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BlackZzzverrR [31]

2 years ago

15

F is between E and G. FE = 1/3 FG and EG = 24. find FG

1 answer:

deff fn [24]2 years ago

5 0

Answer:

FG = 18

Step-by-step explanation:

24

---E--------------F--------------------------------G

1/3FG

4/3FG = 24

FG= 24×3/4

FG= 6×3

FG= 18

Hope this helps!!!

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zimovet [89]

Answer:

m less then 5

Step-by-step explanation:

its telling you itw no less than 5 so you want to use a less than symbol.

7 0

2 years ago

If $1600 earned simple interest of $56.24 in 2 months, what was the simple interest rate? The simple interest rate is % (Do not

Fiesta28 [93]

Answer:

$\$21.1$

Step-by-step explanation:

We know that for principal amount P , time period T and rate of interest $R\%$ , simple interest is given by $S.I. = \frac{P\times R\times T}{100}$ .

Here ,

$P=\$1600\\T=2\,\,months=\frac{2}{12}\,\,years=\frac{1}{6}\,\,years\\S.I=\$56.24$

To find : simple interest rate i.e., $R\%$

On putting values of $P\,,\,T\,,\,S.I$ in formula , we get $S.I. = \frac{P\times R\times T}{100}$

$56.24 = \frac{1600\times R\times 1}{600}\\R=\frac{56.24\times 600 }{1600}=\frac{703\times 3}{100}=\$21.09$

Now we need to round off the answer to the nearest tenth .

So, simple interest rate is % = $\$21.09$ = $\$21.1$

8 0

2 years ago

F(x)=12x2-4x-8. G(x)=11x-6

AlekseyPX

Answer: Second option.

Step-by-step explanation:

Given the functions f(x) and g(x):

$f(x)=12x^2-4x-8\\\\g(x)=11x-6$

You need to divide them in order to find $(\frac{f}{g})(x)$ asked in the exercise. Then:

$(\frac{f}{g})(x) =\frac{12x^2-4x-8}{11x-6}$

Now, it is important to remember that, by definition, the division by zero is not defined. Therefore, the denominator of the function cannot be zero.

Let's find the value of "x" for which the denominator of the function would be zero:

1. You need to make the denominator equal to zero:

$11x-6=0$

2. Finally, you must solve for "x":

$11x=6\\\\x=\frac{6}{11}$

Therefore, as you can see, the answer is:

$(\frac{f}{g})(x) =\frac{12x^2-4x-8}{11x-6}$ , $x=\frac{6}{11}$

4 0

2 years ago

A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the

kramer

Answer:

$18.73ft^3$

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top= $(side)^2=x^2$

Area of one side face= $l\times b=xy$

Cost of bottom=$9 per square ft

Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

Volume of rectangular box= $V=lbh=x^2y$

Total cost= $9(x^2)+5x^2+4(4xy)=14x^2+16xy$

$204=14x^2+16xy$

$204-14x^2=16xy$

$y=\frac{204-14x^2}{16x}=\frac{102-7x^2}{8x}$

Substitute the values of y

$V(x)=x^2\times \frac{102-7x^2}{8x}=\frac{1}{8}(102x-7x^3)$

Differentiate w.r.t x

$V'(x)=\frac{1}{8}(102-21x^2)=0$

$V'(x)=0$

$\frac{1}{8}(102-21x^2)=0$

$102-21x^2=0$

$102=21x^2$

$x^2=\frac{102}{21}=4.85$

$x=\sqrt{4.85}=2.2$

It takes positive because side length cannot be negative.

Again differentiate w.r. t x

$V''(x)=\frac{1}{8}(-42x)$

Substitute the value

$V''(2.2)=-\frac{42}{8}(2.2)=-11.55$

Hence, the volume of box is maximum at x=2.2 ft

Substitute the value of x

$y=\frac{102-7(2.2)^2}{8(2.2)}=3.87 ft$

Greatest volume of box= $x^2y=(2.2)^2\times 3.87=18.73 ft^3$

5 0

3 years ago

Find the minimum sample size needed to be 99% confident that the sample's variance is within 30% of the population's variance.

liq [111]

The Minimum sample size table is attached below

Answer:

$X=173$

Step-by-step explanation:

From the question we are told that:

Confidence Interval $CI=99\%$

Variance $\sigma^2=30\%$

Generally going through the table the

Minimum sample size is

$X=173$

7 0

2 years ago