Determine the following information about each value in a list of positive integers. a. Is the value a multiple of 7, 11, or 13? b. Is the sum of the digits odd or even? c. Is the value a prime number?

Answer:

[tex]s \ne \±2[/tex]

[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]

[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]

Step-by-step explanation:

Given

[tex]3sx_1 +5x_2 = 3[/tex]

[tex]12x_1 + 5sx_2 =2[/tex]

Required

Determine the value of s

Express the equations as a matrix

[tex]A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right][/tex]

Calculate the determinant

[tex]|A|= (3s*5s -5 *12)[/tex]

[tex]|A|= (15s^2 -60)[/tex]

Factorize

[tex]|A|= 15(s^2 -4)[/tex]

Apply difference of two squares

[tex]|A|= 15(s -2)(s + 2)[/tex]

For the system to have a unique solution;

[tex]|A| =0[/tex]

So, we have:

[tex]15(s -2)(s+2) = 0[/tex]

Divide both sides by 15

[tex](s -2)(s+2) = 0[/tex]

Solve for s

[tex]s -2 = 0\ or\ s +2 = 0[/tex]

[tex]s = 2\ or\ s = -2[/tex]

The result can be combined as:

[tex]s =\±2[/tex]

Hence, the system has a unique solution when [tex]s \ne \±2[/tex]

Next, we solve for s using Cramer's rule.

We have:

[tex]mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right][/tex]

Calculate the determinant

[tex]|x_1| = (3 * 5s - 5 *2)[/tex]

[tex]|x_1| = 15s - 10[/tex]

So:

[tex]x_1 =\frac{|x_1|}{|A|}[/tex]

[tex]x_1 = \frac{15s - 10}{15(s -2)(s+2)}[/tex]

Factorize

[tex]x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}[/tex]

Divide by 5

[tex]x_1 = \frac{3s - 2}{3(s -2)(s+2)}[/tex]

[tex]x_1 = \frac{3s - 2}{3(s^2 -4)}[/tex]

Similarly:

[tex]mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right][/tex]

Calculate the determinant

[tex]|x_2| = 3s * 2 - 3 * 12[/tex]

[tex]|x_2| = 6s- 36[/tex]

So:

[tex]x_2 =\frac{|x_2|}{|A|}[/tex]

[tex]x_2 = \frac{6s- 36}{15(s -2)(s+2)}[/tex]

Factorize

[tex]x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}[/tex]

Divide by 3

[tex]x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}[/tex]

[tex]x_2 = \frac{2(s- 6)}{5(s^2 - 4)}[/tex]

Answer:

25.9 ft

Step-by-step explanation:

tan = opp/adj

tan67 = 61 / adj

adj = 61/tan67

use calculator

adj = 25.892963788785889

Rounded

25.9 ft

This question is incomplete, the complete question is;

Suppose that the amount of time it takes to process insurance claims is normally distributed with a mean of 12 weeks and a variance of 9 weeks. What is the probability that the next claim will be processed within; a) 10 weeks, b) 11 weeks, c) 12 weeks.

Answer:

a) the probability that the next claim will be processed within 10 weeks is 25.14%

b) the probability that the next claim will be processed within 11 weeks is 37.07%

c) the probability that the next claim will be processed within 12 weeks is 50.00%

Step-by-step explanation:

Given the data in the question;

mean 12 weeks

Variance = 9 weeks

Standard deviation SD = √Variance = √ 9 = 3 weeks.

Since,  the amount of time it takes to process insurance claims is normally distributed.

z = ( x - mean ) / SD

where x is weeks of next claim.

a) 10 weeks

z = ( x - mean ) / SD

we substitute

z = ( 10 - 12 ) / 3

z = -2/3

z = -0.67

{ from standard normal distribution table }

value of z is 0.2514

Therefore, the probability that the next claim will be processed within 10 weeks is 25.14%

b) 11 weeks

z = ( x - mean ) / SD

we substitute

z = ( 11 - 12 ) / 3

z = -1/3

z = -0.33

{ from standard normal distribution table }

value of z is 0.3707

Therefore, the probability that the next claim will be processed within 11 weeks is 37.07%

c) 12 weeks

z = ( x - mean ) / SD

we substitute

z = ( 12 - 12 ) / 3

z = 0/3

z = 0.00

{ from standard normal distribution table }

value of z is 0.5000

Therefore, the probability that the next claim will be processed within 12 weeks is 50.00%

Answer:

the answer is a

Step-by-step explanation:

Answer:

A, C and G

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the values into the trigonometric ratios:

[tex]\implies \sf \sin(25^{\circ})=\dfrac{a}{c}[/tex]

[tex]\implies \sf \cos(25^{\circ})=\dfrac{b}{c}[/tex]

[tex]\implies \sf \tan(25^{\circ})=\dfrac{a}{b}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric values} \\\\$\sin(90^{\circ}- \theta)=\cos \theta$\\$\cos(90^{\circ}- \theta)=\sin \theta$\\$\tan(90^{\circ}- \theta)=\cot \theta$\\\end{minipage}}[/tex]

Using trigonometric values and the calculated trigonometric ratios:

[tex]\begin{aligned} \sf \sin(90^{\circ}- 25^{\circ})&=\sf \cos (25^{\circ})\\\implies \sf \sin(65^{\circ}) &=\sf \dfrac{b}{c}\end{aligned}[/tex]

[tex]\begin{aligned} \sf \cos(90^{\circ}- 25^{\circ})&= \sf \sin(25^{\circ})\\\implies \sf \cos(65^{\circ}) &=\sf \dfrac{a}{c}\end{aligned}[/tex]

[tex]\begin{aligned}\sf \tan(90^{\circ}- 25^{\circ})&= \sf \cot(25^{\circ})\\\implies \sf \tan(65^{\circ}) &= \sf \dfrac{1}{\tan(25^{\circ})}\\\implies \sf \tan(65^{\circ}) & = \sf \dfrac{b}{a}\end{aligned}[/tex]

Therefore, the true equations are:

[tex]\sf A: \quad \cos(25^{\circ})=\dfrac{b}{c}[/tex]

[tex]\sf C: \quad \sin(65^{\circ})=\dfrac{b}{c}[/tex]

[tex]\sf G: \quad \sin(25^{\circ})=\cos(65^{\circ})[/tex]

Answer:

24

Step-by-step explanation:

Answer:

the remainder is 81

Step-by-step explanation:

so , equate x +3 to 0 , as in x + 3 = 0 then x = -3

so now we know the value of x so just replace it in the expression to get the remainder

♡´･ᴗ･`♡

Answer:

8

Step-by-step explanation:

I'm not too sure, I think it might be 8.

Answer:

4+4 = 8

Step-by-step explanation:

Answer:

so you would actually multiply 32 x 15=480 then subtract 480 - 384= it would have 96 miles left. then divide 96/32= 3

so your answer would be 3 gallons left

Step-by-step explanation:

Answer

0.73

Step-by-step explanation:

73% = 0.73 in decimal form. Percent means 'per 100'. So, 73% means 73 per 100 or simply 73/100.

Answer:

Step-by-step explanation:

73%

=73/100

=0.73

when u divide the percentage with hundred percentage sign will be removed.

Answer: y=-2x-1

Step-by-step explanation:

First let's find the slope by using the formula [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

[tex]\frac{-3--1}{1-0} \\\frac{-2}{1} \\-2[/tex]

The equation for slope intercept form is y=mx+b where m is the slope and b is the y-intercept

The y-intercept is -1 giving us the equation

y=-2x-1

Answer:

2x + 3 ≥ 6

2x + 3 - 3 ≥ 6 - 3

2x ≥ 3

2x ÷ 2 ≥ 3 ÷ 2

x ≥ 1.5

Answer:

It will cost $121.50

Step-by-step explanation:

C = 20 + 25h + .05m

Now plug in the hours and miles

C = 20 + 25(4) + .05(30)

C = 20 + 100 + 1.5

C = 121.50

The total cost rent the truck for 4 hours and 30 miles drive is $121.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Given that, a home improvement store charges $20 to rent a small truck for 1 hour.

Let the number of hours be h and the number of miles be m.

Now, total charge = 20+25h+0.05m

Here, h=4 and m=30

So, total charge = 20+25(4)+0.05(30)

= $121.5

Therefore, the total cost rent the truck for 4 hours and 30 miles drive is $121.5.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

y = 4x² - 4

Step-by-step explanation:

y = a(x - x₁ )(x - x₂)

Plug in the knowns

y = 4(x - 1)(x + 1)

expand

y = 4(x² - 1)

y = 4x² - 4

Answer:

d=4.5

Step-by-step explanation:

d+5.5=10

d=10-5.5

d=4.5

Hope this is helpful

Answer:

wilson swam farther by 0.4 km

Step-by-step explanation:

wilson swam 1.2km

brian swam 0.8km

1.2 - 0.8 = 0.4

Answer:

f(x+3) = 4x + 14

Step-by-step explanation:

f(x+3) = 4(x+3) + 2

f(x+3) = 4x + 12 + 2

f(x+3) = 4x + 14

hope this helps!

Answer:

f(x)=4x+2

f(x+3) means substitute x as (x+3)

f(x+3)=4(x+3) +2

= 4x + 12 + 2

=4x+14.

OPTION C IS LEGIT

Answer:

y = 2( x+5)^2 -4

Vertex (-5,-4)

directrix  y = -33/8

focus (-5, -31/8)

Step-by-step explanation:

First identify the vertex, which is the minimum

Vertex = (-5,-4)

The vertex form is y = a( x-h)^2 + k

y = a( x- -5)^2 -4

y = a( x+5)^2 -4

We need to determine a

Substitute a point on the graph

(-3,4) is on the graph

4 = a( -3+5)^2 -4

4 = a( 2)^2 -4

4 = 4a -4

Add 4 to each side

8 = 4a

Divide by 4

8/4 = a

a=2

y = 2( x+5)^2 -4

To find the focus and directrix, write in standard form

4p(y-k)=(x-h)^2

y+4 = 2(x+5)^2

1/2 (y+4) = (x+5)^2

4p = 1/2

p = 1/8

The focal length is 1/8

Subtract this from the y coordinate to get the directrix

y = -4 -1/8

y = -32/8 - 1/8 = -33/8

Add this to the y coordinate to get the coordinate for the focus the x coordinate the same

(-5, -4+1/8)

(-5, -32/4+1/8)

(-5, -31/8)

Answer:

x = 6.67 inches

Step-by-step explanation:

Set upa s a proportion

x/60 = 1/9

x = 1/9 * 60

x = 6.67 inches

Answer:

A. Tossing 5 coins and getting 4 heads

Step-by-step explanation:

Compound events may be described as events whose occurence has more than one possible outcome, that is the number of possible events is more than one. From the options given above, Rolling 3 on a die, this event has only one possible outcome, which is rolling 3 ; tossing a coin and getting tails also has one obe possible outcome. Drawing 10 diamonds from a deck also focuses on one event which is drwinh diamonds. However, tossing 5 coins and getting 4 heads involves that the 5th toss will be tail. This has more than one event and thus a compound event.

Answer: A.

Step-by-step explanation:

Tossing five coins and getting four heads is a compound event as the coins and cards are different

Answer:

(x-1)^5 (x+1)

Step-by-step explanation:

2 (x-1)^5 + (x-1)^6

Factor out (x-1)^5

2 (x-1)^5 + (x-1)^5 (x-1)

(x-1)^5( 2 + x-1)

Combine like terms

(x-1)^5 (x+1)

Answer:

A

Step-by-step explanation:

factor out (x-1)^5 and you get (x-1)^5(2+x-1)

simplify that to get (x-1)^5(x+1)

Answer:

center=(-6, 1)

radius=√9= 3

Step-by-step explanation:

(x-h)^2 + (y-k)^2=r^2

Answer:The Rule for 10: Numbers that are divisible by 10 need to be even and divisible by 5, because the prime factors of 10 are 5 and 2. Basically, this means that for a number to be divisible by 10, the last digit must be a 0. ... So this number is even and divisible by 5. That means that it is also divisible by 10

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

f(1) is the value of y when x = 1.

Thus, from the graph, we see that when x = 1 on the x-axis, on the y-axis, we have a corresponding y value of -2.

This means y = -2 when x = 1.

Therefore:

f(1) = -2

Answer:

C

Step-by-step explanation:

Answer:

90%

Step-by-step explanation:

present students:40-4=36

36/40*100

=90%

Answer:

90% are present

Step-by-step explanation:

40-4=36

36 are present

36/40 = x/100

36x100=3600

3600/40=90

answer: 90/100 = 90%

No, 4 is not a solution of [tex]9x - 6 = 7x[/tex].

Here's why:-

[tex]9x - 6 = 7x \\ ⇢ 9x - 7x = 6 \\ ⇢ 2x = 6 \\ ⇢ x = \frac{6}{2} \\ ⇢ x = 3[/tex]

Clearly, the value of [tex]x[/tex] is 3.

[tex]{ \bf{ \underbrace{To\:verify:}}}[/tex]

[tex]9x - 6 = 7x \\ ⇢ 9 \times 3 - 6 = 7 \times 3 \\ ⇢ 27 - 6 = 21 \\ ⇢ 21 = 21 \\ ⇢ L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer: 40 coins. Doesn't your profile say college?

Answer:

The probability of rolling a 5 is 1/6.

Step-by-step explanation:

There is only one 5 out of the 6 sides, therefor you can only get it once, so the probability of rolling a 5 would be 1/6.

Answer:

The solution is given below

Step-by-step explanation:

The computation is shown below:

a. The profit margin is

= Operating income ÷ total sales

= $2,828,980 ÷ $23,380,000

= 12.1%

b. The investment turnover is

= Total sales ÷ total assets

= $23,380,000 ÷ $10,000,000

= 2.34

c. The return on investment is

= Profit margin × investment turnover

= 12.1% × 2.34

= 28.29%

d. The residual income is

= Operating income - (minimum rate of return × assets)

= $2,828,980 - (20% of $10,000,000)

= $828,980