if y=6 when x=40 find x when y=24

Answer:

To determine the first term of the geometric progression, let's assume it is 'a'. From the given information, we know that:

Second Term = a + 50

(n + 1)th Term = a + 56

We also have the formula for the nth term of a geometric sequence:

nth term = a * r^(n-1)

where 'r' is the common ratio between consecutive terms. Since the difference between consecutive terms remains constant, i.e., 50 for the second term and 56 for the (n + 1)th term, we can set up the equation:

a + 50 = a * r^1

a + 56 = a * r^2

Solve the equations simultaneously:

a + 50 = a * r^1 => a - 50/r = 0

a + 56 = a * r^2 => a - 56/r = 0

Adding the two equations, we get:

2a - (50/r + 56/r) = 0

2a - (50 + 56)/r = 0

Simplifying the equation further, we obtain:

2a - (106/r) = 0

Now, solve for 'a':

2a - (106/r) = 0

2a = (106/r)

=> 2a = 106/r

The value of 'a' depends on the value of 'r', so we cannot determine its exact value without knowing 'r'. However, once we know 'r', we can calculate the value of 'a'.

The two z values are -1.96 and +1.96 this means that option A is the correct choice.

From the given information we know that P(-z<Z or Z>z) = 5% = 0.05.

Then the table (area under the normal curve) the probability of values smaller than a certain z-score of the standard normal distribution.

Now the standard normal distribution is symmetric about 0.

P(-z<Z)=P(-z<Z or Z>z)/2

P(-z<Z)=0.05/2

P(-z<Z)=0.025

Here we have to determine the corresponding z-score in area under the normal curve table.

The corresponding z-score z is then given in row/column title of area under the normal curve table which corresponding to a probability of 0.025 or the probability closest.

-z = -1.96

Two z -values , positive and negative that are equidistance from the mean so that the area in two tailed total 5% are,

= ±1.967 = ±1.96

z=-1.96,+1.96

Therefore, the correct option is A.

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Answer:

24*10^3=24000

Step-by-step explanation:

Answer:

the answer is 24000 grams

Step-by-step explanation:

hope this helped

Answer:

-9/7.

Step-by-step explanation:

√81 = 9 and √49 = 7

but we need the negative square root

which is -9/7.

Answer:

Step-by-step explanation:

The correct question is attached in the image below;

From there, given that: the earnings = 60x + 50 y ------ (1)

y = -x + 175

for x = 0 ⇒ y = 175 ; Then Point A (0, 175)

y = -2x + 300

for y = 0 ⇒ x = 150 ; Then Point C (150, 0)

For Point B;

y = -x + 175    ---- (a)

y = -2x + 300 ---- (b)

Equating both (a) and (b) from above together; then:

⇒ -x + 175 = -2x + 300

⇒ x = 125

∴

From y = -x + 175

y = -125 + 175

y = 50

So point B ( 125, 50)

Now, the points are O(0, 0), A(0, 175), B(125, 50), C(150, 0)

As such, profit at these points are:

O(0, 0), Profit = 60 × 0 + 50 × 0 = 0

A(0, 175), Profit = 60 × 0 + 50 × 175 = 8750

B(125, 5), Profit = 60 × 125 + 50 × 50 = 10,000

C(150, 0), Profit = 60 × 150 + 50 × 0 = 9000

Hence, maximum profit takes place at B(125, 50) which is = $10,000

Finally, we can conclude that the shop should prepare 125 packages of assortment A and 50 packages of assortment B to maximize profit.

The maximum profit is $10,000

Answer:

K=8

Step-by-step explanation:

The triangles are similar so you can set up the porpotions: 3/6=4/k then you cross multiply and solve for k

A statement which is true about the graph include the following: B: The equation y = 0.5x is correctly represented by the graph.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 0.5x) is characterized by a straight line as shown in the image attached below.

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Answer: The product of two consecutive even numbers is 12 more than the square of the smaller number. The product of the numbers is 6 and 8 is 48. Square of the smaller number (here 6) is 36. so, 12 + 36 = 48.

hope this helps:)

Step-by-step explanation:

The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

When budgeting for housing, it is generally recommended to allocate a certain percentage of your income towards housing expenses. The recommended percentage varies depending on factors such as location, personal financial goals, and individual circumstances.

A common guideline is to spend no more than 30% of your monthly income on housing expenses. To determine the maximum amount Freya should budget for housing, we can calculate 30% of her monthly income:

Maximum housing budget = 30% of $1575

Maximum housing budget = 0.30 × $1575

Maximum housing budget = $472.50

Therefore, Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

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The inputs 4 and 8 have more than one out, the relation is not a function.

A relation is said to be a function if one input is mapped to one output.

that is, each x-value can only have one y-value.

From the table;

Input, output

4 ----- 1

8 ----- 3

4 ------5

8 ----- 4

4  is an input, it has an output of 1.

4 appeared again as input but this time has an output of 5.

This means one input has more than one output.

Also, 8 is an input, it has an output of 3.

8 appeared again as input but this time has an output of 4.

Which also means one input has more than one output.

Therefore, the relation is not a function.

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Answer:

(C) y = 3x

Step-by-step explanation:

Directly proportional relation is one in which the value of x and y gets increases or decreased in same proportion.

example of such relation can be y = kx

where k is the constant of proportionality which depicts by how much value of  y will change in response to change of x.

_______________________________________________

now in the option

A and B

y= 9 , y =1/5

value of y is constant and does not depend on other variable. it value will remain same.

for y = x+4

value of y increases with x but it does not increase proportionally.

let see an example for x =1 , y = 1+4 = 5

x =2 , y = 2+4 = 6

(1,5)  and (2,6) are not proportionally changing also this equation is not of form y = kx

thus, it is incorrect option.

_______________________________

(C) y = 3x

here equation is form y =kx .  in place of k there is 3

let see an example for x =1 , y = 3*1 = 3

x =2 , y = 3*2 = 6

(1,3)  and (2,6) are  proportionally changing (1/3 = 2/6) also this equation is  of form y = kx

thus, it is correct option.

Answer:50.18

Step-by-step explanation:

8x+17+9x+11=102

17x+28=102

-28. -28

17x=74

<CAD=9x+11=50.18

x=74/17

Answer:

Paula get \(\$144\) and Kawai get \(\$168\).

Step-by-step explanation:

Given: Paula and Kawai shared \(\$312\) in the ratio of \(6:7\).

To find: How much money  did each person get?

Solution:

We have,

Paula and Kawai shared \(\$312\) in the ratio of \(6:7\).

So, let Paula get \(\$6x\) and Kawai get \(\$7x\).

As per the question,

\(6x+7x=312\)

\(\implies13x=312\)

\(\implies x=\frac{312}{13} =24\)

Therefore, Paula get \(6\times 24=\$144\), and Kawai get \(7\times 24=\$168\).

Hence, Paula get \(\$144\) and Kawai get \(\$168\).

Answer:

It is a right angled triangle.

so

tan32 = p/b

or, tan32 = x/5

or, tan32×5 = x

so, x = 3.124

for 5 no. the answer is a. 3.124

For y,

cos32 = b/h

or, cos32 = 5/y

or, y = 5/cos32

so, y = 5.895

for 6 no. 5.895 is closest to 5.994, so the answer is c. 5.994.

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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Answer:

1st term: -3

2nd term: 6

3rd term: 21

4th term: 42

Step-by-step explanation:

This problem is unclear if I need to find the first 4 terms or the 4th term. I'm going to assume both possibilities.

To find the value of a term n, you'd just have to plug in that value n into the equation. When finding the first four terms of a sequence, you have to plug in the numbers 1, 2, 3, 4. When you plug in those numbers, you get those said answers.

1st term: 3(1^2)-6=-3

2nd term: 3(2^2)-6=6

3rd term: 3(3^2)-6=21

4th term: 3(4^2)-6=42

When assessing this problem, it is a geometric sequence with a common multiplier.

EXPLANATION:

Given that an = 3n²-6

Put n = 1 then

a1 = 3(1)²-6

⇛a1 = 3(1)-6

⇛a1 = 3-6

⇛a1 = -3

Put n=2 then

a2 = 3(2)²-6

⇛a2 = 3(4)-6

⇛a2 = 12-6

⇛a2 = 6

Put n = 3 then

a3=3(3)²-6

⇛a3 = 3(9)-6

⇛a3 = 27-6

⇛a3 = 21

Put n=4 then

a4 = 3(4)²-6

⇛a4 = 3(16)-6

⇛a4 = 48-6

⇛a4 = 42

Answer: The four terms of the sequence are -3,6,21,42

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Answer:

b. 19.5

Step-by-step explanation:

The approximate measure of angle JGH is 70.529°.

According to this question, we have a right triangle in which lengths of its hypotenuse (\(GH\)), in centimetres, and one leg (\(JH\)) are known and we must determine the measure of an angle (\(m\angle JGH\)), in degrees. A representation of this triangle is included in the image attached below.

By trigonometry we have the following expression for the required angle:

\(\cos m\angle GJH = \frac{HJ}{GH}\) (1)

(\(HJ = 2\), \(GH = 6\))

\(m \angle GJH = \cos ^{-1} \frac{2}{6}\)

\(m \angle GJH \approx 70.529^{\circ}\)

The approximate measure of angle JGH is 70.529°. \(\blacksquare\)

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The DWest company has the lowest rate per minute which is 14.75.

The first company is AB and C

Given that: the price = is $ 19.95 and the time taken is 100 minute

Therefore the rate per unit of time for AB and C companies is

\(\frac{Price}{Time} = \frac{19.95}{100} = 0.1995\)

The second company is Berizon

Given that: the price = is $ 24.95 and the time taken is 150 minute

Therefore the rate per unit of time for Berizon companies is

\(\frac{Price}{Time} = \frac{24.95}{150}= 0.1663\)

The third company is Cinguling

Given that: the price = is $ 9.95 and the time taken is 60 minute

Therefore the rate per unit of time for Cinguling companies is

\(\frac{Price}{Time} = \frac{9.95}{60} = 0.1658\)

The fourth company DWest

Given that: the price = is $ 14.75 and the time taken is 100 minute

Therefore the rate per unit of time for DWest companies is

\(\frac{Price}{Time} = \frac{14.75}{100} = 0.1475\)

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Complete the question in the form of a table:

Answer:

10000

Step-by-step explanation:

100 hugs x 100 hugs

= 10,000 hugs.

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.

The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.

We are also told that Marama plans to fence the garden with 28 feet of wired fencing.

Now, let's break down the problem and find the appropriate values for the domain.

We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:

\(Perimeter = 2t + 2w\),

where t is the length of one side (the width) and w is the length of the other side (the width).

The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:

\(2t + 2w = 28\).

Simplifying this equation, we have:

\(t + w = 14\).

We can express w in terms of t as \(w = 14 - t\).

The area of a rectangle is given by the product of its length and width:

\(Area = t \times w\).

Substituting the expression for w from step 2, we have:

\(A(t) = t \times (14 - t)\).

Simplifying further:

\(A(t) = 14t - t^2\).

To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.

We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).

This shows that the value of t can range from 0 to 14, inclusive.

Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).

To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):

   ^

   |

A(t)|

   |

   |_______________________________

   0              t             14

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

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Answer:

500° celsius = 932.0° fahrenheit....

Answer:

932 fahrenheit

Step-by-step explanation:

500 celsius to fahrenheit is 932 fahrenheit    

The correct expression which is not a rational expression,

⇒ (x+3)(2x-1) / (x+3)

We have to given that;

All the expressions are,

⇒ (x+3)(2x-1) / (x+3)

⇒ (3x²+3x) / (4x+5)

⇒ (3x+4√x-7) / (2x+2)

⇒ (2x²-3x³+5) / 5x

Since, A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Hence, We can simplify all the expressions as,

⇒ (x+3)(2x-1) / (x+3)

⇒ (2x - 1)

Hence, It is not a rational expression.

⇒ (3x²+3x) / (4x+5)

⇒ 3x (x + 1) / (4x + 5)

Hence, It is a rational expression.

⇒ (3x+4√x-7) / (2x+2)

⇒ (3x + 4√x - 7) / 2 (x + 1)

Hence, It is a rational expression.

⇒ (2x²-3x³+5) / 5x

Hence, It is a rational expression.

Thus, The correct expression which is not a rational expression,

⇒ (x+3)(2x-1) / (x+3)

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Answer:

a) The maximum height reached by the ball can be found by taking the derivative of the given equation, setting it equal to 0, and solving for t. We have:

h'(t) = -10t + 20 = 0

Solving for t, we get t = 2. Substituting this value into the original equation, we get:

h(2) = -5(2)² + 20(2) + 0.4 = -10 + 40 + 0.4 = 30.4

Thus, the maximum height reached by the ball is 30.4 meters.

b) The time it takes to reach the maximum height can be found by setting the derivative of the given equation equal to 0 and solving for t, as we did in part (a). In this case, we get t = 2, so it takes 2 seconds for the ball to reach its maximum height.

c) The time at which the ball hits the ground can be found by setting the original equation equal to 0 and solving for t. We have:

h(t) = -5t² + 20t + 0.4 = 0

Solving for t, we get:

-5t² + 20t + 0.4 = 0

This quadratic equation has two solutions, which can be found using the quadratic formula:

t = (-20 ± √(20² - 4(-5)(0.4))) / (2(-5))

= (-20 ± √(400 + 0.8)) / -10

= (20 ± √400.8) / -10

= (-20 ± 20.28) / -10

= -10 ± 10.14

Thus, the ball hits the ground at t = -10 + 10.14 = 0.14 seconds, or at t = -10 - 10.14 = -20.14 seconds. Since the time must be positive, we can conclude that the ball hits the ground at 0.14 seconds.

(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.

(10) The slope of a line parallel to this line, y = 10 -8x is -8.

The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.

Question 9.

f(x) = 0.75x + 6

where;

The slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3

Question 10.

For the equation of another line, y = 10 - 8x

The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;

y = 10 - 8x

where;

slope of a line parallel to the line = -8

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Answer:

\(37\)

\(77\)

Step-by-step explanation:

\(17 \times 2 +3=37\\37 \times 2 +3=77\)

Answer:

37   77

Step-by-step explanation:

2(17) + 3 = 37

2(37) + 3 = 77