Answer:
Father=36 years old
Step-by-step explanation:
5 people 4 children and a father
average age=12
add the ages
3+5+6+10=24
24+12=36
check the work
36 +24=60
60/5=12
answer=36
Answer:
36 years old
Step-by-step explanation:
The average age of father and four children can be expressed in mathematics as:
[tex]\displaystyle \large{\dfrac{f+c_1+c_2+c_3+c_4}{5}}[/tex]
The above expression is what you call average value or mostly known as mean - the mean value is sum of all data values divided by number of data values. The formula reference for mean/average value is:
[tex]\displaystyle \large{\dfrac{x_1+x_2+x_3+...+x_n}{n} = \dfrac{1}{n} \sum_{i=1}^n x_i}[/tex]
Determine or let the following be:
f = father’s agec1 = first child’s agec2 = second child’s agec3 = third child’s agec4 = fourth child’s ageIt is also given in the question that children’s ages are 3, 5, 6 and 10. Hence:
[tex]\displaystyle \large{\dfrac{f+3+5+6+10}{5} = 12}[/tex]
From above, it is also given that average of father’s age and children’s age is 12 years old - that now gives us an equation. What we have to do now is to solve for f.
First, multiply 5 both sides to get rid of denominator.
[tex]\displaystyle \large{\dfrac{f+3+5+6+10}{5} \cdot 5 = 12 \cdot 5}\\\\\displaystyle \large{f+3+5+6+10=60}[/tex]
Evaluate 3+5+6+10 which equals 24.
[tex]\displaystyle \large{f+24=60}[/tex]
Next, subtract both sides by 24 to isolate f-term.
[tex]\displaystyle \large{f+24-24=60-24}\\\\\displaystyle \large{f=36}[/tex]
Finally, we have received the value of term which is f = 36. We know that the term represents father’s age and therefore, father’s age is 36 years old!
If you have any doubts, please let me know in the comment!
What effect does the circled point have on the standard deviation of the residuals? This point will increase the value of the standard deviation of the residuals because it has a large positive residual. This point will increase the value of the standard deviation of the residuals because it has a large negative residual. This point will not affect the value of the standard deviation of the residuals because it has a large positive residual. This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.
The effect of this circled point is that: A. it will increase the value of the standard deviation of the residuals because it has a large positive residual.
What is the standard deviation of residuals?The standard deviation of residuals is also referred to as root mean square deviation and they are typically used in statistics to calculate the rate at which data points spread around a given regression line.
By critically observing the scatter plot shown in the image attached below, we can infer and logically deduce that the circled point will increase the value of the standard deviation of the residuals because it has a large positive residual.
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Complete Question:
A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect does the circled point have on the standard deviation of the residuals?
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
to determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
The correlation coefficient between the student's height and the distance they were able to jump is 0.86.
What is the correlation coefficient?The correlation coefficient is a number that ranges from -1 to 1. It shows the strength of the relationship between two variables. It also shows the direction of the relationship.
Positive correlation is when the two variables move in the same direction. If one variable increases, the other variable also increases. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases. Zero correlation is when there is no relationship between the variables.
The correlation coefficient is calculated using a financial calculator.
Here is the complete question:
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
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Answer:
It's 0.92
Step-by-step explanation:
I took the test already
Martin had 100 trees in his orchard the first year. Each year after that, he
increased the number of trees in his orchard by 10%, rounded to the nearest
whole number. How many trees did he have in his orchard in the sixth year?
So trees after 1 year
100+10=110Trees after 2 years
110+0.1(110)=121Trees after 3 years
121+0.1(121)133(Whole no)Trees after 4years
133+0.1(133)146Trees after 5 years
146+0.1(146)161Trees after 6 years
161+0.1(161)177treesAnswer:
177
Step-by-step explanation:
This scenario can be modeled as an exponential function.
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
If the number of trees increase by 10% each year, then the number of trees each year will be 110% of the number of trees the previous year. Therefore, the growth factor is 110%.
Given:
a = 100 treesb = 110% = 1.10 (in decimal form)x = time (in years)y = number of trees in the orchardSubstituting the given values into the function:
[tex]\implies y=100(1.10)^x[/tex]
(where x is time in years and y is the number of trees in the orchard)
To find how many trees are in the orchard in the 6th year, input x = 6 into the found equation:
[tex]\implies 100(1.10)^6=177.1561=177\: \sf (nearest\:whole\:number)[/tex]
Therefore, Martin had 177 trees in his orchard in the sixth year.
solve for x.
