please can you help me​

Using leaner equation we find that After 12 years from now will Jerry's age be (2/3) of the combined ages of his brother and sister at that time.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Let Jerry's brother present age be X years,

Then Jerry's present age will be 2x

And his sister's present age will be 2X - 6

And let y be  the  number of years from now when Jerry's age = (2/3) of combined age of his brother and sister.

So we have that,

(2X + y)  = (2/3) [(X + y) + (2X - 6 + x)]

simplify the above equation

2X + y = (2/3) [3X + 2y - 6]

multiply through by 3/2

3X + (3/2)y = 3X + 2y - 6

subtract  3X from both sides

(3/2)y = 2y - 6

subtract 2y from both sides

-1/2y = -6

divide both sides by -1/2

y = 12 years

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Answer:

Part A). 25 feet

Part B). 16.25 feet

Step-by-step explanation:

Part A). By applying Pythagoras theorem in ΔABC,

            AC² = AB² + BC²

            AC² = (24)² + 7²

            AC² = 576 + 49

            AC = √625

                  = 25 feet

Part B). By applying Pythagoras theorem in ΔABC,

            AC² = AB² + BC²

           (25)² = (19)² + x²

           625 = 361 + x²

           x² = 625 - 361

           x = √264

           x = 16.25 feet

Answer:

73947.52

Step-by-step explanation:

the equation would be 100000 * (0.988)^25

since time is 25 years, and rate is 0.988, since we are decreasing by 0.012.

The solution to the system of equation are as follows:

System of equation can be solved by using different method such as substitution method, elimination method and graphical method.

Therefore, let's use elimination method to solve the equation.

Hence,

-3x + 2y = 23

5x + 2y = -17

subtract equation(ii) from equation (i)

-8x = 40

x = 40 / - 8

x = -5

5(-5) + 2y = -17

2y = -17 + 25

2y = 8

y = 8 / 2

y = 4

4x+9y = -19

- 4x - 7y = 13

add the equations

-2y = -6

y = -6 / -2

y = 3

Hence,

-4x = 13 + 7(3)

-4x = 13 + 21

-4x = 34

x = 34 / -4

x = - 17 / 2

3x + 7y = 14

2x + 7y = 21

subtract equation(ii) from equation (i)

x = -7

7y = 21 - 2x

7y = 21 - 2(-7)

7y = 21 + 14

7y = 35

y = 35 / 7

y = 5

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Therefore, the particular solution to the differential equation is:

Y(t) = -e^(2t)

To find the particular solution to the differential equation y'' - y' - 6y = 4e^(2t) using the method of undetermined coefficients, we assume a particular solution of the form:

Y(t) = A*e^(2t)

where A is a constant to be determined.

Taking the derivatives of Y(t), we have:

Y'(t) = 2Ae^(2t)

Y''(t) = 4Ae^(2t)

Substituting these derivatives into the differential equation, we get:

4Ae^(2t) - 2Ae^(2t) - 6A*e^(2t) = 4e^(2t)

Simplifying, we have:

-4A*e^(2t) = 4e^(2t)

Dividing both sides by -4e^(2t), we find:

A = -1

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Answer:

The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.

Step-by-step explanation:

Example: What is the HCF of {12,42,14}

Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.

Answer:

-1

Step-by-step explanation:

7-8=-1

Answer:

4

Step-by-step explanation:

3x-5=7x-21

3x-7x=5-21

-4x=-16 ( divide by -4 both sides)

x= 4

Answer:

choice A is better value

Step-by-step explanation:

1/2 Kg = 500 grams

0.7* 5=3.5 dollars for sunflower seeds

prepackaged seeds : 500 mg= 0.5 grams

so 0.5 grams cost 3.95 dollars

Answer:

The correct expression is a.

a) The 99% confidence interval for μ, assuming n = 16 is [76.91, 83.49].

b)  The 99% confidence interval for μ, assuming n = 25 is [77.57, 82.83].

c) Yes, the width of the confidence intervals constructed in parts (a) and (b) decreases as the sample size increases.

a) 99% confidence interval for μ by assuming n=16:

For a sample size of n=16, the standard error is calculated as:

Standard Error, SE

m= σ/√n

= 5.10/√16

= 1.275

Let’s calculate the margin of error for 99% confidence level:

Margin of Error = 2.58 × SE

m = 2.58 × 1.275 = 3.29

Then, the confidence interval for μ is calculated as follows:

Upper Limit= X + ME

= 80.20 + 3.29

= 83.49

Lower Limit= X - ME

= 80.20 - 3.29

= 76.91

Therefore, the 99% confidence interval for μ, assuming n = 16 is [76.91, 83.49].

b) 99% confidence interval for μ by assuming n=25:

For a sample size of n=25, the standard error is calculated as:

Standard Error, SE

m= σ/√n

= 5.10/√25

= 1.02

Let’s calculate the margin of error for 99% confidence level:

Margin of Error = 2.58 × SE

m = 2.58 × 1.02

= 2.63

Then, the confidence interval for μ is calculated as follows:

Upper Limit= X + ME

= 80.20 + 2.63

= 82.83

Lower Limit= X - ME

= 80.20 - 2.63

= 77.57

Therefore, the 99% confidence interval for μ, assuming n = 25 is [77.57, 82.83].

c) Yes, the width of the confidence intervals constructed in parts (a) and (b) decreases as the sample size increases.

It is because as the sample size increases, the standard error of the sample mean decreases, which leads to the decrease in the margin of error, which in turn results in a narrow width of the confidence interval.

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The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly

Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles.

Given,

To prove = ACE is an isosceles triangle

AC = EC  (given)

∠A = ∠C

The characteristics of an isosceles triangle are as follows:

There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

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Answer:

3)

Step-by-step explanation:

An equation is linear if equal changes in x produce equal changes in y.

Let's look at each choice.

1)

A decrease of 10% per year. That means each year, the value of the car is 0.9 times the value of the previous year.

For example, if the original value was $10,000, after 1 year, it is worth 0.9 * $10,000 = $9,000. In 1 year it lost $1,000. In the next year, its value is now 0.9 * $9,000. The value at the end of the 2nd year is $8,100. In the second year, it lost $900 in value. In one period of 1 year it lost $1000 in value. In another equal period of 1 year, it lost $900 in value. A change of 1 year in time produces different changes in loss of value, so it is not linear.

2)

Here, the number doubles every year. Let's say it starts with 100 fish. After 5 years, it has 200 fish. In a change of 5 years in x, the change in y is 100. In the next 5 years, it goes from 200 fish to 400 fish. The change in the second period of 5 years is 200. We see that a change of 5 years can produce a change of 100 fish, but another change of 5 years can produce a change is 100 fish. Since for equal changes in x, the changes in y are not all equal, this is not linear.

3)

Here for every change of 1 day in x, the change in y is 2 liters. Each change of 1 in x always produces a change of 2 in y. This is linear.

4)

Each 2 hours, the amount of caffeine is 2/3 of what it was before. This is similar to the choice 1), and it is not linear.

Answer: 3)

In the given example, composite function f o g can be found by applying the function f onto the output of the function g. This process can be written as f(g(x)) = (6/x-3) (4/7x) = 24/7x - 12/x. Simplifying this equation yields the answer 42x/4 - 21x, option b.  

Composite functions are functions that are composed of two or more other functions combined together. Composite functions can be used to quickly analyze complicated problems. In this problem, calculating f o g is much quicker than analyzing the original functions f and g independently.

By changing the order of operations, it also allows the analyst to quickly determine different results. Therefore, knowing how to combine simple functions allows for faster problem solving for more complex issues.

Correct option is B.

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Answer:

The correct answer is (b.)

A first-order model is not appropriate.

Step-by-step explanation:

If the relationship between the expectation of y and x1 depends on the values of the remaining independent variables, it suggests that there is interaction or dependence between the independent variables. In such cases, a first-order model, which assumes a simple linear relationship between the dependent variable and independent variables, may not capture the complexity of the relationship.

To account for the interaction and dependence between variables, higher-order models or more advanced modeling techniques may be necessary. These techniques could include polynomial regression, interaction terms, or other forms of multivariate analysis. Logistic regression or robust techniques are not specifically mentioned or required based on the given information. The appropriate modeling approach would depend on the specific nature of the relationship and the underlying data.

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Answer:

x = 8

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact A is 90°

then Δ ABP is right at A

using Pythagoras' identity in the right triangle

BP² = AP² + AB² , that is

(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL

x² + 18x + 81 = x² + 225 ( subtract x² from both sides )

18x + 81 = 225 ( subtract 81 from both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Answer:

350

Step-by-step explanation:

It is 350 because 10 ones is 10, 4 tens is 40, and 3 hundreds is 300 if you add them up you get 350.

The required number is 350 which represents 10 ones, 4 tens

and 3 hundred.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We have been given information as

10 ones

4 tens

3 hundred

As per the given question,

Translate the information into an algebraic expression:

It's 350 since 10 ones are 10, 4 tens are 40, and 3 hundred is 300 when added together.

⇒ 1 × 10 + 4 × 10 + 3 × 100

⇒ 10 + 40 + 300

⇒ 350

Therefore, the required number is 350 which represents 10 ones, 4 tens

and 3 hundred.

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Answer:

answer is b

Step-by-step explanation:

Answer:

We can calculate the price with both  sales by multiplying the 75.5 units of money by both percentages (to multiply them, we divide them by 100 first):

75.5 * 0.24 * 0.6 \(\approx.\) 10.8

Answer:

\(\displaystyle y = -4x - 5\)

Step-by-step explanation:

We want to find the slope-intercept form of the equation that passes through the point (-2, 3) and is perpendicular to the line:

\(\displaystyle y = \frac{1}{4} x - 4\)

Note that this line has a slope of 1/4.

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

Since the slope of our old line is 1/4, the slope of its perpendicular line must be -4.

We are also given that it passes through the point (-2, 3). So, we can consider using point-slope form:

\(\displaystyle y - y_1 = m(x - x_1)\)

Let (-2, 3) be (x₁, y₁) and substitute -4 for the slope m. Hence:

\(\displaystyle y - (3)= -4 (x - (-2))\)

Convert into slope-intercept form. Simplify:

\(\displaystyle \begin{aligned} y -3 &= -4 (x + 2) \\ y - 3 &= -4x - 8 \\ y &= -4x -5\end{aligned}\)

In conclusion, the perpendicular line that passes through the point (-2, 3) is given by:

\(\displaystyle y = -4x - 5\)

Answer:

(a)

\(3 \sqrt{5} \)

(b)

\( \frac{6}{ \sqrt{5} } \)

Step-by-step explanation:

A(-3,0)

B(0,6)

\(d = \sqrt{{( - 3 - 0)}^{2} + {(0 - 6)}^{2} } = \sqrt{9 + 36} = 3 \sqrt{5} \)

\(d = \frac{ax0 + by0 + c}{ \sqrt{ {a}^{2} + {b}^{2} } } \)

2x-y+6=0

a=2, b=-1, c=6

x0=0, y0=0

\(d = \frac{6}{ \sqrt{4 + 1} } = \frac{6}{ \sqrt{5} } \)

The items matched in the left column to the items in the right column are

Ratio is the number representing a comparison between two named things or quantities.

1. total to fish

= 8 : 3

2. starfish to fish

= 5 : 3

3. starfish to total

= 5 : 8

4. fish to starfish

3 : 5

In conclusion, the ratio of the total to fish to starfish is 8 : 3 : 5

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answer here!

sry it is a bit messy

Answer:

1) 11001 base 2

2)133 base 5

1) To convert base 10 into base 2

25/2= 12remainder 1

from this point on, the remainders will be replaced by r

12/2= 6r0

6/2=3r0

3/2=1r1

1/2=0r1

The remainders are then written down from the bottom up

= 11001

2) To convert 101011 base 2 into base 5

101011= 1×2⁵ + 0×2⁴+ 1×2³+ 0×2² + 1×2¹ + 1×2⁰

=1×32 + 0×16 + 1×8+ 0×4+1×2+1×1

=32+0+8+0+2+1

=43 base 10

Then convert 43 base 10 to base 5

43/5=8r3

8/5=1r3

1/5=0r1

=133 base 5

Step 1

Ways to choose 5 from 40 multiplied by ways to choose 5 from the other 90 and number of ways to choose 10 in all from 130 as the denominator

Step 2:

Apply combination formula

Step 3:

Ways to choose 5 from 40

Step 4

ways to choose 5 from the other 90

Step 5

ways to choose 10 in all from 130

Step 6

Ways to choose 5 from 40 multiplied by ways to choose 5 from the other 90 and number of ways to choose 10 in all from 130 as the denominator

Answer:

x ≈ 4.4

Step-by-step explanation:

using the tangent ratio in the right triangle

tan43° = \(\frac{opposite}{adjacent}\) = \(\frac{UV}{VW}\) = \(\frac{4.1}{x}\) ( multiply both sides by x )

x × tan43° = 4.1 ( divide both sides by tan43° )

x = \(\frac{4.1}{tan43}\) ≈ 4.4 ( to the nearest tenth )

The value of x, Round to nearest tenth is,

⇒ x = 4.4 units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A triangle is shown in image.

Now, We can formulate;

tan 43° = Opposite / Base

⇒ tan 43° = 4.1 / x

⇒ 0.932 = 4.1 / x

⇒ x = 4.1 / 0.932

⇒ x = 4.39

⇒ x = 4.4 units

Thus, The value of x, Round to nearest tenth is,

⇒ x = 4.4 units

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Answer:

10. =13/6

11. =17/3

12. =76/9

13. =22/7

Hope this helped!!

Answer:

$120 + -33% = $80.40

Step-by-step explanation: