A certain family has a husband, wife, son, and daughter. All together they are 68 years old. The husband is 3 years older than the wife, and the son is 3 years older than the daughter. Four years ago, all together the family was 54 years old. How old is the husband now?

Answer:

1) the domain is all real numbers

2) the range is

[tex]y \geqslant 3[/tex]

Answer:

18 minutes

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is the time,

and T is the half life.

A = 140 when t = 10.  Solve for the half life:

140 = 700 (½)^(10 / T)

0.2 = ½^(10 / T)

log 0.2 = (10 / T) log 0.5

10 / T = 2.32

T = 4.31

When A = 40, t is:

40 = 700 (½)^(t / 4.31)

0.057 = ½^(t / 4.31)

log 0.057 = (t / 4.31) log 0.5

t / 4.31 = 4.13

t = 17.8

Rounded to the nearest whole number, it takes 18 minutes.

The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes.

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

The half-life decay formula is given as,

N(t) = N₀ [tex](1/2)^{(t / T)}[/tex]

Where T is half-life while t is the time taken.

N₀ is the initial amount,

As per the given,

N(t) = 140 when t = 10.

140 = 700 [tex](1/2)^{(t / T)}[/tex]

Take log both sides,

log 0.2 = (10 / T) log 0.5

10 / T = 2.32

T = 4.31 minutes

Put N(t) = 40

40 = 700[tex](1/2)^{(t / 4.31)}[/tex]

Take log both sides,

log 0.057 = (t / 4.31) log 0.5

t / 4.31 = 4.13

t = 17.8 ≈ 18 minutes

Hence "The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes".

For more about exponential function,

https://brainly.com/question/15352175

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Answer:

2.7 in²

Step-by-step explanation:

Area of ∆BAC : ∆Area of EDF = BC² : EF² (based on the area of similar triangles theorem)

Thus:

[tex] 6 in^2 : x in^2 = (3 in)^2 : (2 in)^2 [/tex]

[tex]\frac{6}{x} = \frac{3^2}{2^2}[/tex]

[tex]\frac{6}{x} = 2.25[/tex]

[tex]\frac{6}{x}*x = 2.25*x[/tex]

[tex]6 = 2.25x[/tex]

[tex]\frac{6}{2.25} = \frac{2.25x}{2.25}[/tex]

[tex]2.67 = x[/tex]

Area of ∆EDF = 2.7 in²

Answer:

No, F* < Fc

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I  error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis .

Answer:

Z= 0.253

Z∝/2 = ± 1.96

Step-by-step explanation:

Formulate the null and alternative hypotheses as

H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

Here ∝= 0.005

For alpha by 2 for a two tailed test Z∝/2 = ± 1.96

Standard deviation = s= 15

n= 10

The test statistic used here is

Z = x- x`/ s/√n

Z= 2058- 2046 / 15 / √10

Z= 0.253

Since the calculated value of Z= 0.253 falls in the critical region we reject the null hypothesis.

There is  evidence at the 0.05 level that the doors are too short and unusable.

Answer:

hi

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

3/4=6/8

6/8-1/8=5/8

So 5/8 of the tank is 15 gallons.  This means each 1/8 of a tank is 3 gallons.

The van is currently 6/8 full. We need to add another 2/8 to completely fill the tank.  

2x3=6

You’ll need 6 more gallons to fill the tank.

Answer:

Step-by-step explanation:

Let the number to be found be x

The product of a number and 3 is written as

15 minus twice the number is written as

Now equate the two statements

That's

3x = 15 - 2x

Group like terms

3x + 2x = 15

5x = 15

Divide both sides by 5

the final answer is

Hope this helps you

Answer:

The  probability is  [tex]P(X \le 0.305 ) = 0.01795[/tex]

Step-by-step explanation:

From the question we are told that

      The population mean is  [tex]\mu = 0.966 \ grams[/tex]

       The standard deviation is  [tex]\sigma = 0.315 \ grams[/tex]

Given that the amounts of nicotine in a certain brand of cigarette are normally distributed

    Then the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less is mathematically represented as

        [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(\frac{X - \mu }{\sigma } > \frac{0.305 - \mu }{\sigma } )[/tex]

