The integers less than -2

Beatrice built about 1/3 of a sandcastle. Linda built 4/7 of the same castle. What fraction of the sandcastle did they build tog

wlad13 [49]

Answer

Find out the what fraction of the sandcastle did they build together .

To prove

Let us assume that the fraction of the sandcastle they build together be x .

As given

$Beatrice\ built\ about\ \frac{1}{3}\ of\ a\ sandcastle.$

$Linda\ built\ \frac{4}{7}\ of\ the\ same\ castle.$

Than the equation becomes

$x = \frac{1}{3} +\frac{4}{7}$

L.C .M of (3,7) = 21

solving

$x = \frac{7 + 3\times4}{21}$

$x = \frac{19}{21}$

Therefore the fraction of the sandcastle did they build together be

$x = \frac{19}{21}$

Hence proved

4 0

3 years ago

Is it 80% 70% 50% 60%

nexus9112 [7]

Answer:

50%

Step-by-step explanation:

As there are only two sides of the coin it will be 50% each.

7 0

3 years ago

I NEED HELP PLEASE, THANKS! :) Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withd

Alex

Answer: $5,828.28

Step-by-step explanation:

Use the Compound Interest formula: $A=P(1+\frac{r}{n})^{nt}$ where

A is the accrued amount (balance)
P is the principal (initial amount invested)
r is the interest rate (in decimal form)
n is the number of times compounded each year
t is the time of the investment (in years)

Given: P = 4,900

r = 3.5% (0.035)

n = 2

t = 5

$A=4,900\bigg(1+\dfrac{0.035}{2}\bigg)^{2(5)}\\\\\\.\qquad = 4900(1.0175)^{10}\\\\\\.\qquad = \large\boxed{5,828.28}\\$

5 0

3 years ago

Blake thinks that the mass of a baby mouse will increase similar to what is shown on the

ira [324]

Answer:

Check below for a lucid explanation.

Step-by-step explanation:

The independent variable is the variable whose variation does not depend on another external variable. It is the variable on the x-axis which in this case is the growth of the baby.

Note: The diagram you attached to this question does not include the calibration on the x - axis which will give us the independent variable at point

This, nevertheless, is a very simple task. Locate the point A on the graph and trace it downwards to the x - axis, the value written where the line coincides with the x -axis is the value of the independent variable( growth of the baby) at point A.

6 0

3 years ago

Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1

belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

$F(x) = \int\limits^a_b {f(x)} \, dx$

By using integration formula

$\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c$

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

$\int\limits^6_^-6} (x^{5} + 8 x^{4} + 2 x^{2} + 5 x + 15) )dx$

On integration , we get

= $(\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}$

$F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)$

= $(\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))$