A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?

Answer: c. g may cause h

Step-by-step explanation:

Correlation: It represents the relation between any two or more than two variable.

Causation: It is a kind of correlation where one variable if affected by the other variable.

Therefore , Causation implies correlation.

But correlation does not imply causation.

Hence, if  there were a strong correlation between the variables g and h, then g may cause h.

The price of the basketball on sale is $17.50.

To calculate this:

1. Calculate 50% of $35:

  $35 x 0.50 = $17.50

2. Subtract the discount from the original price:

  $35 - $17.50 = $17.50

When an item is on sale for a percentage off, you first find what that percentage represents of the original price. In this case, 50% of $35 is $17.50. Then, you subtract that amount from the original price to find the sale price. So, the basketball, originally priced at $35, would be $17.50 when it's on sale for 50% off.

Complete question:

Find the price of a $35 basketball that is on sale for 50% off the regular price.

Answer:

Plan B

Step-by-step explanation:

Plan B and plan C start out at the same increase: 10% ($0.50) for the first week. The increase under plan C stays at 10% of the original value, but the increase under plan B increases according to the value the week before, which keeps getting larger.

Hence, plan B gets to $8.00 the fastest — after about 5 weeks.

The answer is [tex]\( 5^{0.75} = 5^{\frac{3}{4}} = \sqrt[4]{5^3} \)[/tex].

To solve[tex]\( 5^{0.75} \)[/tex], we first express 0.75 as a fraction in its simplest form. The number 0.75 is equivalent to [tex]\( \frac{3}{4} \)[/tex]. Therefore, [tex]\( 5^{0.75} \)[/tex] can be rewritten as [tex]\( 5^{\frac{3}{4}} \)[/tex].

Now, we can break down [tex]\( 5^{\frac{3}{4}} \)[/tex] using the properties of exponents. The exponent [tex]\( \frac{3}{4} \)[/tex] indicates that we are looking for the fourth root of 5 raised to the power of 3. Mathematically, this is expressed as [tex]\( \sqrt[4]{5^3} \)[/tex].

To find the value, we first calculate [tex]\( 5^3 \)[/tex], which is [tex]\( 5 \times 5 \times 5 = 125 \)[/tex]. Then we take the fourth root of 125. The fourth root of a number is the number that, when raised to the power of 4, gives the original number. In this case, we are looking for a number that, when raised to the power of 4, equals 125.

The fourth root of 125 is not an integer, but we can approximate it. We know that [tex]\( 2^4 = 16 \)[/tex]and [tex]\( 3^4 = 81 \)[/tex], so the fourth root of 125 must be between 2 and 3. Through calculation or using a calculator, we find that [tex]\( \sqrt[4]{125} \)[/tex] is approximately 3.3019.

Therefore, [tex]\( 5^{0.75} \)[/tex] is approximately 3.3019.

Answer:

Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.

Step-by-step explanation:

Pam read 126 pages of her summer reading book in 3 hours.

[tex]\texttt{Speed of Pam =}\frac{126}{3}=42page/hour[/tex]

Zack read 180 pages of his summer reading book in 4 hours. [tex]\texttt{Speed of Zack =}\frac{180}{4}=45page/hour[/tex]

Number of pages Pam read in 5 hours = 5 x 42 = 210 pages

Number of pages Zack read in 5 hours = 5 x 45 = 225 pages

We need to find will they both finish the 215 page book after 5 total hours of reading,

Here number of pages read by Zack is greater than 215 and number of pages read by Pam is less than 215.

So Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.

we have

[tex]10x^{2}y+ 25x^{2}[/tex]

we know that

[tex]10=2*5\\25=5*5[/tex]

substitute

[tex](2*5)x^{2}y+ (5*5)x^{2}[/tex]

Factor [tex]5x^{2}[/tex]

[tex](5x^{2})(2y+ 5)[/tex]

therefore

the answer is

[tex](5x^{2})(2y+ 5)[/tex]

The equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)

Equivalent expressions are expressions that have equal values

The expression is given as:

10x^2y + 25x^2

Factor out 5x^2 from the expression

5x^2(2y + 5)

Hence, the equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)

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To achieve an annual income of $18,930, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate.

To determine how much a woman should invest at each rate to achieve an income of $18,930 per year, we can set up a system of linear equations. Assuming she invests x dollars at the 10% rate and y dollars at the 18% rate, we can use the following equations:

x + y = $139,700: This equation represents the total amount of money she has to invest.

0.10x + 0.18y = $18,930: This equation represents the annual income from the investments.

To solve:

Multiply the first equation by 0.10:

0.10x + 0.10y = $13,970

Subtract this from the second equation:

0.18y - 0.10y = $18,930 - $13,970

0.08y = $4,960

Divide by 0.08 to find y:

y = $62,000

Substitute y back into the first equation to find x:

x + $62,000 = $139,700

x = $77,700

Therefore, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate to achieve her desired income.

Jim would need 5 years to earn interest equal to half of his original principal at a 10% simple interest rate.

To find out how many years it would take for Jim to earn interest equal to half of his original principal at a 10% simple interest rate, we use the formula for simple interest: I = PRT, where I is the interest, P is the principal, R is the rate of interest per year, and T is the time in years.

In this case, Jim wants the interest I to be half of the principal P. So the equation becomes :

[tex]\frac{P}{2} = P \times 0.10 \times T[/tex] or T

=  [tex]\frac{P}{2 \times P \times 0.10}[/tex], which simplifies to T =[tex]\frac{1}{2 \times 0.10}[/tex]or T = 5 years. Therefore, the correct answer is C. 5 years.

The coordinates of the x-intercept are (B/C,0)

The x-intercept of a graph is defined as the places where the graph crosses the x-axis or the locations where the coordinate of the y-axis equals 0, which are known as the x-intercept of a graph.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Consider the graph of Cx + Ay = B

Here A, B, and C are all positive constants.

To determine the coordinates of the x-intercept

⇒ Cx + Ay = B,

Substitute the value of y = 0 and solve for x

⇒ Cx + A(0) = B,

⇒ Cx = B,

Divide both sides by C

⇒ x = B/C

Hence, the coordinates of the x-intercept are (B/C,0).

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Answer: There would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.

Step-by-step explanation:

Since we have given that

Number of tubes of toothpaste = 56

Number of packets of floss = 112

Number of toothbrushes = 85

We need to find the greatest number of identical dental care bags that dentist can make with the least amount of items leftover.

So, we will find "H.C.F." of 56, 112, 85 which is equal to 1.

So, there would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.

Answer:

The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664

Step-by-step explanation:

It submerges and dives to −972 feet. Then, it ascends 308 feet.

Initially it goes down by 972 feet and then goes up by 308 ft.

Since depth is more than elevation.

Final position is below sea level.

Final depth = 972 - 308 = 664 ft

The integer which represents the submarine's position in feet (depth) after it ascends to avoid the cliff = -664

Answer:

The elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.  

Step-by-step explanation:

We are given the following information in the question:

The elevator descends 500 feet in 20 seconds.

Now, we know that at 0 second the lift was at 0 feet.

To calculate the change in the height of elevator per second, we use the following formula:

[tex]\text{Change in height per second} = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\\= \displaystyle\frac{500-0}{20-0} = \frac{500}{20} = 25\text{ feet per second}[/tex]

Hence, the elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.

The change in the elevator's height per second is -25 feet per second. This is calculated by dividing the total descent (500 ft) by the time taken (20 s). The negative value indicates a descent.

To determine the change in an object's height per second, we can use the formula for velocity, which is the displacement (change in position) divided by the time. In this case, the elevator descends 500 feet in 20 seconds. Therefore, the change in the elevator's height per second is 500 feet divided by 20 seconds.

The change in the elevator's height per second is -25 feet per second

The negative sign indicates that the elevator is descending, as opposed to ascending. It's important to note that this is an average rate of change because the question doesn't specify that the elevator's speed is constant.

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35-3 =32

32/2 = 16

there are 16 pear trees and 19 apple trees

The flux of [tex]\vec f(x,y,z)[/tex] across S is given by the surface integral

[tex]\displaystyle \iint_S \vec f(x,y,z) \cdot d\vec s[/tex]

Join to S the disk D of radius 3 in the plane z = 2, for which we have

[tex]x^2+y^2+2=11 \implies x^2+y^2=9=3^2[/tex]

Let S' = S U D (the union of S and D). Since S' is closed, we can use divergence theorem to compute the flux of [tex]\vec f[/tex] through S' :

[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \iiint_R \mathrm{div}\vec f \, dV[/tex]

Compute the divergence of [tex]\vec f[/tex] :

[tex]\mathrm{div}\vec f = \dfrac{\partial\left(z\tan^{-1}(y^2)\right)}{\partial x} + \dfrac{\partial\left(z^3\ln(x^2+5)\right)}{\partial y} + \dfrac{\partial(z)}{\partial z} = 1[/tex]

Compute the volume integral by converting to cylindrical coordinates. Take

[tex]\begin{cases}x=r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]

Then the flux of [tex]\vec f[/tex] across S' is

[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_2^{11-x^2-y^2} dV = \int_0^{2\pi} \int_0^3 \int_2^{11-r^2} r \, d\zeta \, dr \, d\theta = \frac{81\pi}2[/tex]

To get the flux across S alone, we subtract from this integral the flux of [tex]\vec f[/tex] across D.

Parameterize D by the vector function

[tex]\vec\sigma(\rho,\phi) = \rho \cos(\phi) \, \vec\imath + \rho \sin(\phi) \, \vec\jmath + 2\, \vec k[/tex]

with [tex]0\le\rho\le3[/tex] and [tex]0\le\phi\le2\pi[/tex].

Get the downward-pointing normal vector to D :

[tex]\vec n = \dfrac{\partial\vec\sigma}{\partial\phi} \times \dfrac{\partial\vec\sigma}{\partial \rho} = -\rho\,\vec k[/tex]

Compute the flux across D :

[tex]\displaystyle \iint_D \vec f\cdot d\vec s = \int_0^{2\pi} \int_0^3 \vec f(\vec\sigma) \cdot \vec n \, d\rho\,d\phi = \int_0^{2\pi} \int_0^3 (-2\rho) \, d\rho \, d\phi = -18\pi[/tex]

So the flux of [tex]\vec f[/tex] across S is

[tex]\displaystyle \iint_S \vec f \cdot d \vec s = \frac{81\pi}2 - (-18\pi) = \boxed{\frac{117\pi}2}[/tex]

To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux and evaluate the integral.

To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux: flux = ∫∫(f•n)dA. Here, f(x,y,z) = z tan⁻¹(y²)i + z³ ln(x² + 5)j + zk.

The equation of the paraboloid is x² + y² + z = 11. Using these equations, we can set up the double integral and solve for the flux.

After evaluating the integral, we can find the flux of f across the given surface.

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