If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2?

Hi there!

Convert 36 into 35 and 4/4 since if it is just a number, it can’t be multiply by 3/4.

\(36= 35 \frac{4}{4}\)

Multiply both fractions now but also turn 35 4/4 into a mixed number:

\(36=\frac{144}{4}\)

\(\frac{3}{4} x \frac{144}{4}= \frac{27}{1} = 27\)

Final Result: 27

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

For more such questions on equation visit:

https://brainly.com/question/30451972

#SPJ8

Note: the translated questions is

X = 13, which equation is true?

The y intercept is 0 and the slope of the graph of the equation is 1/2. As the value of y increase by 1, the value of x increases by 2

An equation is an expression that shows the relationship between two or more numbers and variables. Types of equation are linear, quadratic, cubic and so on.

The standard equation of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Given the equation:

y = (1/2)x

The y intercept is 0 and the slope of the graph of the equation is 1/2.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:4

Step-by-step explanation:

Answer:

9 • x + 9 • 3 + 15x

Step-by-step explanation:

You have to divide 9 by each term inside the parenthesis. 15x isnt multiplied or added to anything else so it stays the same.

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

Learn more about the area here:

https://brainly.com/question/27683633.

#SPJ1

The expected value E ( X ) of the probability distribution is E ( X ) = 2.5

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

The mean of probability distribution is also known as expected value. It is denoted by E ( X ). E(X), or mean μ of a discrete random variable X is calculated by multiplying each value of the random variable by its probability and taking the sum of the values.

E ( X ) = μ = ∑x P ( x )

Given data ,

Let the mean of the probability distribution be represented as E ( X )

Now , the expected value E ( X ) is calculated as

The values of x = { 5 , 6 , 7 , 8 , 9 }

The values of P ( X = x ) = { 0.1 , 0.1 , 0.3 , 0.1 , 0.4 }

Now , the expected value E ( X ) is

E ( X ) = ( 5 x 0.1 ) + ( 6 x 0.1 ) + ( 7 x 0.3 ) + ( 8 x 0.1 ) + ( 9 x 0.4 )

On simplifying , we get

The mean of probability distribution is

E ( X ) = 0.5 + 0.6 + 0.21 + 0.8 + 0.36

E ( X ) = 2.47

E ( X ) = 2.5

Hence , the mean of probability distribution is 2.5

To learn more about probability distribution click :

https://brainly.com/question/11425427

#SPJ9

Answer:

\(y=\frac{3}{4}x^2\)

Step-by-step explanation:

Hi there!

Because we're given the vertex of the parabola, we can determine its equation in vertex form:

\(y=a(x-h)^2+k\) where the vertex is \((h,k)\)

Plug in the vertex (0,0)

\(y=a(x-0)^2+0\\y=a(x)^2\\y=a(x-0)^2+0\\y=ax^2\)

Now, we must solve for a. Plug in the given point (-2,3) and solve for a:

\(3=a(-2)^2\\3=4a\\\frac{3}{4} =a\)

Therefore, the value of a is \(\frac{3}{4}\). Plug this back into \(y=ax^2\):

\(y=\frac{3}{4}x^2\)

I hope this helps!

Answer:

16 slices of pizza without 2 olives

Answer:

Scientific notion: 83M meanin million

Answer:

\(8.3\) x \(10^7\)

Step-by-step explanation:

83 000 000  ×  1  =  83 000 000

But 1 can be written as \(\frac{10^7}{10^7}\)

83000000  × \(\frac{10^7}{10^7}\) =  83000000  ×  1  =  83000000

\(\frac{83000000}{10^7}\) x \(10^7\) =  83000000  ×  1  =  83000000

Divide the denominator of \(10^7\) into  83000000

\(8.3\) x \(10^7\) =  83000000

Answer:

140

Step-by-step explanation:

2{ 2[24 + 4(9)-25]}

2{ 2[24 + 36-25]}

2{ 2[35]}

2(70)

140

Answer:

yo- ehm I think itssss 2 > -4

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

Learn more about inverse here:

https://brainly.com/question/30659571

#SPJ1

Answer:

infinite solutions

Step-by-step explanation:

