There exists three consecutive prime numbers whose sum is also a
prime number.

Answer:

with what

Step-by-step explanation:

can you please post the picture

look at the picture to see how to add a pic to a question

Answer:

DG

Step-by-step explanation:

This is a rectangular prism.  BE & AH are also parallel to CF. but they r not in the answers.

The  lengths of the two diagonals of the parallelogram are D1 and D2, where:

D1 = ||A + B||

D2 = ||A - B||

Let's denote the vectors as vector A and vector B. The lengths of the two diagonals of the parallelogram can be calculated using vector operations.

The length of the first diagonal (D1) can be calculated using the formula:

D1 = ||A + B||

The length of the second diagonal (D2) can be calculated using the formula:

D2 = ||A - B||

Here, ||A|| represents the magnitude (length) of vector A, and ||B|| represents the magnitude of vector B.

Therefore, the lengths of the two diagonals of the parallelogram are D1 and D2, where:

D1 = ||A + B||

D2 = ||A - B||

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Answer:

ewanjehehehehejejejjejshs

The two equivalent equations are: 1. s = s equals start fraction l an over pi r end fraction, and 2. s = s equals start fraction pi r over l a endfraction. Hence, 1 and 2 are the required correct statements.

To determine which equations are equivalent, we need to analyze their structures and rearrange them if necessary.

1. s = s equals startfraction l a over pi r endfraction:

This equation represents the relationship between the surface area (s) of a sphere and its radius (r) and lateral area (l a). It is in a valid form and cannot be simplified further.

2. s = s equals startfraction pi r over l a endfraction:

This equation also represents the relationship between the surface area (s) of a sphere and its radius (r) and lateral area (l a). However, it is written in a different order compared to the first equation. By rearranging the terms, we can rewrite it as s = s equals startfraction l a over pi r endfraction, which is equivalent to the first equation.

3. r = r equals startfraction l a over pi s endfraction:

This equation represents the relationship between the radius (r) of a sphere and its lateral area (l a) and surface area (s). It is not equivalent to the first two equations as the variables are in a different order.

4. r = las:

This equation does not match the structure of the previous equations and does not represent a valid relationship between the variables.

Therefore, the two equivalent equations are:

1. s = s equals startfraction l a over pi r endfraction.

2. s = s equals startfraction pi r over l a endfraction.

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The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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Answer:

p = g - 50

Step-by-step explanation:

profit = income - expenses

income = 1 * g = g

expenses = $50

p = g - 50

If g = 50, then

p = 50 - 50 = 0

If she sells 50 glasses of lemonade, she breaks even. That means she makes no profit, but also she loses nothing.

If she sells more than 50 glasses, then she makes a profit.

Answer:

50 is the answer

Step-by-step explanation:

9514 1404 393

Answer:

  f(x) = 6x +1

Step-by-step explanation:

Differences in x-values (first row) are 1, 1, 1.

Differences in y-values (second row) are 6, 6, 6.

The constant ratio of differences (6/1) tells you the function is linear, and has a slope of m = 6/1 = 6.

Using the first point in the form ...

  y = mx + b

we have ...

  y = 6x + b

  7 = 6·1 + b . . . . (x, y) = (1, 7)

  1 = b . . . . . . subtract 6

Then the equation can be written ...

  y = 6x +1

In functional form, this is ...

  f(x) = 6x +1

Based on the given expression, the correct simplification is provided by Sue: 4x + 8z.

To understand why Sue's simplification is correct, let's break down the steps of combining like terms:

The original expression is: 8x + 5z - 4x + 3z + 6.

Step 1: Combine the x terms: 8x - 4x = 4x.

Step 2: Combine the z terms: 5z + 3z = 8z.

Step 3: Bring down the constant term: 6.

Putting it all together, we get the simplified expression: 4x + 8z + 6.

Now, let's evaluate the other given expressions to see why they are incorrect:

Andrea's expression: -32x + 15z + 6

The error in Andrea's simplification arises from subtracting 4x from 8x, which results in -32x. This is incorrect because 8x - 4x equals 4x, not -32x.

Alissa's expression: 4x + 8z + 6

Alissa's simplification is correct and matches Sue's expression, so there is no error in her calculation.

Rachel's expression: 12x + 2z + 6

The error in Rachel's simplification arises from incorrectly adding the x and z terms. The coefficient of x should be 4 (8x - 4x = 4x), but Rachel incorrectly added the coefficients, resulting in 12x. Similarly, the coefficient of z should be 8 (5z + 3z = 8z), but Rachel incorrectly added the coefficients, resulting in 2z.

In conclusion, Sue and Alissa are correct in their simplifications. Sue's expression, 4x + 8z, is the accurate simplification of the given expression. Andrea and Rachel made errors in their calculations by incorrectly adding or subtracting the coefficients of the variables.

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Answer:

C is the answer you are looking for! :)

Step-by-step explanation:

Answer: C

Step-by-step explanation:

it was correct on edge 2022

Answer:

C

Step-by-step explanation:

112 is 35% of the entire book so 112=.35x, x representing the total pages in the book

divide both sides by .35 and you get x=320, making the answer C

Assuming Jayden read 112 pages of a book. The number of pages that  are in Jayden’s book? is :C) 320.

