Austin is 103 years old Raquel is 35 years old how many years ago was Austin age 5 times Raquel age

Answer:

Option 2

Step-by-step explanation:

The question states "the width of the rectangle is 4 less than half the length."  Since we are looking for the value of w, w will be equal to the expression we create.  We start with half the length and than subtract 4 from it.  This is because it says 4 less than half the length, not half of 4-length or another variation.  In many of these problems the best way to solve them is by working backwards.

Answer:

Option 2

Step-by-step explanation:

Translating these words into math, we get w = 1/2l - 4 which is Option 2.

Answer:

89 degrees

Step-by-step explanation:

The angle 1 is the same as angle 3.

Angle 2 is the same as angle 4.

The sum of these four angles is 360 degrees.

We have that:

Angle 2 = Angle 4 = 7x - 14

Angle 3 = Angle 1 = 5x + 14

Finding x:

Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360

2*(5x + 14) + 2*(7x - 14) = 360

10x + 28 + 14x - 28 = 360

24x = 360

x = 15

Angle 1:

5x + 14 = 5*15 + 14 = 89 degrees

Answer:

I think it is B

Step-by-step explanation:

Answer:

x=2           x =8

Step-by-step explanation:

(x-2)(x-8)=0

Using the zero product property

x-2 = 0    x-8 = 0

x=2           x =8

Answer:x = 2 and x = 8

Step-by-step explanation:

( 2 - 2)( 8 - 8)

(0)(0)

=0

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

Answer:

The trip will take 36 minutes.

Step-by-step explanation:

This question can be solved using a rule of three.

The boat maintains a constant speed of 15 knots (nautical miles per hour). How many minutes it will take to return to its home port 9 nautical miles away?

So in 60 minutes, 15 nautical miles. How many minutes for 9 nautical miles?

60 minutes - 15 nautical miles

x minutes - 9 nautical miles

[tex]15x = 60*9[/tex]

[tex]x = \frac{60*9}{15}[/tex]

[tex]x = 36[/tex]

The trip will take 36 minutes.

Answer:

expected profit = $-1.48

Step-by-step explanation:

The required expected value can be solved below.

The total number of ticket they will sell = 500 tickets.

So,

expected profit = expected return - expected cost

1 grand price of 2000 = 1/500 × 2000 = 4

4 second price of $400 = 4/500 × 400 = 3.2

16 third price of $10 = 16/500 × 10 = 0.32

expected return = 4 + 3.2 + 0.32 = $7.52

expected cost = $9

expected profit = expected return - expected cost

expected profit = 7.52 - 9

expected profit = $-1.48

Answer:

give $20 to each person

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B) (0,2)

Step-by-step explanation:

2 ≥ 2(0)-1

2 ≥ 0-1

2 ≥ -1

Answer:

around 68 minutes 31 seconds.

Step-by-step explanation:

10km = miles = 6.21x11 = 68.31

Answer:

She will make 125 dollars

Step-by-step explanation:

First figure out how many hours are in between 8 AM and 6PM

Second multiply that number by the salary she makes per hour. In this case its 12.50*10

Lastly Get the answer and add a dollar sign :D

Answer:

a. P(x≤9)=0.9999

b. P(x=6)=0.0430

c. P(x≥6)=0.0611

Step-by-step explanation:

The question is incomplete:

a.At most 9 will come to a complete stop?

b.Exactly 6 will come to a complete stop?

c.At least 6 will come to a complete stop?

d.How many of the next 20 drivers do you expect to come to a complete stop?

The amount of drivers from the sample that will come to a complete stop can be modeled by a binomial random variable with n=15 and p=0.2.

