Six years ago Matt was four times as old as Brown, and in 3 years the sum of their
ages will be 43 years. Find their present ages.
Answer:
Matt=26
Brown=11
Step-by-step explanation:
Just trust me!!!
The present age of Matt given the information in the question is 26.
The present age of Brown given the information in the question is 8.
What are the linear equations that represent the question?4y - 6 = x equation 1
x + y + 6 = 43 equation 2
Where:
x = Matt's agey = Brown's ageWhat is Brown's age?Subsistute for x in equation 2
4y - 6 + y + 3 = 43
Combine similar terms
5y = 40
y = 8
What is Matt's age?
Subsitute for y in equation 1
4(8) - 6 = x
32 - 6 = 26
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Please help ! Please help!
Pls help me solve this
find the HCF of 12;28 and 32
Answer:
4
Step-by-step explanation:
28 = 22 • 7
12 = 22 • 3
32 = 25
Which model is 85% shaded?
Done
Answer:
I would need to see the models to answer this question.
Answer:
?
Step-by-step explanation:
What is the range of the function on the graph?
Range is the output values which are the y values.
The dot is at y = 2 and the line moves upward to the right off the graph. This means the line will continue to infinity.
The range would be 2 to infinity.
(2, infinity)
A function y(t) satisfies the differential equation dy dt = y4 − 10y3 + 24y2. (a) What are the constant solutions of the equation? (Enter your answers as a comma-separated list.) y = (b) For what values of y is y increasing? (Enter your answer in interval notation.) y (c) For what values of y is y decreasing? (Enter your answer in interval notation.) y
Answer:
[tex](a)\ y =0\ or\ y=4\ or\ y=6[/tex]
[tex](b) \ (-\infty,4)\ u\ (6,\infty)[/tex]
[tex](c)\ (4,6)[/tex]
Step-by-step explanation:
Given
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
Solving (a): The constants
This implies that:
[tex]\frac{dy}{dt} = 0[/tex]
So, we have:
[tex]y^4 - 10y^3 + 24y^2 = 0[/tex]
Factorize:
[tex]y^2(y^2 - 10y + 24) = 0[/tex]
Expand and Factorize the expression in bracket
[tex]y^2(y^2 - 6y - 4y + 24) = 0[/tex]
[tex]y^2(y(y - 6) - 4(y - 6)) = 0[/tex]
[tex]y^2(y - 4)(y - 6) = 0[/tex]
Split
[tex]y^2 =0\ or\ y-4=0\ or\ y-6=0[/tex]
Solve for y
[tex]y =0\ or\ y=4\ or\ y=6[/tex]
The above represents the constants
Solving (b): Increasing values
Here
[tex]\frac{dy}{dx} > 0[/tex]
Follow the same process in (a) but replace all = with >
i.e.
[tex]y^2(y - 4)(y - 6) > 0[/tex]
[tex]y >0\ or\ y>4\ or\ y>6[/tex]
Test the values of each inequality
For [tex]y > 6[/tex]; say [tex]y = 7[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 7^4 - 10*7^3 + 24*7^2[/tex]
[tex]\frac{dy}{dt} = 147[/tex]
[tex]147 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]; This implies that: [tex](6, \infty)[/tex]
For [tex]y > 4[/tex] Say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is false:
Say [tex]y = 3[/tex] i.e. [tex]y < 4[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
[tex]27 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that: [tex](0,4)[/tex]
For [tex]y > 0[/tex]
[tex]y > 0[/tex] implies that: [tex]y < 4[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that [tex](-\infty, 0)[/tex]
We have: [tex](-\infty,0), (0,4)\ and\ (6,\infty)[/tex]
[tex](-\infty,0)\ and\ (0,4)[/tex] can be combined to give: [tex](-\infty,4)[/tex]
So, the interval is: [tex](-\infty,4)\ u\ (6,\infty)[/tex]
Solving (c): Decreasing values
Here
[tex]\frac{dy}{dx} < 0[/tex]
i.e.
[tex]y^2(y - 4)(y - 6) < 0[/tex]
[tex]y <0\ or\ y<4\ or\ y<6[/tex]
Test the values of each inequality
For [tex]y < 6[/tex]; say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is true for [tex]\frac{dy}{dx} < 0[/tex]; This implies that: [tex](\infty,6)[/tex]
For [tex]y < 4[/tex]; say [tex]y = 3[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
This is false
Say [tex]y = 5[/tex] i.e. [tex]y > 4[/tex]
This is the same as: [tex]y < 6[/tex]
So, we have the interval to be: [tex](4,\infty)[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is false
Say [tex]y = 2[/tex] i.e [tex]y > 0[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 2^4 - 10*2^3 + 24*2^2[/tex]
[tex]\frac{dy}{dt} = 32[/tex]
This is also false
So, the intervals are: [tex](4,\infty)[/tex] and [tex](\infty,6)[/tex].
