Jeremy, Sue, and Holly are siblings. Sue was born three years before Holly, and Jeremy was born five years before Sue. The product of Sue's age and Jeremy's age is at most 150.
If x represents the age of Holly, which inequality can be used to find the age of each sibling?

A.
x2 - 11x + 24 ≤ 150
B.
x2 + 8x + 15 ≤ 150
C.
x2 + 8x ≤ 150
D.
x2 + 11x + 24 ≤ 150

Answer:

sandals costed $32.55

Step-by-step explanation:

Final answer:

To find the cost of the sandals, subtract the cost of the T-shirt from the total cost. The equation 8.95 + c = 41.50 leads to c = 32.55, meaning the sandals cost $32.55.

Explanation:

The question asks us to find the cost of sandals that Tina bought, given the total cost of a T-shirt and the sandals combined, and the cost of the T-shirt alone. To solve for the cost c of the sandals, we start with the equation 8.95 + c = 41.50. We then isolate c by subtracting 8.95 from both sides of the equation:

c = 41.50 - 8.95

c = 32.55

Therefore, the cost of the sandals was $32.55.

ANSWER

Quadrant I

EXPLANATION

In the first quadrant all the trigonometric ratios are positive.

This implies that,both tanθ and secθ are positive in the first quadrant.

No two trigonometric ratios are positive in any other quadrant apart from the first quadrant.

Answer:

qaud I

Step-by-step explanation:

ANSWER

y = 3x + 6.50

EXPLANATION

The $3 for each downloaded movie is the unit rate of change.

This is represent the slope of the linear function that models this situation.

The monthly fee of monthly fee of $6.50 the constant rate.

It represents the y-intercept of the function.

The linear function is given by

[tex]y = mx + b[/tex]

The correct choice is y = 3x + 6.50

the answer would be C. y = 3x + 6.50, for every movie you buy (which is x), they would be 3$. therefore it would be 3x, and the monthly fee would just be added with that. :P

he would hove to work 20 hours to meet the second job I think

To make the same total earnings at the first job as the second job (including benefits), Phillip would have to work an additional 4 hours (to account for the $100 benefits). If the workdays are 8 hours each, then for every two days (which is 16 hours) worked at job 2, Phillip would need to work an additional 4 hours at job 1, summing up to 20 hours.

This problem is about comparing the earnings from the two jobs. For the second job, Phillip earns $20 per hour and also gets benefits equivalent to $100 per pay period.

If Phillip wants to earn the same amount in the first job (which does not offer any benefits), we calculate how many hours he would need to work to earn an additional $100 (the value of the benefits).

To do this, we divide $100 (benefits of the second job) by the first job's hourly pay rate ($25) which results in 4 hours.

So, Phillip must work an additional 4 hours to make up for the benefits. Meaning, for any given number of hours he would work at the second job, he would need to work an extra 4 hours at the first job to get the same total earnings.

Therefore, the right answer is not among the choices given because we have an extra step to add to each option. If we consider a standard 8-hour workday, working at the second job for two days gives 16 hours with an additional $100 for benefits. To make the same in the first job, Phillip would need to work, 16 hours (from the second job) + 4 hours (to compensate for the $100 benefits) = 20 hours.

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a) The amount after 2 years with continuous compounding is approximately $6539.48.

b) It will take approximately 2.32 years for the amount to reach $8000 with continuous compounding.

a) To calculate the amount after 2 years with continuous compounding, you can use the formula:

[tex]A = P \times e^{rt}[/tex]

Where:

A = the amount after time 't'

P = the principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = the interest rate (as a decimal)

t = the time in years

Given that P = $5800, r = 6% (0.06 as a decimal), and t = 2 years, we can now calculate the amount (A):

[tex]A = 5800 \times e^{0.06 \times 2}[/tex]

[tex]A=5800 \times e^{0.12}[/tex]

[tex]A=5800 \times 1.1275[/tex]

A=6539.48

Hence,  the amount after 2 years is approximately $6539.48.

b) To find how long it takes for the amount to be $8000, we need to solve for 't' in the formula:

[tex]A = P \times e^{rt}[/tex]

Given that A = $8000 and P = $5800, we can rearrange the formula:

[tex]e^{rt}=\frac{A}{P}[/tex]

[tex]e^{0.06t}=\frac{8000}{5800}[/tex]

Take logarithms on both sides:

[tex]0.006t=log(\frac{8000}{5800})[/tex]

[tex]0.006t=0.139[/tex]

t=0.139/0.06

t=2.327

Hence, it takes 2.32 years for the amount to be $8000.

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After 2 years, the investment grows to approximately $6498.78. It will take around 5.37 years for the investment to grow to $8000.