The probability that exactly k drivers from the sample come to a complete stop is:

[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]

a. We have to calculate the probability that at most 9 come to a complete stop:

[tex]P(x\leq9)=\sum_{k=0}^9P(x=k)\\\\\\P(x=0) = \dbinom{15}{0} p^{0}q^{15}=1*1*0.0352=0.0352\\\\\\P(x=1) = \dbinom{15}{1} p^{1}q^{14}=15*0.2*0.044=0.1319\\\\\\P(x=2) = \dbinom{15}{2} p^{2}q^{13}=105*0.04*0.055=0.2309\\\\\\P(x=3) = \dbinom{15}{3} p^{3}q^{12}=455*0.008*0.0687=0.2501\\\\\\P(x=4) = \dbinom{15}{4} p^{4}q^{11}=1365*0.0016*0.0859=0.1876\\\\\\P(x=5) = \dbinom{15}{5} p^{5}q^{10}=3003*0.0003*0.1074=0.1032\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]

[tex]P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x\leq9)=0.0352+0.1319+0.2309+0.2501+0.1876+0.1032+0.043+0.0138+0.0035+0.0007\\\\P(x\leq9)=0.9999[/tex]

b. We have to calculate the probability that exactly 6 will come to a complete stop:

[tex]P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]

c. We have to calculate the probability that at least 6 will come to a complete stop:

[tex]P(x\geq6)=\sum_{k=6}^{15}P(x=k)\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x=10) = \dbinom{15}{10} p^{10}q^{5}=3003*0*0.3277=0.0001\\\\\\P(x=11) = \dbinom{15}{11} p^{11}q^{4}=1365*0*0.4096=0\\\\\\P(x=12) = \dbinom{15}{12} p^{12}q^{3}=455*0*0.512=0\\\\\\[/tex]

[tex]P(x=13) = \dbinom{15}{13} p^{13}q^{2}=105*0*0.64=0\\\\\\P(x=14) = \dbinom{15}{14} p^{14}q^{1}=15*0*0.8=0\\\\\\P(x=15) = \dbinom{15}{15} p^{15}q^{0}=1*0*1=0\\\\\\P(x\geq6)=0.043+0.0138+0.0035+0.0007+0.0001+0+0+0+0\\\\P(x\geq6)=0.0611[/tex]

Answer:

4

Step-by-step explanation:

A=P0(1+rt).

We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:

A=P0(1+rt)⟹t=A−P0P0r,

and substituting the known quantities gives

r=$3,500−$2,800$2,800×0.075=3.33,

which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.

Answer:

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622

The margin of error is:

M = T*s = 2.2622*0.3 = 0.68

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF

The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

Answer:

Plot the y-intercept at (0, 2). Plot your second point at (-1, -1).

Step-by-step explanation:

I attached an image of what the finished graph should look like when you press done. *rotate the image so the grey is on the bottom*

Answer:

The event of picking a number from 1 to 3 consists of:

Pick number 1

Pick number 2

Pick number 3

The event of choosing red or white card consists of:

Choose a red card

Choose a white card

=> The sample space for picking a number from 1 to 3 and choosing red or white card:

Pick number 1 and choose a red card

Pick number 1 and choose a white card

Pick number 2 and choose a red card

Pick number 2 and choose a white card

Pick number 3 and choose a red card

Pick number 3 and choose a white card

Hope this helps!

:)

Answer:

207.24cm

Step-by-step explanation:

Circumference=2pi*r

=2 (3.14)(33)

=207.24cm

The circumference of the circle is 103.62 cm².

Given that, a circle with diameter of 33 cm.

Radius=d/2=16.5 cm.

The formula to find the circumference of the circle is 2πr.

Now, 2×3.14×16.5=103.62 cm².

Therefore, the circumference of the circle is 103.62 cm².

To learn more about the circumference of the circle visit:

https://brainly.com/question/27177006.

#SPJ2

Answer:

€ 270

Step-by-step explanation:

Since the production cost C(x,y) = 2x² + 5y² + 120 is less than or equal to 250, we have  2x² + 5y² + 120 ≤ 250

The selling price S(x,y) = 40x + 80y

The profit P(x,y) = S(x,y) - C(x,y) = 40x + 80y - 2x² - 5y² - 120

Using the principle of lagrange multipliers, we want to maximize the profit P(x,y) under the condition that C(x.y) ≤ 250.

