population and the time when the population will be doubled.
Suppose the population of bacteria in beginning be x.
The population of bacteria seems like arithmetic progression in which a =x, nth term =3x and n=6.
Aritmetic progression is a sequence which is having common difference.
nth term=a+(n-1)d
3x=x+(6-1)*d
3x-x=5d
2x=5d
d=2x/5
d=0.4x
So now we have to find the value of n where population will be 2x.
nth term=a+(n-1)d
put nth term=2x, a=x,d=0.4x
2x=x+(n-1)*0.4x
2x-x=(n-1)*0.4x
x/0.4x=n-1
2.5=n-1
n=2.5+1
n=3.5
Hence the population of bacteria willbe doubled after 3.5 days.
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Calculate the future value in five years of $8,000 received today if your investments pay future value a. 5 percent compounded annually $ b. 7 percent compounded annually c. 9 percent compounded annually d. 9 percent compounded semiannually e. 9 percent compounded quarterly.
The Future value is:
a) $10,210.25
b) $11,220.41
c) $12,308.99
d) $18,938.90
e) $44,835.28
What is future value?
The future value (FV) of any asset can be understood as an increase in its value at a fixed rate over a period of time. For a given principal sum P, rate of interest r, and time period t, the future value of an asset can be calculated as:
FV=P*(1+r) ^t
We can find future value as shown below:
P=$8,000
t=5 year
a) r=6%=0.06
FV=8000*(1+0.05) ^5
=8000*(1.0) ^5
=$10,210.25
b) r=7%=0.07
FV=8000*(1+0.07) ^5
=8000*(1.07) ^5
=$11,220.41
c) r=9%=0.09
FV=8000*(1+0.09) ^5
=$12,308.99
d) r=9% compounded semiannually
= 0.09
t=2*5=10
FV=8000*(1+0.09) ^10
=8000*(1.09) ^10
=$18,938.90
e) r=9 percent compounded quarterly
=0.09
t=5*4=20
FV=8000*(1+0.09) ^20
=8000*(1.09) ^20
=$44,835.28
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What is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds $401$
The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
According to the statement
We have a given that the maximum sum of the positive integers is 400.
And we have to find the value of n which is a maximum number of integers by which the value of sum become 400.
So, to find the value of the n we use the
A.P. Series'Summation formula
According to this,
S = n (n+1)/2
Here the value of s is 401
Then
S = n (n+1)/2
401 = n (n+1)/2
401*2 = n (n+1)
802 =n (n+1)
n (n+1) = 802
n^2 + n -802 =0
By the use of the Discriminant formula the
value of n becomes n = -28 and n = 27.
The negative value of n is neglected.
Therefore the value of n is 27.
So, The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
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Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button.
A) Sample size of compound event = 25
B) New Sample size = 36
What is Compound event?
A compound event is one that has more than one sample point. Simple events are less complicated than compound events. These occurrences entail the possibility of multiple occurrences. One is the probability of all possible outcomes of a compound event.
An event that consists of two or more simple events is called a compound event. Simple events are those that can only have one result, whereas complex events can have a variety of distinct results. Compound events can consist of several independent or dependent occurrences, where the result of one event has no bearing on the likelihood of the other.
Given,
Number of buttons in a container = 5
Lucas picks one button, replaces it and then picks another.
Therefore,
Sample size of the compound event
n = 5[tex]\times[/tex]5
n = 25
Now, one more button is added in the container and in total there are 6 buttons.
Lucas repeats the same process again and hence,
Sample size of the new compound event will be,
n = 6[tex]\times[/tex]6
n = 36
Full Question is - Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is ___ Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be ____
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Find the interval in which the function is positive.
f(x)=x²-7x + 10
1. (-∞0, 2)
II. (2,5)
III. (5,00)
O I, II
O I, III
O II, III
O II only
Answer:
(b) I, III
Step-by-step explanation:
The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).
General shapeThe leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.
If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.
Specific shapeThe answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).
f(2) = 2² -7·2 +10 = 4 -14 +10 = 0
f(5) = 5² -7·5 +10 = 25 -35 +10 = 0
This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.
A solid oblique pyramid has a square base with edges measuring x cm. the height of the pyramid is (x 2) cm.