2-[x+4(6-x)+16]-10=38-8x
Exact form is x = 86/11
Mixed number form is x = 7 whole number 9/11
Please Help I Don't Understand!
Answer:
a reduction
Step-by-step explanation:
this is because its growing smaller
HELP ASAP
A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.
The correct true statement is the swimmer comes back up 9 seconds after the timer was started.
Maximum height of a functionThe maximum height of a function is the point where the velocity the body is zero.
Given the function that represent the height of the swimmer as h(t)=t^2−12t+27
If the velocity of the function is zero, hence;
h'(t) = 2t - 12
0 = 2t - 12
2t = 12
t = 6secs
Substitute t = 6 into the function as shown:
h(6) = 6^2−12(6)+27
h(6) = 36 - 72 + 27
h(6) = -36 + 27
h(6) = -9 feet
Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.
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Which polynomial function could be represented by the graph below?
A. [tex]f(x) = x^2 - 4x[/tex]
B. [tex]f(x) = x^2 + 4x[/tex]
C. [tex]f(x) = -x^2 - 4x[/tex]
D. [tex]f(x) = -x^2 + 4x[/tex]
Answer:
[tex]f(x) = {x}^{2} + 4x[/tex]
Step-by-step explanation:
The graph is concave up, this means that the leading term x^2 is positive.
[tex]f(x) = {x}^{2} + 4x[/tex]
[tex]y = {x}^{2} + 4x[/tex]
For the x intercept, let y = 0[tex] {x}^{2} + 4x = 0[/tex]
[tex]x(x + 4) = 0[/tex]
[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]
The x intercepts are:
(0 , 0) and (-4 , 0)
For the y intercept, let x = 0
[tex]y = {0}^{2} + 4(0) = 0[/tex]
y intercept :(0, 0)
For the turning point:[tex]t.p = \frac{x1 + x2}{2} [/tex]
[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]
[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]
Turning point:(-2 , -4)
If you connect all these coordinates you will get the parabola shown in the picture.
Solve the system of equations x + y = 14 and 5x - 3y = 38 by combining equations. +y = 14) -3y =38) (5x X +y = 14 5x -3y = 38 try 0x0y= You must answer all questions above in order to submit.
Answer:
6x+2y=52
Step-by-step explanation:
If you just drop down the answers, like for the first set x+5x=6x, so thats the first term and so on.
math 7 grade eog 2022 ansers
What is the slope of the line that passes through the pair of points?
(5, 8), (9,-3)
Answer:
-11/4
Step-by-step explanation:
slope = [tex]\frac{-3-8}{9-5} =\frac{-11}{4}[/tex]
Hope this helps
Answer:
-11/4
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (-3 - 8)/(9 - 5) = -11/4
How can I solve this:
Simplify
Answer:
see the attachment photo!
Answer:
the answer is 7! hope this helps
Step-by-step explanation:
Identify the type of function represented by
f(x) = 4.2x
OA. Decreasing linear
OB. Exponential growth
OC. Exponential decay
OD. Increasing linear
The function is an increasing linear function
How to determine the function type?The function is given as:
f(x) = 4.2x
The above function is a linear function, because linear functions are represented as:
f(x) = mx + b
Where m represents the slope.
A positive slope represents an increasing linear function.
By comparison;
m = 4.2
4.2 is positive
Hence, the function is an increasing linear function
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Is renters insurance a fixed or variable expense?
[tex]\huge\purple{Hi!}[/tex]
renters insurance is a Fixed expenses
I need help in this question if highly appreciate it if someone can help me solve this problem
Answer:
The one you chose is correct.
Step-by-step explanation:
The scale factor is 1.5. We know QP is 5. QP is the corresponding side to KJ. So, we multiply 5 with 1.5 and get 7.5 which is equal to 15/2
I found the scale factor by dividing LK which was 9 and QR which was 6.
9/6=1.5.
Hope this helps
Anyone know how to do this?
