A fountain launches a stream of water directly out of a pool at a vertical speed of 48 feet per second. The water shoots up and then falls back into the pool. The height, h, of the water at time t, in seconds, is given by the equation h = –16t 2 + 48t. The greatest height of the water above the pool is

Answer:

The answer to your question is A.35

The perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2).

Since M, R, and T are midpoints of the sides of ABC, they divide each side into two equal parts. Therefore, AM = MB, BR = RC, and CT = TA.

Now, let's find the lengths of AM, BR, and CT.

1. **Length of AM:**

[tex]\[ AM = \frac{1}{2} \cdot AB = \frac{1}{2} \cdot 18 = 9 \][/tex]

2. **Length of BR:**

 [tex]\[ BR = \frac{1}{2} \cdot BC = \frac{1}{2} \cdot 10 = 5 \][/tex]

3. **Length of CT:**

[tex]\[ CT = \frac{1}{2} \cdot AC = \frac{1}{2} \cdot 14 = 7 \][/tex]

Now, we need to find the perimeter of quadrilateral ACRM:

[tex]\[ \text{Perimeter} = AM + BR + RC + CT \][/tex]

[tex]\[ \text{Perimeter} = 9 + 5 + 7 + 9 = 30 \][/tex]

So, the perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2). Please double-check the answer choices, as the calculated perimeter is not exactly matching any of the provided options.

Answer:

$18

Step-by-step explanation:

The initial price is $25

When the first 10% is off, the new amount is (100 - 10)% x 25

= 0.9 x 25

= 22.5

With an additional 20%

the new amount is (100 - 20)% x 22.5

= 0.8 x 22.5

= $18

The final price of the shirt is $18.00.

To find the final price of the shirt, we need to apply the discounts consecutively to the original price.

 First, we calculate the discount from two weeks ago, which was 10% off the original price of $25.00. A 10% discount is the same as multiplying the price by 0.9 (since 100% - 10% = 90%, or 0.9 in decimal form).

 So, after the first discount, the price of the shirt is:

[tex]\[ \text{Price after first discount} = 25 \times 0.9 = 22.50 \][/tex]

 Next, we apply the additional 20% discount to the original price, not to the already discounted price.

This means we calculate 20% of $25.00 and subtract that from the original price. A 20% discount is the same as multiplying the price by 0.8 (since 100% - 20% = 80%, or 0.8 in decimal form).

 So, after the second discount, the price of the shirt is:

[tex]\[ \text{Price after second discount} = 25 \times 0.8 = 20.00 \][/tex]

However, since the second discount is additional, we need to apply it to the already discounted price of $22.50.

Therefore, we calculate 20% of $22.50 and subtract that from $22.50.

[tex]\[ \text{Additional discount amount} = 22.50 \times 0.2 = 4.50 \][/tex]

[tex]\[ \text{Price after additional discount} = 22.50 - 4.50 = 18.00 \][/tex]

 Thus, the final price of the shirt after both discounts is $18.00.

Answer:

Yes

Step-by-step explanation:

It is a Pythagorean Triple. A Pythagorean Triple is the sides of a triangle that fit perfectly into the Pythagorean Theorem, which is:

a²+b²=c²

12, 13, and 15 are numbers that you should know off the top of your head so if you see a triangle with 2 of those numbers, you instantly know the 3rd number.

~Stay golden~ :)

Answer: Yes

Step-by-step explanation: To determine if these side lengths can form a triangle, I attached a rule in the image provided which is very helpful to look at especially when you're new at this.

If a triangle has sides with lengths of 12, 15, and 13, notice that 12 + 15 or 27 is greater than 13.

So the sum of the lengths of two sides of the triangle is greater than the length of the third side.

This means that the triangle with sides of lengths of 12, 15, and 13, is possible.

Answer:

I'm pretty sure that you would try to find the least common multiple.

Step-by-step explanation:

Final answer:

When adding fractions, you need to find a common denominator using the least common multiple (LCM) of the denominators. In this case, the LCM of 5 and 6 is 30, so you multiply each fraction by a factor to make the denominators the same. Then, you can add the numerators together.

