(A) The weight of cans of vegetables is normally distributed with a mean of 1380 grams and a standard deviation of 80 grams. What is the probability that the sample mean of weight for 15 randomly selected cans is more than 1410

Answer:

Pencils = 325 ; Pens = 975 ; Markers = 650

Step-by-step explanation:

Let :

Number of Pencils = x

Number of pens = y

Number of markers = z

2 times as many markers as pencils

z = 2x

3 times as many pens as pencils

y = 3x

x + y + z = 1950

Write z and y in terms of x in the equation :

x + 3x + 2x = 1950

6x = 1950

Divide both sides by 6

6x / 6 = 1950 / 6

x = 325

Number of pencils = 325

Pens = 3 * 325 = 975

Markers = 2 * 325 = 650

Pencils = 325 ; Pens = 975 ; Markers = 650

Answer:

2.3,5

Step-by-step explanation:

Both the 2nd and 3rd statement is true. Because of both statement is closely analyzed up during design process of automobile.

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Step-by-step explanation:

The answer to 5.04 × 10 eqauls 50.4 , but there are no answers choices that have exactly 50.4 , so the answer is none of these . I hope this helps you :)

Answer: 53.2

Step-by-step explanation:

Using pythagorean theorem, a^2 + b^2 = c^2

40^2 + 35^2 = sqrt of 2825

which is 53.15

rounded up to nearest tenth is 53.2

Answer:

3

Step-by-step explanation:

Given the data :

2, 3, 7, 8, 9, 13

2 5

3 4

7 0

8 1

9 2

13 6

The mean, = Σx / n ; n = sample size

Mean = 42 / 6 = 7

The mean absolute deviation = Σ|x - mean| / n

The mean absolute deviation is Hence,

(5 + 4 + 0 + 1 + 2 + 6) / 6

Mean absolute deviation = 18 / 6

Mean absolute deviation = 3

Answer:

a) P(0) = 80

b) [tex]P(t) = 80(2.2361)^t[/tex]

c) 22,363 cells.

d) The rate of growth after 7 hours is of 18,000 bacteria per hour.

e) 9.7 hours.

Step-by-step explanation:

A bacteria culture grows with a constant relative growth rate.

This means that the population is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.

This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So

[tex]50000 = 400(1+r)^6[/tex]

[tex](1+r)^6 = \frac{50000}{400}[/tex]

[tex](1+r)^6 = 125[/tex]

[tex]\sqrt[6]{(1+r)^6} = \sqrt[6]{125}[/tex]

[tex]1 + r = 125^{\frac{1}{6}}[/tex]

[tex]1 + r = 2.2361[/tex]

So

[tex]P(t) = P(0)(2.2361)^t[/tex]

(a) Find the initial population. P(0)

We have that P(2) = 400. We use this to find P(0). So

[tex]P(t) = P(0)(2.2361)^t[/tex]

[tex]400 = P(0)(2.2361)^2[/tex]

[tex]P(0) = \frac{400}{(2.2361)^2}[/tex]

[tex]P(0) = 80[/tex]

So

[tex]P(t) = 80(2.2361)^t[/tex]

(b) Find an expression for the population after t hours.

[tex]P(t) = 80(2.2361)^t[/tex]

(c) Find the number of cells after 7 hours.

This is P(7). So

[tex]P(7) = 80(2.2361)^7 = 22363[/tex]

22,363 cells.

(d) Find the rate of growth after 7 hours.

We have to find the derivative when t = 7. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t[/tex]

[tex]P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000[/tex]

The rate of growth after 7 hours is of 18,000 bacteria per hour.

(e) When will the population reach 200,000?

This is t for which [tex]P(t) = 200000[/tex]. So

[tex]P(t) = 80(2.2361)^t[/tex]

[tex]200000 = 80(2.2361)^t[/tex]

[tex](2.2361)^t = \frac{200000}{80}[/tex]

[tex](2.2361)^t = 2500[/tex]

[tex]\log{(2.2361)^t} = \log{2500}[/tex]

[tex]t\log{2.2361} = \log{2500}[/tex]

[tex]t = \frac{\log{2500}}{\log{2.2361}}[/tex]

[tex]t = 9.7[/tex]

So 9.7 hours.

Answer:

Step-by-step explanation:

(z)° + (3z + 1)° = 360° - ( 54° + 204° )

z + 3z + 1 = 360 - 258

4z = 101

z = 25.25

Answer:

Step-by-step explanation:

triangol BCD = triangle BDA

so

3x - 1 = 34 - 2x

5x = 35

x = 35 : 5

Answer:

x = 7

Step-by-step explanation:

BD is an angle bisector , so

∠ ABD = ∠ DBC , that is

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Step-by-step explanation:

a1. The shape will be a vertical or horizontal line.

a2. The shape will be shaped like a diagonal line increasing as we go right.

a3. The shape will be shaped like a diagonal line decreasing as we go right.

a4. The shape will be shaped like a U facing upwards.

a5.The shape will be shaped like a U facing downwards.

a6. The shape will look like a S shape and it increases as we go right.

a7. The shape will look like a S shape and it decreases as We go right.

a8. The shape look like a W shape and it facing upwards.

a9. The shape look a W shape facing downwards.

We are given function.

[tex]x {}^{5} - 3x {}^{4} - 5x {}^{3} + 5x {}^{2} - 6x + 8[/tex]

b. We can test by the Rational Roots Test,

This means a the possible roots are

plus or minus(1,2,4,8).

c. If we apply Descrates Rule of Signs,

d. Use Desmos to Graph the Function. Some roots are (-2,1,4).

e.

[tex](x {}^{2} + 1) (x - 1)(x - 4)(x + 2)[/tex]

f. The complex zeroes are

i and -i

Polynomial [tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex] in factor form: (x-1)(x+2)(x-4)(x-i)(x+i)

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Shape of the graph for the following polynomial:

Finding zeros of the polynomial given:

[tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex]

By factor theorem, if f(t) = 0, t is a zero of the polynomial.

Taking t = 1.

f(1) = 1 - 3 - 5 + 5 - 6 + 8 = 0

(x - 1) is a factor of the polynomial f(x).

Divide f(x) by (x-1) using long division to find the other factors.

f(x)/(x-1) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex] is also a factor of f(x).

Factorizing it further:

g(x) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex]

g(-2) = 16 + 16 - 28 + 4 - 8 = 0

(x + 2) is a factor of g(x) and thus f(x).

g(x)/(x+2) = [tex]x^{3} - 4x^{2} +x - 4[/tex] is a factor of f(x).

Factorizing it further:

k(x) = [tex]x^{3} - 4x^{2} +x - 4[/tex]

k(4) = 64 - 64 + 4 - 4 = 0

(x - 4) is a factor of k(x) thus of f(x).

k(x)/(x-4) = [tex]x^{2} +1[/tex]

Factorizing it further:

l(x) = [tex]x^{2} +1[/tex] = (x + i)(x - i)

Zeros of f(x) = 1, -2, 4, ±i

Rational zeros :  1, -2, 4

Positive real zeros: 1, 4

Negative real zeros: -2

Complex zeros: ±i

Polynomial in factor form: (x-1)(x+2)(x-4)(x-i)(x+i).

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Answer:

[tex]B =102[/tex]

[tex]Y = 32[/tex]

Step-by-step explanation:

Solving (47):

To solve for B, we have:

[tex]B + 50 + 28 = 180[/tex] --- sum of angles in a triangle

This gives

[tex]B + 78 = 180[/tex]

Collect like terms

[tex]B =- 78 + 180[/tex]

[tex]B =102[/tex]

Solving (48):

To solve for Y, we have:

[tex]X + Y+ Z = 180[/tex] --- sum of angles in a triangle

This gives

[tex]Y = 180 - X - Z[/tex]

Where

[tex]W+ X=180[/tex] -- angle on a straight line

Solve for X

[tex]X=180 -W[/tex]

[tex]X=180 -100 = 80[/tex]

So, we have:

[tex]Y = 180 - X - Z[/tex]

[tex]Y = 180 - 80 - 68[/tex]

[tex]Y = 32[/tex]

Answer:

Average of the draws equals 420

Standard Error = 11.88

Step-by-step explanation:

Given

[tex]\mu = 420[/tex]

[tex]\sigma = 84[/tex]

[tex]n =50[/tex]

Solving (a): The average of the draws

This implies that we calculate the sample mean

This is calculated as:

[tex]\bar x = \mu[/tex]  --- Sample Mean = Population Mean

So, we have:

[tex]\bar x = 420[/tex]

Solving (b): The standard error

This is calculated as:

[tex]SE=\frac{\sigma}{\sqrt n}[/tex]

So, we have:

[tex]SE=\frac{84}{\sqrt {50}}[/tex]

Using the calculator, we have:

[tex]SE=11.88[/tex]

Answer:

17 don't play any

Step-by-step explanation:

12+9+8+4=33

33-50=17

Answer:

0.7 = 70% probability that the player will score 0 points.

Step-by-step explanation:

For each free throw, we have these following probabilities:

0.3 probability the player makes.

0.7 probability the player misses.

What is the probability that the player will score 0 points?

He is only allowed the second if he misses the first, thus, he ends with 0 points only if he misses the first.

For any free throw:

0.7 probability the player misses, so 0.7 = 70% probability that the player misses the first free throw, and 0.7 = 70% probability that the player will score 0 points.

Answer:

Option C

Step-by-step explanation:

2 and 4 makes the figure look symmetrical

The required lines of symmetry are 2 and 4. option C is correct.

A given picture line of symmetry is to be determined from 1, 2, 3, and 4.

the line is a curve showing the shortest distance between 2 points.

A line of symmetry is defined as the line that draw across any curve or shape, The curve and shape have equal proportion across the line, that line is called the line of symmetry.

