Using a system of equations, it is found that David is 12 years old.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: David's age.Variable y: Dad's age.Variable z: Rebecca's age.David is three times younger than the dad and twice as old as Rebecca, then:
x = y/3 -> y = 3x.x = 2z.Rebecca is 30 years younger than the dad, hence:
z = y - 30.
Then, since x = 2z and z = y - 30 and y = 3x, we solve for x to find David's age.
x = 2(y - 30)
x = 2(3x - 30)
x = 6x - 60
5x = 60
x = 60/5
x = 12.
David is 12 years old.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
If < A and < B form a linear pair, and m< A = x - 21 degrees, and m< B = x + 15 degrees, then find x.
The value of x = 93 degree and value of angle A and B is 72 , 108 degree
What is a Linear Pair ?The pair of triangles that are supplementary and they add to form 180 degree angle are called Linear Pairs.
It is given that
∠ A = x -21
∠ B = x+15
also it is given that
angle A and B form a linear pair
∠ A + ∠ B = 180 degree
To find the value of x
x -21 + x+15 = 180
2x - 6 = 180
2x = 186
x = 93 degree
so
∠ A = x -21 = 93 -21 = 72 degree
∠ B = x+15 = 93+21 = 108 degree
Therefore the value of x = 93 degree and value of angle A and B is 72 , 108 degree.
To know more about Linear Pair
https://brainly.com/question/1757859
#SPJ1
Directions: Find the product and simplify
Answer:
x^4-9x^2+26x-24
Step-by-step explanation:
Answer:
[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]
Step-by-step explanation:
[tex](x - 3)( {x}^{2} - 6x + 8)[/tex]
[tex] {x}^{3} - 6 {x}^{2} + 8x - 3 {x}^{2} + 18x - 24[/tex]
[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]
According to aaa chicago what percentage of crashes involving teen drivers are instigated by distractions like using cell phones, reaching for objects or socializing?.
According to AAA Chicago, 58 percentage of crashes involving teen drivers are instigated by distracted driving.
What does AAA study tell about the distracted driving of teens?
According to the AAA Foundation for Traffic Safety's review of over 1,700 crash films, distracted driving causes 58 percent of car accidents involving juvenile drivers. According to the foundation, this figure is four times higher than earlier projections derived from police records.
The investigation identified 12 different kinds of distracted driving that contributed to collisions, with passenger interaction accounting for 15% of crashes. Twelve percent of the collisions were caused by using a cellphone, which was followed by reaching for something, looking inside the vehicle, gazing outside while not paying attention to the road, singing or dancing, and looking at something outdoors.
According to the study, young drivers were prey to distracted driving by calls, texts, or other mobile device use for an average of 4.1 seconds in the final six seconds before a catastrophic crash.
Learn more about distracted driving here:
https://brainly.com/question/18048790
#SPJ4
Annalise makes rectangular patchwork quilts out of leftover fabric scraps. The first scrap she is using to make a quilt has a width of 2x feet and a length of 5x feet. When finished, the entire quilt will be 5 feet wider and 3 feet longer than the first fabric scrap used. Which of the following functions will give the area, f(x), of the quilt in square feet?
The function that will give the area, f(x), of the quilt in square feet is
Area = f(x) = 10x²+31 + 15
Which of the following functions will give the area, f(x), of the quilt in square feet?Generally, the equation for Area of Rectangle is mathematically given as
A = Length *Width
Therefore
A= (5x+3)(2x+5) square feet.
inconclusion, Area
f(x)= (5x+3)(2x+5)
f(x)=10x+25+ 6+15
(fx) 10x^2 +31x+15
Read more about Area
https://brainly.com/question/27683633
#SPJ1
Answer:
f(x)=10x^2 + 31x + 15
Step-by-step explanation:
Did it and got it right
the other people put so much things for no reason lol
what is 1,987 divide 12 =
The division of 1987 by 12 when solved gives a quotient of; 165.5
How to divide numbers?We want to divide 1,987 by 12. This can be expressed as;
1987 ÷ 12
Now, it must be noted that when dividing, we have the divisor and the dividend. Where the number that is being divided is the dividend which is the numerator, while the number by which we divide is the divisor which is the denominator. Thus, in this question, we have;
Dividend = 1987
Divisor = 12
Thus;
1987/12 = 165.5
Thus, we can conclude that when we divide 1987 by 12, we get 165.5
Read more about division of Numbers at; https://brainly.com/question/1622425
#SPJ1
Determine the equation of the altitude from A.