Answer:
the tangent ratio should be the length of the leg opposite to angle D to the length of the leg adjacent to angle D
Step-by-step explanation:
tangent is opposite over adjacent
Johnni guessed on all 8 questions of a multiple-choice quiz. each question has 4 answer choices. what is the probability that she got exactly 3 questions correct? round the answer to the nearest thousandth. p (k successes) = subscript n baseline c subscript k baseline p superscript k baseline (1 minus p) superscript n minus k. subscript n baseline c subscript k baseline = startfraction n factorial over (n minus k) factorial times k factorial endfraction 0.004 0.208 0.422 0.792
The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
What is Probability ?Probability can be defined as the likeliness of
If you use the formula P(r)=[tex]^nC_r P^rq^{n-r}[/tex]
P is the probability of success = 3/4 = .25
the total number of questions is n = 8
the total number of questions that Johnni got correct is r = 3
the probability of getting an answer wrong is q = 1-0.25 = 0.75
Substituting all of these values
[tex]^8C_3 P^3 (0.75)^{8-3}[/tex]
= .208.
The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
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Answer:
B. 0.208
Step-by-step explanation:
edge 2023
Question 3
the three straight paths, ab, bc, and ac meet each other at three points, a, b, and how do these points of intersection differ from each
other? explain the differences in terms of the angles that you see. also look at the length of the side opposite each angle. what pattern do you see
regarding the measurements? in what situation would all the points of intersection resemble one another modify the triangle in geogebra to
help you with your answers
b
ux
x
font sizes
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characters used: 0 / 15000
submit
airfax county public schools
To find differences in the angles of the intersections we must know how many degrees each angle corresponds to. We must also take into account that the sum of the internal angles must equal 180°.
What is a triangle?A triangle is a polygon that is characterized by having three sides, three vertices, and three angles. An indispensable rule of the interior angles of the triangles is that they must add up to 180º.
Triangles are classified according to their characteristics as shown below:
Equilateral triangle: It is a type of triangle that is characterized by having all equal sides. Consequently, all the angles of an equilateral triangle are 60º. The equilateral triangle is a regular polygon.Isosceles triangle: It is a type of triangle that is characterized by having two equal sides and one different. Consequently, it also has two equal angles.Scalene triangle: A scalene triangle is one that is characterized by having all its sides and angles unequal, that is, different from each other.According to the above, depending on the measurements of the length of the sides and the angles of a triangle, its characteristics and classification change.
Note: This question is incomplete because the image is missing. However I can answer it based on my general prior knowledge.
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Solve 2x + 5y = −13
3x − 4y = −8
(4, 1)
(−4, 1)
(4, −1)
(−4, −1)
Answer:
Step-by-step explanation:
6x + 15y = -39
-6x + 8y = 16
23y = -23
y = -1
2x - 5 = -13
2x = -8
x = -4
(-4, -1)
Option 4
Answer:
(−4, −1)
Step-by-step explanation:
I got it right on the test
PLEASE HELPPPPPPPPPPPP!!!
which unit of measure would be appropriate for the area of a bulletin board that is 2 meters tall and 6 meters wide
Answer:The entire area would be 12 square meters.
Step-by-step explanation:
2 x 6 square meters = 12 square meters. which is the entire area.
the simplification lf (x^3+2x-3)-(x^2-2x+4)
Answer:
x³ - x² + 4x - 7
Step-by-step explanation:
(x³ + 2x - 3) - (x² - 2x + 4)
remove first parenthesis and distribute second parenthesis by - 1
= x³ + 2x - 3 - x² + 2x - 4 ← collect like terms
= x³ - x² + 4x - 7 ← in standard form
To predict the outcome of the vote for the town budget, the town manag assigned random numbers and selected 12F registered voters. He then called these vote and asked how they planned to vote. Is th town manager's sample representative of population? Explain.
The town manager's sample is not representative of population as he only picked females.
What is a sample representative?It should be noted that a sample representative simply means a subset of a population which seeks to reflect the characteristics of the larger group.
In this case, the town manager's sample is not representative of populationas he only picked females. The males too ought to be given an equal chance.
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what is the answer for 0.32+12.965+1.1 and could you explain how you got the answer
answer: 14.385
Add the numbers as if they were whole numbers.Place the decimal point in the sum so that it lines up vertically with the numbers being added.
hope this helps:)
The diagram shows triangles ABC and PQR. ABC is mapped to PQR by combining two single transformations
What is the slope of the line containing (-3, 1) and (1, -2)?
O A
OB.
O C.
O D.
314
413
-
314
43
Slope:-
m=y2-y1/x2-x1m=-2-1/1+3m=-3/4The slope of the given function is -3/4.
What is a slope?Slope is a value that describes the steepness and direction of a line.