We can use the formula for continuously compounded interest, which is A = Pe^(rt), where P is the principal amount ($5800), r is the interest rate (6% or 0.06), t is the time, and e is the mathematical constant approximated as 2.71828.

a) To find the amount after 2 years, sub in $5800 for P, 0.06 for r, and 2 for t to get: A = $5800 * e^(0.06*2). Evaluating this gives approximately $6498.78.

b) To find out when the amount will be $8000, we set A to $8000 and solve for t, getting: t = ln($8000 / $5800) / 0.06. Evaluating this gives approximately 5.37 years.

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this question isn't fully complete. comment a full question below and I'll try for ya ;) - Josie Annette

Answer:

Step-by-step explanation:

(7y)² = 7²×y² = 49y²

In order to simplify the expression (7y)^2, we need to apply the exponent to both the numerical coefficient and the variable inside the parentheses. Here's how to do it step-by-step:
1. The expression (7y)^2 denotes that everything inside the parentheses is to be squared. That means we multiply 7y by itself.
2. When squaring a product, we square each factor separately. So we have to square both the 7 and the y.
3. Squaring 7 gives us 7^2, which equals 49.
4. Squaring the variable y gives us y^2.
5. Now, we multiply 49 by y^2 to combine our results.
Putting these steps together, we see that (7y)^2 simplifies to 49y^2.
The final simplified expression without parentheses is 49y^2.

Answer:

16

Step-by-step explanation:

1 gallon is equal to 8 pints.

2 gallons is equal to 16 pints.

ANSWER

B.

[tex]112\pi \: {units}^{3} [/tex]

EXPLANATION

The volume of a cone is calculated using the formula:

[tex]Volume = \frac{1}{3} \pi {r}^{2}h[/tex]

where r=4 units is the base radius of the cone.

and h=21 units is the vertical height of the cone.

We plug in the values to get;

[tex]Volume = \frac{1}{3} \times \pi \times {4}^{2} \times 21[/tex]

[tex]Volume = 112\pi \: {units}^{3} [/tex]

Answer:

The correct answer is option B.  112π units ³

Step-by-step explanation:

Formula

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the volume of cone

Here radius r = 4 units

Height h = 21 units

Volume = (πr²h)/3

= (π * 4² * 21)/3

= 112π units ²

Therefore the correct answer is option B.  112π units ³

Answer:

  see below

Step-by-step explanation:

The images are mirrored right/left, so the reflection must be across the y-axis. That only leaves two answer choices.

If you translate ABC to the left, you will put it entirely in quadrant II, so reflection across the y-axis will put it in quadrant I. Obviously, that is not the correct sequence of transformations.

If you translate ABC 3 units to the right, it will put line AB on x=2. Then reflection across the y-axis will put that vertical segment on x = -2, exactly where corresponding segment DE is located.

The appropriate choice is the one shown below:

A flat circular plate has the shape of the region x 2 + y 2 ≤ 1. points on the plate have temperature t(x, y) = x 2 + 2y 2 − x. find the temperatures of the hottest and coldest points of the plate

Answer:

  B:  -34

Step-by-step explanation:

The given angles are supplementary, so you have ...

  (2x+146) + (4x+238) = 180

  6x +384 = 180 . . . . . simplify

  6x = -204 . . . . . . . . . subtract 384

  x = -34 . . . . . . . . . . . .divide by 6

_____

Check

angle F is (2·(-34)+146)° = 78°

angle C is (4·(-34)+238)° = 102°

These angles indeed are supplementary, so the answer checks OK.

X=-34; add both expressions together and solve for x

Answer:

Your salary will be $62,500.

Step-by-step explanation:

This is an arithmetic sequence with first term $45,000 and common difference $2,500.

The appropriate formula is a(n) = a(1) + (n-1)d, where a(1) is the first term, n is a counter and d is the common difference.

In this particular case, a(8) = $45,000 + (8-1)($2,500) = $62,500

Your salary will be $62,500.

A function assigns the values. Your salary after completing the 8th year within the company will be $62,500.

A function assigns the value of each element of one set to the other specific element of another set.

Given that the starting salary will be $45,000 while the salary will increase every year by $2,500. Therefore, the function that can represent the salary after (n-1) years can be written as,

y = $45,000 + $2,500(n-1)

Now, the salary after 8th year will be,

y = $45,000 + $2,500(n-1)

y = $45,000 + $2,500(8-1)

y = $62,500

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Answer:

it is the third one (from left to right)

Step-by-step explanation:

no explation

Answer: Permutation; number of ways = 120

Step-by-step explanation:

Answer with explanation:

Number of runner= 5

Number of Distinct Medal = 5

First Medal can be Awarded in 5 ways, second Medal can be awarded in 4 ways and third Medal can be awarded in 3 ways , fourth medal can be awarded in 2 ways and fifth Medal can be awarded in one way.

So, total number of ways =5 × 4×3×2×1=120 way

⇒We will use the concept of Permutation as there are five distinct medal and five different runners

So, Five distinct places can be filled in 5! or [tex]_{5}^{5}\textrm{P}[/tex] ways as order of arrangement is Important because any of the five candidates can win first second, third , fourth or fifth Prize.  

= 5!=5×4×3×2×1=120 ways

Because, n!=n×(n-1)×(n-2)×........1.

ANSWER

The solution is (2,1)

EXPLANATION

The given equations are:

2x+4y=8...(1)

3x-5y=1...(2)

We make x the subject in the first equation to get:

2x=8-4y

This means that,

x=4-2y...(3)

Put equation (3) into equation (2)

3(4-2y)-5y=1

Expand:

12-6y-5y=1

-6y-5y=1-12

-11y=-11

y=1

Put y=1 into equation (3).

x=4-2(1)=2

The solution is (2,1)

Answer:

  $2169.49

Step-by-step explanation:

The mortgage payment is ...

  A = (210,000·0.95)(0.045/12)/(1 -(1 +0.045/12)^(-12·15)) ≈ 1526.16

The monthly set-aside for taxes is ...

  3.5%·200,000/12 = 583.33

The monthly set-aside for insurance is ...

  720/12 = 60

So the total of P&I + taxes + insurance will be ...

  $1526.16 +583.33 +60.00 = $2169.49

Answer:

2202.72

Step-by-step explanation:

just got the answer right on the quiz

The answer is:

The missing step is the step shown in the last option:

D. [tex]324=0.042x+16[/tex]

To find which is the missing step, we need to remember that to cancel a square root, we need to elevate it, so:

Starting from the last step before the missing step, we have:

[tex]-18=-\sqrt{0.042x+16}[/tex]

In order to calculate the value of the variable (x) we need to square both sides of the equation, since squaring a root will cancel the root.

We must remember the following properties:

[tex]\sqrt{a^{m} }=a^{\frac{m}{2}}\\\\(a^{b})^{c}=a^{b*c}[/tex]

Now, finding the missing step, we need to find what to do in order to get the expression of the following step.

So, squaring both sides of the equation in order to cancel the square root and isolate the variable, we have:

[tex]-18=-\sqrt{0.042x+16}\\\\(-18)^{2} =(-\sqrt{0.042x+16})^{2} \\324=0.042x+16\\324-16=0.042x\\\\x=\frac{304}{0.042}=7333[/tex]

Hence, we found the the missing step is:

D. [tex]324=0.042x+16[/tex]

Have a nice day!

Answer:

96in^2

Step-by-step explanation:

because first find the area of two sides (Length*Height)*2 sides.

Find the area of adjacent sides (Width*Height)*2 sides.

Find the area of ends (Length*Width)*2 ends.

Add the three areas together to find the surface area.

Example: The surface area of a rectangular prism 5 cm long, 3 cm.

Answer:

96

Step-by-step explanation:

Did quiz

Answer:

The diameter of the circle is [tex]D=36\ in[/tex] and the radius is [tex]r=18\ in[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

where

D is the diameter of the circle

we have

[tex]C=113.04\ in[/tex]

substitute and solve for D

[tex]113.04=(3.14)D[/tex]

[tex]D=113.04/(3.14)[/tex]

[tex]D=36\ in[/tex]

Find the radius r

[tex]r=36/2=18\ in[/tex] -----> the radius is half the diameter

The work done by the force field  on the object moving on the parabola y=7x^2 from (0,0) to (4,112) is calculated by integrating the force along the path. The total work done is found to be 224 units of work.

To find the work done by a variable force on an object moving along a given curve, we utilize the concept of a line integral in vector calculus. Given the force field F =  and the parabolic path described by y = 7x2, from point (0,0) to (4,112), we want to integrate the force field along the curve. To calculate this line integral, we parameterize the curve using x as the parameter, since y is already expressed as a function of x. We then express the force field in terms of x, evaluate the dot product of the force field and the differential of the position vector, and integrate from the start to the end of the curve.

The work, W, is found by integrating the dot product of F and dx from the initial to the final position:
W = \\int (F . dx).

In our case, the force field becomes F(x, y(x)) = F<7x2, x> = <7x2, x>. The differential displacement along the parabola, expressed in vector form, is dx = <1, 14x>dx because dy/dx = d(7x2)/dx = 14x. Thus, the infinitesimal work is dW = F .dx = 7x2 * 1dx + x * 14xdx = 21x2dx. Finally, we integrate from x = 0 to x = 4 to find the total work:

W = \\int_{0}^{4} 21x2dx = 7x3\\right]_{0}^{4 = 7 * 43 = 224.

Therefore, the work done by the force field along the parabolic path from (0,0) to (4,112) is 224 units of work.

The work required to move an object along the parabola y = 7x^2 from (0,0) to (4,112) under the force field F = <y, x> is approximately 149.33 units.

To find the work required to move an object along a curve under the influence of a force field, we can use the line integral of the force field along the curve. The line integral is given by the formula:

∫ F · dr = ∫ (F1 dx + F2 dy)

Given the force field F = <y, x> and the parabola y = 7x^2, we need to parameterize the curve to express it in terms of a single variable.

Let's parameterize the curve using x as the parameter:

x(t) = t

y(t) = 7t^2

Now, we can calculate the differential elements dx and dy:

dx = x'(t) dt = dt

dy = y'(t) dt = 14t dt

Substitute the expressions for F, dx, and dy into the line integral formula:

∫ F · dr = ∫ (y dx + x dy)

            = ∫ (7t^2 dt + t * 14t dt)

            = ∫ (7t^2 + 14t^2) dt

            = ∫ 21t^2 dt

            = 7t^3 / 3 + C

Evaluate the integral from t = 0 to t = 4:

Work = [7(4)^3 / 3] - [7(0)^3 / 3]

    = (7 * 64 / 3) - 0

    = 448 / 3

    ≈ 149.33

Therefore, the work required to move an object along the parabola y = 7x^2 from (0,0) to (4,112) under the force field F = <y, x> is approximately 149.33 units.

answer for this question is (b)2X

The phrase "the product of 2 and a number" written as a mathematical expression is 2x

Given:

The product of 2 and a number

Let

The unknown number = x

So,

The product of 2 and a number

= 2 × x

= 2x

Therefore, the product of 2 and a number is written as 2x

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Answer:

  68

Step-by-step explanation:

[tex]a_2=2a_1+4=2\cdot 5+4=14\\\\a_3=2a_2+4=2\cdot 14+4=32\\\\a_4=2\cdot 32+4=68[/tex]

  a₄ = 68

_____

The explicit formula is

  an = 9·2^(n-1) -4

Answer:

There were 40 student tickets sold.

Step-by-step explanation:

First I set up equations to represent this situation.

4x+3y=380

x+y=105

x represents the adult tickets and y represents the student tickets.

I can solve this with the elimination method. I want to cancel out the x so I will multiply every term in equation 2 by -4.

4x+3y=380

-4x-4y=-420

Now I combine like terms.

-y=-40

I can divide the negative one from both sides.

y=40

40 Tickets sold.

Thank me later.

Answer:

11.6 cm²

Step-by-step explanation:

The area (A) of the shaded region is

A = area of sector - area of triangle

area of sector = area of circle × fraction of circle

                       = π × 9.28² ×[tex]\frac{68.9}{360}[/tex] ≈ 51.78 cm²

area of triangle = [tex]\frac{1}{2}[/tex] × 9.28 × 9.28 × sin68.9°

                         = 0.5 × 9.28² × sin68.9 ≈ 40.17 cm²

Area of shaded region = 51.78 - 40.17 ≈ 11.6 cm²

The correct answer is A. 46%

Answer:

The three integers are 13,14,15

Step-by-step explanation:

Let x be the first integer

x+1 be the second integer

x+2 be the third integer

The sum of the three integers is 42

x+ (x+1) + (x+2) = 42

Combine like terms

3x+3 = 42

Subtract 3 from each side

3x+3-3 = 42-3

3x= 39

Divide by 3

3x/3 = 39/3

x = 13

x+1 = 14

x+2 = 15

The three integers are 13,14,15

Answer:

y = -2x + 5.

Step-by-step explanation:

The general form is y = mx + b where m = the slope and b = the y-intercept.

So here m = -2 and b = 5 so our equation is:

y = -2x + 5.

Answer:

y = 51.3°

Step-by-step explanation:

tan(y) = Opp./Adj

tan(y) = 10/8

tan(y) = 1.25

y = 51.3°

Answer:

[tex]0.4n+0.1n^2\ miles[/tex]

Step-by-step explanation:

The first time he trains, he runs 0.5 mile, then the first term of the arithmetic sequence is [tex]a_1=0.5.[/tex]

Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time, then the difference of the arithmetic sequence is [tex]d=0.2.[/tex]

The nth term of the arithmetic sequence can be found using formula

[tex]a_n=a_1+(n-1)d,[/tex]

hence

[tex]a_n=0.5+0.2(n-1)\\ \\a_n=0.5+0.2n-0.2\\ \\a_n=0.3+0.2n.[/tex]

The total distance after Miguel has trained n times can be found using formula

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n,[/tex]

thus, the total distance is

[tex]S_n=\dfrac{0.5+0.3+0.2n}{2}\cdot n=\dfrac{0.8+0.2n}{2}\cdot n=(0.4+0.1n)n=0.4n+0.1n^2.[/tex]

Answer:

First answer is C. (0.3+0.2K)

Second one is 15 Times

Step-by-step explanation:

Answer on EDG hope it helps :)