Generally

              [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of X )[/tex]

So  

      [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z > \frac{0.305 - 0.966 }{0.315} )[/tex]

      [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z >-2.0984 )[/tex]

From the z-table(reference calculator dot  net  ) value of   [tex]P(Z >-2.0984 ) =0.98205[/tex]

So  

     [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - 0.98205[/tex]

=>  [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 0.01795[/tex]

=> [tex]P(X \le 0.305 ) = 0.01795[/tex]

Answer:  4  inches

Step-by-step explanation:

1. We gonna find the the length of the right triangle legs using Phitagor theorem.

c²=a²+b²  (1)   , where c is triangle's  hypotenuse

a and b are the triangle's  legs.

Let the leg a =x,    so leg b=x+1 inches

Now we can write the equation using (1)

25=x²+(x+1)²

25=x²+x²+2*x+1

2*x²+2*x-24=0     ( divide by 2 both sides of the equation)

x²+x-12=0

Find the discriminant D=1+12*4=49

√D=7

x1= (-1+7)/2=3     x2=(-1-7)/2=-4 - x2=-4 not possible so length of the leg can not be negative.

So the shorter leg a=x= 3 inches

The longer leg b=x+1=4 inches

Answer: -3

Step-by-step explanation: 2x = -2 then you subtract 1 from that which is the same as adding negative one so -2 - 1 or -2 + -1 = -3

Answer:

[tex]D = 42.5\ inch[/tex]

Step-by-step explanation:

Given

[tex]L = Length[/tex] and [tex]W = Width[/tex]

[tex]L:W = 8: 5[/tex]

[tex]Perimeter = 117[/tex]

Required

Determine the Diagonal

First, the dimension of the screen has to be calculated;

Recall that; [tex]L:W = 8: 5[/tex]

Convert to division

[tex]\frac{L}{W} = \frac{8}{5}[/tex]

Multiply both sides by W

[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]

[tex]L = \frac{8W}{5}[/tex]

The perimeter of a rectangle:

[tex]Perimeter = 2(L+W)[/tex]

Substitute [tex]L = \frac{8W}{5}[/tex]

[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]

Take LCM

[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]

[tex]Perimeter = 2(\frac{13W}{5})[/tex]

Substitute 117 for Perimeter

[tex]117 = 2(\frac{13W}{5})[/tex]

[tex]117 = \frac{26W}{5}[/tex]

Multiply both sides by [tex]\frac{5}{26}[/tex]

[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]

[tex]\frac{5 * 117}{26} = W[/tex]

[tex]\frac{585}{26} = W[/tex]

[tex]22.5 = W[/tex]

[tex]W = 22.5[/tex]

Recall that

[tex]L = \frac{8W}{5}[/tex]

[tex]L = \frac{8 * 22.5}{5}[/tex]

[tex]L = \frac{180}{5}[/tex]

[tex]L = 36[/tex]

The diagonal of a rectangle is calculated using Pythagoras theorem as thus;

[tex]D = \sqrt{L^2 + W^2}[/tex]

Substitute values for L and W

[tex]D = \sqrt{36^2 + 22.5^2}[/tex]

[tex]D = \sqrt{1296 + 506.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = 42.4529150943[/tex]

[tex]D = 42.5\ inch[/tex] (Approximated)

Answer:

2y= 6-3x when x=0

2y= 6-3(0)

2y= 6-0

2y= 6

y= 6/2

y= 3

#i'm indonesian

#hope it helps.

Answer:

[tex] \boxed{y = 3}[/tex]

Step-by-step explanation:

Given, x = 0

[tex] \mathsf{2y = 6 - 3x}[/tex]

plug the value of x

⇒[tex] \mathsf{2y = 6 - 3 \times 0}[/tex]

Multiply the numbers

⇒[tex] \mathsf{2y = 6 - 0}[/tex]

Calculate the difference

⇒[tex] \mathsf{2y = 6}[/tex]

Divide both sides of the equation by 2

⇒[tex] \mathsf{ \frac{2y}{2} = \frac{6}{2} }[/tex]

Calculate

⇒[tex] \mathsf{y = 3}[/tex]

Hope I helped!

Best regards!

