The least multiple of 5 which is divisible by both 3 and 4 is -​

The probability that their second child will be unaffected is 3/4.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. Probability is calculated by the formula:

        P(E) = number of possible outcomes / total number of outcomes

The disease PKU known as Phenylketonuria is a rare inherited disorder. If the mother and father had and passed on the changed gene, then the child can inherit PKU. This is known as autosomal recessive.

The child to be affected by PKU, has to be aa. So, the first child who has the disease is aa. The unaffected child i.e. the second child is AA and Aa.

Here, the number of possible outcomes = 3 and total number of outcomes = 4

P(E)  =  3 / 4

        =  0.75

Therefore, the probability that the second child will be unaffected is 75%.

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One machine can produce 600,000 nails in one hour.

Finding the total number of nails produced by the three machines in a minute and dividing that number by three to obtain the number of nails produced by a single machine in a minute are the first two steps in the solution to this problem.

The number of nails produced by a single machine in an hour can then be calculated by multiplying that number by 60.

Now, we add up the total number of nails produced during :

(15 + 16 + 45 + 48 + 55 + 59 + 3) / 7 = 30

To find the number of nails produced by one machine in one hour, we multiply by 60: 10,000 x 60 = 600,000

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Answer:

10178.7602

Step-by-step explanation:

Volume of cylinder= π·r^2·h = π·9^2·40 ≈ 10178.7602

if 18 is the diameter than 9 would be the radius. to make the formula easier.

The time necessary for p dollars to double when it is invested at interest rate r compounded annually is given by the formula:

t = (ln 2) / (r ln (1 + r))

When compounded monthly, the formula becomes:

t = (ln 2) / (12 r ln (1 + r/12))

When compounded daily, the formula becomes:

t = (ln 2) / (365 r ln (1 + r/365))

When compounded continuously, the formula becomes:

t = ln 2 / (r)

Note that ln is the natural logarithm function.

To use these formulas, you need to know the value of the interest rate r. For example, if r is 5%, then:

When compounded annually, t = (ln 2) / (0.05 ln 1.05) = 13.86 years
When compounded monthly, t = (ln 2) / (12 x 0.05 ln 1.0041) = 14.21 years
When compounded daily, t = (ln 2) / (365 x 0.05 ln 1.000137) = 14.27 years
When compounded continuously, t = ln 2 / (0.05) = 13.86 years

Therefore, the time necessary for p dollars to double depends on the interest rate and the frequency of compounding. Generally, the more frequently the interest is compounded, the shorter the time necessary for p dollars to double.

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Working together, they can complete the task in 4 hours and 48 minutes.

A certain amount of time (T) is taken to complete a certain work (W). The number of units of work done per unit time is called the rate of work (R). Hence, Work (W) = Rate (R) Time (T) Whenever some work is done, the total work itself can be taken as one unit.

Tracy needs 8 hours to complete the task.

Then we can find the ratio of work over time as:

1 task/8 hours = 1/8 task per hour.

This means that she can complete 1/8 of the task per hour.

Dave needs 12 hours to complete the task, then his ratio is:

1 task/12 hours = 1/12 task per hour.

This means that he can complete 1/12 of the task in one hour.

If they work together, then the ratios can be added:

R = \(\frac{1}{8}\) +  \(\frac{1}{12}\)

  = \(\frac{3+2}{24}\)

  = \(\frac{5}{24}\)

So, working together, in one hour they can complete  \(\frac{5}{24}\) of the task, now we can find the number of hours needed to complete the task as:

\(\frac{5}{24}\)×\(x\)= 1 task

x = \(\frac{24}{5}\) hours = 4.8 hours

knowing that an hour is 60 minutes, then 0.8 of an hour is 60*0.8 = 48 minutes.

Then x = 4 hours and 48 minutes.

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The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

Using the segment addition postulate and the bisection concept, the segment EF bisecting RS is given at the end of the answer.

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

From this, the bisection concept is derived, which is when a line crosses a segment exactly at the segment's midpoint, meaning that point A is the midpoint of RS.

