You are driving a 50 foot vehicle at night. although you are on the highway, a bad rainstorm is forcing you to creep along at 35 mph. you should keep ___seconds of distance between you and the vehicle ahead.

Answer:

angle measurements of 40°, 60°, and 80°

side lengths of 4 cm, 6 cm, and 9 cm

Step-by-step explanation:

Answer:

340 cars on her wall

( Brainlyst will help my rank, thanks! <3 )

Answer:

A

Step-by-step explanation:

Multply = 24/105

Divide by 3

8/35

The value of the definite integral ∫(5(f(x) + 2),2,6)dx is 70.

The average value of the function f on the interval 2 ≤ x ≤ 6 is 3. We can use the mean value theorem for integrals to find the value of the definite integral ∫(5(f(x) + 2),2,6)dx.

According to the mean value theorem for integrals, there exists a number c in the interval [2, 6] such that:

f(c) = 1/(6-2) * ∫(f(x),2,6)dx

Since the average value of f on the interval [2, 6] is 3, we have:

3 = 1/(6-2) * ∫(f(x),2,6)dx

Simplifying, we get:

∫(f(x),2,6)dx = 4 * 3 = 12

Therefore, the value of the definite integral ∫(5(f(x) + 2),2,6)dx is:

∫(5(f(x) + 2),2,6)dx = 5 * ∫(f(x),2,6)dx + 5 * ∫(2,2,6)dx

= 5 * 12 + 5 * (6-2)

= 70

Learn more about definite integral here

https://brainly.com/question/27746495

#SPJ11

Answer:

Original: -2g + 1.5 = 17.3

Solving:

-2g = 15.8

-g = 7.9

Answer:

g = -7.9

And don`t worry I only know how to do this because I remember it from a few years ago. I`m not even caught up in my own math class ;--;

Hope that helps

Answer:

its D/ 56.25

Step-by-step explanation:

because the other numbers are too small

Answer:

2280

Step-by-step explanation:

As in understandable steps,

1512x12 = 18144

18144 / 7

= 2592

2592 - 312

= 2280

An equation is formed of two equal expressions. John's salary before the pay raise is $2280.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the pay of John before the raise be x.

As it is stated that John's pay was increased by $312. And he saves 7/12 of his pay which is equal to $1512. Therefore, the equation that can represent the current saving John has,

\(\dfrac{7}{12}(x+312)=1512\\\\(x+312) = \dfrac{1512 \times 12}{7}\\\\x+312= 2592\\\\x =2592-312\\\\x = 2280\)

Hence, John's salary before the pay raise is $2280.

Learn more about Equation:

https://brainly.com/question/2263981

Answer:

24

Step-by-step explanation:

dont exaclty have an explanations - its just the calculations

Answer: (-2,3)

Step-by-step explanation: To figure out where the missing point, D, would go, you have to figure out which side DE is congruent to and what side is missing. I saw that DE is correlates to the base of the triangle because that's the only one of that length. From there, I counted up from the center of the base, DE, to find a good place for the vertex, and made sure it was the same exact distance from DE as C is from the base of the first triangle.

The sorted array after applying the PARTITION algorithm using the first element (5) as the pivot.

To illustrate the operation of the PARTITION algorithm on the given array {5, 1, 2, 7, 9, 3, 7, 8, 4}, we'll follow the steps of the algorithm and show the array at each step.

1: Choose the first element, 5, as the pivot.

{5, 1, 2, 7, 9, 3, 7, 8, 4}

2: Reorder the array so that all elements smaller than the pivot (5) come before it, and all elements larger than the pivot come after it. This is done by swapping elements.

{4, 1, 2, 3, 5, 9, 7, 8, 7}

3: The pivot is now in its final sorted position. Divide the array into two subarrays, one to the left of the pivot (elements smaller than the pivot) and one to the right of the pivot (elements larger than the pivot).

Left subarray: {4, 1, 2, 3}

Right subarray: {9, 7, 8, 7}

4: Recursively apply the PARTITION algorithm to the left and right subarrays.

For the left subarray:

Choose the first element, 4, as the pivot.

{4, 1, 2, 3}

Reorder the array:

{3, 1, 2, 4}

The left subarray is now sorted.

For the right subarray:

Choose the first element, 9, as the pivot.

{9, 7, 8, 7}

Reorder the array:

{7, 7, 8, 9}

The right subarray is now sorted.

5: The entire array is now sorted.

{3, 1, 2, 4, 5, 7, 7, 8, 9}

This is the final sorted array after applying the PARTITION algorithm using the first element (5) as the pivot.

To know more about algorithm:

https://brainly.com/question/30753708

#SPJ4

Answer:

I think it's the last one

Step-by-step explanation:

F(x,y) · r(x,y) = 4(yi - xj) · (xi + yj)= 4xy - 4xy = 0

The two vectors are perpendicular to each other, and the length of F(x,y) is 4, as desired.

A two-dimensional vector field is a vector field in which each point in the plane is associated with a vector.

It is represented by a pair of functions (P, Q), each of which maps (x, y) to a real number, and the vector field itself is written as F = P i + Q j. Let's write a formula for a two-dimensional vector field that has all vectors of length 4 and is perpendicular to the position vector at that point

The formula for a two-dimensional vector field that has all vectors of length 4 and is perpendicular to the position vector at that point is given by:

F(x,y) = 4(yi - xj)

Here, the position vector at any point (x, y) in the plane is given by r(x,y) = xi + yj, and its magnitude is

|r(x,y)| = √(x² + y²).

To see that F(x,y) is perpendicular to r(x,y), take their dot product:

F(x,y) · r(x,y) = 4(yi - xj) · (xi + yj)= 4xy - 4xy = 0

Thus, the two vectors are perpendicular to each other, and the length of F(x,y) is 4, as desired.

Learn more about two-dimensional vector.

brainly.com/question/28931875

#SPJ11

The critical point of S at (0, 1/2) is a local maximum.

To find the critical points of the function S, we need to find the values of (x, y) where the partial derivatives of S with respect to x and y are equal to zero.

Taking the partial derivative of S with respect to x, we have:

∂S/∂x = -2x

Setting this equal to zero, we get:

-2x = 0

x = 0

Taking the partial derivative of S with respect to y, we have:

∂S/∂y = -2y + 1

Setting this equal to zero, we get:

-2y + 1 = 0

2y = 1

y = 1/2

Therefore, the critical point of S is (x, y) = (0, 1/2).

To determine whether this critical point is a local minimum, local maximum, or a saddle point, we need to examine the second partial derivatives of S.

Taking the second partial derivative of S with respect to x, we have:

∂²S/∂x² = -2

Taking the second partial derivative of S with respect to y, we have:

∂²S/∂y² = -2

Taking the mixed partial derivative of S with respect to x and y, we have:

∂²S/∂x∂y = 0

Now, we can use the second partial derivatives to determine the nature of the critical point.

Since both second partial derivatives are negative (-2), and the determinant of the Hessian matrix is positive (-2 * -2 - 0^2 = 4), we can conclude that the critical point (0, 1/2) is a local maximum.

Learn more about local maximum here :-

https://brainly.com/question/27838972

#SPJ11

Answer: (12+5)+2

Step-by-step explanation:

12+5=17

17+2=19

Answer:

12+(5+2)

Step-by-step explanation:

you must do 5 plus 2 first because you are adding 12 to their product. which is the answer to an addition problem. so you are given...

The probability that Cory will win the chess game is described as unlikely. The answer D describes well this probability.

The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

we know that probability of an event always lies between 0 and 1 .

if probability of the event is 0 then we have impossible event.

if the probability of the event is near to 0 means it lies between \(0\) to \(\frac{1}{2}\) ( in the interval \((0,\frac{1}{2} )\) ) then we have unlikely event.

if the probability of the event is 1 then we have a certain event.

if the probability of the event is between \(\frac{1}{2}\) and 1 means it lies in the interval \((\frac{1}{2} , 1)\)  then we have likely event.

if probability of the event is \(\frac{1}{2}\) then the event is neither likely nor unlikely.

we have:

the probability that Cory will win the game is 3/10 which is equal to 0.3,

or 0.3 lies in the interval \((0,\frac{1}{2} )\) so the probability that Cory will win the chess game is described as unlikely.

