A projectile is fired upward from a height of 160 feet above the ground, with an initial velocity of 600ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0. How long will the projectile be in flight? Round your answer to the nearest hundredth.

Answer:

(a) $0.80

(b) 1.25 m

Step-by-step explanation:

(a) Put 1 where L is, and evaluate the equation.

... p = 0.8·1 = 0.8

The cost for 1 meter of rope is $0.80.

(b) Put 1 where p is and solve for L.

... 1 = 0.8L

... 1/0.8 = L = 1.25

The length of rope that costs $1 is 1.25 meters.

Answer:

Well that depends on where you buy it

Step-by-step explanation:

It could cost various things and you didn't add enough context for us to assume where you could have purchased the nylon rope

Answer:

letter A po angsagot terror

Answer:

7.61 meters per second

Step-by-step explanation:

The speed of the wind at x meter i.e. above the ground should be

f(x) = 1.5 ln x  + 5.2

Now to determine the wind speed at 5 meters above the ground substitute

i.e.

x = 5 for the above function

= 1.5 ln (5)  + 5.2

= 7.61

So the speed of the wind above the ground is 7.61 meters per second

And the same is to be considered

Answer:

0.15

Step-by-step explanation:

I don't know if that is right but sorry if it is wrong but I would check with your teacher or someone for help

Given the breadth of the bag is 12 cm and the length is 18 cm, and the assumed height is 6cm, t​he volume of the cooler bag is 1296 ml.

The volume of the cooler bag is determined using the formula;

Volume = length * breadth * height

Data given:

breadth = 12 cm

length = 18 cm

height = ?

The height is not given, therefore, an assumed height of 6 cm is used in the calculation.

Converting the measurements to millimeters:

Breadth = 12 cm * 10 mm/cm = 120 mm

Length = 18 cm * 10 mm/cm = 180 mm

Height = 6 cm * 10 mm/cm = 60 mm

Now, we calculate the volume of the cooler bag:

Volume = 180 mm * 120 mm * 60 mm

Volume = 1,296,000 mm³

To convert the volume from cubic millimeters to milliliters, we divide by 1,000

Volume = 1,296,000 mm³ / 1,000

Volume of cooler bag = 1296 ml

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This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Multiply the 2 denominators which gives you 6. P.S make sure to do cross multiplication for the numerator cause if the rest of the question asks for the full answer then you would get it wrong if you don't.

The statements representing are Gabriel's age is 29/4  and 7 ¼ years old .

This equation can be used to represent the relationship between Dylan and Gabriel's age:

Dylan = 3 ⅓ x Gabriel

24 1/6 =  3 ⅓ x Gabriel

In order to determine Gabriel's age, divide both sides of the equation by  3 ⅓

Gabriel = 24 1/6 ÷ 3 ⅓

145 / 6 x 3/10 = 29/4 =  7 ¼ years old

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Answer:the variable k is the constant of proportionality

Step-by-step explanation:

This can be proven when the equation is used to find different values of y. To find these different values, the x variable is substituted for different values while the k value stays the same. hope this helps!!

Answer:  ln 20 + 5t

Step-by-step explanation:

ln (ab) = lna + lnb

ln (10e⁵ˣ) = ln 10 + ln e⁵ˣ           → (ln e cancels out)

              = ln 10 + 5t        

Hello!

25 wooden ..... 5.5 hours

x wooden ..... 9.9 hours

_____________________

25/x = 5.5/9.9

25 × 9.9 = x × 5.5

247.5 = x × 5.5

x × 5.5 = 247.5

x = 247.5 : 5.5

x = 45 wooden

Good luck! :)

Answer:

45

Step-by-step explanation:

In questions such as these it is implied Anita can and does work at a constant rate. Therefore, we can set up the following proportion:

\(\frac{25}{5.5}=\frac{x}{9.9}\), where \(x\) represents the number of wooden slats she can paint in 9.9 hours.

Multiplying both sides by 9, we get:

\(x=\frac{9.9\cdot 25}{5.5},\\x=\boxed{45}\)

Answer: 17

Step-by-step explanation:

Answer:

Step-by-step explanation:

Q.1.

\(ln\left(4\right)+\:ln\left(x\right)=ln\left(24\right)\)

apply ln rules:

\(ln( 4 * x) = ln (24)\)

cancel ln from both sides:

\(4x = 24\)

divide both sides by 4:

\(x = 6\)

Q.2.

\(2ln\left(x\right)=ln\left(4\right)+ln\left(9\right)\)

apply ln rules:

\(ln\left(x^2\right)=ln\left(4*9\right)\)

cancel ln from both sides:

\(x^2 = 36\)

\(x = \pm6\)

as ln cannot be negative:

\(x = 6\)

The relationship between the amount of flour that Priya bought, x, and the amount of flour that Clare bought

The two relationship are gotten from the word problem

Priya bought x grams of flour. Clare bought 3/8 more than that is interpreted as

let Claire's amount be y

y = x + 3x/8

y = 11x/8

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The equations which represent the relationship between variables x and y as given in the task content are;

It follows from the task content that the answer choices which correctly represents the relationship between both variables are to be determined.

Since x = Amount of flour Priya bought and the amount Claire bought, y is 3/8 more than that.

Therefore, algebraically, the amount Claire bought, y can be expressed in terms of x as follows;

y = x + (3 / 8)x.

The equation above is represented in Choice C.

However, the equivalent expression to the given equation by factorisation is;

y = (1 + 3 / 8) x

y = 11 / 8x.

Therefore, the correct answer choices are; Choice C and Choice E.

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Answer-So the dimensions of the rectangle are width is 4 m and length is 11 m

Step-by-step explanation:

Equation for Perimeter of a rectangle: Perimeter = 2W + 2L

Defining the variables, let

Width = x

Length = 2x+3 (3 more than twice the width)

Plugging everything into the equation

30= 2(x) + 2(2x+3)  using the distributive property,

30=2x+4x+6  combining like terms

30=6x+6  subtracting 6 from both sides,

24=6x  divide both sides by 6

4=x  This means that the width is 4 m

To get the length, use the expression L=2x+3 and plug in x = 4 that was already solved for

L=2(4)+3

L=8+3 = 11 m

So the dimensions of the rectangle are width is 4 m and length is 11 m

The interest after 7 years is $15, 047. 86

The fornula for simple interest is expressed as;

Simple interest = PRT/100

where;

We have the values to be;

P = $3583

R = 6%

T = 7

substitute into the formula for simple interest

Simple interest , I = 3583 × 6 × 7/100

I = 150, 486/ 100

I = $15, 047. 86

Thus, the interest after 7 years is $15, 047. 86

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Answer: 0.49 yards

Step-by-step explanation: First, you do $15-$9.48 to find out how much she spent on the ribbon, which is $5.52. Then, you divide $5.52 by 12 (cents) to figure out how many yards Yolanda could buy with 5.52. 5.52/12=0.49 yards

Answer:

the answer is 2996848

Step-by-step explanation:

The point in the solution set from the graph is (0, 0)

From the question, we have the following parameters that can be used in our computation:

y < -5/2x - 2

y ≥ -1/2x + 2

Next, we plot the graph of the system of the inequalities

The graph is given

From the graph, we have solution to the system to be the shaded region

The point in the solution set from the graph is (0, 0)

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Answer:

y = 3x² + 5x + 1

x = -b±√b²-4ac/2a

a = 3, b = 5 c = 1

x = -5±√5²-4(3)(1)/2(3)

x = -5±√25-12/6

x = -5±√13/6

The number that belongs in the green box is -5.

Given:

Quadratic equation y = 3x² + 5x + 1 into the quadratic formula,

which is \(\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\), determine the values of a, b, and c from the given equation.

Comparing the equation y = 3x² + 5x + 1 with the standard quadratic form y = ax² + bx + c

a = 3

b = 5

c = 1

Now, substitute these values into the quadratic formula:

x = (-(5) ± √((5)² - 4(3)(1))) / (2(3))

x = (-5 ± √(25 - 12)) / (6)

x = (-5 ± √(13)) / 6

Therefore, the quadratic equation y = 3x² + 5x + 1 can be expressed in the quadratic formula as: x = (-5 ± √(13)) / 6

Thus, the number is -5.

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Answer:

$1,000.

Step-by-step explanation:

200 kids divided by 25% or 4 = 50 then 50 x 20 = 1,000.

The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For the lower bound of 93, the z-score is:

z = (93 - 105) / 20 = -0.6

For the upper bound of 117, the z-score is:

z = (117 - 105) / 20 = 0.6

Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:

normalcdf(-0.6, 0.6, 0, 1)

This gives us a probability of 0.6827.

Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

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In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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1.243 is the measure of the value of x from the given expression

Rational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.

Given the following rational equation

√11 x = √17

We need to determine the measure of the value of x.

Taking the square of both sides we will have:

(√11 x)² = (√17)²

11x² = 17

x² = 17/11

x² = 1.545

Take the square root of both sides

√x² = √1.545
x = 1.243

Hence the measure of the value of x from the given equation is 1.243.

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The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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The correct option is The PLUS loan will have a higher balance by $34.10 at the time of repayment. Hence Option B is correct.

Which loan will have a higher balance, and by how much at the time of repayment?

We must compute the total amount owed for each loan to determine which will be paid off first and with which balance.

The compound interest calculation can be used to get the total amount due for the :

\(\rm A = P(1 + r/n)^{(nt) }\)

where A represents the total amount owed, P the borrowed principal, r the yearly interest rate, n the number of times interest is compounded annually, and t the period of time in years.

When we enter the Unsubsidized Stafford Loan values, we obtain:

\(A = 10,958(1 + 0.0385/12)^{(12*1) }= 11387.41\)

Comparing the result above with the PLUS loan balance, the PLUS loan

balance is higher by:

$11,421.51  - $11,387.41

= $34.10

Thus, The correct option is The PLUS loan will have a higher balance by $34.10 at the time of repayment. Hence Option B is correct.

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