i once met six siblings whose ages are 6 consecutive whole numbers. i asked each of them the question how old is your oldest sibling. which of the following could not be the sum of their answers.
A. 95
B. 125
C. 167
D. 205
E. 233

Answer:

Charlotte's mix has a bluer shade of purple

Step-by-step explanation:

Since we are asked whose paint is a bluer shade it would be easier to express the ratios of the paint mix as blue:red

Charlotte: 1 cup red for every 2 cups blue ==> 2 cups blue for every 1 cup red

This can be expressed as the ratio
\(\dfrac{ 2 \;blue}{1\;red} = \dfrac{2}{1} = 2\)

\(-------------------\)

Pablo : 2 cups red for every 3 cups blue ==> 3 cups blue for every 2 cups red

The ratio of blue to red
= \(\dfrac{3 \;blue}{2\;red} = \dfrac{3}{2} = 1\dfrac{1}{2} \;\; (or\; 1.5)\)

Since
\(2 > 1\dfrac{1}{2} \;\;\;(or\; 2 > 1.5)\)  

Charlotte's mix has a bluer shade of purple

Answer:

A. 14z - 28

Step-by-step explanation:

simplify z² - 3z

a. z(z - 3)

the denominator on the right has z(z - 3). but it is also multiplied by (z - 2)

this means the numerator must also be multiplied by (z - 2)

14 x (z - 2) = 14z - 28

hope this helps :)

Answer:

13.6 m²

Step-by-step explanation:

The area of the triangle is equal to

\( \frac{3.2 \times 0.5}{2} = 0.8 \: {m}^{2} \)

Therefore, the area of the figure is equal to

\( (4 \times 3.2) + 0.8 = 12.8 + 0.8 = 13.6 \: {m}^{2} \)

If we had a choice of having our investment compounded annually, semi-annually, or monthly, we choose semi-annually because the interest rate is greater in semi-annually.

In this given question we have to take choice of having your investment compounded annually, semi-annually, or monthly.

We also have to give the reason to chose any of them choice.

The effective annual interest rates of each assuming the annual rate is \(10\%\).

Firstly we know about annually, semi-annually, or monthly investment.

Annually investment means  we get interest in our amount in the annual basis according to rate.

Semi annually means we get interest two time in a year at a half annual rate. In that case we divide annual rate in two part.

Monthly investment means we get interest in our investment twelve time in a year. In this condition we divide annual rate in twelve parts.

Now to choose the investment compounded annually, semi-annually, or monthly we illustrate the rate according to amount.

Since principal amount is same in every condition and rate \(r=10\%\).

The formula of compound amount

\(A=P(1+\frac{r}{100})^n\)

where \(A=\) Amount

\(P=\) Principal amount

\(r=\) rate of interest

\(n=\) time

Condition 1: Considering that we invest on the annually basis for one year. So \(r=10\%\) and \(n=1\).

Putting the value in formula

\(A=P(1+\frac{10}{100})^1\)

\(A=P(1+\frac{1}{10})^1\)

\(A=P(1\times\frac{10}{10}+\frac{1}{10})^1\)

\(A=P(\frac{10}{10}+\frac{1}{10})^1\)

\(A=P(\frac{10+1}{10})^1\)

\(A=P(\frac{11}{10})^1\)

\(A=P(1.1)^1\)

\(A=1.1P\)

Condition 2: Considering that we invest on the semi-annually basis for one year. So \(r=\frac{10\%}{2}=5\%\) and \(n=2\).

Putting the value in formula

\(A=P(1+\frac{5}{100})^2\)

\(A=P(1\times\frac{100}{100}+\frac{5}{100})^2\)

\(A=P(\frac{100}{100}+\frac{5}{100})^2\)

\(A=P(\frac{100+5}{100})^2\)

\(A=P(\frac{105}{100})^2\)

\(A=P(1.05)^2\)

\(A=1.103P\)

Condition 3: Considering that we invest on the monthly basis for one year. So \(r=\frac{10}{12}\%\) and \(n=12\).

Putting the value in formula

\(A=P(1+\frac{10}{12\times100})^{12}\)

\(A=P(1+\frac{1}{12\times10})^{12}\)

\(A=P(1+\frac{1}{120})^{12}\)

\(A=P(1\times\frac{120}{120}+\frac{1}{120})^{12}\)

\(A=P(\frac{120}{120}+\frac{1}{120})^{12}\)

\(A=P(\frac{120+1}{120})^{12}\)

\(A=P(\frac{121}{120})^{12}\)

\(A=P(1.008)^{12}\)

\(A=1.1003P\)

Now if we compare the amount in every condition we get that the amount of condition 2 is greater than all other condition.

So, if we had a choice of having your investment compounded annually, semi-annually, or monthly, we choose semi-annually because the interest rate is greater in semi-annually.

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Answer:

11 and -4

Step-by-step explanation:

Let the required two numbers be x and y

If the sum of two numbers is 7, then

x + y = 7 .. 1

If the difference of their squares is 105, then;

x² - y² = 105 ...2

From 1;

x = 7 -  y... 3

Substitute 3 into 2;

(7-y)² - y² = 105

Expand

49-14y+y² -y² = 105

49-14y = 105

-14y = 105 - 49

-14y = 56

y = -56/14

y = -4

Substitute y = -4 into 3

x = 7 -  y... 3

x = 7 - (-4)

x = 7+4

x = 11

Hence the numbers are 11 and -4

Answer:

17,420

Step-by-step explanation:

It the same on the other side so you would have to multiply 134 and 130 together which u get 17,420 and when u plug it in and divide it u get 130 degrees

Answer: 30 cars left

Step-by-step explanation:

if from 33 cars we subtract 3, we get 30 cars left.

33 - 3 = 30 ...answer

hope that helps...

The number 842 is the number whose digit 4 is ten times larger than in the number 384

To solve the problem, we need to find a number in which the digit 4 is ten times larger than in the number 384.

In the number 384, the digit 4 is in the ones place, which means that its value is 4.

To find a number in which the digit 4 is ten times larger, we need to find a number in which the digit 4 is in the tens place and its value is 10 times larger than 4, which is 40.

The only answer option that fits this description is 842. In this number, the digit 4 is in the tens place and its value is 40, which is ten times larger than its value in the number 384.

Therefore, the correct answer is 842.

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a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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The triple integral using the spherical coordinates is 16 π .

Given :

Use spherical coordinates. Evaluate( x^2 + y^2 + z^2 )^1/2 dv, where B is the ball with center the origin and radius 3.

we know that ,

= ∫∫∫ ( x^2 + y^2 + z^2 )^1/2 dv

= ∫∫∫ x . x^2 .sin Φ dΦ dθ dx

where lower limits and upper limits are ( 0 , 2 ) , ( 0 , 2 π ) , ( 0 , π ) .

= ∫ x^3 . dx ∫ dθ ∫ sin Φ dΦ

= 2^4 / 4 * 2 π * 2

= 4 * 2 π * 2

= 8 π * 2

= 16 π

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0.48

Step-by-step explanation:

to increase an amount by 48%

you divide 48 with 100 to find the multiplier

which is 0.48

multiply 0.48 to an number to find 48%

Nate has a deductible of $1,000, which means he is responsible for paying that amount out of pocket before his insurance coverage kicks in. The cost of repairing his car is $7,000, which exceeds his deductible.

However, Nate's collision coverage limit is $5,000, which is the maximum amount his insurance will cover for repairs.

Since the cost of repairs exceeds Nate's coverage limit, he will have to pay the difference between the coverage limit and the actual repair cost.

In this case, Nate's out-of-pocket expenses would be $7,000 (repair cost) - $5,000 (coverage limit) = $2,000.

Therefore, Nate will have to pay a total of $2,000 out of pocket for this claim, which includes his $1,000 deductible and the additional $1,000 that exceeds his coverage limit.

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Answer:

A.  4

Step-by-step explanation:

Given inequality:

\(x+9 < 4x\)

Rearrange the inequality to isolate x.

Subtract x from both sides of the inequality:

\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)

Divide both sides of the inequality by 3:

\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)

So the values of x that make the inequality true are:

Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.

To check this, substitute x = 4 into the inequality:

\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)

As 13 is less than 16, the inequality is true when x = 4.

$ 573.3

Explanation

to find the total, we need to find the numbers of miles by the cost per mile

so

Step 1

find the total miles:

to do that, do the product of the number of days per year, and the rate of miles per day,l this way:

replace

Step 2

now, replace the total miles value in the expesssion:

therefore, the answer is

$ 573.3

I hope this helps you

Answer:

the answer is 3.6 so I say yes It reasonable it's about there

Answer: Option (2)

Step-by-step explanation:

\(|3k-2| > 7\) means \(3k-2 < -7\) or \(3k-2 > 7\).

Solving each of these cases gives \(k < -\frac{5}{3}\) or \(k > 3\).

So, the answer is Option (2).

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

5 faces

Step-by-step explanation:

V – E + F = 2

We know that V = 5 and E = 8

Substitute these into the equation

5 -8+F = 2

-3+F =2

Add 3 to each side

-3+F+3 = 2+3

F=5

Answer:

d

Step-by-step explanation:

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Temp. 174 176 177 178 178 179 180 181

Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74

Temp. 184 184 184 184 184 185 185 186

Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94

Temp. 186 186 186 188 188 189 190 192

Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16

A)

Using the online linear regression calculator, the lie of best fit which models the data above is :

ŷ = 0.09386X - 15.55523

Where ;

X = independent variable

ŷ = predicted or dependent variable

- 15.55523 = intercept

0.09386 = gradient / slope

B)

Point estimate when tank temperature is 186

ŷ = 0.09386(186) - 15.55523

ŷ = 17.45796 - 15.55523

ŷ = 1.90273

C)

Residual error (y - ŷ), ŷ = 1.90273 when x = 186

(0.94 - 1.90273) = −0.96273

(1.85 - 1.90273) = −0.05273

(2.02 - 1.90273) = 0.11727

(2.64 - 1.90273) = 0.73727

D)

To determine the proportion of observed variation in efficiency ratio, we find the Coefficient of determination R^2, which can be found using the online Coefficient of determination calculator : the r^2 value obtained is 0.4433.

3

x

2

−

3

x

−

60

=

0

Explanation:

A quadratic equation whose roots are

α

and

β

and leading coefficient is

a

is

a

(

x

−

α

)

(

x

−

β

)

=

0

Hence, the quadratic equation whose roots are

5

and

−

4

and leading coefficient is

3

is

3

(

x

−

5

)

(

x

−

(

−

4

)

)

=

0

or

3

(

x

−

5

)

(

x

+

4

)

=

0

or

3

(

x

2

−

5

x

+

4

x

−

20

)

=

0

or

3

(

x

2

−

x

−

20

)

=

0

or

3

x

2

−

3

x

−

60

=

0

Answer:

5x^2+5x-100=0

Step-by-step explanation:

5(x+5)(x-4)=0

(x+5)(x-4)= 0

x= -5

x= 4

Answer:

(4,6)

Step-by-step explanation:

The solution to a system on a graph will be where the lines intersect. The individual graphs have different intercepts and slopes, but they both cross at about (4,6). This point is not an exact intersection, but the question does ask for an approximate solution. This means that the answer should be as close as possible using estimation.

The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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Thus, the mass is increasing at a rate of 0.15625 kg per hour, and the mass on this day is 4.5 kg.

Let's consider a general formula for finding the rate of increase:Rate of increase = k x original valueHere, k is a constant that represents the rate of increase per unit of time, and the original value is the initial value of the quantity being measured.

For example, if the original value is 3.2 kg and the rate of increase is 0.5 kg per hour, we can use the formula to calculate the mass at any time t as follows: Mass at

time t = 3.2 + (0.5 x t)

where t is the time elapsed in hours.In order to find k, we need to know the rate of increase and the original value.

Once we have these values, we can rearrange the formula to solve for

k:k = rate of increase / original value

For example, if the mass is increasing at a rate of 0.5 kg per hour and the original value is 3.2 kg, we can calculate k as follows:

k = 0.5 / 3.2k = 0.15625

To find the rate of increase on a specific day, we need to know how much time has elapsed since the original value was measured. Once we have this information, we can plug it into the formula we derived earlier:Mass at time t = 3.2 + (k x t)For example, if 8 hours have elapsed since the original value was measured, we can calculate the mass on that day as follows:

Mass at time t = 3.2 + (0.15625 x 8)

Mass at time t = 4.5 kg

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Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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Answer:

The rational expression is not written correctly, so i actually can not know the actual expression.

I will try to answer this in a general way, so you can try to apply it to the actual problem.

Now, suppose that our rational expression is:

\(\frac{-12d}{-110d + 5}\)

The numerator is -12d, this part does not have any problem at any value of d, so we don't have any undefined value here.

The denominator is: -110d + 5

Now, a rational expression is undefined if the denominator is eqeual to zero (we can not divide by zero)

So an undefined value will be when:

-110d + 5 = 0

d = -5/110

This means that we can not have the value d = -5/110, because this makes the denominator equal to zero.

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

We have,

To convert 6 kiloliters (kL) to fluid ounces (fl oz), we need to use the conversion factor between these two units.

The conversion factor states that 1 kiloliter is equal to 33814.0227 fluid ounces.

This means that for every kiloliter, there are 33814.0227 fluid ounces.

To convert 6 kiloliters to fluid ounces, we multiply the given value (6 kL) by the conversion factor (33814.0227 fl oz/kL).

= 6 kL x 33814.0227 fl oz/kL

= 202884.1362 fl oz

Therefore,

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

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