Which is true about the relationship between a radius and diameter?

How much must be deposited today into the following account in order to have $35,000 in 7 years for a down payment on a house?

Rom4ik [11]

Answer:

The amount that must be deposited is $ 19973.87.

Step-by-step explanation:

We have a relation between future value present value as:

F= P $(1 +\frac{r}{n} )^{nt}$

F=future value

P=present value

r=rate (as a decimal)

n=number of compounding periods per year

t=number of years

Now,

assume rate as 8%

35000= P $(1+\frac{0.08}{12} )^{12*7}$

or, 35000= P × $1.0067^{84}$

or, P = $\frac{35000}{1.7522}$

or, P = $ 19973.87

So you must deposit $ 19973.87 today.

7 0

3 years ago

Hurry 50 points for correct answer

Ad libitum [116K]

Answer: "7 is a solution to the original equation. The value –1 is an extraneous solution."

Step-by-step explanation:

The equation $x=\sqrt{6x+7}$ can be solved by squaring both sides:

$x^2 = 6x + 7\\\\x^2 - 6x - 7 = 0\\\\(x-7)(x+1) = 0$

We can see that -1 and 7 are solutions, but make sure they are not extraneous by substituting them in the original equation:

$1 = \sqrt{-1}\\ 7 = \sqrt{49}$

The square root of 49 equals 7, but the square root of -1 is an imaginary number.

The correct choice is "7 is a solution to the original equation. The value –1 is an extraneous solution."

4 0

3 years ago

What is ✓ 75 in simplified form? O 5V5 0 2573 O 3V 5 O 3V 25

faust18 [17]

It should be 5√3

Because 25 x 3 = 75

√25=5 so u bring that out and keep the 3 in because it’s a prime number

3 0

3 years ago

What is the approximate diameter of a tire that will make 775 complete rotations in one mile? (Note: there are 5280 feet

GalinKa [24]

Answer:

About 2.17 feet.

Step-by-step explanation:

Let d represent the diameter of the tire.

Then the circumference of the tire will be:

$C=d\pi$

So, the tire will travel dπ miles after one rotation.

After 775 rotations, the total miles traveled should be 5280 feet. Thus:

$775(d\pi)=5280$

Solve for d:

$\displaystyle d=\frac{5280}{775\pi}$

Approximate:

$d=2.1686...\approx2.17$

The circumference of the tire should be about 2.17 feet.

5 0

2 years ago

The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the

kumpel [21]

Answer:

Check the explanation

Step-by-step explanation:

Let X denotes steel ball and Y denotes diamond

$\bar{x_1}$ = 1/9( 50+57+......+51+53)

=530/9

=58.89

$\bar{x_2}$ = 1/9( 52+ 56+....+ 51+ 56)

=543/9

=60.33

difference = d =(60.33- 58.89)

=1.44

$s^2=1/n\sum xi^2 - n/(n-1)\bar{x}^2$

s12 = 1/9( 502+572+......+512+532) -9/8 (58.89)2

=31686/8 - 9/8( 3468.03)

=3960.75 - 3901.53

=59.22

s1 = 7.69

s22 = 1/9( 522+ 562+....+ 512+ 562) -9/8 (60.33)2

=33295/8 - 9/8 (3640.11)

=4161.875 - 4095.12

=66.75

s2 =8.17

sample standard deviation for difference is

s= $\sqrt{[(n1-1)s_1^2+ (n2-1)s_2^2]/(n1+n2-2)}$

= $\sqrt{[(9-1)*59.22+ (9-1)*66.75]/(9+9-2)}$

= $\sqrt{1007.76/16}$

=7.93

sd = $s*\sqrt{(1/n1)+(1/n2)}$

= $7.93*\sqrt{(1/9)+(1/9)}$

=7.93* 0.47

=3.74

For 95% confidence level $Z (\alpha /2)$ =1.96

confidence interval is

$d\pm Z(\alpha /2)*s_d$

=(1.44 - 1.96* 3.75 , 1.44+1.96* 3.75)

=(1.44 - 7.35 , 1.44 + 7.35)

=(-2.31, 8.79)

There is sufficient evidence to conclude that the two indenters produce different hardness readings.

3 0

3 years ago