Todd is 3 years older than his brother Jack. If Jack is x years old and Todd is y years
old, write a rule that relates their ages over time. When Jack is 28 years old, how old will Todd be?

Answer:

0-9(n-1)

Step-by-step explanation:

We can tell the first term of the sequence is 0 and the common difference is -9. So the explicit formula would be h(n)=0-9(n-1)

The explicit formula for h(n) comes to be h(n)=9-9n.

An arithmetic progression is a list of numbers where the difference between consecutive terms is always constant.

[tex]h(n)=h(n-1)-9[/tex]

[tex]h(n)-h(n-1)=-9[/tex]

So the common difference of the arithmetic progression will be -9.

[tex]h(1)=0[/tex] means the first term of the AP is 0.

We know that [tex]n^{th}[/tex] term of an AP is given by:

[tex]h(n)=a+(n-1)d[/tex]

Where a is the first term and d is a common difference.

Fo the given series [tex]a=0[/tex] and [tex]d=-9[/tex]

So, [tex]h(n)=0+(n-1)(-9)[/tex]

[tex]h(n)=9-9n[/tex]

So, the explicit formula for h(n) is [tex]h(n)=9-9n[/tex]

Hence, the explicit formula for h(n) comes to be [tex]h(n)=9-9n[/tex].

To get more about arithmetic progressions visit:

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Answer:

Step-by-step explanation:

h(x) = 2x + 3

f(2x+3)

2x+3 - 7

2x - 4

Answer:

Domain :  0 ≤ t ≤ 3

Range :   -4 ≤ d ≤ 0

Step-by-step explanation:

The graph attached models the depth of submarine as a function of time.

Points on x-axis represent the time and points on y-axis represent increase in height of the submarine.

Domain of a function is represented by the points on x-axis.

Therefore, Domain :  0 ≤ t ≤ 3

Range of function is represented by te points on y-axis.

Therefore, Range :   -4 ≤ d ≤ 0

Answer:

The total length of the tunnel when the crew has finished digging is 1078 meters

Step-by-step explanation:

total length of the tunnel dug by the crew =  573 meters

let the halfway point of the tunnel = h

if the crew digs 34 meters past the halfway point, then we will this equation below;

h + 34 meters = 573 meters

h = 573 - 34

h = 539 meters

halfway point of the tunnel is 539 meters

Then, the total length of the tunnel when the crew has finished digging = 2h

= 2 x 539 meters

= 1078 meters

Therefore, the total length of the tunnel when the crew has finished digging is 1078 meters

Answer:

c) Population parameter or Population statistic

Step-by-step explanation:

Population:-

The totality of observation with which we are concerned , whether this number be finite or infinite is called population

Sample :

A sample is subset of a Population

Given data  the USA today internet poll is called Population

Given data 73 percent of readers are satisfied with their lives.

This is called Population parameter.

Answer:

6 sqrt(5)

Step-by-step explanation:

(3√2) ( √10)

We know that sqrt(a) * sqrt(b) = sqrt(ab)

3 sqrt(2*10)

3 sqrt(20)

3 sqrt(4*5)

We know that sqrt(a) * sqrt(b) = sqrt(ab)

3 sqrt(4) sqrt(5)

3 * 2 * sqrt(5)

6 sqrt(5)

Answer:

a) 120

b) 10

c) 1/12

Step-by-step explanation:

The number of ways that a sample of r can be selected from a population of n is:

nCr = n! / (r! (n−r)!)

a) 3 people selected from a group of 10

₁₀C₃ = 120

b) 3 women selected from a group of 5

₅C₃ = 10

c) Of the 120 committees that can be chose, 10 are all women.  So the probability is 10/120 = 1/12.

Answer:

[tex]P(X \leq 3) = 0.1738[/tex]

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In this question, we have that:

[tex]n = 8, p = 0.6[/tex]

P(3 or fewer)

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.6)^{0}.(0.4)^{8} = 0.0007[/tex]

[tex]P(X = 1) = C_{8,1}.(0.6)^{1}.(0.4)^{7} = 0.0079[/tex]

[tex]P(X = 2) = C_{8,2}.(0.6)^{2}.(0.4)^{6} = 0.0413[/tex]

[tex]P(X = 3) = C_{8,0}.(0.6)^{3}.(0.4)^{5} = 0.1239[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0007 + 0.0079 + 0.0413 + 0.1239 = 0.1738[/tex]

Answer:

  y = 3

Step-by-step explanation:

It can work well to start by eliminating parentheses.

  6(y -1/3) = 4(3y -5)

  6y -2 = 12y -20

  18 = 6y . . . . . . . . . add 20-6y to both sides

  3 = y . . . . . . . . . . . divide by 6

Answer:

y=3

Step-by-step explanation:

6(y−13)=4(3y−5)

(6)(y)+(6)(−13)=(4)(3y)+(4)(−5)(Distribute)

6y+−2=12y+−20

6y−2=12y−20

Step 2: Subtract 12y from both sides.

6y−2−12y=12y−20−12y

−6y−2=−20

Step 3: Add 2 to both sides.

−6y−2+2=−20+2

−6y=−18

Step 4: Divide both sides by -6.

−6y−6=−18−6

y=3

Answer:

it should be 40.5 i believe

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) The distance that Lauren drove to the coast is the same as the distance he drove back from the coast. It means that the total miles that Lauren drove in this round-trip is

75 + 75 = 150 miles

2) time = distance/speed

Time spent in driving to the coast is

75/75 = 1 hour

His return speed is 25 mph

Time spent in driving back from the coast is

75/25 = 3 hours

3) Average speed = total distance/total time

Total distance = 75 + 75 = 150 miles

Total time = 1 + 3 = 4 hours

Average speed = 150/4 = 37.5 mph

Answer:

A: f(x) = (3/4 x)^2 - 1

Step-by-step explanation:

As you can see in the first image i attached, option A is the function that matches the one in your image. the "- 1" in the function is the y-intercept, and the 3/4 is what stretches your parabola which made it larger. You could also use process of elimination to get rid of option B and D since the y-intercepts do not match. Then you are left with A and C. the 4 in "(4x)^2" would make the parabola shrink, as you can see in the second image.

Answer:

ⁱ ʰᵒᵖᵉ ᵗʰⁱˢ ʷᵒᵘˡᵈ ʰᵉˡᵖ ʸᵒᵘ ᵗᵒ ᵍᵉᵗ ʳᵉᵃˡ ᵃⁿˢʷᵉʳ...

Answer:

For 2 loaves of bread, 4 cups of flour, 24 tablespoons of water, and 2 teaspoons of salt are required

For 4 loaves of bread,  8 cups of flour, 48 tablespoons of water, and 4 teaspoons of salt are required

Step-by-step explanation:

Given: A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt

To find: the missing terms in the box

Solution:

As for 1 loaf of bread, 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt are required

So, for 2 loaves of bread, double the quantity.

So, for 2 loaves of bread, 2×2=4 cups of flour, 12×2=24 tablespoons of water, and 1×2=2 teaspoons of salt are required

For 4 loaves of bread, double the quantity used to make 2 loaves of bread.

For 4 loaves of bread,  4×2=8 cups of flour, 24×2=48 tablespoons of water, and 2×2=4 teaspoons of salt are required

See the image attached.

Answer:

10.99 inches

Step-by-step explanation:

7*2=14

diameter=14

circumference=diameter*pi

14*3.14=43.96

quarter circle

43.96/4=10.99

10.99 inches

Answer:

the quarter circle's perimeter = 24.99 inch

Step-by-step explanation:

1. Calculate circumference of a complete circle.

2. Divide by 4 and you have the quarter part. (This is the same as multiplying by 0.25).

3. Just like a pie chart, there are 2 sides from the center to the left and right side edge of the quarter circle. Both are equal to the radius r.

4. Add the numbers found in step 2 and step 3 and you will have found the quarter circle's perimeter.

Given: use 3.14 for pi and r = 7 inch

1. Circumference = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * 7 ) = 10.99 inch

3 Since r = 7 and we have to sides.

So you just add 2 * 7 = 14 inch

4. Add 10.99 + 14 = 24.99 inch

Answer:

a) Check the bar graph in the picture attached

b) The two categorical variables are:

1) Type of owners

2) Likelihood to give CPR

c) Information on the population( in number or percentage) of the dog/cat owners.