Hey there! I'm happy to help!

To find the volume of a cube, you simply take whatever the side length is and multiply it by itself 3 times, which is also known as cubing the number!

16×16×16=4096

You can also write it as 16³=4096

This is because the length is 16, the width is 16, and the height is 16, so you multiply them all together!

I hope that this helps! Have a wonderful day!

Answer:

25 : 63 and 63 : 25

Step-by-step explanation:

This is a complete question

The table shows the educational attainment of the population of Country X, ages 25 and over. Use the data in the table, expressed in millions, to solve the problem. of 10 questions ge 1: Ages 25 and Over, in Miltions 4 Years igh College 4 Years High School (Less than College School Only 4years) Cor Moce) Total Male 29 19 25 89 Female 11 28 23 Total 2 57 42 50 [176 Find the odds in favor and the odds against a randomty selected person from Country X.age 25 and over, with the stated amount of education. four years (or more) of college 21:67, 67:21 63:88, 88:63 25:63, 63:25 25:88, 88:25

According to the question, the relevant data provided in the question for the solution is as follows

Four years or more of college

Number of students = 50

Total = 176 students

Number of students does not belong = 126

So odds in favor is

= 50 : 126

= 25 : 63

And automatically out against the favor is 63 : 25

Answer:

I have not answer

plz follow me....

Answer:

The probability that the sample mean is more than 110 is 0.0384.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sampling distribution of sample mean is given by:

[tex]\mu_{\bar x}=\mu[/tex]

And the variance of the sampling distribution of sample mean is given by:

[tex]\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}[/tex]

The information provided is:

[tex]n=50\\\\\mu=100\\\\\sigma^{2}=1600[/tex]

Since n = 50 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the normal distribution.

The mean variance of the sampling distribution for the sample mean are:

[tex]\mu_{\bar x}=\mu=100\\\\\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}=\frac{1600}{50}=32[/tex]

That is, [tex]\bar X\sim N(100, 32)[/tex].

Compute the probability that the sample mean is more than 110 as follows:

[tex]P(\bar X>110)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{110-100}{\sqrt{32}})[/tex]

                   [tex]=P(Z>1.77)\\=1-P(Z<1.77)\\=1-0.96164\\=0.03836\\\approx 0.0384[/tex]

*Use a z-table.

Thus, the probability that the sample mean is more than 110 is 0.0384.

Answer:

36.9°

Step-by-step explanation:

Sin x = 9/15 = 3/5

x = sin^-1 3/5

x= 36.87

x= 36.9° to nearest tenth

Answer: 0.20

Step-by-step explanation:

The given probability distribution of number of televisions per household in a small town:

x          0       1     2      3

​P(x) ​ 0.05 0.15 0.25 0.55

To find : The probability of randomly selecting a household that has one or two televisions ( in both parts a. and b.).

The computations for this would be :

P( 1 or 2) = P(1)+P(2)

= 0.05+0.15

= 0.20

Hence, the required probability= 0.20

Answer:

Step-by-step explanation:

Answer:

Mean= $21.5067

Median = $15.8

Standard deviation= $19.02

Coefficient of skewness= $0.8991

Step-by-step explanation:

Mean =( $4.0 +$6.0 +$7.4+ $10.6 +$12.5+ $13.6+ $15.4+ $15.8 +$16.8

+$17.4+ $19.1 +$22.3+ $37.1 +$43.2 +$81.4)/15

Mean =$ 322.6/15

Mean= $21.5067

Median= middle number

Median = $15.8

Variance=( ($4.0-.$21.5)²+( $6.0. -.$21.5)²+( $7.4 -.$21.5)²+( $10.6 -.$21.5)²+( $12.5 -.$21.5)²+( $13.6. -.$21.5)²+ ($15.4 -.$21.5)²+( $15.8 -.$21.5)²+ ( $16.8 -.$21.5)²+ ($17.4-.$21.5)² +($19.1 -.$21.5)²+ ($22.3 -.$21.5)²+ ($37.1 -.$21.5)²+ ($43.2-.$21.5)²+( $81.4-.$21.5)²)/15

Variance=$ 5424.79/15

Variance=$ 361.65

Standard deviation= √ variance

Standard deviation= √361.65

Standard deviation= $19.02

Coefficient of skewness

=3( mean-median)/standard deviation

= 3(21.5-15.8)/19.02

= 3(5.7)/19.02

= 17.1/19.02

Coefficient of skewness= 0.8991

Answer:

The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.

