At 10:00 AM a truck started traveling from point A with a speed of 40mph. 3 hours and 10 minutes later a car started to drive from point A in the same direction with an average speed of 60mph. At what time will the car catch up with the truck?

Answer: 5/16

Step-by-step explanation:

First, let's calculate the total number of possible outcomes:

4 options in the first bag      and      4 options in the second bag   = 16

Here is the list:

23   24   25    26

33   34    35   36

43   44    45   46

53   54    55   56

Next, calculate the total number of outcomes which result in the product of 12, 13, 14, or 15.

Here are their products:

6    8     10    12

9   12     15    18

12   16     20   24

15   20    25   30

There are 5 outcomes that include a product of 12, 13, 14, & 15.

Probability is:  (# of satisfactory outcomes)/(total outcomes) = 5/16

[(455 + 180 + 324 + 675)/(65 + 36 + 54 + 75)] = 7.10

Answer is D.

Answer:

7.10% is the answer.

Answer:

a food container and a bowl

Answer: C

y=-5cos(x) is the graphed equation. Cos(x) starts at (0,0) and one period is 2pi or 6.28 and by cos(x) multiplied by -5 starts the cosine wave at (0,-5) and thus corresponds to the graphed equation shown.

Any questions please feel free to ask. Thanks

Answer:

the answer is A.

Step-by-step explanation:

Answer:

A) distance, in miles, between the cities

Step-by-step explanation:

correct on edge

Answer:

45

it is what it is

The cost of basic hokey kit is $45.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit.

Let the cost of the basic kit be x.

Now, 3x+15=150

3x=135

x=$45

Therefore, the cost of basic kit is $45.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ5

Answer:

From the information, we know that Jamal's mother is 28 years older than Jamal, so his mothers age should be:

x + 28 (years)

Also, we know that his uncle's age is twice as much as Jamal's mother age, so we have the following expression:

(x + 28) · 2 = 2x + 56

*Hope this help you

Jamal's uncle's age can be expressed as 2(x + 28), which simplifies to 2x + 56 years.

Jamal is x years old, and his mother is 28 years older than him. Therefore, his mother's age can be represented by x + 28. Jamal's uncle is two times older than Jamal's mother, which means we need to multiply his mother's age by 2 to get the uncle's age. So, the expression for Jamal's uncle's age is 2(x + 28). Simplifying this expression, we get:

2(x + 28)

2x + 2(28)

2x + 56

Thus, Jamal's uncle's age is represented by the expression 2x + 56 years.

Answer:

-4 ≤ f ([tex]\theta[/tex]) ≤ 4

Step-by-step explanation:

The range of a function is the allowed y-values of the function.

We can simply look at the periodic function below and see that the y-value ranges from a negative 4 to a positive 4. It oscillates betwen -4 and 4. That is the range.

We can say -4 ≤ f ([tex]\theta[/tex]) ≤ 4

Last answer choice is right.

*** NOTE: it is a type, not "0", rather "[tex]\theta[/tex]"

Answer: second option.

Step-by-step explanation:

The formula used for calculate the lateral area of a cylinder is this one:

[tex]LA=2\pi rh[/tex]

Where "r" is the radius and "h" is the height

The formula for calculate the area of a circle (which is the base of a cylinder) is:

[tex]A=\pi r^2[/tex]

Knowing the area of the base, you can solve for the radius:

[tex]36\pi=\pi r^2\\\\r=\sqrt{\frac{36\pi units^2}{\pi}} \\\\r=6units[/tex]

Substitute the radius and the height into the formula [tex]LA=2\pi rh[/tex]:

[tex]LA=2\pi (6units)(2units)[/tex]

[tex]LA=24\pi\ units^2[/tex]

Answer:

24π square units (edge)

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

7/2=3.5

Answer:

3.5

Step-by-step explanation:

Ratio of

those who walk : those who ride = 2 : 7

This means that for every 2 students who walk, there are 7 students who ride

Therefore, for every 1 student that walks, (hypothetically) there are 3.5  (7/2) students who ride

Then the number of bus riders is 3.5 times the number of students that walk.

Answer:

4.06 in.

Step-by-step explanation:

                 4

sin(80)= ----------    multiply by X

                 x

x* sin(80)= 4 divide by sin(80)

         4

X=-------------  simplify

      sin(80)

X= 4.06 in.

Answer:

The length of the hypotenuse is 4.1 in

Step-by-step explanation:

By definition, the sine of an angle is:

[tex]sin(x) = \frac{opposite\ side}{hypotenuse}[/tex]

In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.

With this information we can find the length of the hypotenuse h

[tex]sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in[/tex]

Finally the length of the hypotenuse is 4.1 in

Answer:

the numbers are 12, 31

Step-by-step explanation:

Answer:

OPTION B

Step-by-step explanation:

To solve, create a formula.

y= 5(copay)+premium

Using this you get:

Option A: 5(20)+55= $155

Option B: 5(15)+60= $135

Option C: 5(25)+65= $190

Option D: 5(30)+50= $200

Answer:

Option B

Step-by-step explanation:

Option A : 55 + 20(5) = 155

Option B : 60 + 15(5) = 135

Option C : 65 + 25(5) = 190

Option D : 50 + 30(5) = 200

Answer:

Ratio is it rate. Can you do the rate of numbers.