The illustration of this situation is given at the end of the answer.

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Answer:

227

Step-by-step explanation:

nth term = a₁ + (n - 1)d

where a1 = first term , n = # of terms and d = common difference.

here we need to solve for the common difference so we can find the missing term, we do so by plugging in what we are given and solving for d

here we are given an nth term, 456 and we are given the first term, -2.

and from what we see there are 3 terms

So we have nth term = 456 , a1 = -2 and n = 3

==> plug these values into the formula

456 = -2 + (3-1)d

==> add 2 to both sides

458 = (3-1)d

==> subtract 1 from 3

458 = 2d

==>divide both sides by 2

d = 229

We then add the common difference to the term before the missing term to get the missing term

-2 + 229 = 227

Answer:

2+2 = 4

Step-by-step explanation:

Hope this helps.

Answer:

2 + 2 is 4 my guy

Step-by-step explanation:

thx for the points

Answer: There are 25 crates and 15 boxes in the truck when it is full.

Step-by-step explanation:

Let c= Number of crates , b= Number of boxes.

As per given,

\(c+b = 40\)     (i)

\(3c=5b\\\\\Rightarow\ c=\dfrac{5b}{3}\)        (ii)

Put value of c from (ii) in (i)

\(\dfrac{5b}{3}+b = 40\\\\\Rightarrow\ \dfrac{5b+3b}{3}=40\\\\\Rightarrow\ \dfrac{8b}{3}=40\\\\\Rightarrow\ 8b=3\times40\\\\\Rightarrow\ 8b=120\\\\\Rightarrow\ b=\dfrac{120}{8}=15\)

put value of b in (ii),

\(c=\dfrac{5\times15}{3}=5\times5=25\)

Hence, there are 25 crates and 15 boxes in the truck when it is full.

25 boxes 15 crates

We would get this solution by adding up the two sides comparing the ratios, hence: we get room for 3 crates for every 5 boxes that we can hold in the truck.

A ratio is an ordered pair of numbers a and b, written a:b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. hence, if there is 3 crates and 5 boxes you could write the ratio as: 3 : 5 (for every 3 crates there are 5 boxes) 3 / 5 are boys and 5 / 3 are crates.

Answer:

Distance between Gas Station and House = 7.81 miles.

Step-by-step explanation:

The distance between the two locations is 7.81 miles

Given the point at (4,3) represents the location of her house, and the point at (10, 8) represents the location of the gas station.

The distance between the two locations will be determined using the formula

D \(=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Substitute the given coordinate into the formula

\(D=\sqrt{(-6)^2+(-5)^2}\\D=\sqrt{(4-10)^2+(3-8)^2}\\D=\sqrt{36+25}\\ D=\sqrt{61}\\ D=7.81miles\)

Hence the distance between the two locations is 7.81 miles

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Two triangles are similar but not congruent if they have three congruent angles but the side lengths are not equal.

What is the congruency of triangles?

To show how can the triangles be proven similar by the SSS similarity theorem:

The two triangles can be shown to be similar given that the ratios of the corresponding sides ΔWUV and ΔYXZ are constant

Reason:

Known parameters are:

ΔWUV and ΔXZY are shown:

∠VUW ≅ ∠YXZ

∠UWV ≅ ∠XZY

∠UVW ≅ ∠ZYX

Length of side VW = 60

Length of side VU = 50

Length of side UW = 40

Length of side  ZY = 48

Length of side  YX = 40

Length of side  XZ = 32

The ratio of the sides are:

\(\frac{VW}{ZY} =\frac{60}{48} =\frac{5}{4} \\\frac{VU}{YX} =\frac{50}{40} =\frac{5}{4} \\\frac{UW}{XZ} =\frac{40}{32} =\frac{5}{4}\)

Therefore, given that  the angles of ΔWUV and ΔXZY are all congruent, and the sides of triangle ΔWUV and ΔXZY have a constant proportion, we have that the two triangles are congruent by the Side-Side-Side SSS congruency theorem,  and we have:

ΔWUV ~ ΔYXZ given that ΔYXZ is a scaled drawing of ΔWUV.

