a westward moving motorcycle slows down from 24.0 m/a to 12.0 m/s in 3.0 seconds. what is the magnitude and direction of the acceleration

Answer:

[tex]a \cdot b = 1[/tex]

Step-by-step explanation:

[tex] a = 5i + 7j [/tex]

[tex] b = -4i + 3j [/tex]

[tex] a = a_xi + a_yj [/tex]

[tex]b = b_xi + b_yj[/tex]

[tex] a \cdot b = a_xb_x + a_yb_y [/tex]

[tex] a \cdot b = (5)(-4) + (7)(3) [/tex]

[tex] a \cdot b = -20 + 21 [/tex]

[tex]a \cdot b = 1[/tex]

Answer:

[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]

Step-by-step explanation:

[tex]\sf Plug \ in \ the \ values.[/tex]

[tex](5i+7j) \cdot (-4i+3j)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]

[tex]-20i^2 +15ij+-28ij +21j^2[/tex]

[tex]\sf Combine \ like \ terms.[/tex]

[tex]-20i^2 -13ij+21j^2[/tex]

Answer:

Option C

The graph of g is vertically shifted 5 units down

Answer:

X+9=24

Or,x=24-9

:.x=15

Step-by-step explanation:

Answer:

B. x=15

Step-by-step explanation:

To find the solution to the equation, we must get x by itself on one side of the equation.

[tex]x+9=24[/tex]

9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.

[tex]x+9-9=24-9[/tex]

[tex]x=24-9[/tex]

[tex]x=15[/tex]

Let's check our solution. Plug 15 in for x.

[tex]x+9=24 (x=15)[/tex]

[tex]15+9=24[/tex]

[tex]24=24[/tex]

This checks out, so we know our solution is correct. The answer is B. x=15

Answer:

I am going to show you the first steps to complete squares for the given equation: 1) Starting equation: 3x^2 + 9x -4 = 0 2) Add 4 to both sides => 3x^2 + 9x - 4 + 4 = 4 => 3x^2 + 9x = 4 3) Extract common factor 3 in the left side => 3 (x^2 + 3x). Now, compare with a(x^2 + 3x) and you get a = 3. Answer: a = 3.

Answer:

its c

Step-by-step explanation:

Answer:

Sphere Volume = 4/3 * PI * radius^3

Sphere Volume = 4/3 * PI * 8^3

Sphere Volume = 4/3 * PI * 512

Sphere Volume = 2,144.7 cubic inches

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

4,7,12,19

We are adding 3,5,7,9..... each time

The sequence is not arithmetic because we are not adding a constant.  It is not geometric since we are not multiplying by a constant term each time

There is no common difference  or common ratio.

The explicit formula is

an =n^2 +3

The recursive formula is

(n+1)^2 +3 - (n^2 +3)

    n^2 +2n+1+3 - ( n^2+3)

      2n+1

a sub(n+1) = a sub( n) + 2n+1

The 10th term

an      = n^2 +3

Let n=10

an = 10^2+3

    = 100+3

    = 103

summation

see image

since the numbers are increasing and greater than 1 the sum does not exist

Answer: x=29

Step-by-step explanation:

[tex]x-21=8[/tex]

add 21 to both sides

[tex]x-21+21=8+21[/tex]

[tex]21+8=29\\[/tex]

[tex]x=29[/tex]

Answer:

Step-by-step explanation:

tanθ= opp / adj

tan(12) = AC/44

now

AC = tan(12)/44

AC = ...

use calculator to find the value

I just broke mine

Answer:

C, D, E and F

Step-by-step explanation:

Given

4x+5y=18

6x−5y=20

Required

Determine which procedure will result in a single equation in one variable

To do this; we'll test each of the options

A. Subtract the first equation from the second equation.

[tex](6x - 5y=20) - (4x+5y=18)[/tex]

[tex]6x - 4x - 5y - 5y = 20 - 18[/tex]

[tex]2x - 10y = 2[/tex] --- This didn't produce the desired result

B.  Subtract the second equation from the first equation.

[tex](4x+5y=18) - (6x - 5y=20)[/tex]

[tex]4x - 6x + 5y + 5y =18 - 20[/tex]

[tex]-2x + 10y = -2[/tex] --- This didn't produce the desired result

C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.