So, dP/dx = 40 - 4x , dC/dx = 4x, dP/dy = 80 - 10y , dC/dy = 10y

dP/dx + λdC/dx = 0

40 - 4x + 4λx = 0  (1)

4λx = 4x - 40

λ = (x - 10)/x

dP/dy + λdC/dy = 0

80 - 10y + 10λy = 0 (2)

substituting λ into (2), we have

80 - 10y + 10(x - 10)y/x = 0

multiplying through by x, we have

80x - 10xy + 10xy - 100y = 0

80x - 100y = 0

80x = 100y

x = 100y/80

x = 5y/4

substituting x into C(x,y) ≤ 250, we have

2(5y/4)² + 5y² + 120 ≤ 250

25y²/8 + 5y² + 120 ≤ 250

25y² + 40y² + 960 ≤ 2000

65y² ≤ 2000 - 960

65y² ≤ 1040

y² ≤ 1040/65

y² ≤ 16

y ≤ ±√16

y ≤ ± 4 since its quantity, we take the positive value.

So x = 5y/4 = 5(± 4)/4 = ± 5

So, x ≤ ± 5

For the maximum value for the profit, P(x,y), we take the maximum values of x and y which are x = 5 and y = 4. Substituting these values into P(x,y), we have

P(5,4) = 40(5) + 80(4) - 2(5)² - 5(4)² - 120

= 200 + 320 - 50 - 80 - 120

= 520 - 250

= 270

So, the maximum profit obtained is € 270

Answer:

a = 13

b = 0

Step-by-step explanation:

Conjugate of -3 + 2i is -3 - 2i

(-3 + 2i) (-3 - 2i)

We need to expand:

9 + 6i + -6i + -4i^2

-4i^2 =(-4)(-1) = 4

9 + 4 = 13

a = 13

b = 0

Answer:

Hey mate , here is your answer. Hope it helps you

Step-by-step explanation:

Given Zareen has 24min to work on her math homework, and each problem is taking her 2/3 of a minute

As give one problem takes

24*(2/3) minutes = 16

Hence

2/3 divided by 24

Answer:

A. Only the mode makes sense since the data is nominal.

Step-by-step explanation:

Hello!

The objective of the study was to determine if deficiency of carbon dioxide in the soil affects the phenotype of peas.

The variable of study is X: Phenotype of a pea grown in soil with carbon dioxide deficiency.

Possible values of Phenotype codes:

1= smooth-yellow

2= smooth-green

3= wrinkled-yellow

4= wrinkled-green

The absolute frequencies for each phenotype are:

f(1)= 3

f(2)= 4

f(3)= 6

f(4)= 1

n= 14

a) Mean:

X[bar]= (∑xifi)/n= [(1*3)+(2*4)+(3*6)+(4*1)]/14= 33/14= 2.357= 2.36

The average value is always within range of definition of the variable but it does not necessarily correspond to an observation.

b) Median:

To determine the value that corresponds to the median you have to calculate its position:

For even samples the position is:

PosMe= n/2= 14/2= 7

Then you have to arrange the data from least to greatest, in this case, starting from the first category, you have to determine where the seventh observation is within the observed absolute frequencies. The phenotype that corresponds to the 7th observation is 2= smooth-green.

Me= 2= smooth-green.

c) Mode:

The mode corresponds to the most observed category/ value of the variable, i.e. the category with the most observations is 3= wrinkled-yellow

Md= 3= wrinkled-yellow

d) Midrange: (1 + 4)/2= 2.5

e)

As you can see the variable is qualitative and categorical. Even if all central tendency measurements can be calculated, truth is that the only one that shows any valuable information regarding the data set is the mode.

I hope this helps!

Answer:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Class width = 12.375

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

Step-by-step explanation:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Parameter is a measure that describes the entire population.

Statistic basically describes a sample of the population.

From the given information , the entire 1700 professors at a college is the population and only  35 % own a television is a characteristic, called parameter, of population.

Another objective we are to find here is:

Use the given minimum and maximum data entries, and the number of classes, to find the class width, .

Class width = Maximum - Minimum /No of classes

Given that :

Maximum = 120

Minimum = 21

number of classes = 8

Then;

Class width = 120 - 21 /8

Class width = 12.375

From the given information :

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

[tex]answer \\ 9 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

9

Step-by-step explanation:

The ratio of 5 to 5+3 is equivalent to the ratio of 15 to 15+x. This is because when you have a triangle inside of a triangle and both of them share two of the same sides and the third sides are parallel to each other, the side ratios of the triangles are always proportionate.