Clearly,  from observation, it is seen that line 1 and line 3 does not have the same proportion of area across it, so this is not a line of symmetry.
Line 2 and line 4, is lines of symmetry because it has equal proportion of the area across it.

Thus, the required lines of symmetry are 2 and 4. option C is correct.

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9514 1404 393

Answer:

  (-1, -3)

Step-by-step explanation:

Each coordinate is multiplied by the dilation factor when dilation is centered at the origin.

  (1/4)(-4, -12) = (-1, -3) . . . . the image of the given point

Answer:

Step-by-step explanation:

the 3 in 135,864 is 30,000

if you mutiply that by 10 you get 300,000

you just need to write any number with a 3 in the hundred thousands place

Answer:

first: there is a problem in the question in de mentioned quantity u mentioned 10k instead of (10kg).

Step-by-step explanation:

add all your 1uantity afteru divide by 8

Answer:

one fertilizer bag from weight of two kilograms

Step-by-step explanation:

Grams of fertilizer needed = Length in meters * Width in meters * 25

                                            = 8 * 8 * 25

                                            = 1600 grams

Kilograms of fertilizer needed = 1600 / 1000

                                                 = 1.6 kilograms

Therefore, gardener can order 1 fertilizer bag with weight of 2kilpgrams.

Step-by-step explanation:

her it Go i think it is helpful for u

Answer:

u = 6

Step-by-step explanation:

We can use a ratio to solve

3           5

----- = ---------

u             10

Using cross products

3*10 = 5u

30 = 5u

Divide by 5

30/5 = 5u/5

6 = u

Answer: u=6m

Step-by-step explanation:

The 2 triangles, LKO and NMO are similar by AAA congruence. Therefore, we can use ratios to find u.

[tex]\frac{5}{10}=\frac{3}{u}[/tex]

Notice how the 5 and 10 are each inbetween the double and single angle congruence indicators in the image. u and 3 are also both in between the right angle and double line indicator.

When you cross multiply, you get 5u=30, and after simplifying you get u=6 m

Another way you could have done this is by finding the scale factor.

The scale factor between corresponding sides in the 2 triangles is 2. (5 x 2 = 10).

When you multiply 3 by 2, you also get 6 m.

Answer:

4/10=2/5 therefore the answer to 2/5

Answer:

Rate = 10^(log[Ending Amount / Beginning Amount] ÷ time)  -1

Rate = 10^(log(1177 / 1100) ÷ time) -1

Rate = 10^(log( 1.07) ÷ 3) -1

Rate = 10^(0.029383777685 /3) -1

Rate = 10^(0.0097945926) -1

Rate = 1.0228091219 -1

Rate = .0228091219% / hour

Source http://www.1728.org/expgrwth.htm

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

n = 5

f(5) = 6(5)+4

f(5)=34

The fifth term of the sequence is equal to 34.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,

n = 5

f(5) = 6(5)+4

f(5)=34

Therefore, the fifth term of the sequence is equal to 34.

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Answer:

A. H0: p = 0.67; H1: p < 0.67

A. The standard normal, since np > 5 and nq > 5.;

Test statistic = - 0.397 ;

Pvalue = 0.3457;

D. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

B. There is insufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

Step-by-step explanation:

p = 0.67 ; q = 1 - p = 1 - 0.67

Sample size, n = 36

x = 23

Test for normality :

(36*0.67) = 24.12

(36 * (1-0.67)) = 11.88

For a normal distribution :

np ≥ 5 and n(1 - p) ≥ 5

The hypothesis :

H0 : p = 0.67

H1 : p < 0.67

The Test statistic :

Z = (phat - p) / √[(p(1 -p))/n]

Phat = x / n = 23 / 36

Z = ((24/36) - 0.67)) / √[(0.67(1 -0.67))/36]

Z = - 0.031 / 0.0783687

Z = - 0.396983

Z = - 0.397

Usong the Pvalue from Z calculator ;

Pvalue of Z = 0.3457

If Pvalue < α ; Reject H0 ; If otherwise, Fail to reject H0

Answer:

ascending order} an order of numbers from least to greatest like 1 2 3 4

descending order} an order of numbers from greatest to least like 4 3 2 1

Answer:

11/20

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

Given

[tex]-2(5x+8)=14+6x[/tex]

Required

Complete the steps

[tex]-2(5x+8)=14+6x[/tex]

Multiply 5x and 8 by -2

[tex]-10x - 16 = 14 + 6x[/tex]

Subtract by 6x

[tex]-10x - 6x- 16 = 14 + 6x - 6x[/tex]

[tex]-16x- 16 = 14[/tex]

Add 16

[tex]-16x- 16 + 16= 14 + 16[/tex]

[tex]-16x= 30[/tex]

Divide by -16

[tex]x= \frac{30}{-16}[/tex]

[tex]x= -\frac{15}{8}[/tex]

See attachment

Answer:

C. 76 + 7i

Step-by-step explanation:

49 squared is 7 and since it's negative, it is an imaginary number. Therefore, it is 7i. Which leaves C to be the correct option.

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]