-3f + 3f = 0

0=0

This is always true so there are infinite solutions

Answer:

All Real Numbers (infinite Solutions)

Step-by-step explanation:

When you cancel out the -3f and the +3f you get \(0=0\) and since that is true you get all real numbers

Hope this helps

Answer:

∠ U = 22.62°

Step-by-step explanation:

We can use the trigonometric expression to find ∠U by using the ratio:

sin(θ) = opposite/ hypotenuse

=> sin ∠U = 7.5/ 19.5

=> ∠ U = \(sin^{-1}\)( 7.5/ 19.5)

∴ ∠ U = 22.619° ≈ 22.62°

Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

Answer:

The required 97.5% confidence interval is

\(\text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\\text {CI} = 15.5 \pm 2.8412\cdot \frac{0.31}{\sqrt{8} } \\\\\text {CI} = 15.5 \pm 2.8412\cdot 0.1096\\\\\text {CI} = 15.5 \pm 0.311\\\\\text {CI} = 15.5 - 0.311, \: 15.5 + 0.311\\\\\text {CI} = (15.19, \: 15.81)\\\\\)

Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces

.

Step-by-step explanation:

The amounts (in ounces) of juice in eight randomly selected juice bottles are:

15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5

Let us first compute the mean and standard deviation of the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be

\(\bar{x} = 15.5\)

=STDEV(number1, number2,....)

The standard deviation is found to be

\(s = 0.31\)  

The confidence interval for the mean amount of juice in all such bottles is given by

\($ \text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\\\\\)

Where \(\bar{x}\) is the sample mean, n is the samplesize, s is the sample standard deviation and \(t_{\alpha/2}\) is the t-score corresponding to a 97.5% confidence level.

The t-score corresponding to a 97.5% confidence level is

Significance level = α = 1 - 0.975 = 0.025/2 = 0.0125

Degree of freedom = n - 1 = 8 - 1 = 7

From the t-table at α = 0.0125 and DoF = 7

t-score = 2.8412

So the required 97.5% confidence interval is

\(\text {CI} = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\\text {CI} = 15.5 \pm 2.8412\cdot \frac{0.31}{\sqrt{8} } \\\\\text {CI} = 15.5 \pm 2.8412\cdot 0.1096\\\\\text {CI} = 15.5 \pm 0.311\\\\\text {CI} = 15.5 - 0.311, \: 15.5 + 0.311\\\\\text {CI} = (15.19, \: 15.81)\\\\\)

Therefore, we are 97.5% confident that the actual mean amount of juice in all such bottles is within the range of 15.19 to 15.81 ounces.

The combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

To calculate the combined balance of both bank accounts after 3 years, we'll calculate the balance for each account separately and then add them together.

For Bank A, we can use the compound interest formula:

A =\(P(1 + r/n)^(nt)\)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

n = number of times that interest is compounded per year

t = number of years

In this case, Wanda deposited $370 at a 2.25% interest rate compounded annually, so we have:

P = $370

r = 2.25% = 0.0225 (as a decimal)

n = 1 (compounded annually)

t = 3 years

Using the formula, we can calculate the balance for Bank A:

A_A = \(370(1 + 0.0225/1)^(1*3)\)

=\(370(1.0225)^3\)

= 370(1.0678450625)

= $394.76

For Bank B, we can use the simple interest formula:

A = P(1 + rt)

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount

r = annual interest rate (as a decimal)

t = number of years

In this case, Wanda deposited $600 at a 2.5% simple interest rate, so we have:

P = $600

r = 2.5% = 0.025 (as a decimal)

t = 3 years

Using the formula, we can calculate the balance for Bank B:

A_B = 600(1 + 0.025*3)

= 600(1.075)

= $645

Finally, we can calculate the combined balance of both bank accounts:

Combined Balance = A_A + A_B

= $394.76 + $645

= $1039.76

Therefore, the combined balance of both bank accounts at the end of 3 years is closest to $1039.76.

For such more questions on Combined Bank Balances

https://brainly.com/question/28758315

#SPJ11

Answer:

I think the answer is A, good luck have a great day! :D

The transformation from ABC to A'B'C is (x+8, y+4).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have,

Transformed Triangle ABC to A'B'C'.

Now, from the graph the coordinate of A from Triangle ABC is shifted 8 units to the right.

and, moves 4 units upside.

Thus, the transformation applied here is (x+8, y+4).

Learn more about Transformation here:

https://brainly.com/question/13801312

#SPJ2

Answer:

Step-by-step explanation:

D

Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

Answer:

85

Step-by-step explanation:

Answer: he got 80/100 or 80% right

Step-by-step explanation:

24/30 = 12/15

12/15 as a percent:

100/15 = 6.66666666666667

12 x 6.66666666667

15 x 6.66666666667

= 80/100 or 80%

Answer: (1,5)

Analysis = \(\frac{1}{2}(2,10)\)

\(=(\frac{1}{2}\times2,\frac{1}{2}\times10)\)

\(=(1,5)\)

I hope this helps you :D

The values of the functions are:

1. f(2/3) = 2/9

2. f(1/4) = -21/4

If we are given the a function to find the value for which x assumes a given value, substitute the given value of x into the function and solve.

1. To find the value of f(2/3), substitute x = 2/3 into the function f(x) = 2x² - 4x + 2.

f(2/3) = 2(2/3)² - 4(2/3) + 2

f(2/3) = 2(4/9) - 8/3 + 2

f(2/3) = 8/9 - 8/3 + 2

f(2/3) = (8 - 24 + 18)/9

f(2/3) = 2/9

2. To find the value of f(1/4), substitute x = 1/4 into the function f(x) = 4x² + 2x - 6.

f(1/4) = 4(1/4)² + 2(1/4) - 6

f(1/4) = 4(1/16) + 1/2 - 6

f(1/4) = 1/4 + 1/2 - 6

f(1/4) = (1 + 2 - 24)/4

f(1/4) = -21/4

Learn more about function on:

https://brainly.com/question/2284360

#SPJ1

Answer:

Step-by-step explanation:

Jdhbdzbzvdksksskdjdjhdjdjdjjdjdjjfnfndjffjdjxbbx jasjsjs hahahas

After answering the presented question, we can conclude that probability Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

Sketch of exponential probability distribution with mean of 12 seconds:

   |                            

   |                            

   |              .            

   |             . .            

   |             . .            

   |             . .            

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . . .        

   |             . . . .        

   |             . . . .        

   |             . . . . .      

   |             . . . . .      

   |_____________. . . . . . .

        0       12             X

The X-axis represents the time between vehicle arrivals, and the Y-axis represents the probability density. The peak of the distribution is at 12 seconds, which is the mean.

b. Probability of the arrival time between vehicles being 12 seconds or less:

Since the mean of the exponential distribution is 12 seconds, we can use the cumulative distribution function (CDF) to find the probability of the arrival time being 12 seconds or less:

\(P(X < = 12) = 1 - e^(-12/12) = 1 - e^(-1) ≈ 0.6321\)

Therefore, the probability of the arrival time between vehicles being 12 seconds or less is approximately 0.6321.

c. Probability of the arrival time between vehicles being 6 seconds or less:

\(P(X < = 6) = 1 - e^(-6/12) = 1 - e^(-0.5) ≈ 0.3935\)

Therefore, the probability of the arrival time between vehicles being 6 seconds or less is approximately 0.3935.

d. Probability of 30 or more seconds between vehicle arrivals:

\(P(X > = 30) = e^(-30/12) ≈ 0.0498\)

Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Answer: I believe it's A

Hope this helped

Answer:

\(3\sqrt{6}\)

Step-by-step explanation:

We are to determine the limit below.

\(\lim _{x \rightarrow8}\sqrt{7x-2}\)

Plug in 8 into the function.

\(\lim _{x \rightarrow8}\sqrt{7x-2}=\sqrt{7(8)-2}\\=\sqrt{56-2}\\ =\sqrt{54}\\ =3\sqrt{6} \\\lim _{x \rightarrow8}\sqrt{7x-2}=3\sqrt{6}\)