Let x represent the number of pages

35%x=112

Hence:

x=112/35%

x=320

Therefore assuming Jayden read 112 pages of a book. The number of pages that  are in Jayden’s book? is :C) 320.

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Answer:

7 pizzas

Step-by-step explanation:

18 people × 3 slices each = 54 slices

54 ÷ 8 = 6.75

7 pizzas

Answer:

They should order 7 pizzas.

Step-by-step explanation:

18 people x 3 slices per person = 54 slices you will need for everyone

54 slices divided by 8 = 6.75 pizzas.

Round 6.75 to 7 pizzas.

They should order 7 pizzas because you cannot ask the pizza place for 6.75 pizzas.

Louis total distance of 8/5 km. Louis rose his bicycle a total distance of 8/5 km.

Louis rose his bicycle a total distance of 1/2 km + 3/4 km + 7/10 km.

To find the total distance, we need to find a common denominator for the fractions: 2, 4, and 10.

The least common denominator is 20.

So, 1/2 km can be written as 10/20 km, 3/4 km can be written as 15/20 km, and 7/10 km remains the same.

Adding these fractions together, we have:

10/20 km + 15/20 km + 7/10 km = 32/20 km

Simplifying this fraction, we get:

32/20 km = 8/5 km

Therefore, Louis rose a total distance of 8/5 km.

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Louis rode a total distance of 8/5 km or 1 and 3/5 km

Louis rode his bicycle a total of 1/2 km to school, 3/4 km to a ball field, and 7/10 km back home. To find the total distance Louis traveled, we need to add up these three distances.

First, let's add 1/2 km and 3/4 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 4 is 4.

Converting 1/2 to have a denominator of 4, we get 2/4. Now we can add 2/4 + 3/4, which equals 5/4.

Next, we need to add 5/4 km and 7/10 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 4 and 10 is 20.

Converting 5/4 to have a denominator of 20, we get 25/20. Now we can add 25/20 + 7/10, which equals 32/20.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 32/4 and 20/4, we get 8/5.

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The solution to the coupled differential equations dx/dt= 2.x1 +x2 is x1 = t^2 + 2t and x2 = t^2, We can then integrate both sides of the equation to get the following: ln(2.x1 +x2) = t + c

To solve this set of differential equations, we can use the method of separation of variables. This method involves separating the variables in each equation so that they can be solved independently. In this case, we can separate the variables as follows: dx/(2.x1 +x2) = dt

We can then integrate both sides of the equation to get the following: ln(2.x1 +x2) = t + c

where c is an arbitrary constant. We can then exponentiate both sides of the equation to get the following 2.x1 +x2 = e^t.e^c

We can then substitute the initial conditions into this equation to get the following 2.x1 +x2 = e^t.1

where x1(0) = 0 and x2(0) = 0. This gives us the following solution for x1 and x2 x1 = t^2 + 2t and x2 = t^2

Here are some additional explanations:

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Answer:

x = -36

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: See attached.

Step-by-step explanation:

        We see from the given values that for every table there is 3* the number of guests and vise versa (for every 3 guests there is one table). Using this information we can complete the other values by multiplying or dividing.

3 tables * 3 = 6 guests

15 guests / 3 = 5 tables

9 tables * 3 = 27 guests

30 guests / 3 = 10 tables

a) The predicted GPA for a student with Verbal SAT score of 500 is 2.9805.

b) The residual for this student is -0.2805.

To calculate the predicted GPA for a student with Verbal SAT score of 500, we need to plug in the value of 500 into the regression equation:

GPA = 2.0336 + 0.0018929 × VerbalSAT

Thus, the predicted GPA for a student with Verbal SAT score of 500 is

GPA = 2.0336 + 0.0018929 × 500 = 2.9805

To calculate the residual for this student, we subtract the predicted GPA from the actual GPA

Residual = Actual GPA - Predicted GPA

Residual = 2.7 - 2.9805 = -0.2805

Therefore, the residual for this student is -0.2805.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

A straight line linear regression analysis was carried out, using Verbal SAT score, VerbalSAT (values can range from 0 to 800), to predict grade point average in college, GPA, for first-year BU students (GPA values can range from 0 to 4). The sample size is 345 first-year BU students. The following are the least squares estimates of the coefficients of the linear regression model and the estimates of their standard error: Variable DF Parameter Standard Estimate Error 1 2.0336 0.1621 Intercept VerbalSAT (Slope) 1 0.0018929 0.0002709 . . Calculate the predicted GPA and the residual for a student with Verbal SAT score of 500. GPA was 2.7 for this student.

Answer:

-4/5,-1/2,-0.2,0.25

Step-by-step explanation:

To order these, it would be best to convert them into decimals.

-4/5 is equal to -0.8

-1/2 is equal to -0.5

-0.8 is the least, because the further left on a number line, the less the number is.

-0.5 is next and then -0.2

Finally, 0.2 is the greatest

-4/5,-1/2,-0.2,0.25

Hope this helps :-)

Answer:

corresponding angles, alternate exterior angles

Step-by-step explanation:

when you have to parallel lines cut be a transversal, you get different pairs of angles that are either equal or supplementary (add to 180).

