Simplify 3.8x + 11.5

Factor completely 18x2 − 21x −15. 3(2x 1)(3x − 5) 3(2x − 5)(3x 1) 3(2x − 1)(3x 5) 3(6x 1)(x − 5).

sergeinik [125]

The factor of the $18x^{2} -21x-15$ will be 3(3x-5)(2x+1).

<h3>What will be the factor of $18x^{2} -21x-15$ ?</h3>

Given quadratic equation is $18x^{2} -21x-15$

By taking 3 common from whole of the equation it becomes.

$3(6x^{2} -7x-5)$

now by factorization equation will be.

$3(6x^{2} -10x+3x-5)$

3[(2x(3x-5)+1(3x-5)]

Taking (3x-5) common from whole equation it will become

3(3x-5)(2x+1).

Hence the factor of the $18x^{2} -21x-15$ will be 3(3x-5)(2x+1).

To know more about factorization follow.

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3 0

2 years ago

For each level of precision, find the required sample size to estimate the mean starting salary for a new CPA with 95 percent co

Rzqust [24]

Answer:

(a) Margin of error ( E) = $2,000 , n = 54

(b) Margin of error ( E) = $1,000 , n = 216

(c) Margin of error ( E) = $500 , n= 864

Step-by-step explanation:

Given -

Standard deviation $\sigma$ = $7,500

$\alpha$ = 1 - confidence interval = 1 - .95 = .05

$Z_{\frac{\alpha}{2}}$ = $Z_{\frac{.05}{2}}$ = 1.96

let sample size is n

(a) Margin of error ( E) = $2,000

Margin of error ( E) = $Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

E = $Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}$

Squaring both side

$E^{2} = 1.96^{2}\times\frac{7500^{2}}{n}$

$n =\frac{1.96^{2}}{2000^{2}} \times 7500^{2}$

n = 54.0225

n = 54 ( approximately)

(b) Margin of error ( E) = $1,000

E = $Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

1000 = $Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}$

Squaring both side

$1000^{2} = 1.96^{2}\times\frac{7500^{2}}{n}$

$n =\frac{1.96^{2}}{1000^{2}} \times 7500^{2}$

n = 216

(c) Margin of error ( E) = $500

E = $Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

500 = $Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}$

Squaring both side

$500^{2} = 1.96^{2}\times\frac{7500^{2}}{n}$

$n =\frac{1.96^{2}}{500^{2}} \times 7500^{2}$

n = 864

7 0

4 years ago

The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours.

solong [7]

Answer:

A. $1,110

B. 50 units.

Step-by-step explanation:

A. Substitute $x=18$ into the function $T(x)=4x+2$ for calculate the time in hours required for the worker to produce 18 units:

$T(18)=4(18)+2=74$

Now you need to substitute $T=74$ into the function $S(T)=15T$ to calculate the amount in dollars she will be paid for 74 hours:

$S(74)=15(74)=1,110$

She will be paid $1,110.

B. To calculate the number of units that the worker needs to produce to be paid $3,030 , you need to substitute $S(T)=3,030$ into the function $S(T)=15T$ and solve for T (to find the number of hours she requires to work to be paid $3,030)

$3,030=15T\\\\T=\frac{3,030}{15}\\\\T=202$

Now, substitute $T(x)=202$ into $T(x)=4x+2$ and solve for x, to calculate the number of units she produces in 202 hours:

$202=4x+2\\\\202-2=4x\\\\x=\frac{200}{4}\\\\x=50$

She would need to produce 50 units to be paid $3,030

5 0

4 years ago

QUICK PLSS 1. Jabo orders a meal that cost $20.00.

Lelechka [254]

Answer:

$25.80

Step-by-step explanation:

Find the cost of the meal with the sales tax:

20 x 0.075 = 1.5

Add the sales tax to the total

20 + 1.5 = 21.50

Find the tip:

21.5 x 0.2 = 4.3

Add the tip to the total cost so far:

21.50 + 4.30 = 25.80

7 0

3 years ago

Three friends grow groups of sunflowers. Some think that Anna’s flowers are the tallest because the mean height of her flowers i

algol [13]

We have to find the graph where the mean of the flower heights is higher and the median is lower.

1st graph
M = ( 3 + 3 + 3 + 3 + 3 ) / 7
M = 15 / 7
Medium = 3
15 / 7 < 3 ( False )
2st graph
M = ( 2 + 6 + 2 + 1 + 1 + 3 ) / 6
M = 15 / 6
Medium = 4 / 2 = 2
15 / 6 > 2
So this is the requested chart.
Hope this helps, good studies.

7 0

3 years ago