Explanation:

When adding fractions, you need to use the least common multiple (LCM) of the denominators to find a common denominator. In this example, the denominators are 5 and 6. The LCM of 5 and 6 is 30, so you need to find equivalent fractions with a denominator of 30.

To do this, multiply the numerator and denominator of each fraction by a factor that will result in a denominator of 30. For the first fraction, multiply both the numerator and denominator by 6 to get 24/30. For the second fraction, multiply both the numerator and denominator by 5 to get 25/30.

Finally, you can add the numerators together (24 + 25 = 49) and keep the common denominator of 30, giving you the final fraction of 49/30.

Answer:

[tex]3x^{3}-2x^{2} +6x[/tex]

Step-by-step explanation:

The cubic trinomial is in this form :

[tex]Ax^{3}+Bx^{2} +Cx[/tex]

So, instead A, B, and C we can use any number.

We use :

A=3

B=2

C=6

[tex]3x^{3}-2x^{2} +6x[/tex]

A cubic polynomial has a degree of 3.

Since 3 is the highest degree, the polynomial could contain terms with degree 2, 1, or 0 (quadratic, linear, or constant).

A trinomial can have only 3 terms.

Including terms with degrees of 3, 2, 1, and 0 would mean the polynomial has 4 terms.

The cubic trinomial could consist of a cubic, quadratic, and linear term, with no constant term.

Answer:

The measure angle ADB = 180 - (α/2+ β/2) 

Step-by-step explanation:

measure angle A is α degrees, this means that, the angle bisector divides the angle into two equal angles each of measure α/2 degrees

measure angle B is β degrees, this means that the angle bisector divides the angle into two equal angles each of measure β/2 degrees

In triangle ADB, we know that the sum of all measure of a triangle is 180 degrees and we have measure angle MAB = α/2 degrees and measure angle MBA = β/2 degrees

Therefore,

measure angle ADB = 180 - (α/2+ β/2) 

Answer:

The cost of the 20 fruit cup is $ 60  .

Step-by-step explanation:

Given as :

The total students for fruit cup party = 18

The total teachers for fruit cup party = 2

The cost of each fruit cup =$ 3

The delivery charge = $ 10

So, The total number of people for party = Total number of student + Total number of teachers

Or , The total number of people for party = 18 + 2 = 20

∵ each fruit cup cost $ 3

∴ The cost of 20 fruit cup = $ 3 × 20

I.e The cost of 20 fruit cup = $ 60

Hence The cost of the 20 fruit cup is $ 60  . Answer

The range of the function for the fruit-cup party is $10 to $70, including the delivery charge and the cost of the fruit cups.

To find the range of the function for the fruit-cup party, we need to consider the total cost of the fruit cups and the delivery charge. The delivery charge is a fixed cost of $10. The cost of each fruit cup is $3. So, the total cost of the fruit cups for the 18 students and 2 teachers is (18 + 2) × $3 = $60. Therefore, the range of the function is $10 to $70, which includes the delivery charge and the total cost of the fruit cups.

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After the 3% raise she is earning 10,400.

This means 40,400 is 103% of her pay leat year.

To find how much she made last year, divide her new pay amount by 103%:

40,400 / 1.03 = 39,223.30

Her pay last year was $39,223.30

Answer:

$12.09

Step-by-step explanation:

formula; Y= kx

where;    y = $24.18

               x = 2 books

               k = constant of proportionality

Step 1. Do the equation based on the data given

Y = kx

$24.18 = k2

Step 2. Compute the mathematical equation. Divide both sides by 2 to eliminate coefficient in the variable.

