What is the system of equations in this problem

Answer:

factor out 12

[tex]12(14cx - 5 + 2x)[/tex]

Answer:

Yes, the new equipment appear to be effective in reducing the variation of​ weights.

Step-by-step explanation:

We are given that Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065.

A simple random sample of 25 quarters is obtained from those manufactured with the new​ equipment, and this sample has a standard deviation of 0.047.

Let [tex]\sigma[/tex] = standard deviation of weights of new equipment.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \geq[/tex] 0.065      {means that the new equipment have weights with a standard deviation more than or equal to 0.065}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] < 0.065      {means that the new equipment have weights with a standard deviation less than 0.065}

The test statistics that would be used here One-sample chi-square test statistics;

                           T.S. =  [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2}__n_-_1[/tex]

where, s = sample standard deviation = 0.047

           n = sample of quarters = 25

So, the test statistics  =  [tex]\frac{(25-1)\times 0.047^{2} }{0.065^{2} }[/tex]  ~  [tex]\chi^{2}__2_4[/tex]   

                                     =  12.55

The value of chi-square test statistics is 12.55.

Now, at 0.05 significance level the chi-square table gives critical value of 13.85 at 24 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of chi-square as 12.55 < 13.85, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the new equipment have weights with a standard deviation less than 0.065.

yes the answer is( true).

Answer:

The answer is (True)

Step-by-step explanation:

Answer:

Charlie spent 5$ per sandwich

Step-by-step explanation:

He ordered 6 sandwiches

6x5 =30

He spent 2$ on kids meal

30+2 = 32$

Hope this helped, if you want please mark branliest it would be appreciated

Answer:

5

Step-by-step explanation:

remove the kids meal first

32-2=30

now, divided 30 dollars by the 6 sandwiches

30÷6 = 5

each sandwhich is 6 dollars

Answer:

-7. negative

Step-by-step explanation:

49 + -56

49 - 56

-7

Answer:

a) 99.95 grams are remaining after 4 years.

b) The percent of carbon-14 remaining is about 99.95%

Step-by-step explanation:

The amount of carbon 14 remaining after t years is given by the following equation:

[tex]C(t) = 100(0.99988)^{t}[/tex]

a) Amount remaining after 4 years.

[tex]C(t) = 100(0.99988)^{4} = 99.95[/tex]

99.95 grams are remaining after 4 years.

b) Percentage remaining after 4 years:

[tex]p = \frac{100*C(4)}{C(0)} = \frc{100*99.95}{100} = 99.95[/tex]

The percent of carbon-14 remaining is about 99.95%

a) 99.95 grams are remaining after 4 years.

b) The percent of carbon-14 remaining is about 99.95%

a.

The amount of carbon should be

[tex]C=100(0.99988)^4[/tex]

= 99.95 grams

b. The percent is

[tex]= 100 \times 99.95100[/tex]

= 99.95%

Learn more: https://brainly.com/question/6269728?referrer=searchResults

Answer:

240cc

Explanation:

From the expression of the relationship between pressure and volume, we can state mathematical that for two successive volume V1 and V2 and Pressure P1 and P2 we have:

P1V1 = P2V2

V2 = P1V1 / P2

=400×300/500= 240cc

Answer:

The answer is option 1.

Step-by-step explanation:

Firstly, you have to get rid of square root at the denorminator by multiply both side with √8 :

[tex] \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} [/tex]

[tex] \sqrt{a} \times \sqrt{a} = a[/tex]

[tex] \frac{ \sqrt{96} }{ \sqrt{8} } [/tex]

[tex] \frac{ \sqrt{96} }{ \sqrt{8} } \times \frac{ \sqrt{8} }{ \sqrt{8} } [/tex]

[tex] \frac{ \sqrt{96} \times \sqrt{8} }{ \sqrt{8} \times \sqrt{8} } [/tex]

[tex] \frac{ \sqrt{768} }{8} [/tex]

Next, you have to simply by looking which factor is a perfect square :

[tex] \frac{ \sqrt{256 \times 3} }{8} [/tex]

[tex] \frac{16 \sqrt{3} }{8} [/tex]

[tex]2 \sqrt{3} [/tex]

Answer:

its a

Step-by-step explanation:

on edge 2022

Answer:

28.6 × 100

⇒ 286/10 × 100

⇒ 286 × 10

⇒ 2860

Answer:

1) (x+4)2 =49

Step-by-step explanation:

x^2+8x-33 = 0   Factor this equation

(x + 11)(x - 3) = 0     Set each equation equal to 0

x = -11 and 3

Test the first equation to see if it has the same solution

(x+4)2 = 49      Simplify the parentheses

(x+4)(x+4) = 49     FOIL the equation

x^2 + 8x + 16 = 49     Subtract 49 from both sides

x^2 + 8x - 33 = 0       This is the correct solution.

Answer: correct answer is A

Step-by-step explanation:

Answer:

[tex]k=\frac{3}{2}[/tex]

Step-by-step explanation:

Given:

[tex]\frac{k}{4}=\frac{3}{8}[/tex]

To find: value of [tex]k[/tex]

Solution:

Cross-multiplying is a method in which the numerator of each (or one) side is multiplied by the denominator of the other side.

[tex]\frac{k}{4}=\frac{3}{8}[/tex]

On cross-multiplication, the equation becomes [tex]k\times 8=4\times 3[/tex]

[tex]8k=12[/tex]

Divides both sides by 8

[tex]\frac{8k}{8}=\frac{12}{8}\\k=\frac{12}{8}=\frac{3}{2}[/tex]

Answer:

  F ∪ H = {c, d, e, f, g, h}

  F ∩ H = { }

Step-by-step explanation:

The union is the list of elements that are in either of the two sets.

  F ∪ H = {c, d, e, f, g, h}

The intersection is the list of only those elements that appear in both sets. (There are none.)

  F ∩ H = { } . . . . the empty set

Answer:

$405.60

Step-by-step explanation:

If Isaac works for 40 hours will earn $8.45×40=$388. Since he worked 4 extra hours, he will earn $8.45×2×4 since he worked 4 extra hours. $8.45×2=$16.90, which is the amount he earns for every extra hour he works. $16.90×4=$67.60. Now if we add $67.60+$388=$405.60.

Hope this helps!

Answer:

50, 65, 82, 101,122,145,170.

Step-by-step explanation:

hope this helps

(Add two to an odd number and continue doing so)

example: 1+1 =2, 2+3 = 5, 5+5 = 10, 10+7 = 17, and so on so forth.

Answer:

20

Step-by-step explanation:

The rectangle is 2 x 8.

2 + 2 + 8 + 8

Answer:

-6

Step-by-step explanation:

f(x) = 2x + 8

Put x as -7.

f(-7) = 2(-7) + 8

Multiply first.

f(-7) = -14 + 8

Add.

f(-7) = -6

The inclusion-exclusion principle says

P(A1 ∩ A2) = P(A1) + P(A2) - P(A1 ∪ A2)

We know the probability of intersection is 0, so

P(A1) + P(A2) = P(A1 ∪ A2)

which means A1 and A2 are indeed mutually exclusive.

Answer:

118.3

Step-by-step explanation:

area = base * height / 2

The two sides forming a right angle can be used as base and height.

area = 13 m * 18.2 m / 2

area = 118.3 m^2

Answer:it is 118.2977011m^2 because the instruction says do not round

Step-by-step explanation:

Answer:

380

Step-by-step explanation:

Order of operations!

(458+56)-134

(514)-134

514-134

380

done!

Answer:

3.8%

Step-by-step explanation:

After evaluating the expression you get 380. You take 380, and turn it into a percentage, move the decimal to the left twice. Giving you 3.8%

Answer:

  C.  7, 14, 21, 28

Step-by-step explanation:

Since you know your times tables, you know that multiples of 7 are ...

   7, 14, 21, 28

Answer:

Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]

Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]

Test Statistics z = 2.65

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

P- value = 0.004025

Step-by-step explanation:

Given that:

Mean [tex]\overline x[/tex] = 960 hours

Sample size n = 36

Mean population [tex]\mu =[/tex] 937

Standard deviation [tex]\sigma[/tex] = 52

Given that the mean  time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours

Null hypothesis is [tex]\mathbf {H_o: \mu > 937}[/tex]

Alternative hypothesis is [tex]\mathbf {H_a: \mu < 937}[/tex]

Degree of freedom = n-1

Degree of freedom = 36-1

Degree of freedom = 35

The level of significance ∝ = 0.01

SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;

from t-table t(0.99,35), the critical value = 2.438

The test statistics is :

[tex]Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}[/tex]

[tex]Z = \dfrac{23}{8.66}[/tex]

Z = 2.65

The decision rule is to reject null hypothesis   if  test statistics is greater than  critical value.