Step-by-step explanation:

Consider the system of equations:

x + y = 7 ................................(1)

2x - y = 8 ..............................(2)

To eliminate x:

First multiply (1) by 2 to have

2x + 2y = 14 ...........................(3)

Next, subtract (2) from (3) to have

3y = 6

y = 6/3 = 2

To eliminate y:

Add (1) and (2) to have

3x = 15

x = 15/3 = 5

Therefore, (x, y) = (5, 2).

Answer:

6 years

Step-by-step explanation:

A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:

[tex]y=ab^x[/tex]

Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8

[tex]y=ab^x\\8=ab^0\\a=8[/tex]

Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2

Therefore:

[tex]y=ab^x\\y=8(1.2^x) \\[/tex]

To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x

[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]

x = 6 years to the nearest year

Answer:

5 years

Step-by-step explanation:444

Answer:

x = 20°

Step-by-step explanation:

So when I learned it we called it the exterior angle theorem not the angle sum theorem but here goes.

Since exterior angle = 110 Degrees,

--> The Inner 2 angles's sum = 110 Degrees

so, 70 + 2x = 110

=> 2x = 40

x = 20

x = 20°

Hope this helps!

Aqui temos a seguinte divisao de terreno:

creche + banheiros + academia = 45% + 3% + 12% = 60%

O que sobra: Fazendo a conta, 100 - 60 = 40, restará 40%

No enunciado informa que sobraram 960m².

Logo concluimos que 40% = 960m²

Sendo assim, regra de 3:

   m²                %

  960   --------   40

    X     --------   60

40X = 960 . 60

X = 57600/40

X = 1440

Logo 1440m² é destinado para: creche, banheiros públicos e academia

de ginástica comunitária.

O terreno tem um total de 1440 + 960 = 2400m²

para cada espaço - novamente diversas regra de 3:

→ creche = 45%

    m²                  %

  2400   --------   100

    X        --------    45

X = 108000/100 = 1080

→ banheiros públicos  = 3%

    m²                  %

  2400   --------   100

    X        --------    3

X = 7200/100 = 72

→ academia de ginástica comunitária = 12%

    m²                  %

  2400   --------   100

    X        --------    12

X = 28800/100 = 288

provando:

60% = 1440m²  (visto acima)

creche - 1080

banheiros - 72

academia - 288

1080 + 72 + 288 = 1440 (60%)

Answer:

C(4,6)

Step-by-step explanation:

the x turns into its opposite when reflected across y same thing for y when reflected across x

Answer:

c. (4, 6)

Step-by-step explanation:

The rule of an reflection about the y-axis is: [tex]A(x,y)\rightarrow A'(-x,y)[/tex]

Apply the rule to  point (-4, 6):

[tex]\frac{(-4,6)\rightarrow\boxed{(4,6)}}{(x,y)\rightarrow(-x,y)}[/tex]

Option C should be the correct answer.

Answer:

The answer is below

Step-by-step explanation:

The box contains 5 red and 4 white balls.

A) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was (Upper A )Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81

P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81

The probability that at least 1 ball was​ red = 25/81 + 20/81 + 20/81 = 65/81

B) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was not Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)

P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72

The probability that at least 1 ball was​ red = 20/72 + 20/72 + 20/72 = 60/72

Answer:

[tex]a \leqslant 10[/tex]

Step-by-step explanation:

a is less than or equal to 10

less than: <

equal: =

less than or equal to: ≤

Hope this helps ;) ❤❤❤

hope it helps you

imp=draw dark shaded point in thqt line and point towards left

Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:

x=1

Step-by-step explanation:

3(x + 1)= -2(x - 1) + 6.

Distribute

3x+3 = -2x+2+6

Combine like terms

3x+3 = -2x+8

Add 2x to each side

3x+3+2x = 8

5x+3 = 8

Subtract 3 from each side

5x =5

Divide by 5

x =1