First Equation

[tex]18 * (4x+5y=18)[/tex]

[tex]72x + 90y = 324[/tex]

Second Equation

[tex]18 * (6x - 5y=20)[/tex]

[tex]108x - 90y = 360[/tex]

Add Resulting Equations

[tex](72x + 90y = 324) + (108x - 90y = 360)[/tex]

[tex]72x + 108x + 90y - 90y = 324 + 360[/tex]

[tex]72x + 108x = 324 + 360[/tex]

[tex]180x = 684[/tex] --- This procedure is valid

D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.

First Equation

[tex]-6 * (4x+5y=18)[/tex]

[tex]-24x - 30y = -108[/tex]

Second Equation

[tex]4 * (6x - 5y=20)[/tex]

[tex]24x - 20y = 80[/tex]

Add Resulting Equations

[tex](-24x - 30y = -108) + (24x - 20y = 80)[/tex]

[tex]-24x + 24x - 30y -20y = -108+ 80[/tex]

[tex]-50y = -28[/tex]

[tex]50y = 28[/tex]  --- This procedure is valid

E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.

First Equation

[tex]3 * (4x+5y=18)[/tex]

[tex]12x + 15y = 54[/tex]

Second Equation

[tex]-2 * (6x - 5y=20)[/tex]

[tex]-12x + 10y = -40[/tex]

Add Resulting Equations

[tex](12x + 15y = 54) + (-12x + 10y = -40)[/tex]

[tex]12x - 12x + 15y - 10y =54 - 40[/tex]

[tex]5y = 14[/tex]  --- This procedure is valid

F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order

First Equation

[tex]3 * (4x+5y=18)[/tex]

[tex]12x + 15y = 54[/tex]

Second Equation

[tex]2 * (6x - 5y=20)[/tex]

[tex]12x - 10y = 40[/tex]

Subtract equation 1 from 2 or 2 from 1 will eliminate x;

Hence, the procedure is also valid;

Answer:

1.5 hours

Step-by-step explanation:

Set up a proportion:

[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]

Cross multiply:

40x = 60

x = 1.5

= 1.5 hours

Answer:

Y

Step-by-step explanation:

You see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.

Y represents the greater number.

We see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.

A set of values that display an actual role. On graphs it is also a pair of numbers: the first variety indicates the gap along, and the second variety indicates the distance up or down. As an example, the factor (12,5) is 12 units long, and five units up.

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#SPJ2

Answer:

Step-by-step explanation:

Diameter = 26 inches

From the question

1 inch = 25.4 mm

To find it's equivalent in millimeters multiply 26 inches by 25.4 millimeters and divide by 1 inch

so we have 26 inches as

[tex] \frac{26 \: inches \times 25.4mm}{1 \: inch} [/tex]

Simplify

We have

26 × 25.4 mm

We have the final answer as

Hope this helps you

Answer: B.) 26 inches  (25.4 millimeters/ 1 inch)

Step-by-step explanation: i hope this helps :)

Answer:

Translated according to the rule (x, y)⇒ (x+7, y+1)  , reflected across the  x-axis

Step-by-step explanation:

Transformation involves changing the orientation, or even size of a given figure or object to produce its image. The methods of transformation include; translation, rotation, reflection, and dilation.

Comparing the pentagon ABCDE and A”B”C”D”E”, the two transformations applied are reflection across the x-axis first, then translation.

Answer:

wrong position of tan 64

Answer:

Median = 14

Step-by-step explanation:

2, 5, 14, 15, 21, 18, 15, 9, 2

First, order the numbers:

2, 2, 5, 9, 14, 15, 15, 18, 21

Then, cancel out the numbers, starting the first and last number, going outwards in. If there is 1 number left, it is your median. If there are 2 left, add the 2 numbers together and divide them by two:

2, 2, 5, 9, 14, 15, 15, 18, 21

2, 5, 9, 14, 15, 15, 18

5, 9, 14, 15, 15

9, 14, 15

14

The median is 14.

Please tell me if I was wrong! I hope this helps you!

