7. For a dropped object, the function t(h)=√ h/16 can be used to find the distance, h, in feet,
that the object has fallen after a time, t, in seconds. How far has the object fallen after 1.6
seconds?

The simplification of the given estimate above would be = 3 21/40

To simply a mixed fraction, the mixed fraction should be converted to a single fraction. That is;

3⅝ = 29/8

Use the newly converted fraction to solve:

= 29/8 -1/10

Fine the Lowest common denominator = 49

= 145-4/40

= 141/40

= 3 21/40 ( convert to a mixed fraction)

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Leonard gave the correct value of approximate average rate of change of function.

What is a function?

In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.

The average rate of change of  function means the typical rate at which one quantity is changing in respect to another. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

The formula for average rate of change of  function in the interval [a,b] is

[tex]\frac{f(b) - f(a)}{b-a}[/tex].

We are asked to find the rate of change when x = -3 to 6

From graph

when x = -3 , y = -2

when x = 6, y = 2

So average rate of change of function = [tex]\frac{f(6) - f(-3)}{6-(-3)} = \frac{2 - (-2)}{9} = \frac{4}{9}[/tex]

Therefore Leonard gave the correct value of approximate average rate of change of function.

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The number of miles further that Rachel was able to jog on Sunday more than Saturday was 10 miles.

On Saturday, the table shows that Rachel jogged a total of 15 miles. On Sunday, Rachel was able to jog 25 miles.

This means that Rachel was able to jog more miles on Sunday than she was able to jog on Saturday. The difference in the miles was :

= Miles jogged on Sunday - Miles jogged on Saturday

= 25 - 15

= 10 miles

In conclusion Rachel jogged 10 miles more on Sunday than Saturday.

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The graphs of the linear equations will intercept at the point (4, 6)

We know that taxy company a charges $4 plus $0.5 per mile, so the cost for x miles is:

A = 4 + 0.5x

While taxy company be charges $5 plus $0.25 per mile, so the cost for x miles will be:

B = 5 + 0.25x

The graphs will intersect at the x value such that the two linear equations are equal:

A  = B

This happens when:

4 + 0.5x = 5 + 0.25x

0.5x - 0.25x = 5 - 4

0.25x = 1

x = 1/0.25 = 4

And the cost is:

B = 5 + 0.25*4 = 6

So the graphs intercept at the point (4, 6)

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Answer:

[tex]\tan \theta=-\dfrac{\sqrt{5}}{2}[/tex]

[tex]\cos \theta=\dfrac{2}{3}[/tex]

[tex]\sin \theta=-\dfrac{\sqrt{5}}{3}[/tex]

Step-by-step explanation:

To find the exact values of the trigonometric functions of θ, we can use the following trigonometric identities:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\sec x=\dfrac{1}{\cos x}$\\\\\\$\tan x=\dfrac{\sin x}{\cos x}$\\\\\\$\sin^2x+\cos^2x=1$\\\end{minipage}}[/tex]

In quadrant IV, cosine of the angle is positive, whereas sine of the angle is negative.

Given that sec θ = 3/2, and secant is the reciprocal of cosine:

[tex]\sec \theta=\dfrac{3}{2}[/tex]

[tex]\dfrac{1}{\cos \theta}=\dfrac{3}{2}[/tex]

[tex]\boxed{\cos \theta=\dfrac{2}{3}}[/tex]

To find sin θ, we can substitute the found value of cos θ into the Pythagorean identity:

[tex]\sin^2 \theta+\cos^2 \theta=1[/tex]

[tex]\sin^2 \theta+\left(\dfrac{2}{3}\right)^2=1[/tex]

[tex]\sin^2 \theta=1-\left(\dfrac{2}{3}\right)^2[/tex]

[tex]\sin \theta=\sqrt{1-\left(\dfrac{2}{3}\right)^2}[/tex]

[tex]\sin \theta=\dfrac{\sqrt{5}}{3}[/tex]

As sine of the angle is negative in quadrant IV:

[tex]\boxed{\sin \theta=-\dfrac{\sqrt{5}}{3}}[/tex]

Finally, substitute the values of sin θ and cos θ into the tan θ identity to find tan θ:

[tex]\tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]

[tex]\tan \theta=\dfrac{-\frac{\sqrt{5}}{3}}{\frac{2}{3}}[/tex]

[tex]\boxed{\tan \theta=-\dfrac{\sqrt{5}}{2}}[/tex]

Therefore, the exact values of the trigonometric functions for θ are:

[tex]\tan \theta=-\dfrac{\sqrt{5}}{2}[/tex]

[tex]\cos \theta=\dfrac{2}{3}[/tex]

[tex]\sin \theta=-\dfrac{\sqrt{5}}{3}[/tex]

In this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.

What is the quadratic equation?

A quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in the following standard form. a+ bx + c = 0, where a, b, and c are real numbers and a 0.

The Hardy-Weinberg equilibrium is an idealized model of a population that assumes that the frequency of alleles remains constant from generation to generation in the absence of external forces.

According to this model, the frequency of a particular genotype can be calculated using the following formula:

p² + 2pq + q² = 1

where p is the frequency of the dominant allele (C) and q is the frequency of the recessive allele (c). In this case, p = 1 - q = 1 - 0.3 = 0.7, and q = 0.3.

The frequency of individuals with the genotype CC (green hair) is given by p², or 0.7² = 0.49.

The frequency of individuals with the genotype Cc (green hair) is given by 2pq, or 2 * 0.7 * 0.3 = 0.42.

Hence, in this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.

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On evaluating, the function f(x) and g(x) the values of f(g(3)) = - 11 and f(g(x)) = -35x + 22.    

A relation between a collection of inputs and outputs is known as a function. A function is an association between inputs in which each input is connected to approximately one output. To find f(a) for a given function f(x) we simply substitute 'a' instead of 'x' in the given function f(x).

Here we have

f(x) = 7x - 5 and g(x) = - 5x + 4

10. f(g(3))  

To find g(3) take x = 3 in g(x)

=> g(3) = - 5(3) + 4 = - 15 + 4 = 11  

=> g(3) = - 11

To find f(g(3))  take x = g(x) = - 11 in f(x)

f(g(3)) = 7(-11) - 5 =  - 77 - 5 = - 82

∴ The value of f(g(3)) = - 11  

11. f(g(x)

To find f(g(x)) take x = g(x)

=>  f(g(x) = 7(-5x + 4) - 5  

=>  f(g(x)) = -35x + 28 - 5

=>  f(g(x)) = -35x + 22  

∴ f(g(x)) = -35x + 22    

Therefore,

On evaluating, the function f(x) and g(x) the values of f(g(3)) = - 11 and f(g(x)) = -35x + 22.    

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Submarine 2 will reach a depth of -1,056 feet below sea level in the fastest time.

It will take the faster submarine 44 minutes to reach a depth of -1,056 feet below sea level.

Since the proportional equation for Submarine 1 is y = -22x.

In order to determine which submarine will reach a depth of -1,056 feet below sea level in the fastest time, we need to find the proportional equation for Submarine 2 using the graph.

From the graph:

proportionality constant = depth/time

proportionality constant = -120/5 = -24

y = -24x

Since the proportionality constant of Submarine 2 (-24) is greater than that of Submarine 1 (-22). Thus, Submarine 2 will reach a depth of -1,056 feet below sea level in the fastest time.

The faster submarine is Submarine 2:

y = -24x

y = -1,056 feet

-1,056 = -24x

x= 1,056/24

x = 44 minutes

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The solution is,  1/3 ÷ 6, expression shows how much of the pan each person gets.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

wen and five friends equally share 1/3 of a pan of snack bars.

so, we get,

the expression is 1/3 ÷ 6

This is because there are 6 friends in all and you are splitting 1/3 of the pan snack bars to each of them.

So, what your splitting/cutting/dividing would be the dividend (1/3) and then the friends would be the divisor (6)

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Answer:

the age of her mother is 35 yrs old

Step-by-step explanation:

Let the age of daughter be x and mother be 6x

Now,

By question

6x -x=35

or, 5x =35

or,x=35/5

or x =5

Lastly,

age of daughter=x=5

age of mother =6x

=6*5

=35

Answer:

The polygons are similar.

Step-by-step explanation:

The polygons are similar due to the SAS Similarity Theorem.

Hope this helped! :)

Based on the information, it can be inferred that the baby weighed 7.06 pounds at birth.

To calculate how much the baby weighed at birth we must take into account the information we have available

Current Weight: 6.8 lbs.

% lost: 3.7%

According to the above, we must calculate what percentage the current weight is equal to:

100% - 3.7% = 96.3%

Now we must make a rule of three to find the weight of the baby at birth:

96.3 - 6.8

100 - ?

100% * 6.8 pounds / 96.3% = 7.06 pounds

According to the above, the baby was born thinking 7.06 pounds, that is, she lost 0.26 pounds.

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The amount of water a tank can hold is 17155.86 cubuic ft.

Every three-dimensional object occupies some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Now in the given quetion, it is stated that ,

The amount of water that a spherical tank can hold varies directly as the cube of its radius.

Therefore,

[tex]V_1\alpha R^3\\\\\\V_1= aR^3\\\\a=\frac{1767}{7.5^3}[/tex]

Now , for the tank with radius 16 ft.

[tex]V_2\alpha R^3\\\\\\V_2= aR^3\\\\V_2=\frac{1767}{7.5^3}*16^3\\\\V_2=17155.86 ft^3[/tex]

Hence, the amount of water a tank can hold is 17155.86 cubuic ft.

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Answer:

Step-by-step explanation:

I think its A

Answer:

D

Step-by-step explanation:

So the ratio is 8:6 right now and they want to sell 10 each. I can tell you now it's gonna change because neither 6 nor 8 goes into 10 evenly. Now to find out what it'll be

So currently, you found out Terrence has 36 and Jim has 48

So each is going to sell 10. That means...

Jim will have 38 and Terrence will have 26

[tex] \frac{38}{26} [/tex]

Now we'll just simplify until we can't anymore

[tex] \frac{38}{26} = \frac{19}{1 3} [/tex]

19 and 13 are prime numbers... that's the most I can go

The   length of the model is 2 feet

The model is  the actual size. This means that for every 6 feet measured on the actual car, the model will span 1 foot.

Note that the model length is in the numerator and the actual length is in the denominator.

Thus, if the car is 12 feet long and L represents the length of the model, then write the ratio as .

Set the two ratios equal to each other to obtain the proportion below.

The length of the model is given as 2 feet

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Answer:

Step-by-step explanation:

m= 3

Answer:

Part A: What percentage of the survey respondents do not like both hamburgers and burritos? (2 points)

25.6%. 54 out of 205 respondents do not like both hamburgers and burritos. 54/205 = 0.256 or 25.6%.

Part B: What is the marginal relative frequency of all customers that like hamburgers? (3 points)

50.2%. 110 out of 205 respondents like hamburgers. 110/205 = 0.502 or 50.2%.

Part C: Use the conditional relative frequencies to determine which data point has strongest association of its two factors. Use complete sentences to explain your answer. (5 points)

The data point with the strongest association between its two factors is that 29 out of 110 respondents who like hamburgers also like burritos. This is a conditional relative frequency of 26.4%, which is higher than any other combination of the two factors. This suggests that the respondents who like hamburgers are more likely to also like burritos than any other combination of the two factors.

Step-by-step explanation:

The new solid's surface area, which is 490 cm², is created by combining two identical cubes, each of which has a surface area of 294 cm².