For example, corresponding angles are congruent, and alternate exterior angles are congruent.

Gio was able to save approximately $6 from the discount

Data;

This is the ratio of two values to another multiplied by 100.

To solve this, we have to calculate the discounted amount and subtract it from the original price to know how much he saved.

Let's find 31% of 18.99

\(\frac{31}{100}= \frac{x}{18.99} \\x=0.31*18.99\\x=5.889\)

This shows that he got a discount of approximately $5.9.

Gio was able to save approximately $6

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Answer:

$6

Step-by-step explanation:

\(10=2d\)

Given:

The sum of the first three terms of a sequence Is 42.

The fourth term is 24.

To find:

The  u₁ and the common difference

Step-by-step explanation:

nth term of a sequence is

\(u_n=u_1+(n-1)d\)

where, u₁ is first term and d is common difference.

4th term is 24.

\(u_4=u_1+(4-1)d\)

\(24=u_1+3d\)           ...(i)

Sum of nth term of an AP is

\(S_n=\dfrac{n}{2}[2u_1+(n-1)d]\)

Sum of first three terms is 42.

\(S_3=\dfrac{3}{2}[2u_1+(3-1)d]\)

\(42=\dfrac{3}{2}[2u_1+2d]\)

Divide both sides by 3.

\(14=u_1+d\)          ...(ii)

On subtract (ii) from (i), we get

\(10=2d\)

\(5=d\)

Put d=5 in equation (ii).

\(14=u_1+5\)

\(14-5=u_1\)

\(9=u_1\)

Therefore, the first term is \(u_1=9\) and common difference is \(d=5\) .

The equation such that (2, 5) is not a solution is the fourth option:

2x+4y=12

If we have any equation of the form:

ax + by = c

The point (2, 5) is a solution if and only if:

a*2 + b*5 = c

is a true equation.

Then we need to find for which of these given equations, when we replace our point (2, 5), we get a false eqation.

We will see that the correct option is (4).

2x + 4y = 12

replacing the values x = 2 and y = 5 we will get:

2*2 + 4*5 = 12

4 + 20  = 12

24 = 12

That is false, so the correct option is (4).

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Answer:

y = 0.59x

Step-by-step explanation:

Cost per pound of banana = $0.59

If Number of banana's = x

Total Cost of an item = price per item * number of items

Therefore,

Total cost, y = price per pound of banana * number of bananas

y = 0.59 * x

y = 0.59x

The number that is one hundreth less than 3.2 is 3.19

From the question, we have the following parameters that can be used in our computation:

One hundreth less than 3.2

As an expression, we have

3.2 - One hundreth

When represented uisng numbers

We have

3.2 - 0.01

Evaluate the difference

3.19

Hence, the solution is 3.19

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We're given:

To find the area of the garden alone, we can subtract the area of the garden from the combined area of the garden and walkway:

\(4.5(8x + 4)-4(5.5x + 1.5)\)

Open up the parentheses:

\(= 36x +18 -22x - 6\)

Combine like terms:

\(= 36x +18 -22x - 6\\= 14x +18 - 6\\= 14x +12\)

The area of the walkway around the garden is 14x + 12.

The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.

avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.

a)

Hence average value of f(x) on 0≤x≤2

= 1/2 ∫f(x)  with 0 and 2 as intervals

Since integration is basically the area under the curve we get

avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]

Since from 0 to 1, the figure is a triangle and beyond that a straight line we get

1/2[1/2 X 1 X 1 + 0]

= 1/4 sq units

b)

Similarly, the average value of g(x) on 0 ≤ x ≤ 2

1/2[area from 0 to 1 + area from 1 to 2]

= 1/2[0 + 1/2]

= 1/4 sq units

c) here we need to find the average of f(x) . g(x)

Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1

Hence we see that on multiplying the functions, the resultant has to be a 0 function.

Hence its average value will be 0.

d)

Average(f) . Average(g) = 1/4 X 1/4

= 1/16

Average of (f.g) = 0

Hence the statement is false

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Complete Question

The figure attached to the left is a graph of f(x), and below to the right is g(x).

The figure below to the left is a graph of f(x), a

(a) What is the average value of f(x) on 0≤x≤2? avg value = __________

(b) What is the average value of g(x) on 0≤x≤2? avg value = __________

(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________

(d) Is the following statement true?

Average(f) . Average(g)=Average(f.g)

A. Yes

B. No

Answer:

11/18

Step-by-step explanation:

56/144 = cats.

144 - 56 = 88

88/144 are dogs.

Simplified: 11/18

Answer: x=15

Step-by-step explanation:

3x+5=50

3+5=50

Subtract the numbers

3x+5-5=50-5

3x/3=45/5

x=15

Answer:

he equation given in the exercise  is:

Observe that highest exponent of the variable "x" is 2. Therefore, it is a Quadratic equation.

Therefore, making an exponent 1 instead of the exponent 2 would turn the given equation into a Linear function.

Step-by-step explanation: