One number exceeds another by 16. The sum of the numbers is 54. What are the numbers?

Answer:

{58.02007 , 61.97993]

Step-by-step explanation:

Data are given in the question

Sample of cars = n = 121

Average speed = sample mean = 60

Standard deviation = sd = 11

And we assume

95% confidence t-score = 1.97993

Therefore

Confidence interval is

\(= [60 - \frac{1.97993 \times 11}{\sqrt{121} }] , [60 + \frac{1.97993 \times 11}{\sqrt{121} }]\)

=  {58.02007 , 61.97993]

Basically we applied the above formula to determine the confidence interval

Answer:

86

Step-by-step explanation:

Let the number be 10x + y. So, the reversed number is 10y + x.

The sum is 154.

So, (10x + y) + (10y + x) = 154

⇒ 11x + 11y = 154

⇒ x + y = 14 ..... (1)

Again, given that ones digit in the original number is 2 less than the tens digit.

So, y = x - 2 ...... (2)

Now, solving (1) and (2) we get,

x + x -2 = 14

⇒ 2x = 16

⇒ x = 8

So, from equation (2), y = x - 2 = 8 - 2 = 6

Therefore, the original number is 10x + y = 10 × 8 + 6 = 86 (Answer)

Answer:

525 foot is the answer

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.

Answer:

The solutions to the quadratic equation using the quadratic formula will be:

\(x=\frac{1}{2},\:x=\frac{1}{4}\)

Step-by-step explanation:

Given the equation

\(8x^2-6x+1=0\)

solving with the quadratic formula

\(\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\)

\(x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

\(\mathrm{For\:}\quad a=8,\:b=-6,\:c=1\)

\(x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}}{2\cdot \:8}\)

as

\(\sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}=2\)

so

\(x_{1,\:2}=\frac{-\left(-6\right)\pm \:2}{2\cdot \:8}\)

Separating the solution

\(x_1=\frac{-\left(-6\right)+2}{2\cdot \:8},\:x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}\)

solving

\(x_1=\frac{-\left(-6\right)+2}{2\cdot \:\:8}\)

    \(=\frac{6+2}{2\cdot \:8}\)

   \(=\frac{8}{16}\)

   \(=\frac{1}{2}\)

and

\(x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}\)

   \(=\frac{6-2}{2\cdot \:\:\:8}\)

    \(=\frac{4}{16}\)

    \(=\frac{1}{4}\)

Therefore, the solutions to the quadratic equation using the quadratic formula will be:

\(x=\frac{1}{2},\:x=\frac{1}{4}\)

Answer:

1/4 1/2

Step-by-step explanation:

Parallelogram have two pairs of opposite sides that are parallel and congruent.

In a parallelogram, two pairs of opposite sides are parallel and congruent. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Therefore, any pair of opposite sides in a parallelogram satisfies the criteria of being both parallel and congruent.

For example, let's consider a parallelogram ABCD:

These two pairs of opposite sides, AB and CD, and AD and BC, are parallel (they never intersect) and congruent (they have the same length).

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The calculation of this can be done by first determining the future value of the monthly payments of $327.50

The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,

which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.

The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35

This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.

Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.

 for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).

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Using the concept of proportions and ratios on the similar triangles, the value of x is 48 units

Similar triangles are triangles that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are proportional. In other words, the ratios of the corresponding sides of similar triangles are equal.

The concept of similar triangles is based on the fundamental property that corresponding angles in similar shapes are equal, and the corresponding sides are proportional.

To determine the value of x, we can apply the concept of proportions and ratio on the similar triangle;

x / 36 = 64 / x

Cross multiplying both sides

x * x = 36 * 64

x² = 2304

x  = √2304

x = 48 units

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Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

Where are the questions

The equation of the circle is given by (C) (x-3)² + (y + 4)² = 9

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its center.

The equation of the circle in the general form is given by the

(x-a)²+(y-b)²=r²

Where (a,b) is the co-ordinates of the center of the circle and the radius is r.

Now the center of the circle is given at (3,-4) and the radius is r.

We know that the general equation of a circle is  \({\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}\)

Substituting the values in the equation we get:

(x-3)²+(y-(-4))²=(3)²

or, (x-3)²+(y+4)²=9

Hence the equation of the circle is (x-3)² + (y + 4)² = 9.

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Answer:it’s a I think

Step-by-step explanation:

Answer:

b, the division property of equality

Step-by-step explanation:

You are dividing both sides of the equation by 0.36 to solve

Answer:

Here are the angles in each quadrant with a common reference angle of 165°:

First quadrant: angle is 15° (subtract 165° from 180°)

Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)

Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)

Fourth quadrant: angle is 195° (subtract 165° from 360°)

Answer:

7. (5,4) x = 5 y = 4

8. (1,2) x = 1 y = 2

Step-by-step explanation:

This explanation takes too long sry :(

Answer:

what does perpendicular mean again

Answer:

1/6

Step-by-step explanation:

Multiply the fractions to find how much of the whole cake he ate.

1/3 * 1/2

1/6

Best of Luck!

Answer:

1/6

Step-by-step explanation:

He ate 1/2 of 1/3 of the cake, so the fraction of the whole cake he ate is 1/2 x 1/3. Multiplying fractions is easy, simply multiply the numerator of each fraction (the numbers at the top of each fraction) and the denominator of each fraction (the numbers at the. bottom of each fraction). Therefore, 1/2 x 1/3 = 1/6.

Answer:

I) ∠2 and ∠5

Step-by-step explanation:

Answer:I think it is a

Step-by-step explanation:

Answer:

Graph a) is a Euler Path

Odd at D and F

Step-by-step explanation:

A graph has an Euler circuit if and only if the degree of every vertex is even.

A graph has an Euler path if and only if there are at most two vertices with odd degree.

a) Odd at D and F - Euler Path

b) No odds - Euler Circuit

c) Odd at A, C, E, F

d) Odd at A, B, C, D

The original height  of the water in a pool is 5 ft , Option B is the correct answer.

An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.

It is given in the question that

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.

the height of the water is 4.75 feet.

The equation

4.75 = x + (negative 0.25)

can be used to find x, the original height of the water in a pool.

4.75 = x - 0.25

x = 5

Therefore the original height  of the water in a pool is 5 ft , Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

Here we have been given with two equations and we have to calculate the values of x and y. So we would be using elimination method.

★ From Equation No 2:-

>> x - 8y = -13

>> x = 8y - 13

★ In Equation No 1:-

Substituting the value of x which we got above as (8y - 13) here.

>> 2x + 5y = 16

>> 2 (8y - 13) + 5y = 16

>> 2 × (8y - 13) + 5y = 16

>> 16y - 26 + 5y = 16

>> 21y - 26 = 16

>> 21y = 26 + 16

>> 21y = 42

>> y = 42 / 21

>> y = 6 / 3

>> y = 2

★ Finding out value of x:-

>> x = 8y - 13

>> x = 8 (2) - 13

>> x = 16 - 13

>> x = 3

Answer:

CD = 15

x = 5

Step-by-step explanation:

Since BF ≅ FD and AE ≅ EC, then \(EF = \frac{AB + CD}{2}\)

So, \(30 = \frac{x^{2} +20 + x^{2} + 22x - 120}{2}\)

\(60 = 2x^{2} + 22x - 100\)

\(2x^{2} + 22x - 160 = 0\)

\(2(x^{2} + 11x - 80) = 0\)

2(x - 5)(x + 16) = 0

x = 5  or x = -16

If x = 5, then CD = \(5^{2} +22(5) - 120 = 25 + 110 - 120 = 15\)  

Ix x = -16, then CD = will be a negative number which it cannot be.

the 50% concentration of the final solution is a result of mixing the 95% concentration with water, which is 0% concentration.

Multiply the concentration of each liquid times the # of ml you will use, add these and divide by the total ml to get 50%

X = the number of ml of the 95% alcohol mixture

Y = the number of ml of water

X + Y = 855

{.95·X + (0)(Y } / 855 = .50

Again, the 0 above represents the water which is 0% concentration

.95X / 855 = .50

.95X = 427.50

X = 450

plug 450 into the equation X + Y =855

450 + Y =855

Y = 405

Use 450 ml of the 95% solution and 405 ml of water

Answer:

What type of math is this

Step-by-step explanation:

Answer:

$57

Since $71.25 was paid for working 7.5 hours.

That means he was being paid $9.5 per hour.

Which is 71.25÷7.5.

And on tuesday that's 9.5×6 which is $57

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!