How many positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

Answers

Answer 1

Answer:

10,000

Step-by-step explanation:

Answer 2

There are 2970 positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

What is Number system?

A number system is defined as a system of writing to express numbers.

We need to find

positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

Let all 9 numbers ae

a+b+c+d+e+f+g+h+9=13

a+b+c+d+e+f+g+h=13-9

a+b+c+d+e+f+g+h=4

Then we use combinations

(n+k-1)Ck

¹¹C₄

11!/(11-4)!4!

11!/7!4!

330

Three hundred thirty times of nine is two thousand nine hundred seventy.

Now 330 ×9=2970

Hence there are 2970  positive integers less than 1,000,000 have exactly one digit equal to 9 and have a sum of digits equal to 13

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Related Questions

Janine and Thor are both running for class president. Janine goes down a hallway in the school and puts a sticker on every fourth locker. Thor goes down the same hallway, putting one of his stickers on every fifth locker. If there are 130 lockers in the hallway, how many have both students' stickers?

Answers

Answer:

6 lockers have both students' stickers

Step-by-step explanation:

There are 130 lockers in the hallway

Janine goes down a hallway in the school and puts a sticker on every fourth locker.

Janine= 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 52nd, 56th, 60th, 64th, 68th, 72nd, 76th, 80th, 84th, 88th, 92nd, 96th, 100th, 104th, 108th, 112th, 116th, 120th, 124th, 128th.

Thor goes down the same hallway, putting one of his stickers on every fifth locker

Thor= 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, 95th, 100th, 105th, 110th, 115th, 120th, 125th, 130th.

Common multiples of Janine fourth locker and Thor fifth locker= 20, 40, 60, 80, 100, 120

Therefore,

6 lockers have both students' stickers

which equation represents a circle with the center at two, -8 and a radius of 11

Answers

Answer:

( x-2)^2 + ( y +8) ^2 =121

Step-by-step explanation:

The equation of a circle can be written as

( x-h)^2 + ( y-k) ^2 = r^2

where ( h,k) is the center of the circle and r is the radius

( x-2)^2 + ( y- -8) ^2 = 11^2

( x-2)^2 + ( y +8) ^2 =121

Answer:

(x - 2)² + (y + 8)² = 11²

Step-by-step explanation:

General equation for a circle

( x - h )² + ( y - k )² = r², where (h,k) is the center and r ,radius..

with center ( 2,-8 ) and radius 11

(x - 2)² + (y + 8)² = 11²

Actual time in seconds recorded when statistics students participated in an experiment t test their ability to determine when one minute 60 seconds has passed are shown below.Find the mean median mode of the listed numbers. 53 52 72 61 68 58 47 47

Answers

Answer:

53 52 72 61 68 58 47 47 (arrange it)

47 47 52 53 58 61 68 71 (done!)

Mode: 47 (appear twice)

Median: (53+58)/2 = 55.5

Mean = 47+47+52+53+58+61+68+71/ 8

=457/8

=57.12

in the diagram, POS,QOT and ROU are straight lines. find the value of x.​

Answers

Answer: 28

==========================================

Explanation:

Angle UOT is vertical to the angle x. This angle combines with 4x and 40 to get a straight angle of 180 degrees

(angle POU) + (angle UOT) + (angle TOS) = 180

4x + x + 40 = 180

5x + 40 = 180

5x = 180-40

5x = 140

x = 140/5

x = 28

Side note: if x = 28, then 4x = 4*28 = 112.

We see that 112+28+40 = 180, which is the sum of the three angles mentioned earlier. Since we got 180, this confirms the answer.

Solve 2 - (7x + 5) = 13 - 3x (make sure to type the number only)

Answers

Answer:

x = -4

Step-by-step explanation:

2 - (7x + 5) = 13 - 3x

add the binomial (7x +5) to both sides

2 = (7x + 5) + 13 - 3x

combine like terms

2 = 4x + 18

subtract 18 from both sides

-16 = 4x

divide by 4

x = -4

Answer:

-4

Step-by-step explanation:

Distribute the negative signs to the values in the parentheses

2 -7x - 5 = 13 - 3x

Add like terms:

-7x - 3 = 13 - 3x

Add 3x to both sides:

-4x - 3 = 13

Add 3 to both sides:

-4x = 16

Divide both sides by -4:

x = -4

The average daily volume of a computer stock in 2011 was ų=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 30 trading days in 2014, he finds the sample mean to be 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.