Step-by-step explanation:

a) the bar chart is drawn with % of owners likely to give CPR to their pets on the y-axis and the owner types on the x - axis.

b) The two categorical variables are:

1) Type of owners

2) Likelihood to give CPR

c) To construct a 2 x 2 table, the percentage (or number) of either dog owners or cat owners.

Since we know that the total number of pet owners that were sampled = 1166.

If the number of dog owners is known, it can be subtracted from the total number of pet owners to know the number of cat owners and vice versa. If this information is gotten, then the 2 x 2 table can be constructed.

Hi!

So for this you need an equation. It will be 72 • 0.8 - 2.88 • 3

this is bc 12 x 6 is 72 and 3 bc 2 x 3 is 6.

so after you solve it you should get : $48.96..Hope this helped! :))

Answer:

48+25=x

Step-by-step explanation:

Answer:

The answer is D :)

Thank me later.

Answer:

$ 402,722.01

Step-by-step explanation:

Answer:

10.5 minutes

Step-by-step explanation:

Thinking about the problem

The modeling function is of the form P(t)=A⋅Bf(t), where B=4B=4B, equals, 4 and f(t)=\dfrac{t}{10.5}f(t)=

10.5

t

​

f, left parenthesis, t, right parenthesis, equals, start fraction, t, divided by, 10, point, 5, end fraction.

Note that each time f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111, the quantity is multiplied by B=4B=4B, equals, 4.

Therefore, we need to find the ttt-interval over which f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111.

Hint #22 / 3

Finding the appropriate unit interval

fff is a linear function whose slope is \dfrac{1}{10.5}

10.5

1

​

start fraction, 1, divided by, 10, point, 5, end fraction.

This means that whenever ttt increases by \Delta tΔtdelta, t, f(t)f(t)f, left parenthesis, t, right parenthesis increases by \dfrac{\Delta t}{10.5}

10.5

Δt

​

start fraction, delta, t, divided by, 10, point, 5, end fraction.

Therefore, for f(t)f(t)f, left parenthesis, t, right parenthesis to increase by 111, we need \Delta t=10.5Δt=10.5delta, t, equals, 10, point, 5. In other words, the ttt-interval we are looking for is 10.510.510, point, 5 minutes.

Hint #33 / 3

Summary

The number of people who yawned quadruples every 10.510.510, point, 5 minutes.

Answer:

Step-by-step explanation:

(a)

   [tex]= kr^2(r_0 - r )[/tex]

 [tex]= ( kr_0)r^2 - kr^3 \\\\=>v '(r) = ( 2kr_0 )r -3kr^2\\\\= ( -3k)r^2 + ( 2kr_0 )r[/tex]

v has an absolute maximum when v '(r) = 0

v '(r) = 0 =>

( -3k )r2 + ( 2kr0 )r = 0 =>

r = [ -( 2kr0 ) ± sqrt[ ( 2kr0)2 - ( 4 )( -3k )( 0 ) ] ] / [ ( 2 )( -3k ) ]

= [ -2kr0 ± 2kr0 ] / ( -6k)

= 0 or ( -4kr0 / -6k )

= 0 or (2/3)r0

since [tex]r > (1/2)r_0[/tex] in the given interval,[tex]r =(2/3)r_0[/tex], which matches its experimental value.

Answer:

Option C.

Step-by-step explanation:

Solid in the given picture is a rectangular prism and a rectangular prism has 6 faces. Each face is formed by joining 4 vertices of the prism.

All the faces joining four vertices are: AFGB, BGHC, ADEF, DCHE, FEHG, ADCB.

From the given options,

Option (C). ADEF will be one of the face of the solid.

Answer & Step-by-step explanation:

(2/5 + 3/4) * [ 3 - (1/4 : 1/5)]

When you see this sign, : , it usually means to divide the numbers because they represent some form of a ratio. So, we will divide 1/4 by 1/5.

First, do all of the operations in the parentheses ().

