When vector is added to vector , the resultant is vector such that . This resultant vector has components Rx=Ax+BxRx=Ax+Bx and Ry=Ay+ByRy=Ay+By. How do you determine the direction of , the angle the vector makes with the positive x-axis?

Answer:

The initial height of the balloon is 2 feet.

Step-by-step explanation:

The height of the balloon in feet after t seconds is given by the following equation:

[tex]h(t) = -0.08t^{2} + 1.6t + 2[/tex]

What is the initial height of the balloon?

This is h when t = 0, that is, h(0). So

[tex]h(0) = -0.08*0^{2} + 1.6*0 + 2 = 2[/tex]

The initial height of the balloon is 2 feet.

Answer:

the mean service time = 70 minutes

the variance of the total service time for customers arriving during a 1-hour period is 700

the probability that the total service time will exceed 2.5 hours is 0.0012

Step-by-step explanation:

Given that:

Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of 7 per hour.

If it takes approximately 10 minutes to serve each customer

From the given information:

The mean total service time=  [tex]10 \ minutes * \lambda[/tex]  (i.e the average number to turn up during the hour) .

where;

[tex]\lambda =[/tex]  the average rate per hour i.e  7

Thus; the mean service time = 10 × 7  = 70 minutes

For a Poisson Distribution;

The variance of the  the total service time for customers arriving during a 1-hour period can be expressed by  the relation:

[tex]\sigma(aX) = a* \sigma(X). \\ \\ where ; \sigma = {\sqrt{S^2}} \\ \\ \sigma(service \ time) = 10 * \sigma(arrival \ time) \\ \\S^2 (service \ time) = (10* \sigma(arrival \ time))^2 \\ \\ S^2(service \ time) = 100 * S^2(arrival \ time) \\ \\ = 100*\lambda \\ \\ = 100*7 = 700[/tex]

where S² = variance

What is the probability that the total service time will exceed 2.5 hours?

If we convert 2.5 hours to minutes ; we have

2.5 × 60 minutes =150 minutes

The probability that the total service time will exceed 2.5 hours is as follows:

[tex]Z = \dfrac{S-70}{\sqrt {700}} \ \ \ \ follow \ N(0,1) \\ \\ P(S > 150) = \dfrac{S-70}{\frac{\sqrt{700}>(150-70)}{\sqrt{700}}} \\ \\ =P(Z > -2.5512) \\ \\ =0.0012[/tex]

Answer:

6y +52

Step-by-step explanation:

6(2y + 8) - 2(3y - 2)

Distribute

12y + 48 - 6y +4

Combine like terms

6y +52

Answer:

f(x) = 4( x + 3/2)^2

Step-by-step explanation:

F(x) =4 x^2 + 12x + 9

= 4 [ x^2 + 3x] + 9

Add (3/2)^2 - (3/2)^2 to the square bracket, we have:

4 [ x^2 + 3x+ (3/2)^2 - (3/2)^2] + 9

4[ (x + 3/2 )^2 - 9/4] + 9

4( x + 3/2)^2 - 9/4 ×4 + 9

4( x + 3/2)^2 - 9 + 9

4( x + 3/2)^2 +0

4( x + 3/2)^2

Note the (3/2)^2 - (3/2)^2 is decoded by dividing b by 2 and squaring it and then subtracting same. Look at the general equation of a circle given below

ax^2 + bx + c

To form a square expression we adopt (b/2)^2 - (b/2)^2 to the general equation provided a = 1;

To make a = 1; we had to factor out 4 from the coefficient of x; making perfect square is of concern when we have ax^2 + bx ; irrespective of 'c' or not.

This is usually referred to as method of completing the square in solving quadratic equation

Answer:

C. 0.3

Step-by-step explanation:

Answer:

  x = 30°

Step-by-step explanation:

The sum of angles in a triangle is 180°, so you have ...

  60° +2x +60° = 180°

  2x = 60° . . . . . . . . .subtract 120° from both sides

  x = 30° . . . . . . . . . . divide by 2

_____

Since the triangle is isosceles (base angles are congruent), the angle bisector is also an altitude that divides the triangle into congruent 30°-60°-90° triangles. The measure of the angle marked x is 30°.

Answer:

5

Step-by-step explanation:

Area equals bh

So 65 divided by 13

Answer:

h = 5 ft

Step-by-step explanation:

The area of a parallelogram is

A = bh

65 = 13h

Divide each side by 13

65/13 = 13h/13

5 = h

Answer:

22 1/8 mm.

Step-by-step explanation:

First add the whole numbers, then the fractions:

3 + 5 + 5 + 7 = 20

7/8 + 7/8 + 3/16 + 3/16    Change the 7/8's to 14/16:

= 14/16 + 14/16 + 3/16 + 3/16

=  28/16 + 6 /16

= 34 /16

= 2 2/16

= 2  1/8

So the final answer is 20 + 2 1/8

= 22 1/8 mm.