The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The base of the pyramid is x cm while the height is x + 2, hence:
Volume of pyramid = (1/3) * area of square base * height = (1/3) * x * x * (x + 2) = (x³ + 2x²)/3 cm³
The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³
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A local salesman receives a base salary of $975 monthly. He also receives a commission of 6% on all sales over $1200. How much would he have to sell in a month if he needed to have a monthly income of $2500
He has to sell in a month $26616.67.
Given that a local salesman receives a base salary of $975 monthly and he also receives a commission of 6% on all sales over $1200.
A numerical assertion wherein two articulations are delivered equivalent to each other is known as an algebraic condition.
Let the Sales amount be s.
We have:
Sales over 1,200 is written as
s-1200
6% is also 0.06 as a decimal,
so according to question, we have
0.06(s - 1200) + 975=2500
Now, we will apply the distributive property a(b+c)=ab+ac, we get
0.06s-0.06×1200+975=2500
Further, we want to simplify the left-hand side, we get
0.06s-72+975=2500
0.06s+903=2500
Furthermore, we will subtract 903 from both sides, we get
0.06s+903-903=2500-903
0.06s=1597
Now, we will divide both sides with 0.06, we get
0.06s/0.06=1597/0.06
s=26616.67
Hence, he have to sell in a month if he needed to have a monthly income of $2500 is $26616.67.
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Which of the following is the complete factorization of the polynomial below?
2x² +13x² +17x-12
a
jfjoydx9tdzrzfzixitxxytxixutx
Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
The student with the correct list of steps is student B
How to determine the correct student?The list of steps is to create a line parallel to line AB
Both students are correct in step (1).
However, the step (2) of student A is incorrect.
This is so because, the student did not provide how points C and G are created
Hence, the student with the correct list of steps is student B
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Which polynomial is a quintic trinomial?
A. -x^4-5x^2
B. x^3+2x^2−8x+16
C. x² + 4
D. 3x^5+7x^2−9x^4
Answer:
D
Step-by-step explanation:
a quintic polynomial is a polynomial of degree 5
A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )
B is a polynomial of degree 3 (x³ term )
C is a polynomial of degree 2 ( x² term )
D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )
The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the
next few hours, the temperature drops 2 degrees every hour.
Which equation represents the temperature, t, at hour h?
OA. t= 2h+32
B. t= -2h+ 32
C. t = 32h-₂
OD. t= -32h+2
You would multiply the change per hour by number of hours to get -2h
That would be added to the starting temperature.
Answer: B, t = -2h + 32
Answer: The answer is B
Step-by-step explanation:
The question says it drops ( which means subtraction) by 2 degrees every hour, so -2h
Chanda is planning to visit universities over the summer to help decide where she wants to attend college. The first two universities on her proposed route are 6 inches apart on Claudias map. In real life, this distance is 30 miles. What scale does the map use? 1 in = _____ miles.
The map scale to use would be: 1 in. = 5 miles.
What is Map Scale?The scale of a map relates the actual distance of two places to the distance on paper on a scale drawing. It is a ratio between length on the map and distance in real life.
Given that, 6 inches would equal actual distance of 30 miles, let x be the actual distance on ground. We would have:
6/30 = 1/x
Solve for x
x = (30 × 1)/6
x = 5.
Therefore, the scale of the map is: 1 in = 5 miles.
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15. If 3x + 10 = 3y - 2(y + 4), what is the value of y in terms of x? (A) x + 18 (B) 3x+6 (C) 3x + 14 (D) 3x + 18
Answer:
3x + 18
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 18 = y
Answer:
D, 3x + 18.
Step-by-step explanation:
3x + 10 = 3y - 2(y + 4)
3x + 10 = 3y - 2y - 8
3x + 10 = y - 8
y = 3x + 10 + 8
y = 3x + 18.
What additional information is obtained by measuring two individuals on an ordinal scale compared to a nominal scale
The direction of the difference between the 2 measurements.
What is nominal and ordinal scale with example?Examples of data for a nominal scale include a person's gender, ethnicity, and hair color. On the other hand, an ordinal scale requires putting data in a certain order, or in relation to one another and "ranking" each parameter (variable).What is the difference nominal and ordinal?Ordinal data has a preset or natural order, whereas nominal data is categorized without a natural order or rank. A number that can be measured, however, will always be present in numerical or quantitative data.What is an example of a ordinal scale?First place would go to a student with a score of 99 out of 100; third place would go to a student with a score of 92 out of 100; and so on.Learn more about ordinal scale and nominal scale here:
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Solve the inequality. 14 + 10y ≥ 3(y + 14)
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{14+10y\geq 3(y+14) } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Simplify \ both \ sides \ of \ the \ inequality. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{10y+14\geq 3y+14 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Subtract \ 3y \ from \ both \ sides. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{10y+14-3y\geq 3y+42-3y } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{7y+14\geq 41 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ Subtract \ 14 \ from \ both \ sides. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7y+14-14\geq 42-14 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{7y\geq 28 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Divide \ both \ sides \ by \ 7. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{7y}{7}\geq \frac{28}{7} } \end{gathered}$}\\\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{y\geq 4} \end{gathered}$} }[/tex]Find the lateral surface area of the
following prism:
5 cm
5 cm
apothem = 3.44 cm
cm
5 cm
10 cm
5 cm
LSA = [?] cm2
The laterals surface area of the given hexagonal prism is: 250 cm².
How to Find the Lateral Surface Area of Hexagonal Prism?Lateral surface area = 5ah, where:
a = edge length of the baseh = height of the prism.Given the following:
a = 5 cm
h = 10 cm
Lateral surface area of the hexagonal prism = 5ah = 5(5)(10)
Lateral surface area of the hexagonal prism = 250 cm²
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a) The cosine rule can be used to find the value of x in the triangle below.
What number completes the following calculation? x² = 12² +152 - 2 x 12 x 15 x cos(?)
b) What is the value of x? Give your answer to the nearest integer.
Answer:
see explanation
Step-by-step explanation:
(a)
(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )
x² = 12² + 15² - (2 × 12 × 15 × cos71°)
(b)
x² = 144 + 225 - 360cos71°
= 369 - 360cos71° ( take square root of both sides )
x = [tex]\sqrt{369-360cos71}[/tex]
≈ 16 cm ( to the nearest integer )
The product of donnies age and 6 is 72. use variable d to represent donnies age
Answer: D times 6 = 72
D= 12
Step-by-step explanation:
The term product means multiplication. Donnie's age is represented by the letter d, so if the product of d and 6 is 72, or in other words, d times 6 is 72, then d would equal 12
party planners recommend that, for every eight quests, two orders of appetizers be provided. which function reflects this ratio
The ratio guest to appetizers at the party was 4 guest per appetizer.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Ratio of guest to appetizers = 8 guest / 2 appetizers = 4 guest per appetizer.
The ratio guest to appetizers at the party was 4 guest per appetizer.
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Point A is at (3, -8) and point B is at (7, 3). Point M is the midpoint of point A and point B.
The midpoint of point A and point B is (5, -2.5)
How to determine the midpoint?The coordinates are given as:
A = (3, -8)
B = (7, -3)
The midpoint is calculated as:
(x, y) = 0.5 * (x1 + x2, y1 + y2)
So, we have:
(x, y) = 0.5 * (3 + 7, -8 + 3)
This gives
(x, y) = 0.5 * (10, -5)
Evaluate
(x, y) = (5, -2.5)
Hence, the midpoint of point A and point B is (5, -2.5)
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For the following sample, calculate ss. then, compute the sample variance and standard deviation. scores: 5, 2, 2, 7, 9
The sample standard deviation is 7.6 and the sample variance is 2.76.
for the scores 5, 2, 2, 7, 9.
According to the question,
Sample size n = 5
Sample Mean = [5+2+2+7+9]/5
= 5
Formula for sample standard deviation = (x-mean)²/n
= [(5-5)²+(2-5)²+(2-5)²+(7-5)²+(9-5)²]/5
= [0+9+9+4+16]/5
= 38/5
= 7.6
Formula for sample variance = √sample standard deviation
=√7.6
=2.76.
Hence, the sample standard deviation is 7.6 and the sample variance is 2.76.
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How many of the list 729 positive integers are perfect squares, cubes ,or both?
Answer:
there will be 17 integers!
List :
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
They're all squares, like for example, 1^2, 2^2, 3^2, etc
Answer:
cheapt
Step-by-step explanation:
Which graph shows y < x² +1?
O
4) Intro
•
What is inequality?
In Algebra, inequality shows the relation between two expressions using the inequality symbol.
The graph shows the equation y<x^2+1 is attached
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The graph at option 1 shows the given inequality y < x² + 1. The domain and range of the given inequality is {x: x ∈ (-∞, ∞)} and {y: y ∈ [1, ∞)}.
How to graph an inequality?The steps to graph an inequality equation are:
Solve for the variable y in the given equationGraph the boundary line for the inequalityShade the region that satisfies the inequality.Calculation:The given inequality is y < x² + 1
Finding points to graph the boundary line by taking y = x² + 1:
When x = -2,
y = (-2)² + 1 = 4 + 1 = 5
⇒ (-2, 5)
When x = -1,
y = (-1)² + 1 = 2
⇒ (-1, 2)
When x = 0,
y = (0)² + 1 = 1
⇒ (0, 1)
When x = 1,
y = (1)² + 1 = 2
⇒ (1, 2)
When x = 2,
y = (2)² + 1 = 5
⇒ (2, 5)
Plotting these points in the graph forms an upward-facing parabola.
So, all the points above the vertex of the parabola satisfy the given inequality. Thus, that part is shaded.
From this, the graph at option 1 is the required graph for the inequality y < x² + 1. The boundary line is dashed since the inequality symbol is " < ".
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For the real-valued functions f(x)=2x+3 and g(x)=√x-5, find the composition fog and specify its domain using interval notation.
(fog)(x) =
Domain of fog:
Find fog
fog(x)f(g(x))f(√x-5)2√(x-5)+3For real range the domain
x-5≥0x≥5Domain is [5,oo)
use the graph to the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 10
The coordinates of QRTW after dilation by factor 10 are (-20,30),(-30,10),(20,-10),(-20,40).
Given that coordinates of QRTW before dilation are (-2,3),(-3,1),(2,-1),(-2,4) and figure QRTW is dilated by factor 10.
We know that if a figure is dilated its area, increases. The new coordinates can be calculated as x*factor from which it is dilated.
Coordinates are the points on the graph surface.
In our figure Q(-2,3), R(-3,1), S(2,-1), T (-2,4).
We have to just multiply each value with 10 to get the new coordinates of QRTW after dilation.
Q after dilation=(-2*10,3*10)=(-20,30)
R after dilation=(-3*10,1*10)=(-30,10)
S after dilation=(2*10,-1*10)=(20,-10)
T after dilation=(-2*10,4*10)=(-20,40)
Hence the vertices of the image QRTW after dilation are (-20,30),(-30,10),(20,-10),(-20,40).
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A sweatshirt costs $48 at Hollister. The sales tax rate is 7%. How much will it cost to buy the sweatshirt?
Answer:
$ 51.36
Step-by-step explanation:
To find the sales tax multiply the tax rate by the cost of the product and then add to the cost.
Sales tax = tax rate * cost price
= 7% * 48
= 0.07 * 48
= $ 3.36
Cost price = cost of product + sales tax
= 48 + 3.36
= $ 51.36
A researcher randomly assigns participants to complete a crossword puzzle with or without music. The time it takes to complete the crossword puzzle is compared between groups. The experimental group in this example is:
Answer:
The music group
Step-by-step explanation:
The experiment group is the group where something is being modified, so the music group is the one having their environment modified.
What's a venn diagram, how to draw it and the steps too!
What is a Venn Diagram?
Explain : A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
How to draw a Venn Diagram?
Explain : To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram
What is a venn Diagram mostly used for?
Explain : A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
Set notations: The concepts illustrated in Venn ...
Scaled Venn Diagram: Also called Area Propo...
Reuleaux Triangle: Shape formed from the int...
Intersection: The items that overlap in the sets. ...
Here's some question for Venn Diagrams!
A. What's the first step creating a Venn Diagram? https://www.math-only-math.com/practice-test-on-Venn-diagrams.html
B. What's the last step to create a Venn Diagram? https://www.purplemath.com/modules/venndiag4.htm
C. What does a Venn Diagram looks like?
( Try using those questions to partice more about Venn Diagrams! )
( Also, thank you for the points! )