(2/5 + 3/4)*[ 3 - (1/4 : 1/5)]

(23/20) * [ 3 - (5/4)]

(23/20) * (7/4)

Now, we multiply 23/20 by 7/4.

(23/20) * (7/4)

161/80

This number can not be simplified so we will keep it as it is.

So, the answer to this expression is 161/80

Answer:

E) B < A < C

Step-by-step explanation:

Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower.

Initial Values are: A, B and C

After one year, A was up 20%, B was down 25%, and C was unchanged.

Values after one year:

For the second year, A was down 20% from the previous year, B was up 25% from the previous year, and C was unchanged.

Values after the second year

Therefore, from the final values of the stock, we have that:

B<A<C

The correct option is E.

Answer:

There are two possibilities:

[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]

[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]

Step-by-step explanation:

Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:

[tex]x + y = 9.9[/tex]

[tex]x^{2} + y^{2} = 53.21[/tex]

First, [tex]x[/tex] is cleared in the first equation:

[tex]x = 9.9 - y[/tex]

Now, the variable is substituted in the second one:

[tex](9.9-y)^{2} + y^{2} = 53.21[/tex]

And some algebra is done in order to simplify the expression:

[tex]98.01-19.8\cdot y +2\cdot y^{2} = 53.21[/tex]

[tex]2\cdot y^{2} -19.8\cdot y +44.8 = 0[/tex]

Roots are found by means of the General Equation for Second-Order Polynomials:

[tex]y_{1} \approx \frac{32}{5}[/tex] and [tex]y_{2} \approx \frac{7}{2}[/tex]

There are two different values for [tex]x[/tex]:

[tex]y = y_{1}[/tex]

[tex]x_{1} = 9.9-6.4[/tex]

[tex]x_{1} = 3.5[/tex]

[tex]y = y_{2}[/tex]

[tex]x_{2} = 9.9 - 3.5[/tex]

[tex]x_{2} = 6.4[/tex]

There are two possibilities:

[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]

[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]

Answer:

2.9375

Step-by-step explanation:

3/4×47/12

3×47/4×12

141/48

2.9375

Answer:

4x12=48

48+7=55

4 7/12 as an improper fraction is 55/12

multiply the numerator with numerator and denominator with denominator

3x55=165

4x12=48

165/48 can be divided by 3

165/3=55__48/3=16

55/16 is simplified

55/16=3 r 7 so the fraction is 3 7/16

Hope this helps

Step-by-step explanation:

Answer: 2^4*3^5*19

Step-by-step explanation:

You also need to divided by 2 four times, then divided by 3 five times, then the final one is divided by 19.

The largest prime factor of 309² - 147² is, 19.

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The expression is,

⇒ 309² - 147²

Now, We can simplify as;

⇒ 309² - 147²

⇒ (309 - 147) (309 + 147)

⇒ 162 × 456

⇒ 2 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 3 × 19

Thus, The largest prime factor of 309² - 147² is,

⇒ 19

Learn more about the Greatest common factors visit:

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Answer:

  13

Step-by-step explanation:

The line is the hypotenuse of a right triangle that is 5 units high and 12 units wide. The Pythagorean theorem, or the distance formula, tells you the length is ...

  length = √(5² +12²) = √(25+144) = √169

  length = 13

Answer:

D) -7

Step-by-step explanation:

[tex] \because \: PQ + QR = PR \\ \therefore \: 2x + 17 + 12 = 22 + x \\ \therefore \: 2x + 29 = 22 + x \\ \therefore \: 2x - x = 22 - 29 \\ \therefore \: x = - 7 \\ [/tex]

Answer:

Pythagoras theorem: hypotenuse² = opposite² + adjacent²

Step-by-step explanation:

To know if a triangle is a right angle, we need to have the length of each sides of the triangle. Then we would apply Pythagoras theorem to determine if it is truly a right angled triangle.

Pythagoras theorem is a theorem in the form of an equation which shows the relationship between the sides of a right angled triangle.

let the sides of the right angled triangle be:

opposite =a, adjacent = b and hypotenuse = c

Using Pythagoras theorem

hypotenuse² = opposite² + adjacent²

c² = a² + b²

If the left hand side of the equation = the right hand side of the equation, it is a right angled triangle.