Evaluate f(3) if (x) = -4x+5

Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years

mylen [45]

Answer:

The value of annuity is $P_v = \$ 7929.9$

Step-by-step explanation:

From the question we are told that

The periodic payment is $P = \$ 250$

The interest rate is $r = 5\% = 0.05$

Frequency at which it occurs in a year is n = 4 (quarterly )

The number of years is $t = 10 \ years$

The value of the annuity is mathematically represented as

$P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ]$ (reference EDUCBA website)

substituting values

$P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ]$

$P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ]$

$P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ]$

$P_v = \$ 7929.9$

8 0

3 years ago

Find all values of x that make the triangles congruent. Explain your reasoning.

RSB [31]

Answer:

x = $\frac{4}{5},5$

Step-by-step explanation:

If both the triangles ΔABC and ΔBCD are congruent,

Corresponding sides of both the triangles will be proportional.

$\frac{AB}{BD}=\frac{AC}{CD}$

$\frac{5x}{3x+10}=\frac{5x-2}{4x+3}$

5x(4x + 3) = (5x - 2)(3x + 10)

20x² + 15x = 15x² + 50x - 6x - 20

20x² + 15x = 15x² + 44x - 20

20x² - 15x² = 44x - 15x - 20

5x² = 29x - 20

5x² - 29x + 20 = 0

5x² - 25x - 4x + 20 = 0

5x(x - 5) - 4(x - 5) = 0

(5x - 4)(x - 5) = 0

$x=\frac{4}{5},5$

3 0

3 years ago

Noah's oven thermometer gives a reading that is 2% greater than the actual temperature if the actual temperature is 350°F what w

blsea [12.9K]

Answer:

Step-by-step explanation:

Step one:

given data

actual reading= 350°F

thermometer reading 2% of the actual reading

Step two:

Required:

The thermometer reading

let us find 2% of 350°F

2/100*350°

=0.02*350

=7°F

Hence the thermometer reading is 7°F greater than 350°F

The thermometer reading is 350+7=357°F

6 0

3 years ago

what is the equation, in slope-intercept from, of the line that is perpendicular to the line y - 4 = -2/3 (x -6 ) and passes thr

Ne4ueva [31]

Turn y - 4 = -2/3(x - 6) into a linear equation.

y - 4 = -2/3(x - 6)

y - 4 = -2/3x + 4

+4 +4

y = -2/3x + 8

The equation that is perpendicular to y = -2/3x + 8 is y = 3x + 4 as shown in the image below using a graph.

5 0

3 years ago

How much smaller is the sum of the first 1000 natural numbers than the sum of the first 1001 natural numbers?

aleksandr82 [10.1K]

ANSWER

1001

EXPLANATION

The sum of the first n - natural numbers is

$S_n= \frac{n}{2} (2a + d(n - 1))$

The sum of the first 1000 terms is

$S_{1000}= \frac{1000}{2} (2(1) + 1(1000 - 1))$

$S_{1000}=500 (1001)$

$S_{1000}=500500$

The sum of the first 1001 terms is

$S_{1001}= \frac{1001}{2} (2(1) + 1(1001 - 1))$

$S_{1001}= 1001 \times (501)$

$= 501501$

The difference is

$501501 - 500500= 1001$

5 0

3 years ago

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