24.18 =k2

       2

k = $ 12.09 is the constant of proportionality cost in dlooars per book

Answer:

20 liters of 60% acid solution and 60 liters of 80% acid solution

Step-by-step explanation:

Let the amount of 60% solution needed be "x", and

amount of 80% solution needed be "y"

Since we are making 80 liters of total solution, we can say:

x + y = 80

Now, from the original problem, we can write:

60% of x + 80% of y = 75% of 80

Converting percentages to decimals by dividing by 100 and writing the equation algebraically, we have:

0.6x + 0.8y = 0.75(80)

0.6x + 0.8y = 60

We can write 1st equation as:

x = 80 - y

Now we substitute this into 2nd equation and solve for y:

0.6x + 0.8y = 60

0.6(80 - y) + 0.8y = 60

48 - 0.6y + 0.8y = 60

0.2y = 12

y = 12/0.2

y = 60

Also, x is:

x = 80 - y

x = 80 - 60

x = 20

Thus, we need

20 liters of 60% acid solution and 60 liters of 80% acid solution

The expression -y + 9z - 16y - 25z + 4 simplifies to -17y - 16z + 4 by combining like terms, which are the y terms and the z terms separately.

The task is to simplify the expression -y + 9z - 16y - 25z + 4. To do this, we will combine like terms.

First, combine the terms that contain y:

-y - 16y = -17y

Then, combine the terms that contain z:

9z - 25z = -16z

The number without a variable, which is 4 in this case, remains the same since it does not have any like terms to combine with.

Now, we put the simplified terms together:

-17y - 16z + 4

The expression is now simplified to its least terms.

Final answer:

Vertex-edge graphs can model real-world problems, not all graphs can be solved, Euler paths and Hamilton paths are different, and in a Hamilton circuit, all vertices must be used exactly once.

Explanation:

Vertex-edge graphs, also known as graphs or networks, are mathematical structures that consist of vertices (also called nodes) connected by edges. They are widely used to model real-world problems across various fields such as computer science, transportation planning, and social networks, among others (1). While some vertex-edge graphs can be solved, it is not true that all graphs can be solved. Solvability depends on the specific problem being represented by the graph and the algorithms or methods used to solve it (2). Euler paths and Hamilton paths are not the same. An Euler path is a path in a graph that visits every edge exactly once, while a Hamilton path visits every vertex exactly once (3). In a Hamilton circuit, all vertices must be used exactly once, but not in a Hamilton path. There can be more than one Hamilton path in a graph, depending on its structure (4).

Answer:

A.10000

B.25 more trees must be planted

Step-by-step explanation:

⇒Given:

A.

⇒If the total trees per acre is doubled , which means :

total number of trees per acre [tex]t_{f}[/tex] = [tex]2*t_{i}[/tex] = 200

the yield will decrease by : [tex]t_{f}[/tex] - [tex]y_{i}[/tex]

[tex]y_{f}= 150-100= 50[/tex]

⇒total yield = [tex]50*200=10000[/tex]

B.

⇒to maximize the yield ,

let's take the number of trees per acre to be 100+y ;

and thus the average yield per acre = 150 - y;

total yield = [tex](100+y)*(150-y)\\=15000+50y-y^{2} \\[/tex]

this is a quadratic equation. this can be rewritten as ,

     ⇒   [tex]=15000+50y-y^{2}\\=15000+625 - (625 - 50y +y^{2})\\=15625 - (y-25)^{2}[/tex]

In this equation , the total yield becomes maximum when y=25;

⇒Thus the total number of trees per acre = 100+25 =125;

Answer:

16

Step-by-step explanation:

All of the lengths of the rectangle are 4 making the area 4*4=16

Answer:

its 31 when you round to 2 decimal points.

Answer:

BC = 28

Step-by-step explanation:

Since the triangle is equilateral then all 3 sides are congruent.

Equate AB and AC and solve for x, that is

12x + 4 = 8x + 12 ( subtract 8x from both sides )

4x + 4 = 12 ( subtract 4 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2, thus

AC = 8x + 12 = (8 × 2) + 12 = 16 + 12 = 28

Since the 3 sides are congruent then BC = 28

Answer:

The answer is 52%

Step-by-step explanation:

The above data shows that (0.32) 32% of residents support Zhang and live in Cherry Hill.

Since the question asked is to know the percentage of the Cherry Hill residents polled that supported Zhang

We focus on Cherry Hill residents only.