Answer:
y = - 3x + 11
Step-by-step explanation:
the altitude is a line from the vertex A drawn perpendicular to the opposite side BC
calculate the slope of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (- 7, 3 ) and (x₂, y₂ ) = C (- 1, 5 )
[tex]m_{BC}[/tex] = [tex]\frac{5-3}{-1-(-7)}[/tex] = [tex]\frac{2}{-1+7}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ) , then
y = - 3x + c ← is the partial equation
to find c substitute A (4, - 1 ) into the partial equation
- 1 = - 12 + c ⇒ c = - 1 + 12 = 11
y = - 3x + 11 ← equation of altitude from A
can you help me i dont understand this U_U
Answer:
work hours: independent
salary: dependent
Step-by-step explanation:
The independent variable is what is you're "typically" in control of, or it has a constant increase. For example time, you're not really "in control" of time, but it has a constant change. One example where you are in control, is how much money you deposit into your account, you can slightly control it (you obviously can't deposit more than you have), but it's still somewhat in your control.
The dependent variable is what changes as a result of the independent variable changing. So for example in the previous example, where the money deposited was the independent variable, the dependent variable would be the total amount of money in your account
In this case the number of hours during the week is the independent variable and the salary depends on how many hours you work in the week so that is the dependent variable
Find y. right triangles
Answer:
√2
Step-by-step explanation:
Angle ( θ ) = 45
Hypotenuse side = 2
Opposite side = x
Formula : -
sin θ = Opposite side / Hypotenuse side
Note :
The value of sin 45 = 1/√2
sin 45 = x/2
1/√2 = x/2
Cross multiply,
x*√2 = 2*1
x√2 = 2
2 can be simplified as √2 * √2
x√2 = √2*√2
Divide √2 on both sides,
x = √2
If 7846, 7896 and 8802 are rounded to the nearest hundred and then added, the answer will be
Answer:
the answer is 24500
Step-by-step explanation:
7800+7900+8800
=24500
Point o is the center of dilation. triangle x y z is dilated to create triangle x prime y prime z prime. the length of o z is 2 and the length of z z prime is 4. the length of side x prime y prime is 9 and the length of side y prime z prime is 12. triangle xyz was transformed by do,3. what is the length of side xy?
The length of xy in the triangle XYZ is 9 units if xyz is dilated to create triangle x prime, y prime and z prime.
Given triangle xyz is dilated to create x prime, y prime and z prime.The length of oz is 2, the length of Zz Prime is 4,the length of x prime y prime is 9 and the length of side y prime z prime is 12.
Dilation is basically technique of creating similar shapes. Each point is streched outwards from the center point by multiplying the scale.
After dilation the side of the shape used to reduce according to factor. It is reduced by number of times of factor.
The line xy is equal to 9 units after dilation by a factor of 3. So the length of xy is 9/3.
=3 units.
Hence the length of side xy is 3 units if xyz is dilated to create x prime, y prime and z prime.
Learn more about dilation at https://brainly.com/question/3457976
#SPJ4
Answer: 3
Step-by-step explanation: just did it on edge
Consider the diagram.
Triangles L O N and L M N share side L N. Sides O L and M L are congruent. Sides O N and N M are congruent.
The congruence theorem that can be used to prove △LON ≅ △LMN is
SSS.
ASA.
SAS.
HL
The congruence theorem that proves that △LON ≅ △LMN is: A. SSS congruence theorem
What is the SSS Congruence Theorem?According to the SSS congruence theorem, if all three corresponding sides of two triangles are congruent, then both triangles are congruent.