Answers

Answer:

a

   The  null hypothesis is  [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]

    The  alternative hypothesis  [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]

b

 The   95% confidence interval is  [tex]27.475 < \mu < 37.925[/tex]

Step-by-step explanation:

From the question the we are told that

      The  population mean is  [tex]\mu = 35.1 \ million \ shares[/tex]

      The  sample size is  n = 30

       The  sample mean is  [tex]\= x = 32.7 \ million\ shares[/tex]

       The standard deviation is  [tex]\sigma = 14.6 \ million\ shares[/tex]

     

Given that the confidence level is  [tex]95\%[/tex] then the level of significance is mathematically represented as

                  [tex]\alpha = 100-95[/tex]

                  [tex]\alpha = 5\%[/tex]

=>               [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

    The value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

                 [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]

substituting values

                [tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]

                [tex]E = 5.225[/tex]

The 95% confidence interval confidence interval is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

               [tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]

                [tex]27.475 < \mu < 37.925[/tex]

       

Please help me with this

Answers

Answer:

Median; 60

Step-by-step explanation:

For a data plot as shown in the question above, one easier measure of center that can be used for the data set represented is the median.

From the dot plot, we can easily pinpoint the exact median, which can be used as a measure of center.

There are 11 data points represented on the dot plot by 11 dots. The median, that is the median value of the data set, would be the 6th value represented by the 6th dot on the dot plot.

Thus, the middle value is 60.

60 is the median of the data set.

If the random variable X is normally distributed with mean of 50 and standard deviation of 7, find the 9th percentile.

Answers

Answer:

The 9th percentile is 40.52.

Step-by-step explanation:

We are given that the random variable X is normally distributed with a mean of 50 and a standard deviation of 7.

Let X = the random variable

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 50

           [tex]\sigma[/tex] = standard deviation = 7

So, X ~ Normal([tex]\mu=50, \sigma^{2} = 7^{2}[/tex])

Now, the 9th percentile is calculated as;

            P(X < x) = 0.09         {where x is the required value}

            P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-50}{7}[/tex] ) = 0.09

            P(Z < [tex]\frac{x-50}{7}[/tex] ) = 0.09

Now, in the z table the critical value of x that represents the below 9% of the area is given as -1.3543, i.e;

                     [tex]\frac{x-50}{7}=-1.3543[/tex]

                     [tex]x-50=-1.3543 \times 7[/tex]

                     [tex]x=50 -9.48[/tex]

                      x = 40.52

Hence, the 9th percentile is 40.52.

in a gp the sixth term is 8 times the third term, and the sum of the seventh and eighth term is 192. determine the common ratio​

Answers

Answer:

common ratio = 2

Step-by-step explanation:

T6 = ar^5

T3 = ar²

T6 = 8 x T³

ar^5 = 8 x ar²

ar^5/ar² = 8

r³ = 8

r = ³√8

r = 2

If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?

Answers

Answer:

Step-by-step explanation:

positive integer divisible by 3 includes

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...

less than highest possible value is 42

According to the website www.costofwedding, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U. S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.
Choose the statement that is the best interpretation of the confidence interval.
I. That probability that the flowers at a wedding will cost more than $698is greater than 5%.
II. In about 95%of all samples of size 40,the resulting confidence interval will contain the mean cost of flowers at weddings.
III. We are extremely confident that the mean cost of flowers at a wedding is between $701and $767
A) II only
B) I only
C) III only
D) II and III are both correct

Answers

Answer:

D) II and III are both correct.

Step-by-step explanation:

The Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The cost of flowers for a wedding is $698. The 95% of all samples of size is 40 and the confidence interval will be mean cost of flowers at wedding. There is confidence that mean cost of wedding flowers is between $701 to $767.

if (ax+b)(x-3) = 4x^2+cx-9 for all values of x, what is the value of c? a) -9 b) -6 c) 6 d) 9

Answers

Answer:

c=-9

Step-by-step explanation:

Hello,

[tex](ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9[/tex]

We can identify the like terms so:

a = 4

b-3a = c

3b = 9 <=> b = 3

So c = 3 - 3*4 = 3-12 = -9

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

the height of a triangle is 2 centimetres more than the base. if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square. find the base and the height of the original triangle.

Answers

Answer:

Base = 11 cm

Height = 13 cm

Step-by-step explanation:

It is given that the height of a triangle is 2 centimetres more than the base.

Let x cm be the base of triangle. So height of the triangle is x+2 cm.

It is given that if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square.

