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andrew-mc [135]
2 years ago
9

Let K and T be the current ages of two siblings, Katie and Thomas. Katie is currently twice the age of Thomas. In 6 years, Katie

will be 4 times Thomas's current age. How old are Katie and Thomas?
Mathematics
1 answer:
Pavlova-9 [17]2 years ago
6 0

Answer:

Katie is 6 years old and Thomas is 3 years old

Step-by-step explanation:

Given that we should let K and T be the current ages of two siblings, Katie and Thomas.

If Katie is currently twice the age of Thomas then,

K = 2T

and in  6 years, Katie will be 4 times Thomas's current age then

K + 6 = 4T

Solving both equations simultaneously by substituting the value of K given in the first equation into the second

2T + 6 = 4T

Collect like terms

6 = 4T - 2T

6 = 2T

Divide both sides by 2

T = 3

Recall that K = 2T

K = 2 * 3

= 6

Hence Katie is 6 years old while Thomas is 3 years old

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Find the surface area of the triangular prism shown below.
ira [324]

Answer:

150ft²

Step-by-step explanation:

surface area = (2×½×8×3)+(8+5+5)×7

= 24+126

= 159 ft²

7 0
3 years ago
Consumer products are required by law to contain at least as much as the amount printed on the package. For example, a bag of po
Troyanec [42]

Answer:

The average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802

Step-by-step explanation:

We are given that

Standard deviation, \sigma=0.2ounces

We have to find the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.

P(x\geq 10)=0.99

Assume the bag weight distribution is bell-shaped

Therefore,

P(\frac{x-\mu}{\sigma}\geq 10)=0.99

We know that

z=\frac{x-\mu}{\sigma}

Using the value of z

Now,

\frac{10-\mu}{0.2}=0.99

10-\mu=0.99\times 0.2

\mu=10-0.99\times 0.2

\mu=9.802

Hence, the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802

5 0
3 years ago
Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 9x2 y2 and the p
dolphi86 [110]

The vector function is, r(t) =  \bold{ < t,2t^2,9t^2+4t^4 > }

Given two surfaces for which the vector function corresponding to the intersection of the two need to be found.

First surface is the paraboloid, z=9x^2+y^2

Second equation is of the parabolic cylinder, y=2x^2

Now to find the intersection of these surfaces, we change these equations into its parametrical representations.

Let x = t

Then, from the equation of parabolic cylinder,  y=2t^2.

Now substituting x and y into the equation of the paraboloid, we get,

z=9t^2+(2t^2)^2 = 9t^2+4t^4

Now the vector function, r(t) = <x, y, z>

So r(t) = \bold{ < t,2t^2,9t^2+4t^4 > }

Learn more about vector functions at brainly.com/question/28479805

#SPJ4

7 0
2 years ago
Please help me :((!!!!
Alika [10]
This seems like a concept you’re going to learn and use so I’ll do a problem per section and explain.

Well basically this is a concept: if it’s a negative exponent it’s just 1/number^exponent.

So for example:
#1. 1/(10)^2 = 10^-2

The standard notation:
#9: You know that 1/(10)^3 you could either put it in a calculator or realize that you take the number 1, and move the decimal to the left three times. 0.001 would be the answer.

Scientific notation:
combines these topics. Let’s take #17. 0.025. Scientific notation means you write it as a number multiplied by 10^? So let’s see how many places you can move the decimal to get a number without the zeros.

0.025 => move it two places to the right. So that’s 2.5. Now 2.5 multiplied by what 10^? Would give you 0.025? It would be 10^-2. So your answer would be 2.5 x 10^-2.

For all of these, use your knowledge of the power of tens and dividing by tens! ^^ you got this. Let me know if you need help after this explanation.
7 0
3 years ago
Yesterday Andre ate a cup and a half of yogurt. One serving is 2/3 of a cup and 80 calories. How many total calories did Andre e
ZanzabumX [31]
80. there's no mathematical equations, also there's nothing to compare
7 0
3 years ago
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