The answer is D.

Learn more about probability here:

https://brainly.com/question/24756209

#SPJ1

44. A:

A = P(1 + r/n)^(n*t)

(A) To have $6,000 in 3 years from now:

A = $6,000

r = 8% = 0.08

n = 4 (compounded quarterly)

t = 3 years

$6,000 = P(1 + 0.08/4)^(4*3)

$4,473.10

44. B:

________________________________________________

Using the same formula:

$6,000 = P(1 + 0.08/4)^(4*6)

$3,864.12

45. A:

A = P * e^(r*t)

(A) To have $25,000 in 36 months from now:

A = $25,000

r = 9% = 0.09

t = 36 months / 12 = 3 years

$25,000 = P * e^(0.09*3)

$19,033.56

45. B:

Using the same formula:

$25,000 = P * e^(0.09*9)

$8,826.11

__________________________________________________

46. A:

A = P * e^(r*t)

(A) To have $4,800 in 48 months from now:

A = $4,800

r = 12% = 0.12

t = 48 months / 12 = 4 years

$4,800 = P * e^(0.12*4)

$2,737.42

46. B:

Using the same formula:

$4,800 = P * e^(0.12*7)

$1,914.47

__________________________________________________

47. A:

For an investment at an annual rate of 3.9% compounded monthly:

The periodic interest rate (r) is the annual interest rate (3.9%) divided by the number of compounding periods per year (12 months):

r = 3.9% / 12 = 0.325%

APY = (1 + r)^n - 1

r is the periodic interest rate (0.325% in decimal form)

n is the number of compounding periods per year (12)

APY = (1 + 0.00325)^12 - 1

4.003%

47. B:

The periodic interest rate (r) is the annual interest rate (2.3%) divided by the number of compounding periods per year (4 quarters):

r = 2.3% / 4 = 0.575%

Using the same APY formula:

APY = (1 + 0.00575)^4 - 1

2.329%

__________________________________________________

48. A.

The periodic interest rate (r) is the annual interest rate (4.32%) divided by the number of compounding periods per year (12 months):

r = 4.32% / 12 = 0.36%

Again using APY like above:

APY = (1 + (r/n))^n - 1

APY = (1 + 0.0036)^12 - 1

4.4037%

48. B:

The periodic interest rate (r) is the annual interest rate (4.31%) divided by the number of compounding periods per year (365 days):

r = 4.31% / 365 = 0.0118%

APY = (1 + 0.000118)^365 - 1

4.4061%

_________________________________________________

49. A:

The periodic interest rate (r) is equal to the annual interest rate (5.15%):

r = 5.15%

Using APY yet again:

APY = (1 + 0.0515/1)^1 - 1

5.26%

49. B:

The periodic interest rate (r) is the annual interest rate (5.20%) divided by the number of compounding periods per year (2 semiannual periods):

r = 5.20% / 2 = 2.60%

Again:

APY = (1 + 0.026/2)^2 - 1

5.31%

____________________________________________________

50. A:

AHHHH So many APY questions :(, here we go again...

The periodic interest rate (r) is the annual interest rate (3.05%) divided by the number of compounding periods per year (4 quarterly periods):

r = 3.05% / 4 = 0.7625%

APY = (1 + 0.007625/4)^4 - 1

3.08%

50. B:

The periodic interest rate (r) is equal to the annual interest rate (2.95%):

r = 2.95%

APY = (1 + 0.0295/1)^1 - 1

2.98%

_______________________________________________

51.

We use the formula from while ago...

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

P = $4,000

A = $9,000

r = 7% = 0.07 (annual interest rate)

n = 12 (compounded monthly)

$9,000 = $4,000(1 + 0.07/12)^(12t)

7.49 years

_________________________________________________

52.

Same formula...

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

$7,000 = $5,000(1 + 0.06/4)^(4t)

5.28 years

_____________________________________________

53.

Using the formula:

A = P * e^(rt)

A is the final amount

P is the initial principal (investment)

r is the annual interest rate (expressed as a decimal)

t is the time in years

e is the base of the natural logarithm

P = $6,000

A = $8,600

r = 9.6% = 0.096 (annual interest rate)

$8,600 = $6,000 * e^(0.096t)

4.989 years

_____________________________________

Hope this helps.