New height = (x+2)+2 = x+4 cm

Area of a triangle is

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

[tex]82.5=\dfrac{1}{2}\times x\times (x+4)[/tex]

[tex]165=x^2+4x[/tex]

[tex]x^2+4x-165=0[/tex]

Splitting the middle term, we get

[tex]x^2+15x-11x-165=0[/tex]

[tex]x(x+15)-11(x+15)=0[/tex]

[tex](x+15)(x-11)=0[/tex]

Using zero product property, we get

[tex]x=-15,11[/tex]

Base of a triangle can not be negative, therefore x=11.

Base = 11 cm

Height = 11+2 = 13 cm

Therefore, the base of original triangle is 11 cm and height is 13 cm.

Find the area of the shaded regions.

Answers

Answer:

7 pi cm^2 or  approximately 21.98 cm^2

Step-by-step explanation:

First find the area of the large circle

A = pi r^2

A = pi 3^2

A = 9 pi

Then find the area of the small unshaded circle

A = pi r^2

A = pi (1)^2

A = pi

There are two of these circles

pi+ pi = 2 pi

Subtract the unshaded circles from the large circle

9pi - 2 pi

7 pi

If we approximate pi as 3.14

7(3.14) =21.98 cm^2

Answer:

[tex]\boxed{\sf 7\pi \ cm^2 \ or \ 21.99 \ cm^2 }[/tex]

Step-by-step explanation:

[tex]\sf Find \ the \ area \ of \ the \ two \ smaller \ circles.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\sf There \ are \ two \ circles, \ so \ multiply \ the \ value \ by \ 2.[/tex]

[tex](2) \pi (1)^2[/tex]

[tex]2\pi[/tex]

[tex]\sf Find \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\pi (3)^2[/tex]

[tex]9\pi[/tex]

[tex]\sf Subtract \ the \ areas \ of \ the \ two \ circles \ from \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]9\pi -2\pi[/tex]

[tex]7\pi[/tex]

12. Consider the function ƒ(x) = x^4 – x^3 + 2x^2 – 2x. How many real roots does it have?
options:
A) 2
B) 1
C) 3
D) 4

Answers

Answer:

Step-by-step explanation:

Hello, let's factorise as much as we can.

[tex]x^4-x^3 + 2x^2-2x\\\\=x(x^3-x^2+2x-2)\\\\=x(x-1)(x^2+2)[/tex]

So, the solutions are

[tex]0, \ 1, \ \sqrt{2}\cdot i, \ -\sqrt{2}\cdot i[/tex]

There are only 2 real roots.

Thank you.

Answer:

So, the solutions are

There are only 2 real roots.

Step-by-step explanation:

Find the slope of a line perpendicular to the line defined by the equation 3x-5y=12

Answers

Answer:

-5/3

Step-by-step explanation:

Note the slope intercept form: y = mx + b

Note that:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

Isolate the variable, y. First, Subtract 3x from both sides:

3x (-3x) - 5y = 12 (-3x)

-5y = -3x + 12

Next, divide -5 from both sides. Remember to divide from all terms within the equation:

(-5y)/-5 = (-3x + 12)/-5

y = (-3x/-5) + (-12/5)

Simplify.

y = (3x/5) - 12/5

y = (3/5)x - 12/5

You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:

Original m = 3/5

Flipped m = -5/3

-5/3 is your perpendicular slope.

Answer:

          5                                

m =  - ----    perpendicular slope

          3

Step-by-step explanation:

3x - 5y = 12 -------->> convert to y = mx + b

- 5y = - 3x + 12

- 5y = - (3x + 12) --- eliminate the negative

5y = 3x + 12

   

     3x + 12

y = -------------

         5

       3           12

y = -----x  +   -----

       5            5  

the above equation is the form of  y = mx + b

where m is the slope and b is the intercept

   

                            5                                

therefore,  m =  - ----    perpendicular slope

                             3                        

. Simplify the sum. (2u3 + 6u2 + 2) + (7u3 – 7u + 4)

Answers

Answer:

9u^3 + 6u^2 - 7u + 6

Step-by-step explanation:

If y varies directly with x and y = 5 when x = 4, find the value of y when x = -8

Answers

Answer:

-10

Step-by-step explanation:

y : x

= 5 : 4

4z = -8

= -8 / 4 = -2 = z

y : x

= 5 * -2 : 4 * -2

= -10 : -8

The time between consecutive uses of a vending machine is exponential with an average of 15 minutes. a)Given that the machine has not been used in the previous 5 minutes, what is the probability that the machine will not be used during the next 10 minutes

Answers

Answer5

Step-by-step explanation:

f(x )=x square +6x + 5 what is the x intercept to graph f(x)

Answers

Answer:

(-5, 0)

(-1, 0)

Step-by-step explanation:

x-intercepts are points where the graph intersects the x-axis (or when y = 0)

Step 1: Write out function

f(x) = x² + 6x + 5

Step 2: Factor

f(x) = (x + 5)(x + 1)

Step 3: Find binomial roots

x + 5 = 0

x = -5

x + 1 = 0

x = -1

Alternatively, you can graph the function and analyze the graph for x-intercepts:

Which statement best describes what Rutherford concluded from the motion of the particles?

