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Evaluate 10m +\dfrac {n^2}410m+ 4 n 2 10, m, plus, start fraction, n, squared, divided by, 4, end fraction when m=5m=5m, equal

Readme [11.4K]

Answer: $54$

Step-by-step explanation:

Given the following expresion provided in the exercise:

$10m+\frac{n^2}{4}$

You can follow these steps in order to evaluate it when $m=5$ and $n=4$ :

1. You need to substitute $m=5$ and $n=4$ into the given expression:

$10(5)+\frac{(4)^2}{4}$

2. Now you can solve the mutiplication:

$=50+\frac{(4)^2}{4}$

3. Since $4^2=4*4$ , you get:

$=50+\frac{16}{4}$

4. You must solve the division. Divide the numerator 16 by the denominator 4. Then:

$=50+4$

5. And finally, you must solve the addition. So, you get this result:

$=54$

3 0

2 years ago

The nth term of a sequence is 2n2 − 1 The nth term of a different sequence is 40 − n2 Show that there is only one number that is

allsm [11]

Answer:

Step-by-step explanation:

nth term of a sequence = 2n² - 1

Therefore, terms of the sequence will be,

1, 7, 17, 31, 49, ........... n terms

nth term of a different sequence = 40 - n²

Therefore, terms of the sequence will be,

39, 36, 31, 24, 15, 4, -9, -24 .......... n terms

Since, there is no negative number in the first sequence,

Therefore, out of 6 positive terms of second sequence only one number (31) is common in both the sequences.

5 0

1 year ago

The spring has a stiffness k=200n/m and is unstretched when the 25 kg block is at

g100num [7]

To solve this we are going to use the formula fro the force applied to a spring: $F=ks$
where
$k$ is the spring constant
$s$ is the extension

Since we know the $F=ma$ , we can replace that in our formula and solve for $a$ :
$ma=ks$
$a= \frac{ks}{m}$
where
$a$ is the acceleration
$k$ is the spring constant
$s$ is the extension
$m$ is the mass

We know for our problem that $k=200$ , $s=0.4$ , and $m=25$ . So lets replace those values in our formula to find $a$ :
$a= \frac{ks}{m}$
$a= \frac{(200)(0.4)}{25}$
$a=3.5 \frac{m}{s^2}$

We can conclude that the acceleration of the block when s=0.4m is $3.5 \frac{m}{s^2}$ .

7 0

1 year ago

In studying the insurance preferences of homeowners the following conclusions are made: A homeowner is three times as likely to

Ede4ka [16]

Answer:

0.632

Step-by-step explanation:

Given that a homeowner is three times as likely to purchase additional jewelry coverage as additional electronics coverage

If probability of purchasing additional electronics coverage = p, then prob of purchasing jewelry coverage = 3p

The two events are independent hence joint probability is product of these two.

i.e. P(both) = $p(3p) =3p^2$

This is given as 0.2

$3p^2 =0.2\\p = 0.258$

the probability that a homeowner purchases exactly one coverage.

$=P(AUB)-P(A \bigcap B)$

= Prob he purchases I + prob he purchases II-2(prob he purchases both)

$= 0.258+3(0.258)-2(0.2)\\=0.632$

5 0

1 year ago

A company logo is made up of a square and three identical triangles. What is the area of the logo? Enter your answer in the box.

garri49 [273]

Given:
square with sides measuring 7 cm.
3 triangles attached to three sides of the square. A line bisecting one triangle is measured at 4 cm.

Area of a square = s² = (7cm)² = 49 cm²

Area of a triangle = hb/2 = (4cm*7cm)/2 = 14 cm²
Area of the 3 triangles = 14 cm² x 3 = 42 cm²

Total area of the logo = 49 cm² + 42 cm² = 91 cm²

7 0

1 year ago

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