When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard. He measured it once a year and found that it grew by 26 centimeters per year. 4.5 years after he moved into the house, the tree was 292 centimeters tall.

How tall was the tree when Vlad moved into the house?
How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

Using elimination method, the solution to the system of equation is as follows:

x = 2 and y = -5

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's use elimination method to solve the system of equation as follows:

7x + 3y = - 1

4x + y = 3

multiply equation(ii) by 3

Hence,

7x + 3y = - 1

12x + 3y = 9

subtract equation(i) from equation(ii)

5x  = 10

x = 10 / 5

x = 2

Let's find y

7x + 3y = - 1

7(2) + 3y = -1

14 + 3y = -1

3y = -15

y = -15 / 3

y = -5

learn more on system of equation here: https://brainly.com/question/28453461

#SPJ1

Using an exponential function to represent the exponential decay, it will take approximately 4 weeks to reach 320 gallons

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

To solve this problem, we have to write an exponential equation to calculate the exponential decay.

Data;

A = P(1 + r)⁻ˣ

320 = 625(1 + 0.2)⁻ˣ

x = 3.67

Learn more on exponential equations here;

https://brainly.com/question/2456547

#SPJ1

The time t = 3.4209 will it take for the concentration to reach 350,000 material per millimeter.

In an hour, there are 60 minutes. Divide the number of minutes by 60 to convert it to hours. For instance, 120/60=2 means that 2 hours are equal to 120 minutes.

The millimeter, abbreviated mm in the International System of Units (SI), or millimeter, abbreviated mm in the American spelling, is a unit of length that is one thousandth of a metre long, the SI base unit of length. As a result, a metre is made up of 1000 millimeters.

We are going to use formula

y = a * e ^ (b * t)

a and b are constants and t is for time.

Initially there are 100,000 bacteria, so;

100000 = a * e ^ (b * 0)

100000 = a * 1

a = 100000

given condition is that the concentration doubles every 3 hours so

300000 = a * e ^ (b * 3)

As a equals to 100,000

e ^ (b * 3) = 3

b * 3 = ln 3

b = (ln 3) / 3

b = 0.3662

now we have to find value of the time when concentration of bacteria reaches to 350,000:

350000 = 100000 * (e ^ 0.3662 * t)

3.5 = e ^ 0.3662* t

ln 3.5 = 0.3662* t

t = 1.2527 / 0.3662

t = 3.4209

That is the required value of time

To learn more about unit conversion visit:

https://brainly.com/question/19420601

#SPJ4

6️⃣9️⃣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

y = -8x + 23

Step-by-step explanation:

8y=x-16

we need to turn this into slope-intercept form by dividing 8 on both sides

y = x/8 - 2

to make a line perpendicular from another, we must make sure the slope is the negative reciprocal of the original line.

Right now, it's the same as the original. To make it a negative reciprocal, switch the places of the denominator and numerator and flip the signs

-8x is the negative reciprocal of x/8

Does it go through (4,-9)? No.

To make sure it goes through 4,-9, we change it's y-intercept.

Plug in the coordinate given (4,-9) in the y = -8x + b ( we removed -2 since it's not the right answer.

y = -8x + b

(-9) = -8(4) + b

-9 = -32 + b

-9 +32= -32 + b +32

23 = b

plug in b and we get our answer

y = -8x + 23

The amount that Josephine will be paid is $644.30.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.

The amount she'll be paid will be:

= $560 + (10% × $843)

= $560 + $84.3

= $644.30

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

The measure of the interior angles of a polygon is determined by the formula ((n - 2)180)/n = interior angle

measure

Answer: 52.5°

Step-by-step explanation:

sin59 = 45/x

sin59(x) = 45

x = 45/sin59 = 52.5°

Answer:

I'm pretty sure it would be 3:00

Step-by-step explanation:

I could be wrong tho-

Answer:

x=102/25 y=9/5

Step-by-step explanation:

Answer:

[tex]117.8cm ^{2} [/tex]

Step-by-step explanation:

[tex]a = {r}^{2} \theta \: \div 2 \\ = 100 \times 135 \div 2 \\ = 117.8 \: {cm}^{2} [/tex]

It needs to be shown that <W = <H by the SAS congruent theorem

The question is added as an attachment

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

The SSS congruent theorem implies that the corresponding sides of the triangles in question and the angles between them are congruent

From the question, we can see that the following corresponding sides on the triangles have the same mark

W O and H O

AO and AO

This implies that these sides are congruent sides

For the triangle to be congruent by SAS, the following sides must also be congruent

Angle W must be congruent to Angle H

Hence, the additional info is <W = <H

Read more about congruent triangles at

brainly.com/question/1675117

#SPJ1

Complete question

To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that____

If each survey has a sample size of 70, a value which falls within the interval where 95% of the sample means occur is: C) 14.96.

In this scenario, the confidence interval at 95% can be represented by this mathematical expression p - E < p < p + E

Based on the parameters provided, we would determine both the lower limit and upper limit for the interval where 95% of the sample means occur as follows;

Lower limit = 15 - 1.88/√70

Lower limit = 15 - 0.23

Lower limit = 14.77

For the upper limit, we have:

Upper limit = 15 + 1.88/√70

Upper limit = 15 + 0.23

Upper limit = 15.23

For 95% of the sample means to occur, the confidence interval is given by;

Confidence interval = (14.77, 15.23)

Read more on confidence interval here: https://brainly.com/question/22391696

#SPJ1

The minimum sample size needed to guarantee a given margin of error increases , the correct option is (b) .

What is Margin Of Error ?

The term margin of error is defined as an estimate of a small sample that is drawn from a relatively large population data.

the margin of error is usually governed by the parameters such as the standard deviation , sample size and desired confidence level.

to find missing term in the given statement , let us consider the values ,

where σ ⇒ Standard deviation for population

and m as "Margin of error"  and Z as "Empirical value of Z-score" at a given confidence level .

So , minimum sample size for given confidence level is given by

⇒ (Z×σ)²/m²

from above formula we can conclude that minimum sample size is directly related to population's standard deviation.

Therefore, the minimum sample size required would "increase" with the increase in population "standard deviation" .

Learn more about Margin Of Error here

https://brainly.com/question/29982243

#SPJ4

The p-value associated with the null hypothesis = 0.05

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours

Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.

You have the Hypothesis that "students study less than 10 hours, on average, per week"

Symbolically:

H₀:μ≥10hours

H₁:μ<10hours

The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.

The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.

Therefore,

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

The p-value associated with the null hypothesis = 0.05

To learn more about Null Hypothesis visit :

brainly.com/question/16261813

#SPJ4

Answer:

Step-by-step explanation:

y = -2x + 8

perp.: 1/2

y + 5 = 1/2(x - 8)

y + 5 = 1/2x - 4

y = 1/2x - 9

Answer:

It is y = 3/5x - 19/5

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes. Thus, the slope is 3/5x. Plug in -2 as x and solve for the intercept. It ii -19/5.

The ordered pair that describes the location of Q' is (-3, -1)

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

Point Q = (3, -1)

This point can be represented as

(x, y) = (3, -1)

Also, from the question, we have the transformation to be:

Point Q is reflected over the y-axis

Mathematically, this can be expressed as

(x, y) = (-x, y)

So, we have the following representation

Point Q' = (-3, -1)

Hence, the image is (-3, -1)

Read more about transformation at

brainly.com/question/27224272

#SPJ1

Answer: Two dice

Step-by-step explanation:

For the two dice, there are 5 possible: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6)

So two dice, the probability is 5/36 = 30/216

For three dice, the number of favorable cases is 21

The probability is 21/216

So the two dice are more likely

The average rate of change for 3.5 ≤ x ≤ 4 is 2[f(4) - f(3.5)]

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

given:

Interval: 3.5 ≤ x ≤ 4

Now, For average rate

= [f(4) - f(3.5)]/(4 - 3.5)

= 2[f(4) - f(3.5)]

Learn more about Average rate of change here:

https://brainly.com/question/23715190

#SPJ1

Answer:

106

Step-by-step explanation:

A linear pair adds to 180

180 - 74 = 106

Part a: The significance of the piece-wise function is define.

Part b: r(t) be the total amount of snow in cubic ft. is calulated.

Part c: Total volume of the ice is not removed.

For the given question, the rate function is given as;

f(t) = { 0, 0 ≤ t < 6 ,

       125, 6 ≤ t < 7

       108, 7 ≤ 9  }

Part a: The significance of the piece-wise function is-

Part b: r(t) be the total amount of snow in cubic ft.

Part c: total ice accumulated is;

62.5 ft + 54 ft. = 116.5 cubic ft.

Total volume of the ice accumulated = 367.5 cubic ft.

Thus, no total volume of the ice is not removed.

To know more about the rate of change of volume, here

https://brainly.com/question/29504549

#SPJ1

Answer:

Step-by-step explanation:

(0, 2) (4, 0)

(0 - 2)/(4 - 0) = -2/4 = -1/2

y - 2 = -1/2(x - 0)

y - 2 = -1/2x + 0

y = -1/2x + 2

Answer:

1/9

Step-by-step explanation:

The y intercept of a line is when x = 0

y = 1/9

Answer:

y = 1/9

Step-by-step explanation:

y = -10x + 1/9

Substitute 0 for x

y = -10 x 0 +1/9

-10 x 0 = 0

y = 1/9

The probability that the student takes technology given that he is taking Math 8 is 0.075.

What is conditional probability?

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Here, we have

Given:

The probability that a student takes Technology and Math 8 is 0.012.

P(Technology and Math 8) = 0.012

The probability that a student takes Math 8 is 0.16.

P(Math 8) = 0.16

We have to find the probability that a student takes Technology given that the student is taking Math 8

we use conditional probability

P(Technology|Math 8) = P(Technology and Math 8)/P(Math 8)

P = 0.012/0.16

P = 0.075

Hence, the probability that the student takes technology given that he is taking Math 8 is 0.075.

To learn more about the conditional probability from the given link

https://brainly.com/question/10739997

#SPJ1

Min needs to gain 80 marks to raise her average to 75.

Average number is got from sum of all numbers divided by the number of values.

Average value is used to compare among different quantities of same terms.

given, Min receives an average score 70 from 5 math test.

let she needs to gain X in her 6th test to obtain an average of 75 from the total six test.

she gained average 70 from 5 test

if average is 75 then

75 = (X+ 70)/2

X=80

hence, in the 6th test she needs to gain 80 marks.

to learn more about average number visit:

https://brainly.com/question/29983550

#SPJ1

Answer:

A

Step-by-step explanation:

If Monica has $50 dollars to spend on the video arcade, and each game costs $0.25 then we can use an equation that looks something like this:

total = amount of money × cost of one game

50 × 0.25 = 200

Now look at the graphs.

The graph that best matches this equation is A.

Answer: 360 plants

Step-by-step explanation:

90% is equivalent to 0.90.
You multiply 0.90 and get your answer of 360.

The linear equation on the graph shown is:

y = (2/3)*x + 4

We can see that we have a linear equation on the graph, remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

On the graph, we can see that the line intercepts the y-axis at y = 4, then the y-intercept is b = 4

y = a*x + 4

To find the slope we can use another point on the line, for example, we can see that (-6, 0) is also on the line, replacing these values in the linear equation above we will get:

0 = a*-6 + 4

6a = 4

a = 4/6 = 2/3

Thus, the line is:

y = (2/3)*x + 4

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1