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The magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

Sum of vectors in x direction, ∑X = 5 - 1 = 4

Sum of the vectors in y direction, ∑Y = 6 + 14 = 20

Resultant vector = √(∑X² + ∑Y²)

Resultant vector = √(4² + 20²) = 20.4 units

θ = arc tan (ΣY/ΣX)

θ = arc tan (20/4)

θ = arc tan (5)

θ = 78.7⁰

θ ≈ 79⁰

Thus, the magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

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Considering the given function, it is found that:

Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.

The function is:

d = 5t².

Hence:

Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.

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Answer:

Step-by-step explanation:

A new baby grew:

Total inches during two months:

Using continuous compounding, it is found that the value of r is of r = 7.7%.

The amount of money after t years in continuous compounding is:

[tex]P(t) = P(0)e^{rt}[/tex]

In which:

The doubling time of 9 years means that P(9) = 2P(0), which is used to find r, hence:

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]2P(0) = P(0)e^{9r}[/tex]

[tex]e^{9r} = 2[/tex]

[tex]\ln{e^{9r}} = \ln{2}[/tex]

[tex]9r = \ln{2}[/tex]

[tex]r = \frac{\ln{2}}{9}[/tex]

r = 0.077.

r = 7.7%.

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Answer: c) {1,245; 1,224; 1,203; 1,182; …}

Step-by-step explanation:

Concept:

For this question, we just go by eliminating each answer until we get the correct one

Given information

Common difference = -21 (decreasing sequence)

Answer Choice: a) {873, 894, 915, 936, …}

894 - 873 = 21

915 - 895 = 21

936 - 915 = 21

Since the common difference is 21, not -21

[tex]\large\boxed{FALSE}[/tex]

Answer Choice: b) {32, 20, 8, -4, …}

20 - 32 = -12

8 - 20 = -12

-4 - 8 = -12

Since the common difference is -8, not -21

[tex]\large\boxed{FALSE}[/tex]

Answer Choice: c) {1,245; 1,224; 1,203; 1,182; …}

1224 - 1245 = -21

1203 - 1224 = -21

1182 - 1203 = -21

Since the common difference is -21

[tex]\Huge\boxed{TRUE}[/tex]

Answer Choice: d) {1,563; 1,587; 1,611; 1,635; …}

1587 - 1563 = 24

1611 - 1587 = 24

1635 - 1611 = 24

Since the common difference is 24, not -21

[tex]\large\boxed{FALSE}[/tex]

Hope this helps!! :)

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Answer:

x = − 6

Step-by-step explanation:

I have my work

Step-by-step explanation:

[tex] = \frac{6}{7} \times \frac{2}{3} \\ [/tex]

[tex] = \frac{12}{21} \\ [/tex]

Change into lowest term...

[tex] = \frac{4}{7} \\ [/tex]

...

Answer: [tex]48\pi[/tex]

Step-by-step explanation:

[tex](2 \times 24)\pi=48\pi[/tex]

The correct answer is the option A because in one-to-one functions, each y value corresponds to only one x value.

Step-by-step explanation:

A quadratic equation is a  equation with a degree of 2. Below are the 5 ways to solve a quadratic equation.

Answer:

x=-4, x=9

Step-by-step explanation:

We write this into words:

difference = subtraction

square = ^2

a number = x

is equal to = =

5 times that number = 5x

x^2-36 = 5x

write in standard form

x^2-5x-36

what adds to -5 and multiplies to -36?

-9 and 4!

(x-9)(x+4)

x-9 = 0

x= 9

x+4 = 0

x=-4

Answer:

9

Step-by-step explanation:

Let the number = x.

x² - 36 = 5x

x² - 5x - 36 = 0

(x - 9)(x + 4) =0

x = 9 or x = -4

Answer: 9

Answer:

110 [%].

Step-by-step explanation:

if the initial area is 24 m² and final area 50.4 m², then the required percentage can be calculated as:

[tex]\frac{50.4}{24}*100-100=110[/tex] ,  

where 50.4/24*100 - the final percentage.

P.S. It means, the final value of the paint is 3*2.1=6.3 [liters].

Answer:

y = (constant variable x time) + independent variable

y = 60x + 30    ← Health Club B

y = 27x + 50    ← Health Club A

Step-by-step explanation:

I can't see the question at the bottom due to the covering but if you comment I can edit this and give a proper answer. Otherwise this is all I can give you.

Answer:

  $152,419.36

Step-by-step explanation:

The future value of an ordinary annuity is given by the formula ...

  FV = P((1 +r/12)^(12t) -1)/(r/12)

where P is the monthly payment, r is the annual interest rate, and t is the number of years.

For P = 350, r = 0.021, and t = 27 (years to retirement age), the value is ...

  FV = 350((1 +0.021/12)^324 -1)/(0.021/12) ≈ $152,419.36

The value of Jolene's retirement account when she turns 60 will be $152,419.36.

Answer:

It's supplementary angle I think

Answer:

one angle is 20° and the other is 70°

Step-by-step explanation:

Complementary angles add up to 90°.

Here it is given that an angle exceeds 3 times its complement by 10. So, we are taking the complement as x. Since it exceeds its complement 3 times, we are multiplying the complement 3 times. so we get [tex]3x[/tex].

Now we also need to add 10, so we get the final equation [tex]3x+10[/tex], which is the second angle.

As of now, first angle = x and second angle =  3x+10.

Since they are complementary angles, both angles add up to 90°

⇒ 1st angle + 2nd angle = 90°

∴ [tex]x+3x+10 = 90[/tex]  [since 3x and x are like expressions, we should add 3x + x = 4x]

⇒ [tex]4x = 90 - 10[/tex]  [by transposing 10 from LHS to RHS]

⇒ [tex]4x = 80[/tex]

⇒ [tex]x = \frac{80}{4}[/tex]  [by transposing 4 from LHS to RHS]

⇒ [tex]x = 20[/tex]

∴The complementary angle is 20° and the given angle is [(3 × 20) + 10)] = 70°

If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.

Given sample size be 300 and about 5% of the population has a particular genetic mutation.

We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.

Sample size=300

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation=[tex]\sqrt{np(1-p)}[/tex]

Use the known values in the above formula.

Standard deviation=[tex]\sqrt{300*0.05(1-0.05)}[/tex]

=[tex]\sqrt{14.25}[/tex]

=3.77

Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.

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The amount of Harry's loan is $9000.

A loan is when money is lent to another person with the understanding that it would be repaid, along with interest.

According to the question,

A bank loan is taken up by Harry.

After t months, D indicates Harry's outstanding debt (in dollars).

D=-200t+9000

In order to find the initial size of Harry's loan, the time(t)=0, that is, the time when no debts had been paid.

The negative sign in the expression of D denotes the payment of debt.

Substituting t=0, we get,

D=-200*0+9000

D=9000

Thus, the amount of loan taken by Harry is $ 9000.

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Answer:

$20

Step-by-step explanation:

$5.00 = 10miles

$0.25(40) = 40 miles

Remaining miles: 100 - (10 + 40) = 50

0.10(50) = 50 miles

5.00 + 0.25(40) + 0.10(50)

5.00 + 10.00 + 5.00

$20.00 for 100 miles

The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:

Beginning inventory of finished goods $11,850

Cost of goods manufactured                485,310

Ending inventory of finished goods      (12,670)

Cost of Goods Sold                           $484,490

The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.

The cost of goods sold budget is based on the cost of goods manufactured budget.

Direct materials:                            Enamel        Paint     Porcelain      Total    

Total direct materials purchases

budgeted for September            $35,870    $7,530    $139,890  $183,290

Estimated inventory, September 1   1,730        4,150          6,920      12,800 Desired inventory, September 30 (2,980)      (2,710)         (7,150)    (12,840)

Materials used in production                                                          $183,250

Direct labor cost:           Kiln Department    Decorating Department   Total

Total direct labor cost

budgeted for September    $51,550                   $149,500        $201,050

Finished goods inventories:             Dish       Bowl     Figurine             Total

Estimated inventory, September 1  $5,810   $3,310     $2,730        $11,850

Desired inventory, September 30    3,720    4,590       4,360         12,670

Work in process inventories:

Estimated inventory, September 1      $3,540

Direct materials used in production $183,250

Direct labor costs                              $201,050

Total factory overhead costs             $99,450

Desired inventory, September 30       (1,980)

Cost of goods manufactured           $485,310

Indirect factory wages $80,400

Depreciation of plant and equipment 10,550

Power and light 5,110

Indirect materials 3,390

Total 99,450

Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.

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a) The factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The function has a minimum and grows in the + y direction.

d) Marking the two x-intercepts, second, generating a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and estimate the location of the vertex and, finally, creating a parabola with a minimum and growing in the + y direction by matching the points.

In this problem we have a quadratic function in standard form, that is, an equation of the form f(x) = a · x² + b · x + c, where a, b and c are real coefficients. a) First, we need to complete the square and find the roots to determine the factorized form:

4 · x² - 7 · x - 15 = 0

4 · [x² - (7 / 4) · x - (15 / 4)] = 0

x² - (7 / 4) · x - (15 / 4) = 0

x² - 2 · (7 / 8) · x - (15 / 4) + (289 / 64) = 289 / 64

x² - 2 · (7 / 8) · x + 49 / 64 = 289 / 64

(x - 7 / 8)² = 289 / 64

x - 7 / 8 = ± 17 / 8

x = 7 / 8 ± 17 / 8

Then, the factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The end behavior of the graph is inferred from the lead coefficient. A positive coeffcient , which is the case of the function, indicates that vertex of the polynomial is a minimum and parabola grows in the + y direction.

d) In accordance with algebra, we can generate a quadratic equation by knowing three distinct points on Cartesian plane.

First, mark the two x-intercepts, second, generate a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and, finally, generate a parabola with a minimum and growing in the + y direction.

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Step-by-step explanation:

I assume this means exactly one wrong number in the 10 attempts.

the probability to get a wrong number is 0.15 (15%).

therefore, the probability to get a correct number is

1 - 0.15 = 0.85

in 10 tries to get 1 wrong number (and 9 correct numbers) looks like this :

0.15×0.85⁹ = 0.034742542...

this would be the probability to e.g. get a wrong number at the first attempt, and all other attempts are correct.

how many different constellations can we have that way ?

10.

because the wrong number could be given at any of the 10 attempts.

so, the probability to get exactly 1 wrong answer is

10×0.15×0.85⁹ = 0.34742542... ≈ 35%

now, if the question is about the probability to get at least one number wrong, then we can say this is the opposite of the probability to get all 10 numbers correctly.

the probability to get all 10 numbers correctly is

0.85¹⁰ = 0.196874404... ≈ 20%

and therefore, the probability to get at least 1 number wrong is

1 - 0.196874404... = 0.803125596... ≈ 80%

FYI :

this would be, of course, also the result of we did it the complex way :

the sum of the probabilities of

exactly 1 number wrong

exactly 2 numbers wrong

...

exactly 9 numbers wrong

all 10 numbers wrong

and for each of the cases of n wrong numbers the probability is

(10! / (n! × (10-n)!)) × 0.15^n × 0.85^(10-n)

this represents the constellation of n numbers wrong (and 10-n numbers right) multiplied by the number of possible combinations of picking n numbers out of 10.

and again, all this summed up (1 <= n <= 10) is the same as

0.803125596...

The probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Now, Let q = probability of giving out wrong number = 15 % = 0.15

And, p = probability of not giving out wrong number = 1 - q

= 1 - 0.15 = 0.75

Hence, For a binomial probability,

P(x) = ⁿCₓ qˣ pⁿ⁻ˣ.

With n = 10 and x = 1, the probability of getting a number wrong

P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹

          = 10(0.15)(0.75)⁹

           = 1.5(0.0751)

           = 0.1126

           = 11.26 %

b. At most one wrong is P(x ≤ 1) = P(0) + P(1)

= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹

= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹

= 0.0563 + 0.01126

= 0.06756

= 6.756 %

≅ 6.76 %

Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.

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Answer:

75 inches

Step-by-step explanation:

Let x = the short side

Let y = the long side

x + y = 300

y = 3x

Plug 3x for y into the first equation:

x + 3x = 300

4x = 300  Divide both sides by 4

x = 75

Answer:

Rounded to the nearest tenth would be 75.5 degrees

Step-by-step explanation:

The graph of the translated function can be seen in the image below.

For a given function f(x), we define a vertical translation of N units as:

g(x) = f(x) + N

Where if N is positive, the translation is upwards. If N is negative, the translation is downwards.

In this case, we have:

y = f(x) - 2

Then we just need to translate the given graph 2 units below, we will get the graph you can see below.

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Step-by-step explanation:

a)

z = (140 - 118)/16 = 22/16 = 11/8 = 1.375 ≈ 1.38

in the z-table this gives us the p-value : 0.91621

that is the probability of values 140 and below.

for above 140 we need to calculate the value of the other side of the bell-curve :

1 - 0.91621 = 0.08379

b)

z = (90 - 118)/16 = -28/16 = -7/4 = -1.75

in the z-table this gives us the p-value : 0.04006

that is the probability of values of 90 and below.

Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is  less than 0.4

The square root of numbers is is expressed using the square root sign. In order to determine the square root os 0.15 given, we need need to determine the square of perfect square before and after the given number.

For the square root of √0.09

√0.09 = 0.3

Similarly for the square root of √0.16

√0.16 = 0.4

Since the resulting value is 0.3 and 0.4, hence the square root of 0.15 must be between these two values on the number line.

Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is  less than 0.4

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Answer:

$144

Step-by-step explanation:

24*6 = 144

Using the normal distribution, it is found that the percentages are given as follows:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The prorportion of students who receive an A is one subtracted by the p-value of Z = 1.8.

Looking at the z-table, Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359.

3.59% of the grades will be A.

For B, it is the p-value of Z = 1.8 subtracted by the p-value of Z = 1.1, hence:

0.9641 - 0.8643 = 0.0998.

9.98% of the grades will be B.

For C, it is the p-value of Z = 1.1 subtracted by the p-value of Z = -1.2, hence:

0.8643 - 0.1151 = 0.7492.

74.92% of the grades will be C.

For D, it is the p-value of Z = -1.2 subtracted by the p-value of Z = -1.9, hence:

0.1151 - 0.0287 = 0.0864.

8.64% of the grades will be D.

For F, it is the p-value of Z = -1.9, hence 2.87% of the grades will be F.

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Answer:

300 tarts

Step-by-step explanation:

we must solve this equation by going backwards

3/4 of something (as 1/4 was given away) is 150

150 / 3/4 is what you must do

or

150 * 4/3

that is

200

3/5 was sold so 2/5 was left

2/5 of something is 200

200 / 2/5

200 * 5/2

that is

500

3/5 of that was sold

so

500 * 3/5 is 300

300 tarts were sold