a survey was taken of children between the ages 7 and 12. let A be the event that the person rides the bus to school, and let B be the event that the person has 3 or more siblings.

Answer:

unlikely

Step-by-step explanation:

there is less that a 50 % chance

Answer:

unlikely is the answer

Answer:

(d)              

Step-by-step explanation:

Bond's par value = $500

market value of the bond = 88.754% * 500

                                           = 443.77

Commission rate charged by broker A = 3.1%

Commission of broker A = [tex]\frac{3.1}{100}[/tex]*443.77

                                        = $13.75687

Commission of broker B = $24

Difference between the commission of broker A and broker B = 24-13.756

                                                                                                      = $10.24

Hence, (d) Broker A's commission will be $10.24 less then Broker B's.

Answer:He should take the option one of sales commission of 3.1% on

each bond. If he takes the 2nd option, he is required to pay 24$ per

bond. But if he takes the ist option, he is required to pay 15.5$ per bond.

88.754 is the market rate. Total investment is of 500$. Multiply the commission

rate with the amount and you get 15.5 $. There is a difference of 8.5 dollars

between the two options.

The answer is D

Answer:

Mean: 57; Range: 19

Step-by-step explanation:

Answer:

9 + 2n =

Step-by-step explanation:

9 + 2n =

Answer:

It would be 9+2n.

Step-by-step explanation:

Sinve you have not given us an equation, twice a number can also be reresented as 2n. Since 9 is the constant, you can say 9+2n.

5±x[tex]\frac{-3}{√8}[/tex] is an irrational number because there's a radical in the denominator. It wouldn't result in a whole number. It would have to be rationalized or smth

y = x + 4     (*)

x - y = -4    (**)

Substitute (*) to (**):

x - (x + 4) = - 4

x - x - 4 = - 4

- 4 = - 4     TRUE

x ∈ R

y = x + 4

Answer:

x= -8      y= -4

Step-by-step explanation:

SOLVING FOR X

y=x+4

x-y=-4

----------------------

x-x+4= -4

   -4     -4

---------------------

x-x= -8

x= -8

SOLVING FOR Y

plug in the x in any equation

y=(-8)+4

y= -8+4

y= -4

m = 3 is the slope of the given line; also its the slope of anything parallel to the given line

(x1,y1) = (1,3) is the given point the parallel line goes through

y - y1 = m(x-x1) .... point slope form

y - 3 = 3(x - 1) .... plug in the given values; solve for y

y - 3 = 3x - 3

y - 3+3 = 3x - 3 + 3

y = 3x + 0

y = 3x

Final Answer: y = 3x

side note: if you plugged in x = 1 it leads to y = 3 which confirms that (x,y) = (1,3) is on this parallel line.

Answer:

Average rate of change = 2

Step-by-step explanation:

We need to find the average rate of change of f(x) over the interval [-4,-1], so first we need to find the end points at x=-4 and x=-1.

From graph we see that y=-3 when x=-4, So the point is (-4,-3)

From graph we see that y=3 when x=-1, So the point is (-1,3)

Now we can plug these points into average rate of change formula:

[tex]Average\ rate=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]

where (a,f(a)) and (b,f(b)) are the given points.

[tex]Average\ rate=\frac{-3-3}{-4-\left(-1\right)}[/tex]

[tex]Average\ rate=\frac{-3-3}{-4+1}[/tex]

[tex]Average\ rate=\frac{-6}{-3}[/tex]

[tex]Average\ rate=2[/tex]

Hence final answer is 2.

Answer:

Cost of 5 camera cases is $85.

Step-by-step explanation:

First we need to determine what type of function we're dealing with, is it linear, quadratic or exponential?  We can determine this by calculating the first difference.

