Richard and Teo have a combined age of 24. Richard is 9 years older than twice​ Teo's age. How old are Richard and​ Teo?

Answer:

x ≤ 435

Step-by-step explanation:

Given is the following condition.

The sum of a number and 15 is less than and equal to 450.

So, if the number is x, then we have  

x + 15 ≤ 450

⇒ x + 15 - 15 ≤ 450 - 15

⇒ x ≤ 435

Therefore, the solutions of the number are either 435 or less than 435 up to negative infinity. ( Answer )

Answer:

Their mass at the start was 400 kg.

Step-by-step explanation:

Given:

The tyres on a car during a grand prix race are reduced in mass by 3%. Their mass is 388 kg at the end of the race.

Now, to find the mass at the start.

Let the mass at the start be [tex]x[/tex].

According to question:

[tex]x - 3 \%ofx= 388[/tex]

⇒[tex]x-\frac{3}{100}\times x = 388[/tex]

⇒[tex]x-0.03x =388[/tex]

⇒[tex]0.97x=388[/tex]

Dividing both sides by 0.97 we get:

⇒[tex]x=400[/tex]

Therefore, their mass at the start was 400 kg.

To find the original mass of the tyres before the 3% decrease,  we make a simple percentage calculation. By setting up the equation 97/100 * x = 388, we find that the original mass of the tyres was 400 kg.

The question posted is a mathematics problem related to understanding percentages and its application to real-life situations such as a Grand Prix race.

Given that the tyres at the end of the race have a mass of 388 kg, which is 97% of their original mass (since they lost 3%), we can find their original mass by setting up a simple percentage equation. We denote the original mass as 'x' and set up the equation: 97/100 * x = 388. To solve for 'x', we divide both sides of the equation by 97/100, which is equivalent to multiplying by its reciprocal, 100/97.

The solution to the problem is then calculated as following: x = 388 * (100/97) = 400 kg.

Hence, the original mass of the tyres was 400 kg.

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Answer: The y-intercept represents what is the value of y when x=0.

Answer:

8

Step-by-step explanation:

AD is half of AB

1/2 * 16 = 8

Answer:

8

Step-by-step explanation:

CD is an altitude. It is perpendicular to AB, and it splits AB in half. If AB=16, and CD splits AB in half, to find AD you would do this:

1/2AB

1/2·16=8

8 is your answer.

Yu can also see that AD and DB are congruent, so their values must be the same.

~Stay golden~:)

Answer:

Your answer would be 33.7619047619

Step-by-step explanation:

Answer:

The average per cost is $19.25.

Step-by-step explanation:

Given:

The fee paid by cat owner = $269.50. Total visits he made that year 14.

Now, to find the average per cost.

So, to get the average per cost we divide the total fee by total visits:  

Average per cost = Total fee ÷  Total visits

                             =  [tex]269.50\div 14[/tex]

                             =  [tex]19.25[/tex]

Therefore, average per cost is $19.25.

Answer:

The Average cost of per visit to the vet  = $ 19.25

Step-by-step explanation:

Here, the total visits to the vet in a  year = 14

Also, the total amount paid to the vet in a year = $269.50

Now, Let us assume the average cost per vet visit = m

So,[tex]\textrm{Average cost of per visit}  = \frac{\textrm{Total amount paid in n visits}}{\textrm{ n visits}}\\ \implies  m = \frac{269.50}{14}  = 19.25[/tex]

or,  m = $ 19.25

Hence, the Average cost of per visit to the vet  = $ 19.25

Answer:

there are 306 in total

Step-by-step explanation:

Answer:

2750

Step-by-step explanation:

As there are 11 players on the field, each averaging 250 pounds, this means that we can add 250 11 times, 1 for each player. Another way to say this would be to multiply 250 and 11, as we are adding 250 11 times. Our answer is then 250*11 = 2750.

Answer: 1/10

Step-by-step explanation:

There is  1 yellow marble out of the 10 marbles

Answer:

Step-by-step explanation:

1/9

Answer:

35

Step-by-step explanation:

Answer:

the quotient is 4000 and the square is a perfect square

Step-by-step explanation:

120/0.03=4000

40 time 40 is 1600 so its perfectly square.

hope this helps

Answer: the answer is 40

Answer: 10.22

Step-by-step explanation:

Standard Deviation = square root of variance 104.44 = 10.22

Final answer:

To find the standard deviation from the variance of 104.4, you take the square root of the variance, resulting in a standard deviation of approximately 10.22.

Explanation:

If the variance for a data set is 104.4, to find the standard deviation, you take the square root of the variance. The formula to calculate the standard deviation (s) from the variance (σ²) is:

s = √σ²

Applying this formula, the standard deviation would be s = √104.4. Using a calculator, you would get:

s ≈ 10.22

Thus, the standard deviation for the data set with a variance of 104.4 is approximately 10.22.

Answer:

C proportional

Step-by-step explanation:

The answer is c because

proportional means equal

and as u can see in the photo you have represented a proportional relationship because ther line is going in and equal line across the axis and it is increasing at a proportional rate!

and there you go!

Answer:

For [tex]\left | x \right |[/tex] we will have positive values only.

[tex]\left | -2.7 |\right =2.7[/tex]

[tex]\left | -9 |\right =9[/tex]

Rest are positive so will give positive values out of the modulus function.

Step-by-step explanation:

The absolute value of any number is its positive value only.

As for example [tex](-2.7)[/tex] and [tex](2.7)[/tex] both are having equal distance from [tex]0[/tex] in a number line, one on the left other on the right side of the number line but are equidistant from [tex]0[/tex].

So absolute value of a number is its distance on number line from reference point [tex]0[/tex].

One by one we will work with all of our question.

[tex]\left | 10 |\right =10[/tex]

[tex]\left | 0.3 |\right =0.3[/tex]

[tex]\left | 0 |\right =0[/tex]

[tex]\left | -2.7 |\right =2.7[/tex]

[tex]\left | -9 |\right =9[/tex]

So we have to take the positive number out of the modulus function that is also called absolute value.

Answer: -1, 0, and 1

Step-by-step explanation: -1 is an integer and all integers are rational numbers so -1 is rational.

0 is also an integer and all integers are rational numbers. Therefore, 0 is considered a rational number.

1 is a natural number and all natural numbers are rational numbers. Therefore, 1 would be a rational number.

Paying an extra $100 each month on a $60,000 loan with an 8% APR over 25 years will reduce the loan term and total interest paid. To calculate the effect, compute the total cost of the loan with and without the extra payments and subtract these two sums.

The subject at hand pertains to understanding the impact of additional payments on a loan, which falls under the domain of financial mathematics. Let's dissect the impact of paying an extra $100 per month on a $60,000 loan with an 8% annual interest rate over 25 years.

Firstly, we need to calculate the monthly payment for a 25-year loan of $60,000 at 8% interest. This can be calculated by using a loan calculator or the loan payment formula. Then, calculate the total cost of the loan by multiplying this monthly payment by the number of months in the loan term (25 years x 12 months).

You then do a similar calculation, but this time add an extra $100 to the monthly payment. The extra repayment will reduce the loan term and decrease the total interest paid. To see the effect, compare the total cost of the loan with and without the extra $100.

Therefore, the difference between these two sums will give you the saved amount due to the additional $100 monthly payment. This saving is the effect of making additional payments on the loan.

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Making additional monthly payments can shorten the loan term and save money on interest payments.

To calculate the effect of making additional monthly payments on the cost of the loan, we can compare the total interest paid and the duration of the loan with and without the additional payments. Without any additional payments, the monthly payment for a $60,000 loan with an 8% APR and a 25-year term would be $459.18. With an additional $100 each month, the monthly payment would increase to $559.18.

By making the additional $100 payments, the loan would be paid off faster, reducing the term from 25 years to approximately 17 years and saving the borrower 8 years of monthly payments. Additionally, the total interest paid over the course of the loan would also be significantly reduced compared to just paying the required monthly payments.

In summary, making extra monthly payments of $100 can shorten the loan term and save the borrower money on interest payments.

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Answer:

46.125 square feet or [tex]46\dfrac{1}{8}[/tex] sq. feet.

Step-by-step explanation:

The rug is shaped like a parallelogram with a base of [tex]\frac{41}{2} = 20.5[/tex] feet. and a height of [tex]2\dfrac{1}{4} = 2.25[/tex] feet.

Now, the area of a parallelogram is given by the product of one side as the base and the perpendicular distance of that side from the opposite parallel side as height.

Now, the area of the given parallelogram is (20.5 × 2.25) = 46.125 square feet. (Answer)

Answer:

Option 1. Lynn, only

Step-by-step explanation:

The correct question is

Listen Lynn, Jude, and Anne were given the function f(x)=-2x^2+32, and they were asked to find f(3). Lynn's answer was 14, Jude's answer was 4, and Anne's answer was (+/-)4. Who is correct?

1. Lynn, only

2. Jude, only

3. Anne, only

4. Both Lynn and Jude

we have

[tex]f(x)=-2x^{2} +32[/tex]

This is a vertical parabola open downward (leading coefficient is negative)

The vertex is a maximum

we know that

f(3) means, the value of f(x) when the value of x is equal to 3

so

For x=3

substitute in the quadratic equation and solve for f(x)

[tex]f(3)=-2(3^{2}) +32[/tex]

[tex]f(3)=-18 +32[/tex]

[tex]f(3)=14[/tex]

therefore

Lynn's answer is correct

To determine the value of the function f(x) = 2x + 32 at x=3, we substitute x with 3, and solve to obtain f(3) = 38. Therefore, all students' answers were incorrect.

In the function f(x) = 2x + 32, to find the value of f(3), you first need to substitute 'x' with 3. The equation it becomes f(3) = 2 * 3 + 32

By solving the equation, you obtain is f(3) = 6 + 32 which equals to f(3) = 38.

Thus, all the students, Lynn, Jude, and Anne, unfortunately provided incorrect answers.

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Answer:

[tex]5^{10}+8^3[/tex]

[tex]5^{10}=9765625[/tex]

[tex]8^3=512[/tex]

[tex]=9765625+512[/tex]

[tex]=9766137[/tex]

OAmalOHopeO

Answer:

7 x + y = 9

Step-by-step explanation:

8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm' then the ratio of a:b is 1 : 2

Solution:

Given that 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'

Need to find the ratio of a:b

As 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'.  

For sake of simplicity, let volume of 1 sphere of radius a cm is represented by [tex]V_a[/tex] and volume of 1 sphere of radius b cm is represented by [tex]V_b[/tex]

So volume of 8 solid iron sphere with radius 'a cm' = volume of  1 solid iron sphere with radius 'b cm'

[tex]=>8 \times} \mathrm{V}_{\mathrm{a}}=\mathrm{V}_{\mathrm{b}}[/tex]

[tex]\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{b}}}=\frac{1}{8}[/tex]  ---- eqn 1

[tex]\text {Let's calculate } {V}_{a} \text { and } V_{b}[/tex]

Formula for volume of sphere is as follows:

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

Where r is radius of the sphere

Substituting r = a cm in the formula of volume of sphere we get

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

Substituting r = b cm in the formula of volume of sphere we get

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

[tex]\text { Substituting value of } V_{a} \text { and } V_{b} \text { in equation }(1) \text { we get }[/tex]

[tex]\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}[/tex]

[tex]\begin{array}{l}{=>\frac{\frac{4}{3} \pi a^{3}}{\frac{4}{3} \pi b^{3}}=\frac{1}{8}} \\\\ {=>\left(\frac{a}{b}\right)^{3}=\left(\frac{1}{2}\right)^{3}} \\\\ {=>\frac{a}{b}=\frac{1}{2}}\end{array}[/tex]

a : b = 1 : 2

Hence the ratio of a:b is 1 : 2

Final answer:

The ratio of the radius 'a' of the original smaller spheres to the radius 'b' of the new larger sphere formed by melting the 8 smaller spheres together is 1:2, obtained by equating the volumes and simplifying.

Explanation:

The question pertains to using the concept of volumes of spheres in Mathematics to find the ratio of radii of the original smaller spheres to the new larger sphere formed by melting them together. Given that there are 8 solid iron spheres each with radius 'a cm', and they are melted to form one single sphere with radius 'b cm', we preserve the volume during the melting process.

We know that the volume of a sphere is calculated using the formula [tex]V=\frac{4}{3}\pi r^{3}[/tex]. When combining the volumes of the 8 smaller spheres into one large sphere, the volumes on both sides must be equal since no material is lost during melting. The equation to find the volume of the large sphere is [tex]V=8(\frac{4}{3}\pi a^{3}) = \frac{4}{3}\pi b^{3}[/tex].
Simplifying this equation, we obtain the cubic ratio of radii a³/b³ = 1/8. Taking the cube root of both sides, the simple ratio of the radii is a/b = ∛[1/8], which simplifies to a/b = 1/2. Therefore, the ratio of the radius of the smaller sphere to the radius of the larger sphere, a:b, is 1:2,

Answer:

Well, we know x has to add up to 180 degrees since a triangle has 180 degrees in it!

63 + 36 = _99__

180 - 99 = 81

81 = x

180 - 81 = 99

99 is z

99 + 13 = 112

180 - 112 = 68

68 is y

Since 13 is an angle measurement. We add to get 180.

68 = y

99 = z

81 = x

Answer: 292.50 dollars

Work Shown:

P = 650 is the the principal.

r = 0.09 is the interest rate in decimal form.

t = 5 is the number of years.

i = P*r*t

i = 650*0.09*5

i = 292.50 is the simple interest.

Given values:

Principle,

Rate,

Time,

As we know,

→ [tex]i = R\times r\times t[/tex]

By substituting the values, we get

      [tex]= 650\times 0.09\times 5[/tex]

      [tex]= 292.50[/tex]

Thus the response above is right.

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Answer:

Linear

Step-by-step explanation:

Because it has no exponents

If it has no exponents than its always linear

Answer:

Linear

Step-by-step explanation:

It is in Slope-Intercept Form [y = mx + b], and this formula is ALWAYS a linear function [NO EXPONENTS].

I am joyous to assist you anytime.

There are 165 different subcommittees possible.

To calculate the number of different subcommittees possible, we can use the combination formula. The number of different subcommittees is equal to the number of ways to choose 3 members out of 11. This can be calculated using the formula C(n, r) = n! / (r! (n - r)!), where n is the total number of members and r is the number of members in the subcommittee.

Plugging in the values, we have C(11, 3) = 11! / (3! (11 - 3)!) = 165. Therefore, there are 165 different subcommittees possible.

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Answer:

-33

Step-by-step explanation:

x-6b when b=5 and x=-3

-3-6(5)=-3-30=-33

Answer:

here  you go If the slope is undefined, it means that it is a vertical line.  This means that it passes through all points in the y direction.  Since the x value is -4, and the line is vertical, that's the only x value on that line.  So you just say the equation of the line is x=-4  

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

y-y1=m(x-x1)

m=0

y-8=0(x-(-4))

y-8=0(x+4)

y-8=0

y=0+8

y=8

Answer:

3:31 PM

Step-by-step explanation:

When the planes arrives in San Francisco, the time is 4:91 or 5:31 PM(central time/yellow). From Central time period to pacific time period, the time decreases by 2 hours. 5:31 - 2 hours is 3:31. The time is still PM. Answer is 3:31 PM.

Answer:

3:31pm

Step-by-step explanation:

Because each 60mins=1hr

51+40=91 which equals an hour and thirty 1 minutes plus an hour and 40 minutes which equals 3:31

Hope I'm right good luck!!1