What is the only prime number that is a factor of 16

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:

7 x + y = 9

Step-by-step explanation:

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

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:

there are 306 in total

Step-by-step explanation:

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.

Answer:

-33

Step-by-step explanation:

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

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

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:

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:

Your answer would be 33.7619047619

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:

35

Step-by-step explanation:

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

Answer:

The number of students who actually went for the skiing is 0.75 times the total number of students .

Step-by-step explanation:

Given as :

Students were surveyed about their wither break plans

The percentage of students who did not go for skiing = 25 %

So, The percentage of students who did not go for skiing =100 % - 25 % = 75%

Let The total number of students = x

So, The number of students actually went for the skiing = 75% of the total number of students

I.e The number of students actually went for the skiing = [tex]\frac{75}{100}[/tex]× x

Or, The number of students actually went for the skiing = 0.75× x

∴ The number of students actually went for the skiing = 0.75 x

Hence The number of students who actually went for the skiing is 0.75 times the total number of students . Answer

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:

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!

28 tablets will be required for course of therapy.

One tablet is of 400-mg and prescription is for 200 mg for every 6 hours for 14 days. total number of tablets to be find out.

Arithmetic operation are Addition, subtraction, division, and multiply in order to achieve mathematical solution of the statement.

Here, tablet for a day = 200-mg/400-mg x 24 hr/6 hr
                                    =  1/2 x 4
                                    = 2 Tablets a day
Now, for number of tablets for 14 days course,
= 14 x 2
=  28 Tables in 14 days

Thus, 28 tablets will be required for course of therapy.

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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:

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:

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

The length of playing field is 58.9 feet

Solution:

Given that, the diagonal length of a rectangular playing field is 76 feet,  

And its width is 48 feet.  

To find: length of playing field

Now, we know that, diagonal, width and length of a rectangle will form an right angle triangle with diagonal as hypotenuse.

So, now, in a right angled triangle  we can use pythagorean theorem to find the length

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, In a right angled triangle ABC we get

[tex]c^2 = a^2 + b^2[/tex]

Where "c" is the length of hypotenuse

"a" is the length of one leg of right angled triangle

"b" is the length of other leg of right angled triangle

[tex]\begin{array}{l}{\text {Then, diagonal = width }^{2}+\text { length }^{2}} \\\\ {76^{2}=48^{2}+\text {length }^{2}} \\\\ {\text {Length }^{2}=76^{2}-48^{2}} \\\\ {\text {Length }^{2}=5776-2304}\end{array}[/tex]

[tex]\begin{array}{l}{\text { Length }^{2}=3472} \\\\ {\text { Length }=\sqrt{3472}} \\\\ {\text { Length }=58.92}\end{array}[/tex]

Hence, the length of the rectangular field is 58.9 feet

Answer:The answer is 3,472

Step-by-step explanation:

I GOT THIS CORRECT TRUST ME!! :)

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:

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:

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.

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:

e-1/25

Step-by-step explanation:

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: the answer is 40

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)