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The complete question is given here:

Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.

How can the triangles be proven similar by the SSS similarity theorem?

Answer:

Please refer to the attachment

The value of x in the triangle is 46.40° .

The angle of a triangle can be found using sine rule.

Therefore, applying sine rule,

a / sin A = b / sin B = c / sin C

Hence,

5 / sin x = 6.9  / sin 88°

cross multiply

5 sin 88° = 6.9 sin x

5 × 0.99939082701 = 6.9 sin x

4.9969541351 = 6.9 sin x

divide both sides by 6.9

sin x = 4.9969541351  / 6.9

sin x = 0.72419625146

x = sin⁻¹ 0.72419625146

x = 46.4020264383

Therefore,

x = 46.40°

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Answer:

B.  \(Cos ^{-1}\) \(\frac{6.3}{9.8}\)

E.  \(Sin^{-1}\) \(\frac{7.5}{9.8}\)

Step-by-step explanation:

The trigonometric functions are applied when given a side and one of the angles of a right angled triangle.

Sine θ = \(\frac{opposite}{hypotenuse}\)

Cosine θ = \(\frac{adjacent}{hypotenuse}\)

Tangent θ = \(\frac{opposite}{adjacent}\)

Given that; hypotenuse = 9.8, opposite side = 7.5 and adjacent side = 6.3.

Then,

Sin θ = \(\frac{7.5}{9.8}\)

⇒ θ = \(Sin^{-1}\) \(\frac{7.5}{9.8}\)

Also,

Cos θ = \(\frac{6.3}{9.8}\)

⇒ θ = \(Cos ^{-1}\) \(\frac{6.3}{9.8}\)

So, the appropriate answers to the given questions are options B and E.

Answer:

b

Step-by-step explanation:

Answer:

y=\(\frac{3}{8}\)x

Step-by-step explanation:

First, let's understand what the question is asking us. The question is asking us to find the equation for the line shown in the graph in slope-intercept form (y=mx+b). In slope intercept form, m is the slope and b is the y-intercept. So, to find the equation of the line, we will need to find the slope and y-intercept.

Slope (m):

Slope can be found by rise over run. In other words, slope is the amount you go up or down divided by the amount you go to the left or right. To find slope, you need to look at 2 points. I'm choosing to look at the points (0,0) and (8,3). To get from (0,0) to (8,3), we need to go up 3 and to the right 8. This means that our slope is 3/8.

Y-intercept (b):

To find the y-intercept, you need to find where the line crosses the y-axis. In the graph shown, the line crosses the y-axis at y=0. This means that our y-intercept is 0.

Slope-intercept form equation:

Now, let's use the information we found to create the equation for the line!

y=mx+b

y=\(\frac{3}{8}\)x+0 or just y=\(\frac{3}{8}\)x

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".

What is judicial activism?

Judicial activism is a judicial philosophy that is sometimes referred to as "legislating from the bench". It is an exercise of judicial review and generally refers to the willingness of a judge to strike down legislative or executive actions regarding constitutional issues. Judicial restraint is generally thought of as the opposite of judicial activism.[1]

Earlier in the january of 1947 ,Arthur Schlesinger Jr. introduced the term "judicial activism" .An article by Keenan Kmiec says that in its early usage, it was sometimes used with a positive connotation akin to the term "civil rights activist".

Thus , Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".

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the question requires:

the time t required.

the equation of the inverse variation.

how do find t:

first we determine how much the tank holds by multiplying 120 by 40.

the tank holds 4800 gallons.

so now to find t we can use the formula v = d/t where d is the 4800 gallons.

so: t = d/v

t = 24 minutes

now for the equation of the inverse variation.

we can say that the equation is t = d/v since t and v are inversely proportional.

note that v and t stand for velocity and time respectively.

make sure to ask if you need any further guidance!!