The total area of a cube's faces that cover it is the surface area of the object. The cube's surface area is calculated as six times the square of its side lengths. 6a², where an is the cube's side length, serves as its representation. In essence, it is the overall surface area.

Total surface area of a cube = 6a², where a is the length of each of the sides.

Let the surface area of each identical cube = 294 cm²

The length of each side be

6a² = 294

simplifying the above equation, we get

a² = 294/6

a² = 49

a = √49

a = 7 cm

Surface area of the new solid

= surface area of the two identical cubes - 2(area of the surface where both are joined)

Surface area of the new solid = 2(294) - 2(7²) = 490 cm²

Therefore, the surface area of the new solid be 490 cm².

The complete question is;

Two identical rectangular prisms and two identical cubes are joined. Answer the questions to find the new solid’s surface area. The numbers are 9 and 4.

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It will it take Lainey 7 seconds to travel from the top to the bottom of the slide. Option C

Using the formula for calculating speed

The formula for Speed is given as [Speed = Distance ÷ Time].

To calculate the time, the speed formula can be molded as:

Time = Distance ÷ Speed].

Given Distance = 336 feet

Given speed = 48 feet per second

Time = Distance ÷ Speed

= 336 ÷ 48 = 7 seconds

Hence, the time it will  take Lainey to travel from the top to the bottom of the slide is 7 seconds

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The total number of winning hands are 276.

Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The probability of an event can be calculated using the following formula.

Probability of an event = Number of favourable outcomes/Total number of outcomes = x/n.

In the given question,

If the first card drawn is a 10, then there are

[tex]P_9^2=\frac{9!}{(9-2)!} =9*8=72 hands[/tex]

There are 9 possible numbers if the second card is a 10, and there are 8 possible numbers if the third card, giving us,

[tex]9*8= 72 hands[/tex]

If the third card is 10 then there are 9 possible numbers for the first card and 8 possible numbers for

second card, it gives us

[tex]9*8= 72 hands[/tex]

And there are 5 odd cards, and it gives us:

[tex]P_5^3=\frac{5!}{(5-3)!} =5*4*3=60 hands[/tex]

So, we have that in total we have

72+72+72+60=276 winning hands.

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Answer:

[tex]x\geq 5\\x > 4\\[/tex]

Answer:

x ≥ 5

x > 4

x < 6

Step-by-step explanation:

The inequalities for which 5 is the lowest integer value that x could take are:

Therefore, the correct options are:

x is greater than or equal to 5.

x > 4.

x is less than 6.

Answer:

start by using the formula for the area of a rectangle:

Area = length × width

We know that the area of the farm is given as square miles, so we can write:

lw =

Solving for w, we can divide both sides by l:

w =

Therefore, the width of the rectangular farm is miles.

To simplify the expression, we can multiply the numerator and denominator by 2:

w =

So the width can also be expressed as the fraction __.

Answer: 36

Step-by-step explanation:

to find the length, find the hypotenuse of a triangle formed by the x-axis and the distance the parallelogram is from the x-axis.

hypotenuse= [tex]a^{2}+b^{2} =c^{2}[/tex]

the distance from -6 to -3 is 3 units

the distance from 0 to 4 is 4 units

[tex]3^{2} +4^{2} =9+16=25[/tex]

then [tex]\sqrt{25} =5[/tex]

therefore the length of the parallelogram is 5 units

repeat on other side

the distance from -3 and 9 is 12 units

the distance from 0 and 5 is 5 units

[tex]12^{2} +5^{2} =144+25=169[/tex]

then [tex]\sqrt{169} =13[/tex]

therefore the width of the parallelogram is 13 units

now to find the perimeter add all side lengths of the given shape

since parallelograms have equal lengths and widths add 13+13+5+5

therefore the perimeter of the parallelogram is 36

Answer:

$13,488.50

Step-by-step explanation:

annual rate 6%

so every month = 6/12 = 0.5%

compounding monthly so every month the money grows at (1+0.5%)

for 5 years, it's 60 months

10,000 *  (1+0.5%)^60 =  $13,488.50

The complete question

A model rocket is launched with an initial upward velocity of 50m/s. The rocket's height h (in meters) after t seconds is given by the following. h=50t-5t².

Find all values of t for which the rockets height is 20 meters.

The values of t for which the rockets height is 20 meter are, (10 + 2√21) / 2  and (10 - 2√21) / 2

Velocity is a vector quantity that represents the rate of change of an object's position. It is defined as the derivative of the position vector with respect to time and has units of meters per second (m/s). Velocity includes both speed and direction, and is an important concept in physics and engineering.

We can find the values of t for which the rocket's height is 20 meters by setting h equal to 20 and solving for t.

h = 50t - 5t² = 20

Expanding the equation, we have:

50t - 5t² = 20

Adding 5t² to both sides:

50t = 20 + 5t²

Dividing by 5 both the sides,

10t = 4 + t²

t² - 10t + 4 = 0

t = (10 + 2√21) / 2

and t = (10 - 2√21) / 2

So the values of t for which the rocket's height is 20 meters are

(10 + 2√21) / 2  and (10 - 2√21) / 2

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They reach their location at 9:24 the next morning.

The relative speed is the net speed of two different objects with respect to each other.

If two objects move in the same direction we take the difference between their speeds.

If two objects move in the opposite direction we take the sum of their speeds.

We can utilize the following parameters in our calculation based on the question,

Time = 4 pm

Distance = 64 km

Calculate how long it took the father to ride his horse and the son to walk the first 32 miles.

Time = Distance / (Difference between rates of father and son)

Time = 32 km / (8 km/h - 3 km/h)

Time = 32 km / 5 km/h

Time = 6.4 hours

Determine how long it will take the father to walk the final 32 miles and the son to ride the horse.

Time = Distance / (Difference in Speed)

Time = 32 km / (8 km/h - 4 km/h)

Time = 32 km / 4 km/h

Time = 8 hours

Therefore,

Total time = 6.4 hours + 8 hours + 3 hours break + 4 pm is 9:24 am the next day.

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 140000\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 67.2\%\to \frac{67.2}{100}\dotfill &0.672\\ t=years\\ \end{cases}[/tex]

[tex]140000 = 16000(1 + 0.672)^{t} \implies \cfrac{140000}{16000}=1.0672^t\implies \cfrac{35}{4}=1.0672^t \\\\\\ \log\left( \cfrac{35}{4} \right)=\log(1.0672^t)\implies \log\left( \cfrac{35}{4} \right)=t\log(1.0672) \\\\\\ \cfrac{\log\left( \frac{35}{4} \right)}{\log(1.0672)}=t\implies 33.35\approx t\qquad \textit{about 33 years and 128 days}[/tex]

The area of the triangle ABC is 6√6 cm².

Triangle ABC is depicted in the given diagram, where AB = 7 cm, BC = 6 cm, and AC = 5 cm.

Heron's formula, which claims that the area is provided by: for a triangle with sides of lengths a, b, and c, can be used to determine the triangle's area.

(s(s-a)(s-b)(s-c)) = area

where s is the triangle's semi perimeter and is determined by:

s = (a + b + c)/2

Here are the facts:

7 cm for a and 6 cm for b.

c = 5 cm

The semi perimeter is as follows:

s = (7 + 6 + 5)/2 = 9

When we apply Heron's formula, we get:

Area = √(9(9-7)(9-6)(9-5)) = √(9 × 2 × 3 × 4) = √216

When we reduce the square root, we obtain:

= 6√6 cm²

As a result, the triangle ABC has a 6√6 cm² area.

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Answer: he will need an area of 6*4 fencing

Step-by-step explanation: if 6+4 is 10 times that by 2 and you have 20

I hope this helped