Answers

Answer:

some particle traveled through empty spaces between atoms and some particles were deflected by electrons

Step-by-step explanation:

The motion of particles will be

some particle traveled through empty spaces between atoms and some particles were deflected by electrons.

What was Rutherford Experiment?The vast majority of the alpha particles simply passed through the gold foil.Some of the alpha particles had a slight angle of deflection.Only a tiny fraction of the alpha particles rebounded.

So, the observation made the stamement

He came to the conclusion that the majority of space in an atom was unoccupied since there was very little alpha particle deflection.The fact that very few particles were diverted from their course led him to the further conclusion that positive charge takes up very little space in an atom.

Then, motion of particles will be

some particle traveled through empty spaces between atoms and some particles were deflected by electrons.

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Literal Equations: 5(x + y) = 2x +7y, Solve for x

Answers

Answer:

x=2y/3

Step-by-step explanation:

Answer:

x = 2y/3

Step-by-step explanation:

5(x + y) = 2x + 7y

5x + 5y = 2x + 7y

5x - 2x = 7y - 5y

3x = 2y

x = 2y/3

Thus, The value of x = 2y/3


A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?
A. 6 + 30π m
B. 6 x 30π m
C. 6 x 30π m
D. 6 x (30π) m
PLZ HURRY IM TIMED

Answers

Answer:

Below

Step-by-step explanation:

The formula of the volule of a cone is:

● V= (1/3) × Pi × r^2 × h

h is the height and r is the radius.

■■■■■■■■■■■■■■■■■■■■■■■■■■

We are given that the volume is 30 Pi m^3

● V = 30 Pi

● 1/3 × Pi × r^2 × h = 30 Pi

If we multiply h by 6 we should do the same for 30 Pi since it's an equation

● 1/3 × Pi × r^2 × h = 30 × Pi × 6

Answer:

REVIEW: B is Correct    Exit

A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?

A. 6 + 30π m

B. 6 x 30π m

C. 6 x 30π m

D. 6 x (30π) m

Step-by-step explanation:

The answer is be all i did was dig into what the other person was saying and got b it is correct:)

A charity organization is holding a food drive with a goal to collect at least 1,000 cans of
food by the end of the month. It currently has 565 cans from donations and is having an
event where 87 guests will attend and bring cans. Which solution set represents the
number of cans each guest must bring to meet the goal?
+
OA
++
0
1
2
3
4
5
6
7
8
9
10
---
+
OB. 4
+
0
1
2
3
4
5
6
7
8
9
10
OC.
+
1
2
3
5
6
7
8
9
10
OD. +
+
++
-
6
+
7.
+
0
1
2
3
4
5
8
9
10

Answers

Answer:

Each guest must bring 5 cans.

Step-by-step explanation:

1000-565=435

435/87=5

Please Hurry ...Which expression is equivalent to

Answers

Answer:

[tex]\huge\boxed{\sf \frac{160rs^5}{t^6}}[/tex]

Step-by-step explanation:

[tex]\sf 5r^6t^4 ( \frac{4r^3s^tt^4}{2r^4st^6} ) ^5[/tex]

Using rule of exponents [tex]\sf a^m/a^n = a^{m-n}[/tex]

[tex]\sf 5r^6t^4 ( 2 r^{3-4} s^{2-1}t^{4-6})^5\\5r^6t^4(2r^{-1}st^{-2})^5\\5r^6t^4 * 32 r^{-5}s^5t^{-10}[/tex]

Using rule of exponents [tex]\sf a^m*a^n = a^{m+n}[/tex]

[tex]\sf 160 r^{6-5}s^5t^{4-10}[/tex]

[tex]\sf 160 rs^5 t^{-6}[/tex]

To equalize the negative sign, we'll move t to the denominator

[tex]\sf \frac{160rs^5}{t^6}[/tex]

Allison bought jelly beans to share with her friends. She bought pounds of blueberry jelly beans and pounds of lemon jelly beans. If she gave pounds of jelly beans away to her friends, how many pounds of jelly beans does Allison have left?

Answers

Answer: [tex]1\dfrac{11}{12}\text{ pounds}[/tex]

Step-by-step explanation:

The complete question is provided in the attachment.

