Answer:
6 years
Step-by-step explanation:
So each person's age can be represented as a linear equation, since each year our age increases by 1. It can be represented in the slope-intercept form: y=mx+b. The slope in this case is going to be 1, since the time is going to be years, and each year everyone's age goes up by 1 (of course if you're still alive...) and y-intercept in this case represents their current age.
So the father can be represented as: y=x+38
The sons can be represented as: y = x+13 and y=x+5
The daughter can be represented as: y=x+8
So adding up all his children you get:
(x+13)+(x+5)+(x+8)
This gives you the equation:
3x+26
Now set this equal to the father's age to solve for x (in this context it's years)
3x+26=x+38
Subtract from both sides
2x+26=38
Subtract 26 from both sides
2x=12
Divide both sides by 2
x=6
So in 6 years the father will be the same age as his children put together
Select all the correct answers.
3x
If the measure of angle is 4, which statements are true?
The measure of the reference angle is 60°.
□ sin(0) = 2
The measure of the reference angle is 45°.
Otan(8) = 1
cos(8) = √2
The measure of the reference angle is 30°.
If the measure of angle θ is 3π/4, the true statements are:
sin(θ) = √2/2.The measure of the reference angle is 45°.How to determine the true statements?In Trigonometry, an angle with a magnitude of 3π/4 (radians) is equivalent to 135° (degrees) and it's found in the second quarter. Thus, we would calculate the reference angle for θ in second quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 135
Reference angle = 45°.
Also, a terminal point for this angle θ is given by (-√2/2, √2/2) which corresponds to cosine and sine respectively. This ultimately implies that sin(θ) = √2/2.
tan(θ) = cos(θ)/sin(θ)
tan(θ) = [(-√2/2)/(√2/2)]
tan(θ) = -1
In conclusion, we can logically deduce that only options A and B are true statements.
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Complete Question:
If the measure of angle θ is 3π/4, which statements are true. Select all the correct answers.
A. sin(θ)=sqrt2/2
B. The measure of the reference angle is 45
C. The measure of the reference angle is 30
D. The measure of the reference angle is 60
E. cos(θ)=sqrt2/2
F. tan(θ)=1
Use synthetic division to find the expression for the area of the base of a rectangular prism with height x 4 and volume x3 2x2 – 17x – 36. 2x2 – 9x x2 6x – 24 x2 – 2x – 9 –4x2 8x 36
The expression for the area of the base of Prism is x2 – 2x – 9
The volume of a rectangular prism is this
Volume = Area x Height
Substituting the given expressions
x3 + 2x2 - 17x - 36 = Area x (x + 4)
Area = (x3 + 2x2 - 17x - 36) / (x + 4)
Now, let's use synthetic division
-4 | 1 2 -17 -36
---- __-4___8___36
1 -2 -9 0
The expression for the area is
Area = x2 - 2x - 9
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The population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 20% in 10 years. what will be the population in 20 years? (round your answer to the nearest person.)
The population in 20 years is 719 people.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
According to the question
[tex]\frac{dP}{dt} = kP[/tex] where P is population at any time
solving equation,
[tex]\int[/tex][tex]\frac{dP}{dt} =\\[/tex] [tex]\int kP[/tex]
[tex]lnP=kt+C[/tex] -(1)
Applying the conditions,
at t=0, P = 500
[tex]ln500=C[/tex] -(2)
at t=10, P= 600
putting it in equation gives
[tex]ln(600) = k(10)+ln(500)[/tex]
ln(6/5) = k(10)
[tex]k = \frac{ln(6/5)}{10}[/tex]
at t=20 , P= ?
[tex]lnP=(\frac{ln(6/5)}{10})20 + ln500[/tex]
[tex]lnP=({ln(6/5)}{2 + ln500[/tex]
On putting the values of ln(6/5) , ln(500)
[tex]lnP=0.182(2) + 6.214[/tex]
[tex]P = e^{6.578}[/tex]
P = 719.099
On rounding off
P ≈ 719 people
Thus the population in 20 years is 719 people.
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Select the correct answer. The steps for solving the given equation are shown below. -3-7 T 11 C 4 Steps 7 4 114 -3x7 44 -3x7 + 7 = 44 + 7 -3x = 51 3r = I = -17 Justifications 1. multiplication property of equality 2. simplification 3. 777 4. simplification 5. division property of equality 6. simplification Select the correct property for the missing justification in the table. addition property of equality division property of equality multiplication property of equality subtraction property of equality Select the correct answer . The steps for solving the given equation are shown below . -3-7 T 11 C 4 Steps 7 4 114 -3x7 44 -3x7 + 7 = 44 + 7 -3x = 51 3r = I = -17 Justifications 1. multiplication property of equality 2. simplification 3. 777 4. simplification 5. division property of equality 6. simplification Select the correct property for the missing justification in the table . addition property of equality division property of equality multiplication property of equality subtraction property of equality
The property for the missing justification is: A. addition property of equality.