In the image given, we have:
ON ≅ MN LO ≅ LMLN ≅ LN (reflexive property)This means all three corresponding sides are congruent, therefore, the congruence theorem that proves both triangles are congruent is:
A. SSS.
Learn more about the SSS congruence theorem on:
https://brainly.com/question/2102943
#SPJ1
Answer: Option 1 or A. SSS
Step-by-step explanation: The congruence theorem that can be used to prove △LON ≅ △LMN is SSS.
Trust me!
If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.
If you found any of my answers helpful please like and subscribe. I mean choose my answer as Brainliest. I would appreciate it! :)
In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20 winning numbers are randomly selected from numbers 1 to 80. A win occurs if the player has correctly selected 3, 4, or 5 of the 20 winning numbers. (Round all answers to the nearest hundredth of a percent.) what is the percent chance of winning
The percentage of winning if 20 winning numbers are randomly selected from numbers 1 to 80 is 12.48%.
Given There are 80 numbers from which 20 numbers are selected randomly in a game of Keno by player and after selection of 20 winning numbers again 20 numbers are selected and player wins if the player has correctly selected 3,4,or 5 of the 20 winning numbers.
Probability is the chance of happening an event among all the events possible.
Probability of winning is calculated as under:
Probability=[tex]C(20,3)C(60,17)/C(80,20)[/tex]
We have taken C(20,3) because player will win if 5 numbers are selected from 20 winning numbers.
We have taken C(60,17) because after selection of 20 numbers 60 numbers will left from 80 and after winning from 3 numbers 17 numbers left and from total 80, 20 numbers are taken.
=C(20,3)C(60,17)/C(80,20)
=(20!/3!17! * 60!/17!43!)/80!/20!60!
=1140*387221678682300/35353161422121743200
=12.48%
Hence the probability of winning is 12.48%.
Learn more about probability at https://brainly.com/question/24756209
#SPJ4
d = 6 when v = 20 Work out an equation connecting d and v work out the value of d when v =30
The value of d is 27/2 when v =30
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal
Suppose that d is directly proportional to the square of v.
So the equation is, d ∝ v² equals to d = kv², where k is a constant.
So in order to find the value of k,
d = k v²
d = 6, v = 20,
Substitue the value of d and v into the equation :
6 = k(20)²
k = 6/400
k = 3/200
Substitue the value of k and v =30 into the equation,
d = 3/200(30)²
d = 2700/200
d = 27/2
Hence, the value of d is 27/2 when v =30
Learn more about equation
https://brainly.com/question/10413253
#SPJ1
Write equations for the vertical and horizontal lines passing through the point (5,3)
Answer:
Horizontal line - y=3
Vertical line - x=5
Step-by-step explanation:
See both graphs below
Write the product in its simplest form:
-4y²• 8y4
Consider a deck with 2626 black and 2626 red cards. You draw one card at a time and you can choose either guess on whether it is red beforehand or simply observe the result. If the card is red you get \$1$1 and the game ends whenever you decide to guess. What is your strategy to play this game and the expected earnings
The maximum earning is v(r,b)
Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.
Then v(r,b) satisfies the recursion
and
The stopping rule is simple: Stop when v(r,b)=0.
To explain the recursion . . .
If r,b>0, and the player elects to play a card, then:
The revealed card is red with probability [tex]\frac{r}{r+b}[/tex], and in that case, the player gets a score of +1, and the new value is V(r-1,b)The revealed card is black with probability [tex]\frac{b}{r+b}[/tex], and in that case, the player gets a score of −1, and the new value is V(r,b-1)Thus, if r,b>0, electing to play a card yields the value f(r,b).
But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).
Implementing the recursion in Maple, the value of the game is
v(26,26)=41984711742427/15997372030584
v(26,26) ≈2.624475549
and the optimal stopping strategy is as follows . . .