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

The P-value can be calculated as follows:

find P(z < - 2.65) from normal distribution tables

= 1 - P (z ≤ 2.65)

= 1 - 0.995975     (using the Excel Function: =NORMDIST(z))

= 0.004025

Answer:

50%

Step-by-step explanation:

45 cents is 15 cents more than 30 cents. The increase in cents is 15.

15 is half of 30. Half is also 0.5, 1/2, or 50%. The increase is 50%.

You can also answer this using the percent change formula.

percent change = (new number - old number)/(old number) * 100%

percent change = (45 - 30)/30 * 100%

percent change = 15/30 * 100%

percent change = 0.5 * 100%

percent change = 50%

If the result is positive, it is a percent increase.

If the result is negative, it is a percent decrease.

Answer:

B

Step-by-step explanation:

The sample must be represenatative of whole population. Random selection ensures this.

Answer:

Take an example in a triangle:

The orthocenter is the intersection point of 3 altitudes.

The centroid is the intersection point of 3 medians.

The circumcenter is the intersection point of 3 bisectors.

Centroid, orthocenter, and circumcenter are collinear.

Hope this helps!

:)

Answer:

(c) Yes, since the p-values associated with each predictor are less than 0.05

(d) 22.093 cubic feet

(e) underestimate

Step-by-step explanation:

Our main objective is to determine the following

(c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONE Only diameter is a significant predictor since it has the smallest p-value

Yes, since the p-values associated with each predictor are less than 0.05

No, since the p-values associated with each predictor are less than 0.05

Assuming our significance level ∝ = 0.05

From the data given;

p-value for height is = 0.00

p - value for diameter = 0.01

where, p-value ( = 0.01 and 0.00 ) <  ∝ (= 0.05 )

Hence, according to the rejection rule; the null hypothesis is rejected and  the predictors "height" and " diameter" are significant predictors of volume.

Thus

The answer is :

Only diameter is a significant predictor since it has the smallest p-value

Yes, since the p-values associated with each predictor are less than 0.05

(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________

[tex]\hat y = -57.99+ 0.34 \ \mathbf{height }+4.71 \ \mathbf{diameter}[/tex]

[tex]\hat y = -57.99+ 0.34 \ \mathbf{(79)}+4.71 \ \mathbf{(11.3)}[/tex]

[tex]\hat y = 22.093 \ cubic foot[/tex]

(e)

A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONE

overestimate

underestimate

We can posits that the model gives an underestimate of the volume of this tree due to the fact that the predicted value is 22.093 and which is less than the observed value of 24.2 cubic feet.

Answer:

(i) [tex]80-x[/tex]

(ii) [tex]S(x) = 40 - 0.10x[/tex]

(iii) $36.5

Step-by-step explanation:

Given that:

1. Total Number of fruits = 80

2. Number of mangoes = x

3. Both mangoes and oranges are there in the basket.

Solution (i):

Only mangoes and oranges are there in the basket and the basket is full.

so, Number of mangoes + Number of oranges = Total number of fruits

x + Number of oranges = 80

Number of oranges = [tex]80 -x[/tex]

Solution (ii):

Given:

Cost of an orange = 50 cents = $0.50

Cost of a mango = 40 cents = $0.40

Cost for x mangoes = [tex]\$ 0.40x[/tex]

Cost for ([tex]80-x[/tex]) oranges = [tex]\$ 0.50 \times (80-x)[/tex]

[tex]\Rightarrow S(x) = 0.50 (80-x) + 0.40x\\\Rightarrow S(x) = 40 -0.50x + 0.40x\\\Rightarrow S(x) = 40 - 0.10x[/tex]

Solution (iii):

Put value of x = 35 in S(x)

[tex]S(35) = 40 - 0.10 (35)\\\Rightarrow S(35) = 40 - 0.35\\\Rightarrow S(35) =\$ 36.5[/tex]

Hence, answers are:

(i) [tex]80-x[/tex]

(ii) [tex]S(x) = 40 - 0.10x[/tex]

(iii) $36.5

Answer:

19.7 or 20 rounded

Step-by-step explanation:

A = $ 1,861.65

A = P + I where

P (principal) = $ 630.00

I (interest) = $ 1,231.65

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pe^rt

Calculate Principal Amount, solve for P

P = A / e^rt

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r

Answer:

32.738ft³

32.7ft³

Step-by-step explanation:

This is half a sphere therefore volume=4/3πr³×1/2

4/3×22/7×2.5³×1/2

=32.738ft³