For example, if we say: If the car was very high to acceleration at least, 1,000 km/h.

If Usain Bolt was won on the Olympics, he has 27 km/h.

Hmm, the ratio isn't rate at all. This method can do the non rate. For example, if we say: If the gas price at BP, there's $100 per year.

Step-by-step explanation:

With this method, you must solve the ratio isn't rate.

For there's the group, this was what do you say, it's GCF, or greatest common factor. With this GCF method, for example: if we say, the European Parliament, and the MPs, are divided by gender, if we divide by male and female. For more examples, see the answer at the above with the picture

With this method of the rate, there are no of speed, price, or something else.

There are some examples like the km/h, representing the Kilometers per hour.

Hopefully with this helpful example

Answer:

g(x), and the maximum is 5

Step-by-step explanation:

for given function f(x), the maximum can be seen from the shown graph i.e. 2

But for the function g(x), maximum needs to be calculated.

Given function :

g (x) = 3 cos 1/4 (x + x/3) + 2

let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)

g(x)= 3 cos1/4(0 + 0) +2

    = 3cos0 +2

     = 3(1) +2

     = 3 +2

     = 5 !

Answer:

[tex]x=\frac{5\pi}{4}[/tex]

Step-by-step explanation:

We want to solve;

[tex]\cscx=-\sqrt{2}[/tex] in the 3rd quadrant

Recall that;

[tex]\sin x=\frac{1}{\csc x}[/tex]

We use the reciprocal ratio to get;

[tex]\sin x=-\frac{\sqrt{2}}{2}[/tex]

In the third quadrant the solution is

[tex]x=\pi+\sin^{-1}(\frac{\sqrt{2} }{2} )[/tex]

[tex]x=\pi+\frac{\pi}{4}[/tex]

[tex]x=\frac{5\pi}{4}[/tex]

I'm not sure what to make of the "h" and "i" in your question, so I'll just ignore them (and the 3). Looks like we have

[tex]\vec f(x,y,z)=(x+y,x-y,x^2+y^2-2z)[/tex]

and a surface parameterzied by

[tex]\varphi(u,v)=(u+2v,u-2v,u^2+2v^2)[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Then

[tex]\varphi_u\times\varphi_v=(4u+4v,4u-4v,-4)[/tex]

so that the flux is given by the integral

[tex]\displaystyle\iint_S\vec f\cdot\mathrm d\vec S=\int_0^1\int_0^1(2u,4v,4v^2)\cdot(4u+4v,4u-4v,-4)\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle8\int_0^1\int_0^1(u^2+3uv-4v^2)\,\mathrm du\,\mathrm dv=\boxed{-2}[/tex]

To calculate the flux of the given vector field through the surface S, you need to calculate the partial derivatives of the parametrization, then find the cross product of these partial derivatives, and finally evaluate the double integral over the surface using the flux formula.

To calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y2 − 2zi through the surface S parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v2 with 0 ≤ u, v ≤ 1 and oriented by φu × φv:

Answer:

The center is (0,0) and the radius is 5

Step-by-step explanation:

To find the center of a circle, you need to look at the equation

In this case this equation could be written as

[tex](x-0)^2+(y-0)^2=5^2[/tex]

The x value is x=0 for the center and the y values is y=0

The radius can be found by looking at the constant that is squared, so r=5

In the case of an equation like this

[tex](x-1)^2+(y+1)^2=3^2[/tex]

The center point would be (1,-1) and r=3

Final answer:

The quadratic expression 3x^2-48 can be completely factored as 3(x-4)(x+4) by first factoring out the common factor and then utilizing the difference of squares.

Explanation:

To factor this expression completely, we first need to look for common factors and any patterns that might help simplify the expression. Both terms in the expression 3x2−48 have a common factor of 3. Factoring out this common factor gives us:

Notice that the expression inside the parenthesis, x2 − 16, is a difference of squares, which can be factored further into (x − 4)(x + 4). Therefore, the fully factored form of the original expression is:

This shows how identifying common factors and utilizing the difference of squares helps in completely factoring the given expression.

Answer:

The scale is 7

Step-by-step explanation:

Divide 12 from 84 to get the answer.

Hope this helps! :)

Answer:

Step-by-step explanation:

Answer:

61-25=n

Step-by-step explanation:

A) The formula for surface area of a sphere is A = 4*PI*r^2

using 3.14 for PI:

Surface area for Earth = 4 * 3.14 x 3960^2 = 196,960,896 miles^2

Surface area of the moon: 4 * 3.14 * 1080^2 = 14,649,984 miles^2

B)Divide the Surface of the Earth by the moon:

196,960,896 / 14,649,984 = 13.44

The Earths surface is 13.4 times larger than the moon.