Answer: The median is 14

Step-by-step explanation: The median is the number that is halfway into the data set. To find the median, the data should be arranged in order from least to greatest. For this example.  2,2,5,9,14,15,15,18,21. Find the number that is halfway. which is 14

Answer:

Divide the diameter by 2.

Step-by-step explanation:

The radius of any circle is always the end to the center.

The diameter is a point of the circle to the opposite side.

This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.

Hope this helped!

Answer:

Divide the diameter by 2. d/2=r

Step-by-step explanation:

If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.

If the diameter was 10, the radius would 10/2=5.

Answer:

Solution : y = 4x - 8

Step-by-step explanation:

The first thing we want to do is isolate t², rather than t. Why? As you can see when we substitute t² into the second equation, it will be easier than substituting t, as t is present in the form t². So, let's isolate t² in the first equation --- ( 1 )

x = t² + 2,

t² = x - 2

Now let's substitute this value of t² in the second equation --- ( 2 )

y = 4t²,

y = 4(x - 2),

y = 4x - 8 ~ And hence our solution is option c.

Answer:

Because it increases the risk of Type 1 error

Step-by-step explanation:

ANOVA is the analysis of the variance .

When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error  .

For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.

This has two disadvantages .

First the procedure is too lengthy  and tediuos.

Second the overall level of significance greatly increases as the number of t- tests increases.

The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.

Answer:

For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value

Step-by-step explanation:

Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.

Mathematically, the null hypothesis is as expressed as below;

H0: μ = 1,200

The alternative hypothesis H1 would be;

H1: μ > 1,200

Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics

For us to reject the null hypothesis, one of two things, or two things must have occurred.

The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.

If this happens, then we can make a rejection of the null hypothesis

Full question attached:

Answer and explanation:

A) B2*B10: cell B2 and B10 have the values regular swear costs and number of swears respectively and we need to multiply these two values to get our answer

B) =IF(B10>10,(B10-10)*B3,0): Sam is supposed to pay an extra $2 for swear words over 10 and so we check if his swear words are above 10 and if they are we find out how many they are by subtracting 10 from them and then we multiply the value gotten by the cost for extra swear words($2)

C) =IF(B10<5,B10*B4,0): here we check if swear words are less than 5 and if they are we multiply number of swears words less than by 5 by the cost ($0.50)

D) F10=C10+D10+E10: to calculate total money in jar(F10), we simply add up regular cost(C10), extra cost(D10) and refund(E10)

Answer:

C) 3/2x-1/8

Step-by-step explanation:

We can see that it has a generally positive slope, which rules out B and D.

Plugging in a few numbers for x, we can quickly see that 6 is too high of a slope. (If we plug in 6 for x, the y value would be almost 35, not 10).  This rules out A.

While it doesn’t fit perfectly, C is by far the closest.

Answer:

B. An obtuse scalene triangle

Step-by-step explanation:

Polygons are plane figures bounded by three or more straight sides. Examples are: trigon, quadragon, hexagon, nonagon etc.  They are  named with respect to their number of sides.

An obtuse triangle has one of its angles greater than [tex]90^{0}[/tex] but less than [tex]180^{0}[/tex]. While a scalene triangles has non of its sides to be equal in length.

The valid description of the classes of polygons is: an obtuse scalene triangle. Which implies that the triangle has one of its angles to be obtuse, and non of its sides equal.

Answer:

$7,415.99

Step-by-step explanation:

Hello, please consider the following.

[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]

So it gives $7,415.99

Thank you.

Answer:

Step-by-step explanation:

Given that :

population Mean = 15000

standard deviation= 1200

sample size n = 100

sample mean = 16000

The null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o : \mu = 15000 }\\ \\ \mathtt{H_1 : \mu > 15000}[/tex]

Using the standard normal z statistics

[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]z = \dfrac{16000 -15000}{\dfrac{1200 }{\sqrt{100}}}[/tex]

[tex]z = \dfrac{1000}{\dfrac{1200 }{10}}[/tex]

[tex]z = \dfrac{1000\times 10}{1200}[/tex]

z = 8.333

degree of freedom = n - 1 = 100 - 1 = 99

level of significance ∝ = 0.05

P - value from the z score = 0.00003

Decision Rule: since the p value is lesser than the level of significance, we reject the null hypothesis

