one number is four greater than another number.the sum of two numbers is 78.what are the two numbers?

If each cube has a side measure of 12 inch, what is the volume of the rectangular prism?

barxatty [35]

Answer:

nii pata didi plz dil dedo

5 0

3 years ago

Read 2 more answers

Determine whether the data described in the tables is best modeled by a linear function or an exponential function.

Leviafan [203]

Answer:

Electric car = Exponential function (decreasing cost)

Gasoline car = Exponential function (increasing cost)

Step-by-step explanation:

The given data the Electric car, we have;

Time (years) ${}$ Cost (thousands of dollars)

0 ${}$ 35

5 ${}$ 27

10 ${}$ 21

15 ${}$ 16

20 ${}$ 12.5

The difference between successive term is such that each term decreases by approximately the same percentage given as follows

1st and 2nd term (35 - 27)/35 × 100 ≈ 22.8571% decrease

2nd and 3rd term (27 - 21)/27 × 100 ≈ 22.222% decrease

3rd and 4th term (21 - 16)/21 × 100 ≈ 23.81% decrease

4th and 5th term (16 - 12.5)/16 × 100 ≈ 21.875% decrease

Therefore. the electric car is best approximated by exponential function

The given data the Gasoline car, we have;

Time (years) ${}$ Cost (thousands of dollars)

0 ${}$ 35

5 ${}$ 40.2

10 ${}$ 46.3

15 ${}$ 53.2

20 ${}$ 61.2

The difference between successive term is such that each term increases by approximately the same percentage given as follows

1st and 2nd term (40.2 - 35)/35 × 100 ≈ 14.857% decrease

2nd and 3rd term (46.3 - 40.2)/40.2 × 100 ≈ 15.174% decrease

3rd and 4th term (53.2 - 46.3)/46.3× 100 ≈ 14.9% decrease

4th and 5th term (61.2 - 53.2)/53.2× 100 ≈ 15.03% decrease

Therefore. the Gasoline car is best approximated by exponential function

4 0

3 years ago

Milk is a good source of many vitamins that can help us stay healthy. FDA recommends that the average vitamin A concentration fo

Lelechka [254]

Answer:

The degrees of freedom for this sample are 27.

The sample size to get a margin of error equal or less than 0.3656 is n=4450.

Step-by-step explanation:

The degrees of freedom for calculating the value of t are:

$df=n-1=28-1=27$

With 27 degrees of freedom and 95% confidence level, from a table we can get that the t-value is t=2.052.

The sample size to get a margin of error equal or less than 0.3656 can be calculated as:

$MOE=t\cdot s/\sqrt{n}\\\\n=\left(\dfrac{t\cdot s}{MOE}\right)^2=\left(\dfrac{2.052\cdot 11.8841}{0.3656}\right)^2=66.7^2\\\\\\n=4449.13\approx4450$

6 0

3 years ago

Find the values of x and y

Mkey [24]

Answer:

x = 78º

y = 35º

Step-by-step explanation:

These are isosceles triangles

two angles are congruent

-----------------------------

x + 51 + 51 = 180

x = 180 - 102

x = 78º

y + y + 110 = 180

2y = 70

y = 35º

3 0

2 years ago

in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Nimfa-mama [501]

Answer:

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

Step-by-step explanation:

Let $\vec u$ and $\vec a$ , from Linear Algebra we get that component of $\vec u$ parallel to $\vec a$ by using this formula:

$\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a$ (Eq. 1)

Where $\|\vec a\|$ is the norm of $\vec a$ , which is equal to $\|\vec a\| = \sqrt{\vec a\bullet \vec a}$ . (Eq. 2)

If we know that $\vec u =(2,1,1,2)$ and $\vec a=(4,-4,2,-2)$ , then we get that vector component of $\vec u$ parallel to $\vec a$ is:

$\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

Lastly, we find the vector component of $\vec u$ orthogonal to $\vec a$ by applying this vector sum identity:

$\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}$ (Eq. 3)

If we get that $\vec u =(2,1,1,2)$ and $\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$ , the vector component of $\vec u$ is:

$\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

$\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

4 0

3 years ago