Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.

Answer:   25 km

Step-by-step explanation:

500 km / 5 = 100 km up stream

500 km / 4 =  125 km down stream

125 - 100 = 25 km in still water

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$350\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=350\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=350(1.03)^2\implies A=371.315[/tex]

Answer:

7/15

Step-by-step explanation:

odd numbers are those that do not have divides ie1,2,3,5,7,11,13

The probability of randomly selecting an odd number from the numbers 1-15 is 8/15.

Probability is used to know the odds that an event would happen.  The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability that a randomly selected number would be odd = number of odd numbers / total numbers

Odd numbers between 1 and 15 = 1 , 3, 5, 7, 9, 11, 13, 15

Probability that a randomly selected number would be odd = 8/15

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Answers:

1. x[tex]\geq[/tex] [tex]\frac{y+4}{3}[/tex]

2. x [tex]\neq[/tex][tex] \frac {y} {2} [/tex]

3. x<y-5

4. x>2(y+3)

5. x [tex]\leq[/tex] [tex]\frac{y-2}{4}[/tex]

6. x < [tex]\frac{5-y}{5}[/tex]

Make me brainiest!!!!!!!!!!

Answer:

Step-by-step explanation:

1. x\geq\frac{y+4}{3}

2. x \neq \frac {y} {2}

3. x<y-5

4. x>2(y+3)

5. x \leq\frac{y-2}{4}

6. x < \frac{5-y}{5}

Answer:

6 in^2.

Step-by-step explanation:

The area of 2 similar figures are in the ratio of the squares of corresponding sides. So we have the equation:

3^2 / 6^2 = x / 24

9/36 = x /24

1 / 4 = x / 24

x =  24/4 = 6 in^2 (answer).

Answer:

18 combinations

Step-by-step explanation:

Assuming you can only have one slice of cheese per cracker, then you would have to multiply the number of types of crackers by how many types of cheeses there are to find the total amount of combinations.

3 crackers * 6 cheeses = 18 combinations

Answer:

d^2y/dx^2 = 2

Step-by-step explanation:

We take the derivative with respect to x twice here.  Find the first derivative, simplify the results and then differentiate that result again with respect to x.

(d/dx)(2x^2+2y=17+  →  4x + 2(dy/dx) = 0.  Simplifying, we get:

dy/dx = -2x

Now take the derivative of this new equation, obtaining:

d^2y/dx^2 = 2

Como? No entiendo perdón

Answer:

B. -14

Step-by-step explanation:

If you solve the system using the method of elimination, the y terms will automatically cancel each other out without any manipulation at all.  So go with it and solve for x first.  If the y terms cancel out, you're left with x = -3.

If x = -3, sub that value in for x in eitheer one of the original equations and solve for y:

[tex]3x-y=5[/tex] becomes

[tex]3(-3)-y=5[/tex] and

[tex]-9-y=5[/tex] so

[tex]y=-14[/tex]

Answer:

Step-by-step explanation:

The sum of those numbers is 14.  Let's divide 14000 by 14 to get the number of parts (each part will be an investment in dollars) and we get 10,000.  So if a person invests 2 parts, he invests 2(10,000).  A person that invests 5 parts invests 5(10,000), and likewise for the person investing 7 parts: 7(10,000).  That gives us 20,000 + 50,000 + 70,000 = ?  

(140,000)

The difference in investment between the largest and the smallest is 50,000

Final answer:

To find out the investments of three friends in a ratio of 2:5:7, one part is calculated as $10,000. The smallest investor contributes $20,000 and the largest investor contributes $70,000. Hence, the difference in their investments is $50,000.

Explanation:

The question is asking to determine the individual investments of three friends in a food truck business based on their total contributions amounting to $140,000 and the ratio of their investments being 2:5:7. First, we find the total number of parts in the ratio (2+5+7=14 parts). To find the value of one part, we divide the total investment by the number of parts ($140,000 \/ 14 = $10,000 per part).

Now, we can calculate each friend's investment:

The difference in investment between the smallest and the largest investor is $70,000 - $20,000 = $50,000.

Replace the x and y values in the given equation.

1. d = √((6-0)^2 + (8-0)^2

= √(6^2 + 8^2)

= √(36 + 64)

= √100

= 10

2. d = √((3-(-3))^2 + (5-2)^2

=√((3+3)^2 + 3^2)

=√(6^2 + 3^2)

= √(36 + 9)

= √45

=3√5 ( exact ) or as a decimal 6.7082 (round as needed)

3.  d = √((4-(-1))^2 + (-5-(-1))^2

= √((4+1)^2 + (-5+1)^2)

= √(5^2 + -4^2)

=√(25 + 16)

= √41 (exact) or as a decimal 6.4031 (round as needed)

Product 4 after the third year is 27 which is higher than the rest after 3 years.