Conclusion: There is sufficient evidence  that the Dean claim for his graduate students earn more than average salary of $15,000

Dean's Claim of Average Salary = 16000, ie greater than 15000 : is correct

Null Hypothesis [ H0 ] : Average Salary = 15000

Alternate Hypothesis [ H1 ] : Average Salary > 15000

Hypothesis is tested using t statistic.

t = ( x - u ) / ( s / √ n ) ; where -

x = sample mean , u = population mean , s = standard deviation, n = sample size

t = ( 16000 - 15000 ) / ( 1200 / √100 )

= 1000 / 120

t  {Calculated} = 8.33,

Degrees of Freedom = n - 1 = 100 = 1 = 99

Tabulated t 0.05 (one tail) , at degrees of freedom 99 = 1.664

As Calculated t value 8.33 > Tabulated t value 1.664 , So we reject the Null Hypothesis in favour of Alternate Hypothesis.

So, conclusion : Average Salary > 15000

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

In a 6 sided die, the numbers that are possible to be rolled are

1, 2, 3, 4, 5, and 6.

We know that the numbers 2, 3, and 5 are prime, while 1, 4, and 6 are not.

3 out of the 6 numbers are prime, therefore 3 out of the 6 numbers are not prime.

So the fraction is [tex]\frac{3}{6}[/tex]

This simplifies to [tex]\frac{1}{2}[/tex].

Hope this helped!

Answer:

1/2

Step-by-step explanation:

the prime numbers between 1 and 6 inclusive are:  2, 3, 5  (i.e 3 possible outcomes)

the non prime numbers are : 1, 4 and 6 (i.e 3 possible outcomes)

for each roll, the total number of possible outcomes is 6 (because its a 6-sided die)

P(does not roll a prime number) = P (rolls 1, 4 or 6)

= number of possible non-prime outcomes / total number of outcomes

= 3/6

= 1/2

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

Answer:

Step-by-step explanation:

[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]

Answer:18 ft

Step-by-step explanation: Perimeter=2(L+B)

Perimeter=2(7 + 2)

2×9=18

Answer:

18feet.

Step-by-step explanation:

To find the perimemter of a rectangle, you just add all the sides.

A rectangle has 4 sides in total, where 2 are equal, and the other 2 are als equal.

So, you just add 7+2+7+2, which gives 18.

This is why, the perimeter of this rectangle is 18feet.

Hope this helped, have a nice day!

Answer:

Step-by-step explanation:

step one :

Given that the equation of the circle is described as

[tex]x^2 + y^2 = 64[/tex]

To correctly identify the center of the circle we have to place the equation in the standard form.

the standard equation for a circle is

[tex](x-h)^2+(x-k)^2= r^2[/tex]

step two :

let us re-write the given equation so that we can compare it with the general equation of circle

[tex](x-0)^2+(x-0)^2= 8^2[/tex]

step three:

From this above equation in step two we can see that the circle has a radius of 8

Answer:

a. Pr(They both have type O)

= Pr(They both have type O)

= 0.35 x 0.45

= 0.1575 = 15.75%

b. Pr( they both have the same blood type)

= Pr( they both have the same blood type)

= 2/8

= 0.25 = 25%

c. Pr( at least one person has type O)

= Pr (at least one person has type O)

= 1 - 0.3575

= 0.6425 = 64.25%

Step-by-step explanation:

a) Data:

                   O       A         B       AB

Chinese   0.35   0.27    0.26     0.12

American 0.45   0.4      0.11       0.04

b) Calculations:

i. Pr(They both have type O)

= Probability of Chinese with O multiplied by Probability of American with O

= 0.35 * 0.45

= 0.1575 = 15.75%

ii. Pr( they both have the same blood type)

= Probability of two out of 8 outcomes

= 2/8

= 0.25 = 25%

iii. Pr( at least one person has type O)

= Probability of (1 – p(none) )

The probability of none = p(none O blood type)

= p(none)

for Chinese = (0.27 + 0.26 + 0.12) * for American ( 0.4 + 0.11 + 0.04)

= 0.65 * 0.55 = 0.3575

Pr (at least one person has type O) = 1 - 0.3575

= 0.6425