[tex]\frac{5}{5+3} =\frac{15}{15+x}[/tex]   Starting equation

[tex]\frac{5}{8} =\frac{15}{15+x}[/tex]   Simplify

[tex]5(15+x)=8*(15)[/tex]   Cross multiply

[tex]75+5x=120[/tex]   Distributive Property on left and simplify on right

[tex]5x=45[/tex]   Isolate the variable

[tex]x=9[/tex]   Divide both sides by 5 (Division Property of Equality)

Answer:

1,085

Step-by-step explanation:

The calculation of  number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-

[tex]= N\times (2 \times documentaries\ and\ 1\ horror \ movies)+N\times (3\ documentaries)[/tex]

[tex]=(6C_1)\times (15C_2)+(6C_0)\times (15C_3)[/tex]

= 630 + 455

= 1,085

Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.

Answer:

“It is a binomial with a degree of 3”

Step-by-step explanation:

Since it has just two different coefficients, it would be considered “binomial” for that reason. As you can notice, the highest degree is 3. So match those up and the correct answer would be the second choice “It is a binomial with a degree of 3”

Answer:

B

Step-by-step explanation:

Answer:

[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]

And we can find the probability with this difference and using the normal standard table:

[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]

Step-by-step explanation:

Let X the random variable that represent the wages, and for this case we know the distribution for X is given by:

[tex]X \sim N(17.15,2.25)[/tex]  

Where [tex]\mu=17.15[/tex] and [tex]\sigma=2.25[/tex]

We want to find this probability:

[tex]P(15<X<20)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we have:

[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]

And we can find the probability with this difference and using the normal standard table:

[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]

The answer to your problem is: X=17

Answer:

17

Step-by-step explanation:

x + 10 + 9x=14x-58

x + 9x + 10 =14x-58

10x + 10 =14x-58

By grouping like terms by moving 14x to the left and 10 to the right of the equation; we have:

10x - 14x =-58-10

-4x=-68

x=-68/-4=17{ dividing both sides by -4}

Answer:

AC = 198

Step-by-step explanation:

Since all these points are collinear, we know that the addition of AB plus BC should give the same as AC. We can then set an equation that addresses this identity:

AB + BC = AC

5x +8 +6x - 1 = 12x - 11

Now re-arranging like terms in order to combine them:

8 - 1 + 11 = 12x - 5x - 6x

19 - 1  = 12x - 11x

18 = x

Now that we know the value of 'x", we can determine the value of AC:

AC = 12x - 11

AC = 12 (18) - 11

AC = 216 - 18

AC = 198

Answer:

2044

Step-by-step explanation:

just follow the story

a person uses a

hanger (2)

to pop a

ball  (0)

then flies

two kites (44)

Answer:

1). 2044

Step-by-step explanation:

The story includes: a hanger, a ball, and two kites (in that order)

From the information given, a hanger is 2, a ball is 0, and a kite is 4.

So it would be 2044.

Answer:

The  90% confidence interval for the difference between proportions is (0.115, 0.228).

As the value 0 is not included in the interval, we can conclude that there is significant difference in the proportion of youger adults that use the horn and older adults that use the horn.

Step-by-step explanation:

We want to calculate the bounds of a 90% confidence interval.

For a 90% CI, the critical value for z is z=1.645.

The sample 1 (younger adults) , of size n1=501 has a proportion of p1=0.521.

[tex]p_1=X_1/n_1=261/501=0.5210[/tex]

The sample 2 (older  adults), of size n2=352 has a proportion of p2=0.3494.

[tex]p_2=X_2/n_2=123/352=0.3494[/tex]

The difference between proportions is (p1-p2)=0.1715.

[tex]p_d=p_1-p_2=0.5210-0.3494=0.1715[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{261+123}{501+352}=\dfrac{384}{853}=0.4502[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4502*0.5498}{501}+\dfrac{0.4502*0.5498}{352}}\\\\\\s_{p1-p2}=\sqrt{0.0005+0.0007}=\sqrt{0.0012}=0.0346[/tex]

Then, the margin of error is:

[tex]MOE=z \cdot s_{p1-p2}=1.645\cdot 0.0346=0.0569[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.1715-0.0569=0.115\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.1715+0.0569=0.228[/tex]

The  90% confidence interval for the difference between proportions is (0.115, 0.228).