Given, Amount blueberry jelly beans= [tex]1\dfrac{1}{4}[/tex] pounds

[tex]=\dfrac{5}{4}[/tex] pounds.

Amount lemon jelly beans = [tex]2\dfrac{1}{3}[/tex]pounds

[tex]=\dfrac{7}{2}[/tex] pounds

Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans

[tex]=(\dfrac{5}{4}+\dfrac{7}{3})[/tex] pounds

[tex]=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}[/tex]

Amount of jelly beans she gave away = [tex]1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}[/tex]

Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away

=[tex]\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}[/tex]

She has left [tex]1\dfrac{11}{12}\text{ pounds}[/tex] of jelly beans.

Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x

Answers

Answer:

[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]

Step-by-step explanation:

Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:

1) [tex]t = 2-x[/tex] Given

2) [tex]y = 5\cdot x +11[/tex] Given

3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties

4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property

5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property

6) [tex]y = -5\cdot (-x)+11[/tex]  [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]

7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property

8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse

9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties

10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property

11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]

12) [tex]y = (-5)\cdot t +21[/tex] By 1)

13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result

14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition

15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition

16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property

17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property

18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].

*please help* If multiple forces are acting on an object, which statement is always true?


The acceleration will be directed in the direction of the gravitational force.

The acceleration will be directed in the direction of the applied force.

The acceleration will be directed in the direction of the net force. <-- MY ANSWER

The acceleration will be directed in the direction of the normal force.

Answers

Answer: You are correct. The answer is choice C.

The sum of the vectors is the resultant vector, which is where the net force is directed.

An example would be if you had a ball rolling on a table and you bumped the ball perpendicular to its initial velocity, then the ball would move at a diagonal angle rather than move straight in the direction where you bumped it.

Acceleration is the change in velocity over time, so the acceleration vector tells us how the velocity's direction is changing.

The direction of the acceleration on a body upon which multiple forces are applied depends on the direction of the netforce acting on the body.

When multiple forces acts on a body, such that the different forces acts in different directions.

The acceleration will be in the direction of the netforce.

This is the direction where the Cummulative sum of the forces is greatest.

Acceleration due to gravity is always acting downward, if the upward force is greater than the Gravitational force, then the acceleration won't be in that direction.

Therefore, acceleration will be due in the direction of the netforce.

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If the normality requirement is not satisfied​ (that is, ​np(1​p) is not at least​ 10), then a​ 95% confidence interval about the population proportion will include the population proportion in​ ________ 95% of the intervals. ​(This is a reading assessment question. Be certain of your answer because you only get one attempt on this​ question.)

Answers

Answer:

less than

Step-by-step explanation:

If the normality requirement is not satisfied​ (that is, ​np(1​ - p) is not at least​ 10), then a​ 95% confidence interval about the population proportion will include the population proportion in​ _less than__ 95% of the intervals.

The confidence interval consist of all reasonable values of a population mean. These are value for which the null hypothesis will not be rejected.

So, let assume that If the 95%  confidence interval contains the value for the hypothesized mean, then the sample mean  is reasonably close to the hypothesized mean. The effect of this is that the p- value is going to be greater than 0.05, so we fail to reject the null hypothesis.

On the other hand,

If the 95%  confidence interval do not contains the value for the hypothesized mean, then the sample mean  is far away from the hypothesized mean. The effect of this is that the p- value is going to be lesser than 0.05, so we reject the null hypothesis.

A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular box. What size square should be cut from each corner to obtain a maximum volume

Answers

Answer:

the size of the square to be cut out for maximum volume is 1.5695 inches

Step-by-step explanation:

cardboard that measures 8 by 12 inches.

We need to determine What size square should be cut from each corner

We were given given the size of the cardboard.

let us denote the length of the square as 'x'.

Then our length, width and height will be:

Length = 8 − 2x

Width = 12− 2x

Then our Height = x

So now, the volume= length×width ×height

Volume = (8 − 2x) x (12− 2x) x (x)

After calculating volume comes out to be:

V = (96 − 40x + 4x²) (x)

V = 4x³ − 40x² + 96x

Now, we can use differentiation to equate it to zero.

So differentiate it with respect to x, we get

dV/dx = 12x² − 80x + 96

12x² − 80x + 96 = 0

So, after solving this, x comes out to be:

x = 5.097 and x = 1.5695

Looking at it the size of the square cut out cannot be 5.097 because we cannot cut out of both sides of the width, since the width is 5 inches.

Therefore, the size of the square to be cut out for maximum volume is 1.5695 inches.

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