Use all the six numerals 4, 5, 6, 7, 8 and 9 to form two 3-digit even numbers whose sum is smallest, and what is the sum? ​

Given:

Jack's scores in five successive rounds were 25,-5,-10, 15 and 10.

To find:

The total score at the end.​

Solution:

It is given that the scores in five successive rounds were 25,-5,-10, 15 and 10. So, the sum of the scores at the end is:

[tex]Sum=25+(-5)+(-10)+15+10[/tex]

[tex]Sum=(25+15+10)+(-5-10)[/tex]

[tex]Sum=50+(-15)[/tex]

[tex]Sum=50-15[/tex]

[tex]Sum=35[/tex]

Therefore, the total score at the end. is 35.

Answer: 65 have passport and 30 have passport and voter ID so the remainder of people with voter ID only would be 20

Step-by-step explanation

Step-by-step explanation:

1.

[tex]qr - pr \: + qs - ps[/tex]

[tex]r(q - p) + s(q - p)[/tex]

[tex](r + s)(q - p)[/tex]

2.

[tex] {x}^{2} + y - xy - x[/tex]

[tex] {x}^{2} - x - xy + y[/tex]

[tex]x(x - 1) - y(x - 1)[/tex]

3.

[tex]6xy + 6 - 9y - 4x[/tex]

[tex] - 4x + 6 + 6xy - 9y[/tex]

[tex]2( - 2x + 3) - 3y( - 2x + 3)[/tex]

[tex](2 - 3y)( - 2x + 3)[/tex]

4.

[tex] {x}^{2} - 2ax - 2ab + bx[/tex]

[tex]x(x - 2a) - b(x - 2a)[/tex]

[tex]-(x +b)(2a-x)[/tex]

5.

[tex]axy + bcxy - az - bcz[/tex]

[tex]xy(a + bc) - z(a + bc)[/tex]

[tex](xy - z)(a + bc)[/tex]

Answer:

2

Step-by-step explanation:

(n+1)!=1×2×...×(n-1)×n×(n+1)

6*(n-1)!=1×2×...×(n-1)

--> n×(n+1)=6

-->n=2

Answer:

f (n + 1) = -2 f(n)

Step-by-step explanation:

Answer:

b 25x6 = 150

25 decreases every month so

150 decreses every 6 month

800-150

650 are the bees remaining after 6 month

Answer:

104 m^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w = 10*8 = 80

Then find the area of the triangle

A = 1/2 bh = 1/2 (8) * 6 = 24

Add the areas together

80+24 = 104 m^2

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

The two right triangles share angle A, so the similarity statement can be written ...

  ΔABC ~ ΔADE

Corresponding sides are proportional, so we have ...

  BC/DE = AB/AD

  x/12 = 3/(3+9)

  x = 3 . . . . . . . . . . multiply by 12

Answer:

x=3

this is correct!!!

-2y=10-5x

-2y/-2=(10-5x)/-2

Y=5/2x-2

Answer:

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Step-by-step explanation:

A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.

Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.

According to the Pythagorean Theorem:

[tex]\displaystyle x^2+y^2=1521[/tex]

Let's take the derivative of both sides with respect to time t. Hence:

[tex]\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right][/tex]

Implicitly differentiate:

[tex]\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]

Simplify:

[tex]\displaystyle x\frac{dx}{dt} + y \frac{dy}{dt} = 0[/tex]

The area of the triangle formed will be given by:

[tex]\displaystyle A = \frac{1}{2} xy[/tex]

Again, let's take the derivative of both sides with respect to time t:

[tex]\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right][/tex]

From the Product Rule:

[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)[/tex]

At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.

[tex]\displaystyle y = \sqrt{1521-(15)^2}=36[/tex]

The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:

[tex]\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}[/tex]

Evaluate for dy/dt:

[tex]\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}[/tex]

Finally, using dA/dt, substitute in appropriate values:

[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)[/tex]

Evaluate. Hence:

[tex]\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}[/tex]

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Answer:

Step-by-step explanation:

B because the vertex is at point (3, 4) which is greatest.