If 24≤b≤26, play while r≥b−5.If 17≤b≤23, play while r≥b−4.If 11≤b≤16, play while r≥b−3.If 6≤b≤10, play while r≥b−2.If 3≤b≤5, play while r≥b−1.If 1≤b≤2, play while r≥b.If b=0, play while r>0.So, The maximum earning is v(r,b)
Learn more about PROBABILITY here
https://brainly.com/question/24756209
#SPJ4
←
2. What is the five-number summary for (34, 47, 51, 11,7,9,13, 49, 22)?
Answer: 47
Step-by-step explanation:
For a 4-units class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on students, and the distribution of total study hours per week is bell-shaped with a mean of 15 hours and a standard deviation of 3 hours. a) 95% of the students have study hours that are between_____and_____hours.
b) What percentage of the students have study hours that are above 12?
95% of the students have study hours between 10.75 and 13.25 hours and the percentage of the students have study hours that are above 12 is 92%.
Given average of 12 % studying required, population mean of 15 hours, standard deviation of 3 hours.
We have to find the confidence interval for 95% students and the percentage of the students that have studied above 12 hours.
Margin of error=z*σ[tex]\sqrt{n}[/tex]
z value for the p value 0.95 is 1.96.
Margin of error=1.96*3/[tex]\sqrt{22}[/tex]
=5.88/4.69
=1.25
Upper interval=Mean +margin of error
=12+1.25
=13.25
Lower interval=Mean- margin of error
=12-1.25
=10.75
The confidence interval (10.75,13.25).
Now we will calculate the percentage of the students that are above 12.
z value when X=12, z=12-15/15
=-3/15
=-0.2
p value of -0.2 will be =0.5+0.4207=0.9207
=0.9207*100
Percentage=92.07%
Approx=92%.
Hence the confidence interval is (10.75 , 13.25) and 92% students have studied above 12.
Learn more about confidence interval at https://brainly.com/question/15712887
#SPJ4
Question is incomplete as it should include sample size of 22.
For which of the given p-values would the null hypothesis be rejected when performing a level 0. 05 test?.
Using a significance level of 0.05, the null hypothesis would be rejected for p-values less than 0.05.
What is the relation between the p-value and the conclusion of test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.Hence, the null hypothesis would be rejected for p-values less than 0.05.
More can be learned about hypothesis tests at https://brainly.com/question/16313918
#SPJ1
The legths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in., find the width, perimeter an area of this rectangle.
Step-by-step explanation:
when given a ratio like this 4:7, it means that one item represents 4 units, and the other 7 units.
let's assume that length is larger than width, so the given 31.5 in are these 7 units.
that means 1 ratio unit is
31.5 / 7 = 4.5 in
the width is 4 units, therefore
width = 4×4.5 = 18 in
the perimeter is
2×length + 2×width = 2×31.5 + 2×18 = 63 + 36 = 99 in
the area is
length × width = 31.5×18 = 567 in²
Professor Nwamabi is conducting an experiment in which he is examining the effects of air conditioning on sleep habits. 100 participants are randomly assigned into two groups, one of which sleeps for a week in an air conditioned setting and of which sleeps in a room without air conditioning. After a week he has various physiological markers assessed to see if the groups are different. In this research, the use of air conditioning represents a(n) ________ variable.
In the research of Professor Nwamabi the use of air conditioning represents independent variable.
Given 100 participants are randomly selected in a research in which effects of air conditioning on sleep habits is studied.
Dependent variable is the variable whose value is dependent on the other variables like increase in profit and production.
Independent variable is the variable whose value is not dependent on the other variables.
In the research of Professor Nwamabi in which he is examining the effects of air conditioning on sleep habits, use of air conditioning represents independent variable. In this study the effect is on sleep habits means the value of sleep habits will change due to use of air conditioning. It shows that the use of air conditioning is not depending on other variable in the research.
Hence the use of air conditioning represents the independent variable.
Learn more about independent and dependent variables at https://brainly.com/question/25223322
#SPJ4
1. On the number line above, the ratio of AE to
AG is equal to the ratio of DF to which of the
following?
Answer:
(C) BE
Step-by-step explanation:
AE = 4
AG = 6
-> AE/AG = 2/3
DF = 2
We need a segment that is 3/2 the length of DF, which is 2.
The only option that works is (C) BE
+
Which statement is true?
UV LAB and WXZY
ZYLWX and AB 1 WX
OUVI AB and UV || ZY
AB|| UV and AB || WX
Answer:
the answer is c
Step-by-step explan
UV ⊥ AB and UV ║ ZY is the correct statement about the given figure.
What is a parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.
As we can observe in the graph Line ZY is parallel to the UV and WX is parallel to AB.
Similarly, WX is perpendicular to ZY and UV(Parallel)
And AB is perpendicular to UV and ZY(Parallel)
Therefore, the correct statement is
UV ⊥ AB and UV ║ ZY
Learn more about parallelograms here:
https://brainly.com/question/29147156
#SPJ2
A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.
Which system of linear equations represents the beverage sales on Saturday?
c = 4 times h
Linear equation: 1.5c + 2h = 360
Hello!
Your answer should be..
c=4h ( as there are 4 hours )
1.5c+2h=360
c is 1.50 and h is 2.00 so you must add them to reach 360
Hope this helps! :)
If a gallon of gas costs 368 9/10 cents, how much does 1/2 gallon cost?
Answer:
[tex]737\frac{4}{5}[/tex]cents
Step-by-step explanation:
1 Gallon of Gas = 368.9 cents (Note: 9/10 = 0.9)
1/2 Gallon of gas = [tex]\frac{368.9}{\frac{1}{2} }cents\\ =368.9 * 2\\= 737.8 cents[/tex]
or [tex]737\frac{4}{5}[/tex] cents (Reduced to simplest form)
Order from least to greatest. 10/8, 1.2, 0.556, 0.8%
The order from least to greatest is 0.8%, 0.556, 1.2 and 10/8
Ordering of numbersIn order to order the given numbers, we will first have to write them as a percentage as shown.
Given the number below
10/8, 1.2, 0.556, 0.8%
Convert to percentage
10/8 = 125%
1.2 = 120%
0.556 = 55.6%
0.8%
Hence the order from least to greatest is 0.8%, 0.556, 1.2 and 10/8
Learn more on ordering here; https://brainly.com/question/12399107
#SPJ1
Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem?
O xx-5
0 x>-5
O x>-1
O x<-1
Answer:
x > -5
Step-by-step explanation:
[tex] \frac{2}{5} (x - 1) < \frac{3}{5} (x + 1)[/tex]
[tex]2(x - 1) < 3(x + 1)[/tex]
[tex]2x - 2 < 3x + 3[/tex]
[tex] - 5 < x[/tex]
[tex]x > - 5[/tex]
Wade wants to buy two shirts and a tie and must spend no more than $60.00. The tie he likes costs $12.50. If the two shirts are the same price, how much can he pay for each shirt?
Answer:
$23.75
Step-by-step explanation:
first, we know the tie he bought is $12.50, so we want to subtract that from the total ($60). Now we have 47.50 dollars left and if he wants to buy two shirts, we divide $47.50 by 2, which is $23.75. So if the two shirts are the same price, he can pay $23.75 for each shirt.
What is the solution for w in the equation?
w+1/2=1/4w+2
A. 4
B. 2
C. 10/3
D. 9/3
Answer:
B. 2
w=2
Step-by-step explanation:
hope this helps!
Samuel invested money in his bank account. he had a principal, p, of $100 in his account at the beginning of the period, which increased at a rate, r, of 0.15 per year. at the end of the period, he had interest, i, of $105 in his account. use the simple interest formula i = prt, to solve for the time, t, in months that it took to earn this amount. (1 point) 7 months 58 months 84 months 700 months
The correct answer is 700 months .
What is simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account. Simple interest doesn't compound, which means a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.Given,
I = 105
P = 100
r = 0.15
Now use simple interest formula,
[tex]S.I. = \frac{p * r* t}{100}[/tex]
105=100×(0.15)×(t)
Swap sides so t is on the left.
100 ×(0.15)×(t)=105
Divide both sides by 100.
0.15t=1.05
Divide both sides by 0.15
t=700
So, we see that it takes 700 months to earn this amount.
Learn more about Simple interest
brainly.com/question/25845758
#SPJ4