(0.62) 62% of residents surveyed live in Cherry Hill

So you would divide 32% by 62% and that would be approximately 0.52  

Convert 0.52 to percentage

0.52 x 100 = 52%

Answer:

About 52%

Step-by-step explanation:

Answer: 210

Step-by-step explanation: because 9 times 15 =135

and then you add 75

and then add them together and get 210 for the long distance phone call

Answer:

https://cdn.flvs.net/assessment_images/educator_algebra2_v19/02_07_14_flvs.gif

Step-by-step explanation:

the correct answer is: ( x ) equals negative 1 plus or minus 2 I square root of 2

To solve the equation [tex]\( x^2 + 2x + 9 = 0 \)[/tex], you can use the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

In this case, [tex]\( a = 1 \), \( b = 2 \), and \( c = 9 \)[/tex]. Substituting these values into the formula:

[tex]\[ x = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(9)}}{2(1)} \]\[ x = \frac{-2 \pm \sqrt{4 - 36}}{2} \]\[ x = \frac{-2 \pm \sqrt{-32}}{2} \]\[ x = \frac{-2 \pm 4i\sqrt{2}}{2} \]\[ x = -1 \pm 2i\sqrt{2} \][/tex]

So, the correct answer is: ( x ) equals negative 1 plus or minus 2 I square root of 2.

Answer:

The sales price of the camcorder is  $742.41 .

Step-by-step explanation:

The Cost Price of camcorder  = $678

The sales Tax = 9.5%

Now, 9.5% of the cost price $678 =  [tex]\frac{9.5}{100} \times (678) = 64.41[/tex]

⇒ The sales tax on the camcorder = $64.41

SALES PRICE = COST PRICE + SALES TAX

                       =   $678 + $64.41

                       = $742.41    

or, sales price   =$742.41  

Hence, the sales price of the camcorder is  $742.41 .

Answer:

14.6%

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

Here, n = 10, r = 4, and p = 1/4.

P = ₁₀C₄ (1/4)⁴ (1−1/4)¹⁰⁻⁴

P = 210 (1/4)⁴ (3/4)⁶

P ≈ 0.146

There is an approximate 14.6% probability that exactly 4 of the 10 adults are on a diet.

Answer:

-3 and 6

Step-by-step explanation:

-3 + 6 = 3

-3 * 6 = -18

Final answer:

The two numbers that add up to 3 and multiply to -18 are 6 and -3. By setting up equations based on these conditions and solving them, we determine these two numbers.

Explanation:

The question asks about two numbers that when added together equal 3, and when multiplied together equal -18. To find these numbers, we need to set up a system of equations based on the given conditions:

Let the two numbers be x and y.

The sum of x and y is 3: x + y = 3.

The product of x and y is -18: xy = -18. Let's use factorization and proceed as follows:

Assume y = 3 - x.

Substitute y into the second equation: x(3 - x) = -18.

This simplifies to x2 - 3x - 18 = 0.

Factor the quadratic: (x - 6)(x + 3) = 0.

So, x = 6 or x = -3.

Using x + y = 3, if x = 6, then y = -3. If x = -3, then y = 6.

The two numbers that satisfy the given conditions are 6 and -3.

Answer:

Step-by-step explanation:

From the given diagram we notice that

1. Line AB is equal to Line DE.

2. Line AC is equal to line DF.

3. Angle A is equal to angle D

Then, it shows that 2 sides of the triangle are similar and 1 of it's angle is also similar. Then, it is SAS

Where, S- represent sides and A- represents angle

NOTE : we have SSS, ASA, AAS and SAS, we don't have SSA

To write the similar triangle equation

∆ABC ≈ ∆DEF

Since AB is equal to DE, the we replace It with DE and also Angle A is equal to angle D. Also AC is equal to DF, then we replace C with F.