Answer:

[tex]\text{b. } y=-(x-3)^2+4[/tex]

Step-by-step explanation:

Algebraically, we want to compare the y-coordinates of the vertex, since all the functions shown are parabolas that are concave down.

Let's break the format down:

The negative sign in front of each of the functions indicate that the parabolas will be concave down (open downwards), which means the vertex represents the function's maximum. The term inside the parentheses when applicable to just indicates the horizontal/phase shift.

Since the first term being squared is negative, we want to minimize its value to produce the greatest possible y-value.

Therefore, substitute whatever value of [tex]x[/tex] that makes each [tex]x^2[/tex] term equal to 0. (Maximum value of [tex]-x^2[/tex] is 0).

Therefore, we can simplify compare the last terms in each equation.

Equation A's last term is 3.

Equation B's last term is 4.

Equation C's last term is -5.

Equation D's last term is 0.

Since equation B has the greatest last term, it will have the greatest possible y-value.

The distance from the origin is a.

Step-by-step explanation:

If the point is located at the coordinate [tex](a\cos \alpha, a\sin \alpha)[/tex], then its distance from the origin is given by

[tex]r = \sqrt{x^2 + y^2} = \sqrt{(a\cos \alpha)^2 + (a\sin \alpha)^2}[/tex]

[tex]\:\:\:\:=\sqrt{a^2(\cos^2\alpha + \sin^2 \alpha)}[/tex]

[tex]\:\:\:\:= a[/tex]

Answer:

The answer is C, no solution.

Step-by-step explanation:

Answer: Around 37.3

Step-by-step explanation:

[tex]tan(63)=\frac{x}{19} \\\\x=19*tan(63)=37.2895996...[/tex]

Answer:

37.3

Step-by-step explanation:

tan (63)=x/19

x=19×tan(63)=37.3

Answer:

Step-by-step explanation:

BC/AB = DE/AD

1/2 = x/(2+1)

x = 1.5

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

See this attachment

Answer:

a) Their average weight is of 187 pounds.

b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?

8228/44 = 187

Their average weight is of 187 pounds.

b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For men, we have that [tex]\mu = 186, \sigma = 60[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]

This probability is 1 subtracted by the p-value of Z when X = 187. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

1 - 0.5438 = 0.4562

0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For women, we have that [tex]\mu = 157, \sigma = 69[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]

[tex]Z = 2.88[/tex]

[tex]Z = 2.88[/tex] has a p-value of 0.998.

1 - 0.998 = 0.002.

0.002 = 0.2% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

He,smixing x and y values and averaging them. You add x of one point and add to the x value of the second point. Then divide by 2. Do the same with the y values.

Answer:

21 degrees

Step-by-step explanation:

I did it on the calculator

Answer:

2sqrt(x)-2x^3

Step-by-step explanation:

f(x) - g(x) = sqrt(x)-x-(2x^3)+sqrt(x)+x=2sqrt(x)-2x^3

The difference of the two functions f(x) and g(x) is -

f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]

We have - two functions of [tex]x[/tex] :

[tex]f(x)=\sqrt{x} -x\\g(x) = 2x^{3} - \sqrt{x} -x[/tex]

We have to find -

[tex]f(x)-g(x)[/tex]

The term [tex]y=f(x)[/tex] indicates that [tex]y[/tex] is expressed as a function of [tex]x[/tex], where [tex]x[/tex] is a independent variable and [tex]y[/tex] is a dependent variable which depends on [tex]x[/tex].

According to question -

[tex]f(x)-g(x)=\sqrt{x} -x - (2x^{3} - \sqrt{x} -x)\\f(x)-g(x)=\sqrt{x} -x-2x^{3} + \sqrt{x} +x\\f(x)-g(x)=-2x^{3} + 2\sqrt{x}[/tex]

Hence, f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]

To solve more questions on operations of functions, visit the link below-

https://brainly.com/question/12688480

#SPJ2

Answer:

Step-by-step explanation:

The vertex is either the highest point on the parabola or the lowest point. We have a positive parabola, so the vertex is a low point. It sits at (2, -4). Locate that point and see what I mean by the lowest point on the parabola.