And because x is raised to the third, the amount would Increase by being raised to the 3rd every year.

The answer is Product 4.

Julius bought a total of 2 gallons of beverages, including 2 quarts of orange juice and 16 cups of chocolate milk.

To find out how many gallons of beverages Julius bought, we need to convert each quantity to gallons and then sum them up:

1. **2 pints of milk**:

  - 1 pint = 0.125 gallons

  - 2 pints = [tex]\(2 \times 0.125 = 0.25\)[/tex] gallons

2. **2 quarts of orange juice**:

  - 1 quart = 0.25 gallons

  - 2 quarts = [tex]\(2 \times 0.25 = 0.5\)[/tex] gallons

3. **16 cups of chocolate milk**:

  - 1 cup = 0.0625 gallons

  - 16 cups =[tex]\(16 \times 0.0625 = 1\)[/tex] gallon

4. **32 ounces of lemonade**:

  - 1 ounce = 0.0078125 gallons

  - 32 ounces = [tex]\(32 \times 0.0078125 = 0.25\)[/tex] gallons

Now, let's sum up the quantities:

[tex]\[ 0.25 + 0.5 + 1 + 0.25 = 2 \][/tex]

So, Julius bought a total of 2 gallons of beverages.

Answer:

(x, y)-->(x-7, y+4)

Step-by-step explanation:

To get from T to T', you have to move the image 7 units to the left of the preimage.  From that point, you have to move up 4.

Answer:

255

Step-by-step explanation:

1. 75% is actually 0.75, and you want to find 75% of 340.

2. Multiply 0.75 and 340. 0.75 x 340 = 255

3. Answer = 255

Answer: 119°

Step-by-step explanation:

A circle equals 360° degress. If you subtract the two angles shown in the picture you'll get 238°.

Now vertical angles are congurent thus if we divide 238 into 2 we get 119°.

Answer:

it's 119

step explanation:

i guessed and got it rt, lol.

Step-by-step answer:

A line with slope (or gradient) m, passing through a point (x0,y0) can be represented by the equation:

(y-y0) = m(x-x0)  ......................(1)

Here,

(x0,y0) = (1,7), and

slope/gradient = -2

Substitute values into (1) above gives

(y-7)=2(x-1)

Expand and simplify

y-7 = 2x-2

y =2x -2 + 7

y=2x+5

is the final answer.

Answer:

Step-by-step explanation:

⇒ sin (49°) = cos (90° - 49°) = cos (41°)

Sinus is a periodic trigonometric function, defined in the context of a right triangle as the ratio of the opposite leg to the hypotenuse.

Cosinus is a periodic trigonometric function, defined in the context of a right triangle as the ratio of the adjacent leg to the hypotenuse.

Final answer:

To find the value of x where sin49° equals cosx, we utilize the identity sin(90° - x) = cos x, which yields the answer x equals 41°.

Explanation:

To find the value of x where sin49° = cosx, we use the trigonometric identity sin(90° - x) = cos x. Since sin49° is given, we can set up our equation as:

sin(90° - x) = sin49°.

This reveals that 90° - x = 49°

Solving for x, we get:

x = 90° - 49°

x = 41°

Therefore, the value of x is 41°.

Answer:

The answer is 12. There are 12 pens in each pack.

Step-by-step explanation:

The constant of proportionality between the number of packs and the number of pens that Frank buys is 12 pens per pack, calculated by dividing the total pens by the number of packs in both given scenarios.

The student asks about the constant of proportionality between the number of packs of pens and the number of pens. To find this, we divide the number of pens by the number of packs for each given scenario to ensure the ratio is consistent.

Given Frank buys three packs and ends up with 36 pens, we divide 36 pens by 3 packs to get 12 pens per pack.

When he buys five packs and has 60 pens, we again divide 60 pens by 5 packs and get the same result, 12 pens per pack. Therefore, the constant of proportionality is 12 pens per pack.

Answer: -4 . 2ⁿ⁻¹

Step-by-step explanation: This is a geometric progression

the nth term is given by arⁿ⁻¹

a = the first term of the sequence

r = common ratio

n=  number of terms

for this sequence

a = -4

r = -8/-4 = 2

nth term, an = -4 . 2ⁿ⁻¹

Answer:

an = 2 ● (-4)n-1

Step-by-step explanation:

Just got it right

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

Note Is a 1/4 of a pastry instead of 14 of a pastry

we know that

To find the fraction of the original pastry that represents each of the 3 pieces cut by Joanne, divide 1/4 by 3

so

[tex](1/4)/3=\frac{1}{12}[/tex]

Answer:

1/12

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

Given

f(x) = - (x - 3)(x + 11)

Find the zeros by setting f(x) = 0, that is

- (x - 3)(x + 11) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 11 = 0 ⇒ x = - 11

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros

[tex]x_{vertex}[/tex] = [tex]\frac{3-11}{2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4

Substitute x = - 4 into f(x) for y- coordinate of vertex

f(- 4) = -(- 7)(7) = 49 ← y- value of vertex

Answer:

C

GX is reflected across the X-axis

g(x) is reflected across the X-axis if f(x) is the original function.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here we have f(x) is the original function, the true value of g(x) is that g(x) is reflected across the X-axis.

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First, you have to find the 52% of the 30%(chance that he gets a dividend) .Then you simply have to subtract the result (15.6%) from the 30%. Your result is 14.4% chance that he wont get a divident.

Answer:

14.4%

Step-by-step explanation:

An investment advisor believes that there is a 30% chance of making money by investing in a specific stock. If the stock makes money, then there is a 52% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money but does not receive a dividend.

Probability is the chance/likelihood that an event will occur or not

The chances that one makes money from a stock is 30%

Chances that one will not=70%

Chances that there will dividend among those who made money is =52%

chances that there wont be dividend is =100%-52%=48%

the probability that One will make money and not receive a dividend

is 30%*(100%-52%)

14.4%

Answer:

$348.29

Step-by-step explanation:

The payment is calculated by multiplying the rate per hundred times the number of hundreds. The latter is found by dividing the loan amount by $100.

$2.41 × $14,452/$100 ≈ $348.29

Answer:$299.16

Step-by-step explanation:

Financed amount = $14452

APR  = 8.9%

Period / time = 5 years

monthly payment = $100 for every $2.07

To calculate the monthly payment of a financed amount we multiply the financed amount by the ratio of the given amount paid per $100

The monthly payment would be =  14452 * 2.07/100 = 14452 * 0.0207

= $299.16 approximately

therefore the monthly payment of a financed amount of $14452 is equal to $299.16

Answer:

1. $60

2. $240

Step-by-step explanation:

Use the formula for simple interest. Put your numbers in the formula and do the arithmetic.

i = Prt . . . . where i is the interest amount, P is the principal, r is the rate, t is the time period

1. P = $600, r = 0.05, t = 2, so you have ...

i = $600·0.05·2 = $60

__

2. P = $1500, r = 0.04, t = 4, so you have ...

i = $1500·0.04·4 = $240

$21 it will cost for lollipop

Answer:

$1.10

Step-by-step explanation:

1.10 times 10

Answer:

Option C. linear: slope = -5, y-intercept = 50

Step-by-step explanation:

Let

b ----> is the automatic decrease on the gift card balance

m ---->  is the number of months beyond two years

we know that

The equation of the line into slope intercept form is equal to

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

where

m is the slope

b is the y-intercept

In this problem the linear equation that represent this situation is

[tex]b=-5m+50[/tex] ---> equation of the line into slope intercept form

so

The slope is -5

The y-intercept is 50

Answer:

This function is linear. True

The slope of this function is 50. False

The y-intercept of this function is 50. True

Answer:

Option B is correct.

Step-by-step explanation:

Given:

A Solid Figure made up pf cuboid and a triangular based prism.

To find: Total Surface area of the figure.

Total Surface Area = Area of front + Area of top + Area of Back + 2 × Area of side + Area of bottom

Area of Front = Area of Square + Area of rectangle

                      = 10 × 10

                      = 100 in.²

Area of top = Area of Rectangle

                   = 13 × 10

                   = 130 in.²

Area of back =  Area of square in down + Area of rectangle in up

                      = 10 × 10 + 5 × 10

                      = 100 + 50

                      = 150 in.²

Area of the bottom = Area of the rectangle

                                = 12 × 10

                                = 120 in.²

Area of the side = Area of rectangle + Area of the triangle

                           = 12 × 10 + 1/2 × 5 × 12

                           = 120 + 5 × 6

                           = 120 + 30

                           = 150 in.²

Total Surface Area = 100 + 130 +150 + 120 + 2 × 150

                               = 500 + 300

                               = 800 in.²

Therefore, Option B is correct.

Answer:

Without any studying, the score would be about 328

Step-by-step explanation:

The y-intercept of an equation represents the point where its graph crosses the y-axis. At this point the value of x is always equal to 0.

The y-intercept of the equation in this context would represent the Math SAT score of a student who did not do any studying, that is the number of hours spent studying, x = 0.

Substitute x = 0 in the given equation and solve for y;

y = 24.387(0) + 328.182

y = 328.182

Therefore, Without any studying, the score would be about 328