Let A be the event that we choose an adult chaperone and let B be the event that we pick a male student. Then, we want to calculate the following probability.

where the symbol between A and B means the union of events, which could be understood as "or". Using the properties of probability, we have

where the symbol on the right, between A and B, is the intersection, which can be understood as "and". Since we are going to pick only one person, it is impossible that we pick an adult chaperona and a male student. So,

So we have

Now, we want to calculate P(A) and P(B).

To calculate the probability of each event, we first count the number of possibilities that the event is true.

Note that since we have 6 adult chaperones, we have 6 possibilites such that the event A is true. Now, to calculate the probability of A, we simply divide this number by the total number of people on the bus (which is 50). So we get

In the same manner, for event B, we have a total of 23 possibilities such that the event B is true. Then

Finally, by replacing this values in the original expression, we have

Answer:

You need 4 severing's of 1 1/2 quarts and 3/4 of grape juice to make 9 quarts of grape juice

Step-by-step explanation:

(1 1/2 + 3/4) x 4= 9

Answer:

104 degrees

Step-by-step explanation:

90 + 54 + 132 = 276

360 - 276 = 104

Answer:

n=-5

Step-by-step explanation:

Do the equation backwards:

-26 - 4 = -30

-30 / 6 = -5

Check:

-5*6 = -30

-30+4 = -26

Hope this helps!

The expression given 5g times 7h as required to be rewritten in the task content is; 35gh.

It follows from the task content that the rewritten form of the expression 5g times 7h is to be determined.

Since the given expression can be written algebraically as; 5g × 7h

i.e 5 × 7 × g × h

= 35gh.

Consequently, the rewritten form using the fewest number of symbols and characters is; 35gh.

Read more on multiplication of algebraic expressions;

https://brainly.com/question/32318047

#SPJ4

option A, f(x) = 4(x − 2)² + 4, is the quadratic function that has a vertex of (2,4).

How to solve the question?

The vertex form of a quadratic function is given by f(x) = a(x-h)² + k, where (h,k) represents the vertex of the parabola. Therefore, to find the quadratic function that has a vertex of (2,4), we need to substitute h=2 and k=4 in the given options and see which one satisfies this condition.

Option A: f(x) = 4(x − 2)² + 4

Here, h=2 and k=4. Therefore, the vertex is (2,4). Hence, this option satisfies the condition and could be the correct answer.

Option B: f(x) = 3(x + 2)² + 4

Here, h=-2 and k=4. Therefore, the vertex is (-2,4), which is not the required vertex. Hence, this option is not correct.

Option C: f(x) = 2(x-4)² + 2

Here, h=4 and k=2. Therefore, the vertex is (4,2), which is not the required vertex. Hence, this option is not correct.

Option D: f(x) = 2(x + 4)² + 2

Here, h=-4 and k=2. Therefore, the vertex is (-4,2), which is not the required vertex. Hence, this option is not correct.

Therefore, option A, f(x) = 4(x − 2)² + 4, is the quadratic function that has a vertex of (2,4).

To know more about quadratic equation visit :-

https://brainly.com/question/1214333

#SPJ1

Answer:

SA = 10,800 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 40

w = 60

h = 30

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 60(40) + 30(40) + 30(60) )

SA = 2 ( 2400 + 1200 + 1800 )

SA = 2 ( 5400 )

SA = 10,800 ft²

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

A. vertex B

B. Side BC and BD

C. Angle EBD

Step-by-step explanation:

An angle is an undefined term in plane geometry.

Vertex of \(\angle 4\)

The vertex of an angle is the point where the rays that form the angle meet.

From the diagram, rays BE and BA meet at point B to form \(\angle 4\).

Hence, the name of the vertex is B

Sides of \(\angle 1\)

The sides of an angle are the rays or sides that form the angle

\(\angle 1\) is formed by rays BC and BD

Hence, the sides are BC and BD

Another name for \(\angle 5\)

An angle can be named by combining the sides and the vertex.

The sides of \(\angle 5\) are DB and BE, while the vertex is B

This means that rays DB and BE meet at point B

Hence, another name is \(\angle DBE\)

Classify the angles

Angles are classified based on the measure

\(\angle FBC\) is a right angle, because \(\angle FBC = 90^o\)

\(\angle EBF\) is an obtuse angle because \(\angle EBF\) is greater than \(90^o\) but less than \(180^o\)

\(\angle ABC\) is a straight angle, because \(\angle ABC= 180^o\)

Angle bisector

The line or ray that divides an angle into equal halves is an angle bisector.

Ray BE is an angle bisector, because it divides \(\angle DBA\) into two equal halves.

Find \(\angle EBC\)

We have:

\(\angle EBD = 36\)

\(\angle DBC = 108\)

\(\angle EBC\) is calculated using:

\(\angle EBC = \angle EBD +\angle DBC\)

\(\angle EBC = 108+36\)

\(\angle EBC = 144\)

Find \(\angle ABE\)

We have:

\(\angle EBF = 117\)

\(\angle DBC = 108\)

\(\angle ABE\) is calculated using:

\(\angle EBF = \angle ABE +\angle EBD + \angle ABF\)

Where

\(\angle ABF = 90\)

\(\angle ABE = \angle EBD\)

So, we have:

\(117 = \angle ABE +\angle ABE + \angle 90\)

\(117 = 2\angle ABE + 90\)

Collect like terms

\(2\angle ABE =117 - 90\)

\(2\angle ABE =27\)

Divide both sides by 2

\(\angle ABE =13.5\)

Read more about angles at:

https://brainly.com/question/13954458

To verify that all sales that have been shipped to customers have been recorded, a test of transactions should be completed on a representative sample drawn from the sales records or shipping records.

The sample should be chosen randomly and be large enough to provide a reasonable level of confidence in the accuracy of the recorded transactions. This test will help ensure that all sales have been properly recorded in the accounting system and that there are no unrecorded sales. It is important to perform this test on a regular basis to maintain the integrity of the financial records.

More on transactions test: https://brainly.com/question/15392308

#SPJ11

To prove angle abd and angle cbd are congruent using a proof by contradiction, the assumption statement that starts the proof is Angle abd and angle cbd are not congruent.

Proof by contradiction is a technique used in logic and mathematics to verify the truth or validity of a claim by demonstrating how presuming the proposition to be incorrect results in a contradiction.

A proof by contradiction first starts with the negation, or opposite of the hypothesis.

In context of the problem, the proof by contradiction will start by the opposite . Since we are to prove that angle abd and angle cbd are congruent, the opposite is Angle abd and angle cbd are not congruent.

Learn more on proof by contradiction at:

https://brainly.com/question/16813112
#SPJ1

6/(n² - n - 3) is the expanded form of the expression 6/(n-1)(n-3)

To expand the expression 6/(n-1)(n-3)

we can use the distributive property.

Let's break it down step by step:

6/(n-1)(n-3) = 6/[(n-1) × (n-3)]

Using the distributive property:

= 6/(n² - 4n + 3n - 3)

Combine the like terms in the denominator

= 6/(n² - n - 3)

Now, let's find the sum of this expression. we need to specify the range of values for the variable n.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

The Venn diagram of the 66 students in the drama group is illustrated below.

Venn Diagram:

Basically, a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by intersections of the circles.

Given,

All 66 students in a drama group take part in at least one of the four activities given below. acting (4) dancing (D) singing (S) stage management (M) Of these 66 students 11 take part in acting, dancing and singing 17 take part in acting and singing 14 take part in dancing and singing 16 take part in acting and dancing 33 take part in singing 37 take part in acting 29 take part in dancing Any student who takes part in stage management does not take part in acting, dancing or singing.

Here we need to show all this information on the Venn diagram, giving the number of students in each subset.

While we looking into the given information,

Total number of students = 66

Here A refers acting, D refers dancing and S refers singing

=> All three activities count = 11

=> Acting and singing = 17

=> Dancing and singing = 14

=> Acting and dancing = 16

=> Singing = 33

=> Acting = 37

=> Dancing = 29

Based on these details we have drawn the following Venn diagram.

To know more about Venn diagram here.

https://brainly.com/question/29301560

#SPJ1