Answer: D

Step-by-step explanation:

When a coordinate is reflected over the y-axis, it changes from (x, y) to (-x, y)

The three coordinates of ΔCDE are

After the y-axis reflection, they'll become:

I hope this is correct :\

You're right, this problem is asking for the least and greatest values. But, we have to take a bit of a closer look at the stem and leaf plot.

The left side is the ones place and the right side is the tenths place.

Using that information, the least data value is 2.5, and the greatest data value is 5.7.

Hope this helps!

Answer:

En matemáticas, especialmente en la teoría de números hay una proposición que vincula tres conceptos: primalidad, factorial de un número entero no nulo y congruencia de números respecto de un módulo.

answer-Wilson's theorem, in number theory, theorem that any prime p divides (p − 1)! ... + 1, where n! is the factorial notation for 1 × 2 × 3 × 4 × ⋯ × n. For example, 5 divides (5 − 1)!

Answer:

Moving upwards with an acceleration.

Step-by-step explanation:

weight of the person  = 195 pounds

Apparent weight = 205 pounds

As the weight increases so the scale is moving upwards with some acceleration.

The scale is in elevator which is moving upwards.

Answer:

46.38

Step-by-step explanation:

all the answer are not same but buy calculating its the right answer

Answer:

The half-life of this substance is of 569.27 days.

Step-by-step explanation:

Amount of a substance after t days:

The amount of a substance after t days is given by:

[tex]P(t) = P(0)e^{-kt}[/tex]

In which P(0) is the initial amount and k is the decay rate, as a decimal.

Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.

This means that [tex]P(300) = 0.694P(0)[/tex]. We use this to find k.

[tex]P(t) = P(0)e^{-kt}[/tex]

[tex]0.694 = P(0)e^{-300k}[/tex]

[tex]e^{-300k} = 0.694[/tex]

[tex]\ln{e^{-300k}} = \ln{0.694}[/tex]

[tex]-300k = \ln{0.694}[/tex]

[tex]k = -\frac{\ln{0.694}}{300}[/tex]

[tex]k = 0.0012[/tex]

So

[tex]P(t) = P(0)e^{-0.0012t}[/tex]

What is the half-life (in days) of this substance?

This is t for which P(t) = 0.5P(0). So

[tex]0.5P(0) = P(0)e^{-0.0012t}[/tex]

[tex]e^{-0.0012t} = 0.5[/tex]

[tex]\ln{e^{-0.0012t}} = \ln{0.5}[/tex]

[tex]-0.0012t = \ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.0012}[/tex]

[tex]t = 569.27[/tex]

The half-life of this substance is of 569.27 days.

Answer:

9.42

Step-by-step explanation:

The circumference of a circle is calculated using the following formula:

C=2πr (C: circumference, r : radius)

radius here is 6 and π  is given as 3.14

2*(3.14)*6 = 18.84 now divide this by 2 to find the length of semicircle

18.84/2 = 9.42

Answer:

6π

Step-by-step explanation:

Given:

In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.

To find:

The length of the missing side.

Solution:

In a right angle triangle,

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.  

Substituting Perpendicular = 8 inches and Base = 12 inches, we get

[tex]Hypotenuse^2=8^2+12^2[/tex]

[tex]Hypotenuse^2=64+144[/tex]

[tex]Hypotenuse^2=208[/tex]

Taking square root on both sides, we get

[tex]Hypotenuse=\sqrt{208}[/tex]

[tex]Hypotenuse=14.422205[/tex]

[tex]Hypotenuse\approx 14.4[/tex]

The length of the missing side is 14.4 inches. Therefore, the correct option is D.