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3 years ago

Twenty-six is what percent of 40?

Mathematics

1 answer:

barxatty [35]3 years ago

8 0

C. 65% is the answer
The equation is 26/40=%
(26/40) = (13/20)
(13/20) • (5/5) = 65/100
which equals 65%

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Area of the rhombus shown below?

liraira [26]

Answer:

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = $\frac{1}{2}$ product of diagonals

Here AC = 13 and BD = 15 are the diagonals, hence

A = 0.5 × 13 × 15 = 97.5 units² → A

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3 years ago

Which set of documents do you need to correct a mistake on a filed tax return?

dsp73

Answer:

Plato: C. 1040X, original return, and any supporting forms.

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2 years ago

Two objects are ________ when they have the same size and shape. What’s the blank?

iren2701 [21]

Answer:

I think the answer is 'congruent'. :)

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

The vector (a) is a multiple of the vector (2i +3j) and (b) is a multiple of (2i+5j) The sum (a+b) is a multiple of the vector (

kow [346]

Answer:

$\|a\| = 5\sqrt{13}$ .

$\|b\| = 3\sqrt{29}$ .

Step-by-step explanation:

Let $m$ , $n$ , and $k$ be scalars such that:

$\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}$ .

$\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}$ .

$\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}$ .

The question states that $\| a + b \| = 34$ . In other words:

$k\, \sqrt{8^{2} + 15^{2}} = 34$ .

$k^{2} \, (8^{2} + 15^{2}) = 34^{2}$ .

$289\, k^{2} = 34^{2}$ .

Make use of the fact that $289 = 17^{2}$ whereas $34 = 2 \times 17$ .

$\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}$ .

$k^{2} = 2^{2}$ .

The question also states that the scalar multiple here is positive. Hence, $k = 2$ .

Therefore:

$\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}$ .

$(a + b)$ could also be expressed in terms of $m$ and $n$ :

$\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}$ .

$\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}$ .

Equate the two expressions and solve for $m$ and $n$ :

$\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}$ .

$\begin{cases}m = 5 \\ n = 3\end{cases}$ .

Hence:

$\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}$ .

$\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}$ .

6 0

2 years ago

PLEASE PLEASE HELP IM BEING TIMED The two-way table represents data from a survey asking students whether they plan to attend co

lara31 [8.8K]

Answer: 82%

Step-by-step explanation:

- - - - - - - - college - - not college - - - - total

Travel - - - - 43 - - - - - - - 10 - - - - - - - - 53

Not travel - 24 - - - - - - - 5 - - - - - - - - - 29

Total - - - - 67 - - - - - - - 15 - - - - - - - - - 82

Marginal relative frequency of students who plan to attend college:

(Number of students who plan to attend the college / Total number of the students)

Number of students who plan to attend college = 67

total number of students = 82

Marginal relative frequency = 67/82

= 0.8170731

= (0.8170731) * 100%

= 81.7% = 82%

8 0

2 years ago