We can translate the number of cameras to correspond to the x axis and cost to the y axis.  By doing this we can come up with the ordered pairs of (2,25), (4,59),(10,305).  Let's get the first two ordered pairs and calculate the first difference:

[tex]\frac{59-25}{4-2}=17[/tex]

And now the second and third value:

[tex]\frac{305-59}{10-4}=41[/tex]

Notice how these values do not match, this means that this function is not increasing at a constant rate meaning that this function is not linear.  Now let's calculate the second difference:

[tex]\frac{41-17}{10-2}=3[/tex]

This means our function is quadratic with a=3.  Remember that generally speaking a quadratic function is such that:

[tex]y=ax^2+bx+c[/tex]

Where a,b,c are coefficients and in this case a=3.  Now, let's solve for b and c values by using the coordinates given.  Let's use the coordinates (2,25) where x=2 and y=25 and so:

[tex]f(x)=ax^2+bx+c\\\\25=3(2)^2+b(2)+c\\25=3(4)+2b+c\\25=12+2b+c\\13=2b+c\\\\b=\frac{13-c}{2}[/tex]

Now let's solve for "c" by using different coordinates (4,59) where x=4 and y=59 and also use the "b" value that we calculated above and so:

[tex]f(x)=ax^2+bx+c\\\\59=3(4)^2+(\frac{13-c}{2})(4)+c\\59=48+\frac{52-4c}{2}+c\\11=\frac{52-4c+2c}{2}\\11=26-2c+c\\-15=-c\\\\c=15[/tex]

Now that we know the value of "c" we can use the equation for b to solve for b and so:

[tex]b=\frac{13-c}{2}=\frac{13-15}{2}\\\\b=-1[/tex]

So this means in the quadratic equation a=3, b=-1 and c=15 therefore by using the general equation of a quadratic function we obtain or final equation:

[tex]f(x)=ax^2+bx+c\\\\f(x)=3x^2-x+15[/tex]

Since we want to find the total cost of producing 5 camera cases x=5 and so:

[tex]f(x)=3x^2-x+15\\\\f(5)=3(5)^2-(5)+15\\f(5)=75-5+15\\\\f(5)=85[/tex]

And so the cost of 5 camera cases is $85.

Answer:

B. c <_ 250

Step-by-step explanation:

NO MORE THAN 250 =  AT MOST 250 = less or greater than.

Answer:

[tex]a \geq \frac{1}{\sqrt{2} -1}[/tex]

Step-by-step explanation:

This equation is more intimidating than the problem you have to solve.

You know that the sine of everything is always between -1 and +1. So for the entire expression to be >= 0, the a*tan(pi/8) bit has to be 1 at least. Given this, we can forget about the sin(...) term of the equation for the remainder of solving it.

You already figured out that tan(pi/8) is sqrt(2)-1.

So what we're saying is a * (sqrt(2) - 1) has to be 1 at least.

If we solve a(sqrt(2)-1) >= 1 for a we get:

a = 1/(sqrt(2)-1)

[tex]c)\\\tan\left(\dfrac{\pi}{8}\right)=\tan\left(\pi-\dfrac{7\pi}{8}\right)=\tan\left(-\dfrac{7\pi}{8}\right)=-\tan\left(\dfrac{7\pi}{8}\right)\\\\=-(1-\sqrt2)=\sqrt2-1\\\\y=\sin(2x-1)+a\tan\dfrac{\pi}{8}\\\\\text{We know}\ -1\leq\sin(2x-1)\leq1.\\\\y\geq0\ \text{therefore}\ a\tan\dfrac{\pi}{8}\geq1\\\\\text{We have to move the graph at least one unit up}\\\\a(\sqrt2-1)\geq1\qquad\text{divide both sides by}\ (\sqrt2-1)>0\\\\a\geq\dfrac{1}{\sqrt2-1}\cdot\dfrac{\sqrt2+1}{\sqrt2+1}\\\\a\geq\dfrac{\sqrt2+1}{(\sqrt2)^2-1^2}[/tex]

[tex]a\geq\dfrac{\sqrt2+1}{2-1}\\\\a\geq\dfrac{\sqrt2+1}{1}\\\\a\geq\sqrt2+1\\\\Answer:\ \boxed{a=\sqrt2+1}[/tex]

Answer:

[tex] \dfrac{5^7}{2} = \dfrac{78125}{2} [/tex]

Step-by-step explanation:

[tex] \left( \dfrac{4}{5} \right)^2 \times 5^4 \times \left( \dfrac{2}{5} \right)^{-2} \div \left( \dfrac{5}{2} \right)^{-3} = [/tex]

[tex] = \dfrac{4^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]

[tex] = \dfrac{(2^2)^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]

[tex] = \dfrac{2^4}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]

[tex] = 2^{4 - 2 - 3} \times 5^{- 2 + 4 + 2 + 3} [/tex]

[tex] = 2^{-1} \times 5^{7} [/tex]

[tex] = \dfrac{5^7}{2} [/tex]

[tex] = \dfrac{78125}{2} [/tex]

Answer:

The rate of change per year equals: (125.000-180000)/ 5= -11000

That means that the business loses 11000 $ each year

Step-by-step explanation:

[tex]\text{Use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\27x^3-125=3^3x^3-5^3=(3x)^3-5^3=(3x-5)[(3x)^2+(3x)(5)+5^2]\\\\=\boxed{(3x-5)(9x^2+15x+25)}[/tex]

Answer:

60

Step-by-step explanation:

anwser: B.

see explanation

Answer:

V = [tex]\frac{4}{3} \pi r^3[/tex]

Step-by-step explanation:

Final answer:

To find the volume of a sphere, use the formula: Volume = 4/3 (pi) (radius)^3

Explanation:

The volume of a sphere can be calculated using the formula:

Volume = 4/3 (pi) (radius)^3

To find the volume, you need to know the radius of the sphere. Plug in the value for the radius and then evaluate the expression using the order of operations. Finally, multiply the result by 4/3 and pi to find the volume of the sphere.

Answer:

Your answer would be 2.35. All you have to do id divided how many meters you have by 1000. Hope it Helped

Step-by-step explanation:

km=m times 1000

Answer:

B. 2x^2 − x

Step-by-step explanation:

3x^2 + x − x^2 − 2x

We need to combine like terms

3x^2 -x^2+ x − 2x

2x^2 -x

The expression 3x² + x - x² - 2x simplifies to 2x² - x, which is Choice B.

To simplify the expression 3x² + x - x² - 2x, you can combine like terms. The equation has two terms involving x squared (x²) and two terms involving x to the first power.

Combine the x² terms: 3x² - x² = 2x².

Next, combine the x terms: x - 2x = -x.

Putting them together, the simplified expression is 2x² - x.

Therefore, the answer is Choice B: 2x² - x. This step-by-step process demonstrates the importance of combining like terms and simplifying expressions to arrive at the correct solution.

Answer:

A) 25.872

Step-by-step explanation:

A tip when multiplying numbers that are decimals, make the numbers whole numbers without decimals:

862.4 * 10 = 8624

0.03 * 100 = 3

8624 * 3 = 25,872

Then divide by the amount you multiplied the numbers by:

25,872 ÷(100 * 10) = 25.872

So your answer is A) 25.872

Answer:

25.872

Step-by-step explanation:

you just line up the desimals and do your regular multipication.

Answer:

144 is the answer

Answer:

144

Step-by-step explanation:

Steps:

a times b = 3 times 4. That equals 12.

Then you put 12^2. 12 times 12 equals 144.

Answer:

It will take Chris 13 weeks of allowance to save enough to buy the computer.

Step-by-step explanation:

Chris needs $858 to buy a computer.

She has already saved $575.

She gets $15 an hour for babysitting and will babysit 12 hours in the next month, then she will get for babysitting:

($15/hour)(12 hours)=$180

Then, Chris will need:

A=$858-$575-$180→A=$103

She can save &8 a week form her allowance, then she will need:

Number of weeks: n = $103 / ($8/week) → n=12.875 weeks

Rounding:

n=13 weeks

Chris will need 13 weeks of saving her allowance to have enough money to buy the computer.

Chris needs to save a total of $858 for a computer and has already saved $575.

To determine how many weeks she will need to save her allowance to purchase the computer, we must first calculate the additional amount she will earn from babysitting.

Chris earns $15 an hour for babysitting and will babysit for 12 hours in the next month, earning her an additional 15 x 12 = $180.

Adding this to her current savings of $575 gives us a total of $575 + $180 = $755.

The remaining amount needed to buy the computer is $858 - $755 = $103.

Since Chris saves $8 per week from her allowance, we divide the remaining amount by her weekly savings to find the number of weeks required: $103 / $8 = 12.875 weeks.

Since partial weeks of savings are not possible, we round up to the nearest whole number, which means Chris will need 13 weeks to save enough from her allowance to buy the computer.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (7, 6) and (-7, -6). Substitute:

[tex]m=\dfrac{-6-6}{-7-7}=\dfrac{-12}{-14}=\dfrac{12}{14}=\dfrac{6}{7}[/tex]

Final answer:

The slope of the line passing through the points (7, 6) and (-7, -6) is 6/7, which is not reflected in the provided options, hinting at an error in the question or the answer choices.

Explanation:

To find the slope of the line passing through the points (7, 6) and (-7, -6), we use the slope formula, which is:

m = (y2 - y1) / (x2 - x1)

Substituting the given points into the formula gives us:

m = (-6 - 6) / (-7 - 7)

Which simplifies to:

m = (-12) / (-14)

And further simplifies to:

m = 6/7

However, this result is not among the provided options, which suggests there may have been an error in the question or in the options given. The correct slope calculated from the provided points is 6/7, not any of the options presented (A, B, C, D).

Answer:

7 years

Step-by-step explanation:

Let x  be number of years the populations be equal

City A's population of 1115000 is decreasing at a rate of 15000 per year.

The population is decreasing at a constant rate so we use equation

y= mx + b

where m is the slope(rate), b is the initial population

m= -15000 (decreasing) , b= 1115000

y= -15000 x + 1115000

City B's population of 698000 is increasing at a rate of 45000 per year.

m= 45000 (increasing) , b= 698000

y= 45000 x + 698000

Now we set the equations equal and solve for x

45000 x + 698000 = -15000 x + 1115000

Add 15000 on both sides

60000 x + 698000 = 1115000

Subtract 689000 on both sides

60000 x = 417000

Divide by 60000 on both sides

x= 6.95

So after 7 years the population will be equal.

Final answer:

To find the number of years until the populations are equal, set up an equation based on the population change per year for both cities. Solve for the variable representing years, and round to the nearest whole number. The populations of City A and City B will be equal in approximately 7 years.

Explanation:

To solve for the number of years until the populations of City A and City B are equal, let's set up an equation. Begin with the populations at the starting point: City A has 1,115,000 residents and is losing 15,000 per year, while City B has 698,000 residents and is gaining 45,000 per year. Let x represent the number of years after which the populations will be equal.

For City A, the population after x years will be 1,115,000 - 15,000x. For City B, the population after x years will be 698,000 + 45,000x. Therefore, we can set up the following equation to find when they are equal:

1,115,000 - 15,000x = 698,000 + 45,000x

To solve for x, combine like terms and get all the x terms on one side:

1,115,000 - 698,000 = 45,000x + 15,000x

417,000 = 60,000x

Divide both sides by 60,000 to solve for x:

x = 417,000 / 60,000

x ≈ 6.95

Since we round to the nearest whole number, the populations will be equal in approximately 7 years.

Answer:

We have 45 dogs when we have 30 cats

Step-by-step explanation:

If the ratio of dogs to cats is 3:2

We want to get to 30 cats so we need to multiply by 15  (2*15 =30)

What we do on one side we do on the other

3*15 : 2 * 15

45 :30

We have 45 dogs when we have 30 cats

Answer:

36 fruit tarts

Step-by-step explanation:

90 x .40 = 36

Answer: Choice A)

y + 3 = (2/3)(x - 5)

====================================================

Explanation:

Point slope form is

y - y1 = m(x - x1)

m = 2/3 is the given slope

(x1,y1) = (5,-3) is the point the line goes through

So we have

y - y1 = m(x - x1)

y - (-3) = (2/3)(x - 5)

y + 3 = (2/3)(x - 5)

Answer:

It would be 1 and 2/5 or 1.4 per minute.

Step-by-step explanation:

Answer:

x=22

Step-by-step explanation:

1408/64

Answer:

22

Step-by-step explanation:

1,408/64

Answer:

true

Step-by-step explanation:

The angle bisector and perpendicular bisector of a triangle are distinct concepts.

False: The angle bisector and perpendicular bisector of a triangle are distinct concepts.

The angle bisector of a triangle divides the opposite angle into two equal angles, while the perpendicular bisector of a segment is a line perpendicular to a segment at its midpoint.

It is possible for the angle bisector of a triangle and the perpendicular bisector of different segments within the triangle to coincide, but in general, they are not the same.