This can be merged as: [tex](4,6)[/tex]
Hence, the interval for [tex]\frac{dy}{dt} < 0[/tex] is [tex](4,6)[/tex]
MUST HELP!!!! (+50 POINTS +BRANILEST +5 STARS +THANKS ON PROFILE)
Answer:
Personification is your answer.
Hope it helps!!!
Li’s family is saving money for their summer vacation. Their vacation savings account currently has a balance of $2,764. The family would like to have at least $5,000.
The inequality 2764 + x Greater-than-or-equal-to 5000 can be used to determine the amount of money the family still needs to save. What is the solution to the inequality?
x Greater-than-or-equal-to 2236
x Greater-than-or-equal-to 7764
x Less-than-or-equal-to 2236
x Less-than-or-equal-to 7764?
Answer: x greater-than or equal-to 2,236
Step-by-step explanation:
5,000-2,764= 2,236
so Li's family still needs to save at least $2,236
Answer:
A
Step-by-step explanation:
bc
Jamie placed $2800 in a savings account which earns 4.3% interest, compounded continuously. How much will she have in the account after 9 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answer:
4123
Step-by-step explanation:
A=Pert,
where A is the balance of the account, P is the principal, r is the annual interest rate (as a decimal), and t is the time (in years). We are given that P=2800, r=0.043, and t=9. Substituting the values into the formula and using a calculator to evaluate, we find
A=Pert=2800e(0.043)(9)≈4123.16
A rectangular prism is 4 cm long, 3 cm wide and 8 cm tall. What is the volume of the prism?
Answer:
96 cm³
Step-by-step explanation:
v = 4 x 3 x 8 = 96 cm³
Answer:
The volume of the prism is 96cm^3
Step-by-step explanation:
You multpily 4*3*8=96
A box contains 3 black pens, 7 blue pens and 5 red pens. Without replacing the first pen,
what is the probability of pulling a red or blue pen?
Answer:12/15
Step-by-step explanation: first you add 7+5=12
then add 12+3=15
I NEED HELP PLEASE ASAP!
Answer:
Step-by-step explanation:
Solve for the following by
FACTORING:
x2 + 15x + 56 = 0
Answer:
17x + 56 = 0
Step-by-step explanation:
add 2x and 15x
hi can you please help me with my work
Answer:
3 expodent 12
Step-by-step explanation:
PLEASE HELp ME U GET ALOT OF POINTS 97points
circumference and Area of circles
7. Demi measured the wheels on her brother's wagon. The diameter of each
wheel is 15 inches. To the nearest inch, how far will the wagon travel each
time the wheels make a complete turn?
8.The radius of circle A is 6 ft. The diameter of circle B is 6 ft. To the nearest
foot, how much greater is the circumference of circle A as compared to the circumference of circle B?
9. The larger circle in the design at the right has a radius of 40 in.
What is the area of the shaded part of the design?
30 in.
10. Max knows that the circumference of a circular pool is 12 ft.
He estimates that the diameter of the pool is between 3 ft and 4 ft. Is this reasonable? Explain.
Answer:
#7
C = πd = 3.14*15 in = 47 in (rounded)#8
C₁ = 2πr = 2*3..14*6 ft = 37.68 ftC₂ = πd = 3.14*6 ft = 18.84 ftThe difference:
C₁ - C₂ = 37.68 - 18.84 = 19 ft (rounded)#9
No picture attached#10
C = 12 ftd = C/πd = 12/3.14 = 3.82 ft3 ft < 3.82 ft < 4 ftMax is right
1. Find the slope of the graph. Slope:
Answer:
I think the answer is 5 down and over to the left 3.
Step-by-step explanation:
I just counted from the point on the (4,3) and counted down until it was line up with the other point. Next, I counted from there to the other point.
Question 7Partially correct answer. Your answer is partially correct. Try again.An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.(a) Is there evidence that the success rate is greater for longer tears
This question is incomplete, the complete question is;
An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.
a) Is there evidence that the success rate is greater for longer tears? Use alpha=0.05
Answer:
P-value = 0.6443
Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.
Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ = [tex]p[/tex]₂
Step-by-step explanation:
Given the data in the question;
Sample of tears greater than 25;
number of successive repairs X₁ = 13
number of repair n₁ = 19
proportion of successive repairs [tex]p[/tex]₁ = 13/19 = 0.68
q₁ = 1 - [tex]p[/tex]₁ = 1 - 0.68 = 0.32
Sample of tears shorter than 25;
number of successive repairs X₂ = 22
number of repair n₂ = 30
proportion of successive repairs [tex]p[/tex]₂ = 22/30 = 0.73
q₂ = 1 - [tex]p[/tex]₂ = 1 - 0.73 = 0.27
so;
H₀ : There is no significant difference in the successive proportions; [tex]p[/tex]₁ = [tex]p[/tex]₂
Hₐ : The successive rate is greater for longer tears [tex]p[/tex]₁ >
Significance level ∝ = 0.05
Test Statistics
Z = ([tex]p[/tex]₁ -
so we substitute
Z = ( 0.68 - 0.73 / √[ (0.68 ×0.32 / 19) + ( 0.73×0.27 / 30 ) ]
Z = -0.05 / √[ 0.01802 ]
Z = -0.05 / 0.1342
Z = -0.37
P-value for the given test, p = P( Z > -0.37 )
= 1 - P( Z ≤ - 0.37 )
= 1 - 0.35569
P-value = 0.6443
Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.
Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ = [tex]p[/tex]₂
Jamal's car averages 18.4 miles per gallon. How far can he expect to drive on 9.2 gallons of gas?
Answer:
169.28
Step-by-step explanation:
18.4x9.2=169.28
Can someoneee please help me
9514 1404 393
Answer:
37°
Step-by-step explanation:
The diagonals of a rhombus are angle bisectors. Angle 1 matches the other half of angle L.
∠1 = 37°
__
Angle 2 is the complement, 53°, and angle 3 is the same as angle 2, 53°.
The diagonals of a rhombus are perpendicular bisectors of each other, so angle 4 is 90°.
David invests $7000 in two different accounts. The first account paid 2 %, the second account paid 5
% in interest. At the end of the first year he had earned $182 in interest. How much was in each
account?
Answer:
3,990
Step-by-step explanation:
9.3+b=−42 , you would subtract 9.3 to isolate the variable.
Answer:
yeh you are correct so it will be b is equal to minus 42 minus 9.3 that will be equal to -51.3 so that is the value of b
You moved 7 units left, 8 units up, and ended at point W
Where did you begin?
OA) (1.8)
OB) (9.1)
OC) (81)
OD) (9.8)
Please help me I’m tired
Answer:
C. (8,1)
Step-by-step explanation:
Geometry Question!!!
9514 1404 393
Answer:
12.5 cm
Step-by-step explanation:
Triangle IDA is a 3-4-5 right triangle with a scale factor of 5. That is, segment AI is 25 cm long. Since IS is half the length of the diagonal, it is ...
IS = (25 cm)/2
IS = 12.5 cm
__
If you like, you can work out the length of AI using the Pythagorean theorem:
AI² = DI² +DA²
AI = √(15² +20²) = √(225 +400) = √625 = 25
Can you help me thanks!
Carl paid $40 for 12.5 gallons of gas.After calculating,he said that the cost per gallon was about 31 cents per gallon.Is there anything wrong with Carl's thinking?.
Answer:
Well yes, because it should have cost $3.2 PER gallon
Step-by-step explanation:
Divide 40 by 12.5 to find out how much of a per gallon costs! Hope it helps.
twenty subtract from 28
Answer:
8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
20-28= -8
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9 What is the confidence interval for the population mean μ? <μ
Answer:
Confidence Interval = ( 5.6 < μ < 8.2 )
The interval shows that the mean attractiveness is Above average on a scale of 1 to 10
Step-by-step explanation:
Data Given : 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9
a) construct a confidence interval at a 95% confidence level
confidence interval = x ± tcritical ( s / √ n ) ------ ( 1 )
n = 12
μ (mean) = ( 5+8+2+8+7+6+6+8+9+9+6+9 ) / 12 ≈ 6.92
std ( s ) = √ 1/11 *∑( xi- X )^2
= √ 1/11 * ( 5 - 6.92)^2 + ( 8 - 6.92)^2 + ( 2 - 6.92)^2 + ( 8 - 6.92)^2 + ( 7-6.92)^2 + ( 6 - 6.92)^2 + (6 - 6.92 )^2 + ( 8 - 6.92 )^2 + ( 9 - 6.92)^2 + ( 9 - 6.92)^2 + ( 6 - 6.92 )^2 + ( 9 - 6.92 )^2
= √ 1/11 * 46.92 = 2.07
tcritical at ∝ 0.05 , df = 11 = 2.20
Back to equation 1
6.92 ± 2.2 ( 2.07 / √ 12 )
( 6.92 ± 1.31 )
Confidence Interval = ( 5.6 < μ < 8.2 )
Which of the following is NOT an example of a right angle?
Ο Α.The corner of a door
O B.The corner of a book
C.The point of a pencil
D.The corner of a piece of notebook paper
Answer:
The point of a pencil
Step-by-step explanation:
all other three mesure 90 the point of pencil is not square shape in order for it to be right angle its gotta be square shape hope this helps! may i be marked brainliest?
−8≤2/5(k−2) negative 8 is greater than/equal to 2/ fifths (k minus 2)
Answer:60
Step-by-step explanation: