Answer:
[tex]F = 45.4[/tex]
[tex]S = 12.68[/tex]
Step-by-step explanation:
Given
Represent the sons age with S and the father's age with F
[tex]S * F = 576[/tex]
[tex]F = 5S - 18[/tex]
Required
Determine F and S
Substitute 5S - 18 for F in the first equation
[tex]S * (5S - 18) = 576[/tex]
Open Bracket
[tex]5S\² - 18S = 576[/tex]
Equate to 0
[tex]5S\² - 18S - 576 = 0[/tex]
Solve using quadratic formula:
[tex]S = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 5[/tex]
[tex]b = -18[/tex]
[tex]c = -576[/tex]
[tex]S = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]S = \frac{-(-18)\±\sqrt{(-18)^2 - 4*5*-576}}{2 * 5}[/tex]
[tex]S = \frac{18\±\sqrt{324 + 11520}}{10}[/tex]
[tex]S = \frac{18\±\sqrt{11844}}{10}[/tex]
[tex]S = \frac{18\±\108.8}{10}[/tex]
[tex]S = \frac{18+108.8}{10}[/tex] or [tex]S = \frac{18-108.8}{10}[/tex]
[tex]S = \frac{126.8}{10}[/tex] or [tex]S = \frac{-90.8}{10}[/tex]
[tex]S = 12.68[/tex] or [tex]S = -9.08[/tex]
Since, age can't be negative.
We have that:
[tex]S = 12.68[/tex]
Recall that:
[tex]F = 5S - 18[/tex]
[tex]F = 5 * 12.68 - 18[/tex]
[tex]F = 45.4[/tex]
Hence:
The father is 45 years old and the son is 13 years old (Approximated)
Can someone help me solve this ?
Answer:
$182
Step-by-step explanation:
Let x be the number of students going
Let y be the total cost
Then,
7x=y
7(26)=y
$182=y
Therefore, the total cost would be $182 for 26 students to go.
Hope this gives you an A
Answer:
expression: 7 × (S which is 26)
Total cost: 182
Step-by-step explanation:
The capacities (in ampere-hours) were measured for a sample of 120 batteries. The average was 178 and the standard deviation was 12. Find a 95% lower confidence bound for the mean capacity of this type of battery. Round the answer to two decimal places. The lower confidence bound is .
Answer: A 95% lower confidence bound for the mean capacity of this type of battery = 175.85
Step-by-step explanation:
Given: The capacities were measured for a sample : n= 120 batteries.
[tex]\overline{x}=178[/tex] and [tex]\sigma=12[/tex]
lower confidence bound= [tex]\overline{x}-z^c\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Critical z value for 9%% confidence = 1.96
So, a 95% lower confidence bound for the mean capacity of this type of battery will be :
[tex]178-(1.96)\dfrac{12}{\sqrt{120}}\\\\=178-(1.96)(1.0954451)\\\\=(1.96)(1.0954451)\approx175.85[/tex]
Hence, a 95% lower confidence bound for the mean capacity of this type of battery = 175.85
The expression on the left side of an equation is shown below.
-6x+6-0
If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the
equation?
-6
1
-6x
- 6x+6
D: -6x +6
Step-by-step explanation: Told ya.............
The amount dispensed by a soft-drink dispensing machine has a normal distribution with mean μ and standard deviation 0.155 ounce. The mean amount dispensed, μ , can be controlled. At what value should μ be set so that a 16 ounce cup will overflow with probability 0.01? Round your answer to two decimal places.
Answer: [tex]\mu=15.64[/tex]
Step-by-step explanation:
Let x be a random variable that represent the amount dispensed by a soft-drink dispensing machine which has a normal distribution with mean μ and standard deviation [tex]\sigma=[/tex] 0.155 ounce.
To find : μ such that P(X>16)=0.01
Consider P(X>16)=0.01
[tex]P(\dfrac{X-\mu}{\sigma}>\dfrac{16-\mu}{0.155})=0.01[/tex]
Since, [tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
Also, z-table , one -tailed z-value for p-value of 0.01= 2.326
Then, [tex]\dfrac{16-\mu}{0.155}=2.326[/tex]
[tex]\Rightarrow {16-\mu}=0.155\times2.326\\\\\Rightarrow {16-\mu}=0.36053\\\\\Rightarrow\ \mu=16-0.36053=15.63947\approx15.64\\\\\Rightarrow\ \mu=15.64[/tex]
Find the divergence of each of the following vector fields at all points where they are defined. (a) div(x(x2 y2 z2)1.5i y(x2 y2 z2)1.5j z(x2 y2 z2)1.5k)
Answer: the divergence of the vector fields at all points its defined is 0
Step-by-step explanation:
Given that;
div ( [x / (x²+ y² + z²)^1.5]i + [y / (x² + y² + z²)^1.5]j + [z / (x² + y² + z²)^1.5]k )
= d/dx [x / (x²+ y² + z²)^1.5] + d/dx [y / (x² + y² + z²)^1.5] + d/dx [z / (x² + y² + z²)^1.5]
= [1 / (x²+ y² + z²)^1.5] - [3x² / (x²+ y² + z²)^2.5] + [1 / (x²+ y² + z²)^1.5] - [3y² / (x²+ y² + z²)^2.5] + [1 / (x²+ y² + z²)^1.5] - [3z² / (x²+ y² + z²)^2.5]
= [3 / (x²+ y² + z²)^1.5] - [(3x² + 3y² +3z²) / (x²+ y² + z²)^2.5]
= [2 / (x²+ y² + z²)^1.5] - [3 / (x²+ y² + z²)^1.5] = 0
therefore the divergence of the vector fields at all points its defined is 0
y=3/4x -1 find the slope and the y intercept PLEASE ALOT OF POINTS
Answer:
slope 3/4
y intercept -1
Step-by-step explanation:
y=mx+b
m=slope
b=y intercept
Answer:
Slope-3/4
Intercept-(0,-1)
Step-by-step explanation:
Evaluate the expression when x=4 and y=1: 5y
Answer:
5
Step-by-step explanation:
5(1) = 5
Answer:
5
Step-by-step explanation:
There is no x so we only replace y with 1
5(1)=5*1=5p
plz help as soon as you can
A: -16 < -4
B: 40 > 8
C: -45 < 15
D: 35 > -20
E: Reverse
Find equation for a vertical line passing through the point (-12,-4)
Answer:
x = -12
Step-by-step explanation:
This is a vertical line, so the equation will be of the form x = k, where k is any x-value.
The conclusion that x = -12 was found because the x-value in the point was -12.
g The probability of rolling a single die and obtaining a two is one-sixth. The probability of rolling a single die and obtaining a five is one-sixth. What is the probability of rolling a single die and obtaining either a two or a five
Answer:
33.33% or [tex]\frac{2}{6}[/tex]
Step-by-step explanation:
A single die has a total of six different possible outcomes (1, 2, 3, 4, 5, 6). Since the numbers two and five are only two of the six possible outcomes that means that the possibility of getting one of these two numbers on a single roll is [tex]\frac{2}{6}[/tex] . If we divide this fraction and multiply the result by 100 (0.333 * 100 = 33.33) we see that there is a 33.33% chance of you rolling either a two or a five.
Using exponents, what is the simplified form of 15x6/3x2
F. 5x"
G. 5x3
H. 5x
I. 5
Answer:
[tex] \frac{15 {x}^{6}}{3 {x}^{2} } = 5 {x}^{4} [/tex]
Find x.
P
40
600
L
R
1345753 yessssssssssss
A manufacture has been selling 1300 television sets a week at $390 each. A market survey indicates that for each $25 rebate offered to a buyer, the number of sets sold will increase by 250 per week. a) Find the demand function p ( x ) , where x is the number of the television sets sold per week.
Answer:
P = - 0.1x+520
Step-by-step explanation:
Finding the demand function p ( x ) , where x is the number of the television sets sold per week.
each $25 rebate offered to the buyer, the number of sets sold will increase by 250 , hence slope = -25/250 = -1/10 Equation will be
P-390/x-1300 = -25/250
Cross multiplying
250(P-390) = -25(x-1300)
250p-97500 = -25x+32500
250p = -25x+32500+97500
250p = -25x + 130000
Divide both sides by 250
250p/250 = (25x + 130000)/250
P = - 0.1x+520
Hence, the demand function p(x) is
= - 0.1x+520
The curved part of this figures is a semicircle.
What is the best approximation for the area of this figure?
14+16.25π units²
28+16.25π units²
14+8.125π units²
28+8.125π units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 4 comma negative 2 to negative 4 comma 2. Another segment extends from negative 4 comma 2 to 3 comma 2. A semicircle extends from 3 comma 2 to negative 4 comma negative 2.
The area of a shape is the amount of space on the shape.
The best approximation for the area of the figure is [tex]14 + 16.25\pi[/tex]
How to determine the area of the figureStart by calculating the diameter of the semicircle using the following distance formula:
[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2}[/tex]
So, we have:
[tex]d = \sqrt{(-4 -3)^2 +(-2 -2)^2}[/tex]
[tex]d = \sqrt{65}[/tex]
Divide by 2, to calculate the radius
[tex]r = \frac{\sqrt{65}}{2}[/tex]
So, the area of the semicircle is:
[tex]A = \frac{\pi r^2}{2}[/tex]
This gives
[tex]A = \pi (\frac{\sqrt{65}}{2})^2[/tex]
[tex]A = \frac{65}{4}\pi[/tex]
[tex]A = 16.25\pi[/tex]
Next, we calculate the area of the triangle using:
[tex]A = 0.5 * B * H[/tex]
Where:
[tex]B = 3 -(-4)[/tex]
[tex]B = 7[/tex]
[tex]H= 2 - (-2)[/tex]
[tex]H = 4[/tex]
So, we have:
[tex]A = 0.5 * 7 * 4[/tex]
[tex]A = 14[/tex]
The area of the figure is then calculated as:
[tex]A = 14 + 16.25\pi[/tex]
Hence, the best approximation for the area of the figure is [tex]14 + 16.25\pi[/tex]
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(4, 3); 4x − 5y = 30
HeLp
What is the equation of the graphed line written in
standard form?
O x=-3
O y=-3
O x + y = -3
O x-y=-3
Answer: y=-3
Step-by-step explanation:
please answer asap!!
Answer:
MON= 15
Step-by-step explanation:
9x+44+6x+3=77
15x+47=77 subtract 47 from both sides
15x=30 divide both sides by 15
x=2
6x+3
(6*2)+3
12+3=
15
Hope this helps
If f(x)=6x2-4, what is f(1)?
Answer:
f−1(x)=√6(x+4)6,−√6(x+4)6
Plz let me know if im wrong!!!
Answer:
are u sure this is written correctly?
Helppppppppppppppppp
Answer:
16
Step-by-step explanation:
since the triangle is the same on both sides, if one side is 16 then the other side is the same.
Ed's goal is to jog no more than 8 miles this week. He jogged 4 3/4 miles on Monday and 3 3/8 miles on Wednesday.
Answer:
8.125
Step-by-step explanation:
He jogged over 8 miles so he needs to stop jogging he already completed his goal.
In 2016, humans produced 29 billion tonnes of carbon dioxide. This is set to grow by around 40% by the year 2035. How many tonnes of carbon dioxide will be produced by humans in 2035? Give your answer in standard form.
Answer:is it 40.6 billion tonnes of carbon dioxide
Step-by-step explanation:
Andre and Elena are solving this system of equations: y=3x,
y=9x−30
Andre's first step is to write: 3x=9x−30
Elena’s first step is to create a new system: {3y=9xy=9x−30
Do you agree with either first step? If so which one and explain your reasoning
It should be noted that when Andre and Elena are solving this system of equations, the first step is correct but the others are wrong.
How to illustrate the information?It should be noted that an equation is used.to show the relationship between the expressions that are given.
It should be noted that Andre and Elena are solving this system of equations: y=3x, y=9x−30.
This will be equated to this:
3x = 9x - 30
Collect like terms
9x - 3x = 30
6x = 30
Divide
x = 30 / 6
x = 5
Note that y = 3x = 3 × 5 = 15
Therefore, it should be noted that when the value of y is 15 and only the first step is correct.
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16m^2+60m-54
Factor
HELP PLEASE WILLMARK BRAINLIEST
Answer: D
Step-by-step explanation:
Subtract 2(1/2) - 4(1/4)
A. -2(1/4)
B. -1(3/4)
C. 1(3/4)
D. 7(3/4)
Solve the equation.
512^x= 8
O {3}
O {1/3}
O {-1/3}
O {-3}
Answer:
it's the 2nd one
Step-by-step explanation:
its 1/3
ratios. 12 yards to 9 feet
Since one yard is equivalent to three feet, you can multiply the number of yards by 3 to convert from yards to feet. 36 feet are equal to 12 yards times 3 feet per yard. Consequently, 12 yards are equal to 36 feet.
What does the term "yard" mean?A unit of length equivalent to 3 feet, or around 0.914 metres.
Both the US Customary and British Imperial Systems of Measurement use yards as a measure of length. Yd is its symbol. The length of medium-sized objects is frequently measured using it.
What is an illustration of one yard?About half the length of a bed is a yard. wider than a huge refrigerator. the elevation of a countertop.
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How do I divide a fraction?
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed
Answer:
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.
Step-by-step explanation:
All of the following expressions are equivalent to 12w + 6, except:
(3 + 6 w)2
6(1 + 2 w)
-1(-12 w - 6)
-1(12 w - 6)
Answer:
Except for -1 (12w - 6).
Steve made 50$ raking leaves 75$ mowing lawns. He gave 60% of his earnings to his mother. How much did Steve give to his mother?