Step-by-step explanation:

the perimeter of this

3 7/8 + 5 3/16 + 5 3/16 + 7 7/8

= 31/8 + 83/16 + 83/16 + 63/8

= 62 + 83 + 83 + 126/ 16

= 354/16 ans

Answer:

The 90​% confidence interval for the population​ mean is between 27.34 months and 39.84 months.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645*\frac{19}{\sqrt{25}} = 6.25[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 33.59 - 6.25 = 27.34 months

The upper end of the interval is the sample mean added to M. So it is 33.59 + 6.25 = 39.84 months

The 90​% confidence interval for the population​ mean is between 27.34 months and 39.84 months.

Answer:

1/2 or 0.5

Step-by-step explanation:

4x+8=10tothefirstpower x=1/2 or 0.5

Answer:

[tex]\frac{-4}{5}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5} - \frac{7}{5} = \frac{3-7}{5} = \frac{-4}{5}[/tex]

The sum of the fractions is -4/5.

The real numbers arranged in order on a geometric line form a number line. The points on the geometric line represent real numbers.

On the number line, the addition of a positive number a to a number b moves the point at b to the right by a units.

The addition of a negative number -a to a number b moves the point at b by a units to the left.

The point H in the diagram is at the number 3/5, third stick to the right of 0.

Adding -7/5 to 3/5 means moving the point H to the left by 7 sticks. Doing so we find the point at -4/5 as shown in the figure.

The final position of the point after addition is -4/5.

The value of 3/5 - 7/5 is, thus, -4/5.

Learn more about number line here

https://brainly.com/question/25230781

#SPJ2

Answer:

B 63 degrees

Step-by-step explanation:

180 - 54 = 126

126 / 2 = 63

Answer:

the first and the second answer

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

This is correct believe me it is.

Answer:

31200 dollars

Step-by-step explanation:

you multiply 13 by 4, because its last week and this week, then find 60 percent of that. Proportion: x/52000=60/100. When solved, it is $31200

The solution is, $31200 should she plan to spend on advertising next week.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

Last week Malia spent $13,000 on advertising.

This week, she plans to spend three times as much.

Next week, she wants to spend 60% of what she spent the previous two weeks.

now, we have,

you multiply 13000 by 4,

i.e.  13000 *4 = 52000

because its last week and this week,

then find 60 percent of that.

let, she plan to spend on advertising next week is x .

Proportion:

x/52000=60/100.

When solved, it is $31200.

Hence, The solution is, $31200 should she plan to spend on advertising next week.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ6

Answer:

0.7 + 0.4 - 0.2 = 0.9

Step-by-step explanation:

Let's denote the probabilities as following:

The probability that the show had animals is

P(A) = 0.7

The probability that the show aired more than 10 times is

P(B) = 0.4

The probability that the show had animals and aired more than 10 times is

P(A⋂B) = 0.2

The probability that a randomly selected show had animals or aired more than 10 times is P(A⋃B)

The correct form of  addition rule to determine the probability that a randomly selected show had animals or aired more than 10 times is:

P(A⋃B) = P(A) + P(B) - P(A⋂B) = 0.7 + 0.4 - 0.2 = 0.9

=> Option B is correct

Hope this helps!

Answer:

B;3

Step-by-step explanation:

That is because to complete the box you need the sum to subtract from one of the addends to be able to find the other and

28.42-24.72=3.7

Hope this helps:)

The missing number is 3.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:

Operands: The numbers used in an operation are called operands. Depending on the type of operation, different terms are applied to the operands.

Operator: An operator is the sign used to represent a mathematical operation, such as + for addition, subtraction, multiplication, and division.

Given adding certain number to 24.72 gives 28.42

24.72 + [?].7 = 28.42

let the number be x + .7

equation is

24.72 + x +.7 = 28.42

x = 28.42 - 0.7 - 24.72

x = 3

Hence 3 is the missing digit.

Learn more about Mathematical operators;

https://brainly.com/question/8959976

#SPJ5

Answer:

√2

Step-by-step explanation:

(-5, 0) and (-4, 1)

[tex]d=\sqrt{(x_{2}-x_{1} )^{2}+ {(y_{2}-y_{1} )^{2}}}[/tex]

[tex]d= \sqrt{(-4-(-5))^{2} + (1-0)^{2}} =\sqrt{1+1} =\sqrt{2}[/tex]

Answer:

y=3(x+2)^2-5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

eifufjdbeiixjfbdbsisifbfbfbidid

Answer:

228incubed

Step-by-step explanation:

Area of prism is area of cross section x length.

So, área of trapezium is a plus b times h divided by 2.

Times that by height. Gives you 228

Answer:

Z = 1.96.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

The value of z that should be used is Z = 1.96.

Answer:

C and E

Step-by-step explanation:

ANP = BNP = 90 WILL PROVE THAT CD IS PERPENDICULAR TO AB.