So the answer is C

∆ABC ≈ ∆DEF SAS

Answer:

9.4m

Step-by-step explanation:

Let the diagram of the rectangular pyramid be as shown in the attached

If a point C' is selected midway between C and B and F' is selected midway between D and C as shown in pyramid 2

FC can then be computed using pythagoras theorem such that

FC^2 = FC'^2 + CC'^2

FC^2 = (14.6/2)^2 + (9.8/2)^2

FC^2 =53.29 + 24.01

FC^2 = 77.3

FC = sqrt(77.3) = 8.8

To determine the height of the attic, we estimate EF, Pythagoras theorem can be used for triangle EFC

such that EC^2 = EF^2 + FC^2

therefore EF^2 = EC^2 - FC^2

EF^2 = 12.9^2 - 8.8^2

EF^2 = 166.41 - 77.44

EF^2 = 88.97

EF = sqrt(88.97)

EF = 9.4

The height of the attic is therefore 9.4m

Answer:

The company's profit be in the year 2008 is $8.3 million.

Step-by-step explanation:

Given:

In the year 2006, a company made $7 million in profit, their profit increased by 9%.

So, we need to calculate the company's profit be in the year 2008.

Now, by putting the formula to find the profit(P) after the two year:

Difference between the year = 2008 - 2006 = 2 year.

So, number of years(n) = 2 year

Rate of profit increasing(r) = 9%

Amount company made in 2006 (A) = $7 million.

[tex]P=A(1+\frac{r}{100})^{n}[/tex]

[tex]P=7(1+\frac{9}{100})^{2}[/tex]

[tex]P=7(1+0.09)^{2}[/tex]

[tex]P=7(1.09)^{2}[/tex]

[tex]P=7\times 1.188[/tex]

[tex]P=8.316[/tex]

Profit in the year 2008 would be 8.316 million, and nearest to the tenth of a million dollars is $8.3 as 3 is in the tenth place of the decimal and 1 in the hundredth so rounding will change $8.316 to $8.3.

Therefore, the company's profit be in the year 2008 is $8.3 million.

Final answer:

To find the company's profit in 2008 after a 9% increase each year from 2006, we calculate compound growth over two years. The profit in 2008 would be $8,316,700, which rounds to $8.3 million.

Explanation:

To calculate the company's profit in the year 2008 after it increased by 9% each year following 2006, we can use the formula for compound interest which is similar to calculating compounded profit growth. The formula is:

[tex]P = P_0 \times (1 + r)^t[/tex]

Where:

P is the future profit

P₀ is the initial profit ($7 million)

r is the annual growth rate (9% or 0.09)

t is the number of years since 2006 (2008 - 2006 = 2 years)

Let's calculate the profit for 2008:

P = $7,000,000 × (1 + 0.09)²

First, calculate the growth factor for one year:

1 + 0.09 = 1.09

Now, apply the growth factor for two years:

1.09² = 1.1881

Multiply the initial profit by the growth factor:

P = $7,000,000 × 1.1881 = $8,316,700

To the nearest tenth of a million dollars, the company's profit in 2008 would be $8.3 million.

Answer:

We can conclude that Δ ABC ≅ Δ DEF by AAS postulate.

Step-by-step explanation:

Δ ABC and Δ DEF are congruents because:

1. Their non-included sides BC and EF are equal (7 units = 7 units)

2. Their angles ∠A and ∠D are equal (39° = 39°)

3. Their angles ∠C and ∠F are equal  (64° = 64°)

Now, we can conclude that Δ ABC ≅ Δ DEF by AAS postulate.

Answer:

32

Step-by-step explanation:

4 x 8 = 32

Answer:

32 quarters

Step-by-step explanation:

if there are 4 stack with 8 quarters in each stack, then we know that all we have to do is multiply 4 x 8 which equals 32

Answer:

x > - 2

Step-by-step explanation:

Given

7 + x > 5 ( subtract 7 from both sides )

x > - 2

Answer:

a = - 17

Step-by-step explanation:

Given

- 2(a + 16) = 2 ( divide both sides by - 2 )

a + 16 = - 1 ( subtract 16 from both sides )

a = - 17

Answer:

a=-17

Step-by-step explanation:

-2(a+16) =2

-2a-32=2

+32 +32

-2a=34

divided in both sides by -2

a=-17

Hello.

Answer: -55. When adding two negatives, you add like you would any positive number.