What is the Addition Property of Equality?If b - a = c, based on the addition property of equality, we can isolate b by adding a to both sides, i.e. b - a + a = c + a, to give us b = c + a.
Using the addition property of equality, 7 was added to both sides of the equation as shown in step 3.
Therefore, the missing justification is: A. addition property of equality.
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A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is
The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
Sample size (n) = 16.
Sample mean = 2.8 minutes.
Sample standard deviation (σ) = 1.2 minutes.
Confidence interval given = 95%.
The degree of freedom (df) can be calculated as n - 1.
df = n - 1 = 16 - 1 = 15.
Since, the level of confidence is 95%, the level of significance α = 1 - 0.95 = 0.05.
From the T-Distribution table, we take the value at critical value α/2 with the degree of freedom 15.
[tex]t_{\frac{\alpha }{2} ,15}[/tex] = 2.131.
Now, the margin of error can be shown as follows:
[tex]E = t_{\frac{\alpha }{2} ,15} * \frac{\sigma}{\sqrt{n} } \\\Rightarrow E = 2.131 * \frac{1.2}{\sqrt{16} }\\ \Rightarrow E = 0.6393[/tex]
The width at the confidence interval of 95%, is twice the margin of error, that is:
Width = 2*E = 2*0.6393 = 1.2786.
Thus, the width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
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Which choices are equivalent to the expression below? Check all that apply.
√8√8
A. √8
B. 8
C. √√8.8
D. 64
E. √16
F. 64
I hope this photo will help you.
To wire the entire new addition, max and fred have 6 rolls of wire with 9 2/5 feet per roll and 7 rolls of wire with 16 3/4 feet per roll. how many feet of additional wire do they need in order to complete the job if it requires 200 feet of wire? write the result as a mixed number.
Additional wire of 26 7/20 feet, in the form of a mixed fraction, is required to complete the job.
What is the length of additional wire required, in the form of a mixed fraction?A mixed fraction is represented by both its quotient and remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Max has total 6*9 2/5feet of wire, that is, 282/5 feet of wire.
Fred has total 7*16 3/4 feet of wire, that is, 469/4 feet of wire.
The total amount of wire required=200 feet
The total amount of wire available=282/5+469/4
=3473/20
An additional amount of wire is required=200-3473/20
=(4000-3473)/20
=527/20
Thus, the additional amount of wire required is expressed as a mixed fraction= 26 7/20 of feet.
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If AABD
ACBD,
LA = 32° and ZC = 5x - 13
A
C
x =
B
D
[?]
Answer: 9
Step-by-step explanation:
By CPCTC,
[tex]32=5x-13\\\\45=5x\\ \\ x=9[/tex]
Ryan Massey wants to deposit the following into his savings account: 28 ten-dollar bills, 9 five-dollar bills,
20 quarters, 85 dimes, 32 pennies, and three checks for $654.24, $100.00, and $458.92. He wants to
receive $50.00 in cash.
After he withdraws $50.00 in cash the bank reconciliation shows that Ryan would have: $1 501.98 in bank balance.
What is the solution to the above?Add all the deposits
Total = $338.82
Add the checks
654.24 + 100.00 + 458.92
= $1,213.16
Total amount deposited is: Cash + Check
1,213.16 + 338.82
Total Deposit = $1,551.98
Less withdrawal of $50
$1,551.98 - $50
Balance left = 1 501.98
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Full Question:
Ryan Massey wants to deposit the following into his savings account: 28 ten-dollar bills, 9 five-dollar bills, 20 quarters, 85 dimes, 32 pennies, and three checks for $654.24, $100.00, and $458.92. He wants to receive $50.00 in cash.
How much cash would he lave left after he withdraws $50.00 in cash?
What is the radius of the circle with equation (x + 1/5) ^ 2 + (y - 2/5) ^ 2 = 1/25
Answer:
1/5
Step-by-step explanation:
In the circle equation shown, the 1/25 all by itself on the right side of the equation is r^2.
r^2 = 1/25
Squareroot both sides.
r = 1/5
A book seller gains 30% on the cost price by selling a book for $130.Calculate the cost price of the book.
Answer:
Let the cost price be x
Selling price, S.P. = 130Gain % = 30%[tex]\rm{C.P. = \dfrac{S.P. \times 100}{100+ gain \% }}[/tex]
[tex]\rm{C.P. = \dfrac{130 \times 100}{100+30}}[/tex]
[tex]\rm{ C.P. = \dfrac{130}{30} }[/tex]
[tex]\large{\boxed{\rm{ C.P. = \dfrac{13}{3}}}}[/tex]
Given the following graph of a point on the polar plane, name another set of coordinates that could also represent this point using a
positive "value and a negative "O" value, where -360 ≤ 0 ≤ 0. State your answer in the form: (r,0) with "O" in degrees without the
degree symbol.
Answer:
(r,0)
Step-by-step explanation:
HELP PLSSSSS! 10 points for whoever and good ratings
Answer:
Hello! The answer is 19.25 m²
Step-by-step explanation:
A = 1/2(4 + 7)3.5
A = 1/2(11)3.5
A = (5.5)3.5
A = 19.25 m²
Answer:
19.25 m²
Step-by-step explanation:
A = (1/2)(b1 + b2)h
A = (1/2)(7 m + 4 m)(3.5 m)
A = 19.25 m²
A bucket is in the shape of a frustum with top diameter 20cm and bottom diameter 12cm. If the height of the bucket is 8cm, calculate the volume of the bucket
Answer: V≈1642 cm³.
Step-by-step explanation:
D=20 cm d=12 cm h=8 cm V=?
[tex]R=\frac{D}{2}=\frac{20}{2} =10 \ (cm).\\ r=\frac{d}{2}=\frac{12}{2}=6 \ (cm).\\ \boxed {V=\frac{1}{3} *\pi *h*(R^2+R*r+r^2)} \ \ \ \ \ \Rightarrow\\V=\frac{1}{3}*\pi *8*(10^2+10*6+6^2)\\V=\frac{1}{3}*\pi *8*(100+60+36)\\ V=\frac{8}{3} *\pi *196\\V=\frac{8*196*\pi }{3} \\V\approx1642\ cm^3.[/tex]
what postulate is this?
A. SSS (side side side)
B. SAS (side angle side)
C. ASA (angle side angle)
D. AAS (angle angle side)
Answer:
the answer is c ASA
Step-by-step explanation:
i think I. not sure
Robert, Richard and David were working on a project to redesign coke cans. First, Robert measured the original coke can and found the circumference to be 8.6 inches. Richard measured the height to be 15.2 cm.
David calculated the volume to be 131.3 cm3.
Choose the true statement(s) below.
Select one or more:
a.David's calculations are incorrect, he needed to convert centimeters to inches before finding the radius then use the area of the base times the height .
b.David is correct.
c.David's calculations are incorrect, he used the circumference and the height to find the volume.
The true statement is David's calculations are incorrect, he used the circumference and the height to find the volume.
VolumeCorrect calculation:
Height = 15.2 cmCircumference = 8.6 inchesC = 2πr
8.6 = 2 × 3.14 × r
8.6 = 6.28r
r = 8.6/6.28
r = 1.36942675159235 inches
convert 1.36942675159235 inches to cm
= 3.478343949044569 cm
Approximately,
r = 3.5 cm
Volume = πr²h
= 3.14 × 3.5² × 15.2
= 3.14 × 12.25 × 15.2
= 584.668 cm³
Approximately,
volume = 584.7 cm³
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What is the slope of each of these three graphs?
[5] No slope (or a slope of 0)
There is no incline or decline to the line, so there is no slope.
[6] 1
We can use "rise over run" since we have clear points on the graph. See attached.
[7] Undefined slope
This slope of this line is undefined. The formula for slope is [tex]\frac{\text{change in y}}{\text{change in x}}[/tex] which becomes [tex]\frac{0}{0}[/tex] in a case like this. You cannot divide by 0, giving a slope of undefined.
A grandfather is 51, while his grandson is 11. in how many years will the grandfather's age be twice the age of his grandson?
Answer:
29 years
Step-by-step explanation:
In 29 years the grandson will be 40 and the grandfather will be 80. 80 is twice as much as 40.
Answer: 29 years
Step-by-step explanation: if the grandfather is 51 when the grandson is 11 then the grandfather was 40 when his grandson was born. This mean the grandfather will be 80 when the grandson is 40. 40-11=29
What is the area of a square with radius 7.5m
Answer:
48.375
Step-by-step explanation:
Area of square- area of circle
Side^2 - pieR^2
(15)^2 - 3.14*7.5*7.5
225 - 176.625
= 48.375
Hope this helps
The area of the square is 56.25 m².
The area of the square is:
Area = Side²
Area = (7.5 m)²
Area = 56.25 m²
{ Pisces04 }
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50. The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5. If she has a total of 30 notes, how many notes of each denomination she has.