Answer:

t = 24

Step-by-step explanation:

The cubic inches that the fish tanks will hold is 13,824 inches³.

In order to determine the cubic inches that the fish tanks would hold, multiply the volume of one of the fish tanks by 3.

Volume of a rectangular prism  = length x width x height

The feet has to be converted to inches

1 feet = 12 inches

2 x 12 = 24 inches

Volume = 16 x 24 x 12 = 4,608 inches³

Volume of the fish tanks =  4,608 inches³ x 3 = 13,824 inches³

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Answer:

5x + 40

Step-by-step explanation:

At the start, he has 40 tennis balls.

He also buys x amount of boxes which holds 5 tennis balls each

The amount of tennis balls in x number of boxes is 5x

5x + 40 is the number of tennis balls he will have after buying x number of boxes

-Chetan K

Answer:

Step-by-step explanation:

One of four in number form is 1/4 this is the only thing I can tell you without knowing what the answer choices are or what the question is

4 square 6 in surd form​ is  4√6

A number system is defined as a system of writing to express numbers.

4 square 6 in surd form​

Any number of the form n √a, which cannot be written as a fraction of two integers is called a surd.

4 square 6 in surd form​ is 4√6

Decimal Form is 9.8

Hence, 4 square 6 in surd form​ is  4√6

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Answer:

Step-by-step explanation:

The Y-intercept is (0,-1)

The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.

When charged electrons (current) are forced through a conducting loop by the weight of an electrical raceway power source, they can perform tasks like lighting a lamp. In a nutshell, voltage equals pressure and is expressed in volts (V).

Here,

The voltage generated by the uv spectrophotometer is inversely proportionate to the amount of light present and linearly proportional to the sample's absorbance.

This indicates that as the sample's absorbance rises, so does the energy the colorimeter generates.

Similar to this, the voltage generated by the colorimeter rises as light strength falls.

The Beer-Lambert Law, which says that a sample's absorbance is directly proportional to its concentration of the absorbing substance and its path length and inversely proportional to incident light intensity, describes this connection.

The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.

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Given equation is a first-order nonlinear ordinary differential equation (ODE): y' - (x + y - 1)^2 = 0

What is differential equation ?

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

This equation can be solved using various methods, such as numerical methods or analytical methods like the implicit function theorem or the method of characteristics. However, finding an exact solution can be challenging and may not always be possible.

If you would like to find an approximate solution to this ODE, you could use numerical methods such as Euler's method, Runge-Kutta method, or the finite difference method. These methods can provide a numerical approximation to the solution for a given range of x and a specified initial condition.

The given equation is a first-order nonlinear ordinary differential equation (ODE):

y' - (x + y - 1)^2 = 0

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The statements for the function f( x) = 3x ²- 5 are

f( 5)< 1( false)

f( 0) = 1( false)

Statements for the function f(x) = 3x ²- 5

To find the true or false statement we have to substitute the value for x

First, x= 3

f(x) = 3x ²- 5

f(3)= 3( 5)²- 5

f(3) = 75- 5

f(3)= 70.

Thus, the statement" f( 5)< 1" is false.

Now, at x =0

f(x) = 3x ²- 5

f(0) = 3( 0)²- 5

f(0)= 0- 5

f(0)= -5.

Thus, the statement" f( 0) = 1" is false.

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Answer:

the green box is 0

Step-by-step explanation:

we are asked to find the x-intercept, which means y = 0

(x, y)

Another way to test this is plug it in 1 for x!  (1, y) where x = 1

\(y = \frac{2x^{2} -3x+1}{2x^{2} +8x+6} \\\\\)

\(y = \frac{2(1)^{2} -3(1)+1}{2(1)^{2} +8(1)+6}\)

\(y = \frac{2(1) -3(1)+1}{2(1) +8+6}\)

\(y = \frac{2 - 3 + 1}{2 + 8 + 6}\)

\(y = \frac{-1+1}{10 + 6}\)

\(y = \frac{0}{16}\)

y = 0