Answer:

IQR = 274

Step-by-step explanation:

Given the unit sales for the months as:

148, 329, 491, 167, 228, 285, 441

Let's rearrange in ascending the values in ascending order (from lowest to highest), we have:

148, 167, 228, 285, 329, 441, 491

Here the total number of data, n is 7

Let's find the quartile locations using the formula:

[tex] Lq = (n + 1) * (\frac{q}{4}) [/tex]

where q is quartile index.

For first quartile, Q1:

[tex] Lq = (7 + 1) * (\frac{1}{4}) [/tex]

[tex] Lq = 8 * (\frac{1}{4}) = 2 [/tex]

Thus, the 2nd observation in the data is 167.

Q1 = 167

For third quartile, Q3:

[tex] Lq = (7 + 1) * (\frac{3}{4}) [/tex]

[tex] Lq = 8 * (\frac{3}{4}) = 6 [/tex]

Thus, the 6th observation in the data is 441.

Q3 = 441

The interquartile range, IQR will be:

Q3 - Q1

= 441 - 167

= 274

IQR = 274

Answer:

  44

Step-by-step explanation:

Put 8 where x is and do the arithmetic.

  f(8) = 6·8 -4 = 48 -4

  f(8) = 44

Answer:

No

Step-by-step explanation:

Although two sides are equal, the 32 is simply too big for it to be a triangle.

Answer:

No it is not the sides of right angled triangle.

Step-by-step explanation:

IF a²+b²=c² then the triangle is right

3²+3²=32²

9+9=1024

18=1024

Answer:

Step-by-step explanation:

here are some of the graph points:

(-2,-2)

(-1,-3)

(0,-4)

(1,-5)

(2,-6)

(3,-7)

(4,-8)

The graph should have a negative slope and the slope should be -1, and the y-intercept should be -4.  The pic you put is not the correct graph.

Answer:

Answers are below in bold

Step-by-step explanation:

1) A = 1/2bh          Use this equation to find the area of each triangular base

A = 1/2(8)(6)         Multiply

A = 1/2(48)           Multiply

A = 12cm²           Area of each triangular base

2) A = L x W        Use this equation to find the area of the bottom rectangular face

A = 20 x 8          Multiply

A = 160 cm²       Area of the bottom rectangular face

3) A = L x W        Use this equation to find the area of the back rectangular face

A = 20 x 6          Multiply

A = 120 cm²       Area of the back rectangular face

4) A = L x W        Use this equation to find the area of the sloped rectangular face

A = 20 x 10         Multiply

A = 200 cm²      Area of the sloped rectangular face

5) To find the total surface area of the triangular prism, add together all of the numbers.

A = 12 + 12 + 160 + 120 + 200       Add

A = 504 cm²       Total area of the triangular prism

Answer:

see explanation

Step-by-step explanation:

Given

A = bh ( isolate h by dividing both sides by b )

[tex]\frac{A}{b}[/tex] = h

-----------------------------

Given

V = 3k + 2 ( subtract 2 from both sides )

V - 2 = 3k ( divide both sides by 3 )

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

Corrected Question

Find a number in between 35.76 and 35.8 and make the inequality 35.76<________<35.8 a true statement?

Answer:

One example is 35.77

Step-by-step explanation:

Given the numbers 35.76 and 35.8

To make the inequality [tex]35.76< x <35.8[/tex] a true statement, we look for a value of x such that:

[tex]x>35.76; and\\x<35.8\\$Let x=35.77\\Cearly:$\\35.77 > 35.76;$ and$\\35.77<35.8[/tex]

Therefore:

[tex]35.76< 35.77 <35.8[/tex] is a true statement.

Answer:

Option 3 is correct.

The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games.

Step-by-step explanation:

Before anything else, we first give the null and alternative hypothesis for this question.

Null hypothesis would be that there isn't significant evidence to conclude that the mean point spread of home games is higher than that of away games.

H0: µ1 = µ2

And the alternative hypothesis would be that there is significant evidence to conclude that the mean point spread of home games is higher than that of away games.

Ha: μ1 > μ2

The data from the output of the analysis of the hypothesis test is missing from the question. It was obtained online and is attached to this solution of the question.

The table consists of the difference, the sample mean, the standard error of the mean, degree of freedom, the test statistic and most importantly, the p-value. It is the p-value that absolutely gives us the concluding statement of the hypothesis testing.

When the significance level for a test isn't provided, the convention is usually to use 5% significance.

Interpretation of p-value

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.4351

0.4351 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that 'The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread of home games is higher than that of away games'.

Hope this Helps!!!

Answer:

Minutes= 90

Step-by-step explanation:

Brady will take care of 24 cows in 120 minutes.

Rate of Brady = 24/120

Mc Kenna takes care of same 24 cows in 360 minutes.

Rate of Mc Kenna = 24/360

Sum of rates = 24/120 + 24/360

Sum of rates =( 72+24)/360

Sum of rates = 96/360

Sum of rates = 96/360

Let's determine how many minutes it will take them total to take of Same 24 cows

Minutes = 24/rate

Minutes = 24/(96/360)

Minutes =( 24*360)/96

Minutes= 90