Tessa did 3/5 of her homework problems on Saturday. On Sunday, she did 1/3 of what was left plus the last 4 problems. How many problems did Tessa do over the weekend?

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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Answer:

The polygons are similar.

Step-by-step explanation:

The polygons are similar due to the SAS Similarity Theorem.

Hope this helped! :)

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 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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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

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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Answer:

Step-by-step explanation:

m= 3

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

Answer:

okay have a nice day haha

It is given that 2/5 of all patients admitted to ward 17.

Remining fraction is:

So 3/5 of patients admitted to ward 18.

Since 1/6 of all patients moved to another ward, and the reminder assigned as before, the initial fraction becomes:

Now, 3/5 of the new fraction, 5/6 is admitted to ward 18.

That is:

This is half of the patients.

The difference of the number of the patients admitted to ward 17 is the same fraction of the number of infected:

So the difference of patients is 4.

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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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 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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[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]

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 two values of y such that the barn is 50 yards from the well

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-1, 1) and (-1,, y) is calculated to be 50 yards and hence we solve for y

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

50 =√{(-1 - -1)² + (1 - y)²}

50 =√{ (1 - y)²}

2500 = (1 - y) (1 - y)

2500 = 1 - 2y + y²

y² - 2y - 2499 = 0

solving the quadratic equation gives

y = 51 OR -49

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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 __.

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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Answer:

[tex]x=42; \ y=14\sqrt{5}.[/tex]

Step-by-step explanation:

1. if the angles of the given triangle are 30-60-90°, then

2. y=0.5*28√5=14√5;

[tex]3. \ x=28\sqrt{5}*sin(60)=28\sqrt{3}*\frac{\sqrt{3} }{2}=42.[/tex]

4. finally, x=42; y=14√5.

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:

[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:

[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]

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:

Length = 10cm, Width = 9 cm

Step-by-step explanation:

Let's call the amount that both the length and width are increased by "x". So, the new length is 5 + x and the new width is 4 + x.

The original area of the rectangle was 5 * 4 = 20 cm2.

The new area of the rectangle after the increase is (5 + x) * (4 + x) = 20 + 70 + 2x^2.

Expanding the right-hand side, we have 20 + 70 + 2x^2 = 90 + 2x^2.

Equating the two areas, we get:

20 + 70 + 2x^2 = 90 + 2x^2

Subtracting 2x^2 from both sides:

20 + 70 = 90

Subtracting 20 from both sides:

70 = 70

So x^2 = 50 / 2 = 25.

Taking the square root of both sides, we get:

x = 5

So the length of the longer rectangle is 5 + x = 5 + 5 = 10 cm, and the width is 4 + x = 4 + 5 = 9 cm.

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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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

Answer:100 or it just means 10 times

Step-by-step explanation: you need to learn the angles when the number are put on each side and then your answer will come!

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   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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