C) Multiply the surface of the Earth by 70%:

196,960,896 * 0.70 = 137,872,627.2 million square miles of water.

Calculating surface areas of Earth and the moon, comparing them, and determining the amount of water on Earth's surface.

a. Find the surface area of Earth and the moon:

b. Compare the surface areas of Earth and the moon: Earth's surface area is approximately 13.5 times greater than the Moon's surface area.

c. About 70% of Earth's surface is water: There are approximately 137.9 million square miles of water on Earth's surface.

Answer:

  A|  12, 3

Step-by-step explanation:

The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...

  y = (x -12)(x -3)

A quick check shows this product is ...

  y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required

The factors are zero when x is either 12 or 3.

The zeros of the equation are 12 and 3.

____

Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).

Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.

90 degrees

3 ( square root sign) 10

                 10√2

Then b = ------------ = 5√2

                     Answer:

5√2

Step-by-step explanation:

Notice that the sine function links side b, the hypotenuse (10) and the 45° angle:

                 1

sin 45° = ------ = b/10

                √2

Then b = 10√2 / 2  = 5√2

Answer:

[tex]\boxed{7k + 3}[/tex]

Step-by-step explanation:

Average cost = total cost/number of items = (35k² + 29k + 6)/(5k + 2)

Perhaps the best way to solve this problem is to use long division.

                       7k  + 3  

5k + 2)35k² + 29k + 6

          35k² +  14k              

                       15k + 6

                       15k + 6

                                0

Thus,

[tex]\frac{35k^{2}+29k+ 6}{5k + 2} = 7k+3[/tex]

The average cost per item is [tex]\boxed{7k+3}[/tex].

Answer:7k+3

Step-by-step explanation:

Answer:

h

Step-by-step explanation:

Answer:

C) √5(cos(117°) +i·sin(117°))

Step-by-step explanation:

The rectangular number a+bi can be written in polar form as ...

√(a^2+b^2)×(cos(arctan(b/a)) + i·sin(arctan(b/a)))

Here, we have a=-1, b=2, so the magnitude is ...

√((-1)^2 +2^2) = √(1+4) = √5

and the angle is ...

arctan(2/(-1)) = arctan(-2) ≈ 116.565° . . . . . a 2nd-quadrant angle

Then you have ...

-1 +2i = √5(cos(117°) +i·sin(117°)) . . . . . . customary "polar form"

_____

Comment on the answer

The "polar form" is generally written as ...

(magnitude)·(cos(angle) +i·sin(angle))

You may also see it as ...

(magnitude) cis (angle) . . . . . . . where "cis" is shorthand for "cos + i·sin"

In my engineering courses, we often used the form ...

(magnitude) ∠ (angle)

The form used by my calculator is ...

(magnitude)·e^(i·angle) . . . . . where angle is usually in radians

Answer:

3.30 for apple and 2.00 for an orange

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. We can then solve this system using the elimination method to find the cost of an apple and an orange.

To solve this problem, we can set up a system of linear equations to represent the charges for apples and oranges at the fruit stand. Let's use x to represent the cost of an apple and y to represent the cost of an orange.

From the given information, we can set up the following equations:

111x + 111y = 5.30

111x + 222y = 7.30

Next, we can solve this system of equations by using substitution or elimination. Let's use the elimination method:

Multiply the first equation by 2, and multiply the second equation by 1:

222x + 222y = 10.60

111x + 222y = 7.30

Subtract the second equation from the first:

111x = 3.30

Divide both sides by 111:

x = 0.03

Substitute this value back into either equation to solve for y:

111(0.03) + 222y = 7.30

3.33 + 222y = 7.30

222y = 3.97

y = 0.01

Therefore, the cost of an apple is $0.03 and the cost of an orange is $0.01 at the fruit stand.

Answer:

480 = x(6)

Step-by-step explanation:

Given in the question that,

distance travelled by the train = 480 miles

time taken by the train to travel 480 miles = 6 hours

Suppose speed of train = x miles/hour

Formula to use to drive the equation

480 = x(6)

x = 480/6

x = 80 miles/hour

Answer:

The question is incomplete, the complete question is Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 12 ft³ of fluffy material. The base is 3 ft, the height is 2 ft, what is the length of the pillow?

The length of the pillow is 4 feet

Step-by-step explanation:

The formula of the volume of the wedge is [tex]V=\frac{1}{2}bhl[/tex] , where

∵ The pillow in the shape of a wedge

∵ The pillow is filled with 12 ft³ of fluffy material

∴ The volume of the wedge = 12 ft³

∵ The base = 3 feet

∵ The height = 2 feet

- Use the formula of the volume above to find its length

∵ [tex]V=\frac{1}{2}(2)(3)l[/tex]

∴ V = 3 l

∵ V = 12 ft³

- Equate 3 l by 12

∴ 3 l = 12

- Divide both sides by 3

∴ l = 4 feet

∴ The length of the pillow is 4 feet