Answer:
Given that,
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50.
The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5.
She has a total of 30 notes with her.
Let assume that
Number of Rs 10 notes be 2x
Number of Rs 20 notes be 5x
Number of Rs 50 notes be 30 - (2x + 5x) = 30 - 7x
So,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad\sf \:Denomination \: of \: Rs \: 10=2x\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=5x\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=30 - 7x\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
Now,
Amount in form of Rs 10 = 10 × 2x = Rs 20x
Amount in form of Rs 20 = 20 × 5x = Rs 100x
Amounts in form of Rs 50 = 50 × (30 - 7x) = Rs 1500 - 350x
Now, According to statement
[tex]\begin{gathered}\sf \: 20x + 100x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 120x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 1500 - 230x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \:- 230x = - 460 \\ \\ \end{gathered}[/tex]
[tex]\sf \: \implies x = 2 [/tex]
Hence,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Denomination \: of \: Rs \: 10=4\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=10\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=16\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
━━━━━━━━━━━━━━━━━━━━━22/11,594 I need a step by step answer
Answer:
1.89753
Step-by-step explanation:
22/11,594
Multiply the numerator and denominator by 1000 to remove decimal[tex]\frac{22}{11.594} * 1000 = \frac{22000}{11594}[/tex]
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ion 9
ret
ered
ed out of
g
ion
Given circle A with radius 15, find the length of arc FD. Give your answer rounded to the nearest hundredth.
Answer:
20°
156°
46°
my
E
D
B
The length of arc FD with a radius of 15 and angle of 120° is 10π units.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The length of an arc is given by:
arc length = (Ф/360) * 2π*radius
Let us assume that the angle is 120°
arc FD = (135/360) * 2π(15) = 10π
The length of arc FD with a radius of 15 and angle of 120° is 10π units.
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A circle has a circumference of 6. It has an arc of length 1.
What is the central angle of the arc, in degrees?
Answer:
Central Angle (Radians)=
1.0482
Central Angle (Degrees)=
6.0058e+1
Sector Area Equals
0.477
Step-by-step explanation:
PLEASE HELP!!!
Determine the measure of the angle formed by the line y=3/2x and the positive x-axis.
Answer:
the angle = ~56.3 degrees
Step-by-step explanation:
1. y=3/2(x) and y=0
2. say x is equal to 4. the length along the x axis is 4. you would plug x=4 into y=3/2x to get the length along the y axis (which would be 6). then you would use these lengths to find the angles value with tan. tan^-1(6/4), so the answer would be ~56.3 degrees
Please help me Ill mark you brainlest
Answer:
Step-by-step explanation:
what does I mean in a equation
Iota, also known as the symbol , is denoted as being the square root of -1. Since square roots of negative numbers do not exist, there is a variable that represents it complexly. In fact, every real number (a) can be represented using the form (a) + (0).
On occasion, variables can also use and it does not have to be talking about the square root of -1. However, this rarely ever happens to avoid confusion. Check instructions in questions to see how is defined.
The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours. How many total miles did the Ramos family drive?
ASAP
Anyone is here
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours -> They drove a total of 55 x 3 = 165 miles.
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours -> They drove a total of 45 x 2 = 90 miles.
So, the total amount of miles the Ramos family drove is 165 + 90 = 255 miles.
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours.
[tex]\longrightarrow \tt{55*3=165}[/tex]
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.
[tex] \longrightarrow \tt{45*2=90}[/tex]
Total miles the Ramos family drive
[tex] \longrightarrow \tt{165+90=255}[/tex]
[tex]answer : \pink{255} \: \tt{miles}[/tex]
I really need help on this question
Answer:
24Step-by-step explanation:
Since 20 is 4/3 * 15, the answer must be 4/3 * 18
4/3 * 18 = 24, so the answer is 24
A triangle has one side length of 2x
2 + 5x + 3. The other two sides of the triangle have lengths x
2 + 2x and
3x − 2. Determine the simplified expression that represents the total perimeter of the triangle.
The simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
How to determine the perimeter?The side lengths are given as:
2x^2 + 5x + 3, 2 + 2x and 3x - 2
Add these lengths to determine the perimeter (P)
P = 2x^2 + 5x + 3 + 2 + 2x + 3x - 2
Collect like terms
P = 2x^2 + 5x + 2x + 3x + 3 + 2 - 2
Evaluate the like terms
P = 2x^2 + 10x + 3
Hence, the simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
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What second degree polynomial function has a leading coefficient of -2 and root 4 with a multiplicity of 2
The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
How to write the polynomial?
A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:
[tex]p(x) = a*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]
Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.
Then this polynomial is equal to:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
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