Given are the points that lie on line, we need to find the slope of the line,
So,
m = y₂ - y₁ / x₂ - x₁
The ordered pairs are :-
(-3, 1) and (1, -2)
So, the slope (m) = -2-1 / 1+3 = -3/4
Hence, the slope of the given function is -3/4.
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Please help y’all I’ll do anything!!
Answer:
555
Step-by-step explanation:
If each side of a square is 15 miles, we can find the total distance travelled by finding how many sides of squares were travelled.
You could either count the boxes, or, as I'm going to do, you could calculate the length of each straight line.
I switch between the y axis and the x axis, because we are travelling in different directions (if moving up/down we pay attention to y-axis, if moving right/left we pay attention to x-axis)
From 'Home' to the 'Restaurant', we are travelling from 6 to -7 on the grid. So, if we want to know the distance between them, we need to figure out how far apart they are. This is similar to figuring how far apart any two numbers are--we find the difference. (6) - (-7) [6 + 7] = 13. So, the amount of squares travelled from home to the restaurant is 13.
[I pay attention to the values along the x-axis for these two points because we are considering the distance along the x-axis]
[y-axis because it is vertical travel]
Restaurant (at -5) to campground (at 2) has a distance of : 7
[x-axis because it is horizontal travel]
Campground (at -7) to Rest Area (at -3) has a distance of : 4
[y-axis travel]
Rest Area (at 2) to the endpoint of that line segment (at 8) has a distance of: 6
[x-axis travel]
Endpoint of line segment (at -3) to endpoint below destination (at 3) has a distance of : 6
[y-axis travel]
Endpoint below destination (at 8) to destination (at 9) has a distance of : 1
We can then add all of the distance travelled:
13 + 7 + 4 + 6 + 6 + 1
= 37
37 sides of boxes were travelled, so we can multiply:
37 x 15
= 555
because each box length is 15 miles.
So, the family travelled 555 miles
If x1 = 4, then x² + 1/x² =
Answer:
257/16
Step-by-step explanation:
Given :
x¹ = 4Then :
x² + 1/x²(x¹)² + 1/(x¹)²(4)² + 1/(4)²16 + 1/16257/16Write the following ratio using two other notations.
[tex] \frac{1}{3} [/tex]
Answer:
1:3
1 to 3
Step-by-step explanation:
The other notations a ratio [tex]\frac{a}{b}[/tex] can be written in are a:b and a to b.
From what we are given, a = 1 and b = 3, so in the form a:b, the ration would be 1:3 and in the form a to b it would be 1 to 3.
Any ideas for this question
===========================================================
Explanation:
Let x = length of side BC
This is the height of the cylinder. Think of a can that is laying on its side. The radius of this can or cylinder is CD
If point B has x coordinate of 12, and BC is 12 units long, this must mean point C has x coordinate of 12-x. This is plugged into the function to show that CD has a length of exactly [tex]\sqrt{12-x}[/tex]
This is the radius of the cylinder
The volume of a cylinder is [tex]V = \pi*r^2*h[/tex]
Plug in the radius and height mentioned to get this function in terms of x
[tex]V = \pi*\left(\sqrt{12-x} \ \right)^2*x[/tex]
That simplifies to
[tex]V = \pi(12-x)x[/tex]
or
[tex]V = \pi(12x-x^2)[/tex]
Ignore the pi portion for now.
We wish to maximize the function f(x) = 12x-x^2
Use either calculus (specifically derivatives) or a graphing calculator to find that the vertex is at (6, 36)
This means x = 6 leads to the largest f(x) value being 36.
Therefore, the volume V is maxed out when x = 6 and we get a max volume of 36pi cubic units.
Write in point-slope form an equation of the line that passes through the given point and has the given slope. Point: (4, 8); m = 3/4
Answer:
[tex]\mathsf{y-8=\cfrac{3}{4}(x-4)}[/tex]
Step-by-step explanation:
Hi student, let me help you out!
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ..... ........ ...... ... ......... .... ....
First, let's recall the point-slope form equation: ↪ [tex]\mathrm{y-y_1=m(x-x_1)}[/tex].
where: y₁ = y-coordinate of the point (the second coordinate), m=slope, x₁=x-coordinate (the first coordinate).
Let's stick in the values accordingly. We obtain the following: [tex]\mathrm{y-8=\cfrac{3}{4}(x-4)}[/tex], which is our point-slope form equation.
Hope this helped you out, ask in comments if any queries arise.
Best Wishes!
[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{4}}[/tex]