Solve system of equations.
1/3x-3 y=-4
x-9 y=-12

Answer: 7, 28, 112

Step-by-step explanation: The first three terms in the sequence can be found by using the formula an = 4an-1, starting with the initial value a1 = 7:

a2 = 4a1 = 4 * 7 = 28

a3 = 4a2 = 4 * 28 = 112

So, the first three terms in the sequence are 7, 28, 112.

Answer:

The simplified expression is given as

\(8x^2y^4(17x^2-2)\)

Step-by-step explanation:

step one:

Given the expression

\(x^2y^4(x^2 - 16) - 9y^4(x^4 - 16)\)

step two:

First, let us open the bracket we have

\(x^2y^4(x^2 - 16) - 9y^4(x^4 - 16)\\\\x^4y^4-16x^2y^4-9x^4y^4+144x^4y^4\\\\\)

step three:

collect like terms we have

\(x^4y^4-16x^2y^4-9x^4y^4+144x^4y^4\\\\x^4y^4-9x^4y^4+144x^4y^4-16x^2y^4\\\\-8x^4y^4+144x^4y^4-16x^2y^4\\\\136x^4y^4-16x^2y^4\\\\\\\)

step four:

we can now factor out \(8x^2y^4\)we have

\(8x^2y^4(17x^2-2)\)

The completed statement obtained using the proportional relationship between the recipes and the number of bags of snack mix made are presented as follows;'

A proportional relationship is one in which the output variable is a constant multiple of the input variable.

The possible recipe to make 6 bags of snacks obtained froma similar question is presented as follows;

3 cups of granola

1 cup of raisins

1.5 cup of almonds

0.5 cup of cranberries

0.75 cup of chocolate chips

The evaluation of the possible statements in the question that requires completion using proportional relationships of the recipe, are presented as follows;

1. To make 18 bags of snack mix, Sherry needs ___ cups of almonds

18 = 3 × 6

Therefore, the amount ingredients required to make 18 bags of the snack mix is 3 times the amount of ingredients in the recipe, which indicates;

The number of cups of almonds Sherry needs = 3 × 1.5 = 4.5

2. Sherry needs 6 cups of granola to make ___ bags of the snacks

The number of granola required for 6 bags = 3 cups

6 = 2 × 3

The number of bags of the snack mix 6 cups of granola can make is twice the number made by 3 cups, of granola or 2 × 6 = 12 bags of snack mix.

3. If Sherry uses 1 cup of cranberries, she will need to use ___ cups of resins

The number of cups of cranberries in the recipe = 0.5 cups

Number of cups of resins in the recipe = 1 cup of resin

Therefore, 1 cup of resin is required for 0.5 cups of cranberries

2 × 1 = 2 cups of resins will be required for 2 × 0.5 = 1 cup of cranberries

4. The recipe will make ___ bags of snack mix if Sherry  uses only 1 cup of granola

3 cups of granola are required for 6 bags of snack mix

Therefore; 3/3 = 1 cup of granola will be required for 6/3 = 2 bags of the snack mix

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\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.8\% of 25}}{\left( \cfrac{3.8}{100} \right)25}\implies \text{\LARGE 0.95}\)

Answer:

To find 3.8% of 25, we can convert the percentage to a decimal and then multiply it by 25:

3.8% = 0.038 (converting percentage to decimal)

0.038 x 25 = 0.95

Therefore, 3.8% of 25 is 0.95.

Answer:

the answers are (-80+28-56) and (4(-20+7y-14))

Step-by-step explanation:

Answer:

64 is the fourth term

Step-by-step explanation:

Note : -

First term : 2

Second term : 8

Third term : 4

Fourth term : 64

Fifth term : 256

Sixth term : 1024

The point P is (9, 2, 12).

To find the point P, we need to add the vector v = PQ to the given point 0.

Given that v = PQ has the components (7, 6, 9) and the point 0 has the components (2, -4, 3), we can calculate the coordinates of point P as follows:

P = 0 + v = (2 + 7, -4 + 6, 3 + 9) = (9, 2, 12)

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Answer:

400 tiles

Step-by-step explanation:

Calculate the area of each tile, in m^2:

30 cm = 0.30 m

(0.30 m)^2 = 9.0 x 10^-2 m^2

Divide this into the total area:

(36m^2)/(9.0 x 10^-2 m^2)= 400 tiles

====

Another approach is to note that 6m^2 could be envisioned as a square with sides of 6 m.  Calculate the tiles needed to stretch along one side:

6 m = 600 cm

600 cm/30 cm  = 20 tiles

It takes 20 tiles to cover one direction

It would also take 20 tiles for the other direction, so a mosaic of 20 by 20 tiles would cover the 36 m^2.

20 x 20 = 400 tiles

The table of values that represents exponential decay is (c)

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

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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The proportion of a normal distribution located in the tail beyond z = 1.00 is 0.1587.

The normal distribution is a continuous probability distribution, and the area under its curve is 1.0. The normal distribution is symmetric with respect to the mean, which is zero, and has a bell-shaped curve. The tails of the normal distribution approach the horizontal axis, but they never meet it. The curve is entirely above the horizontal axis, and its total area equals 1.The standard normal distribution's curve, which is a normal distribution with a mean of 0 and a standard deviation of 1, has a total area of 1.0. Half of the total area is located on each side of the mean. Half of the area of the standard normal distribution is located in the right-hand tail beyond z=0. The area of the standard normal distribution located in the left-hand tail beyond z=0 is also half. Half of the tail area of the standard normal distribution beyond z=1.00 is located in the right-hand tail beyond z=0. The left-hand tail area beyond z= -1.00 is also half of the total area beyond z= -1.00. Therefore, the proportion of a normal distribution located in the tail beyond z = 1.00 is 0.1587.

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Answer:

12/5 = 2.4 miles

2.4 x (15/16) = 2.25 miles.

2.25, or 9/4 miles

Answer:

28

Step-by-step explanation:

if he was 3 years old 10 years ago that would make him 13 and then add 15 so 13+15=28

Answer:

y = 3x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (4, 5) into the partial equation

5 = 12 + c ⇒ c = 5 - 12 = - 7

y = 3x - 7 ← equation of line

A company seeking to estimate the time required to produce 100 units of a product based on past production rates should utilize regression analysis. This statistical method is the most effective among the given choices because it focuses on identifying the relationship between variables, such as production rates and time, and uses this relationship to make predictions.

Regression analysis will enable the company to develop a model that quantifies the relationship between the production rates (independent variable) and the time taken to produce units (dependent variable). By analyzing historical data, the company can establish a mathematical equation to predict future production times based on the past performance.

Hypothesis testing and confidence intervals are less suited for this purpose, as they primarily focus on determining the significance of relationships or differences between groups rather than predicting future outcomes. Similarly, correlation analysis measures the strength of a relationship between variables but does not predict future values based on past data.

In summary, regression analysis is the most effective statistical method for a company to estimate the time required to produce 100 units of a product based on past production rates. This method enables the company to create a predictive model, which can help optimize production processes and enhance overall efficiency.

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The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

Given that,

We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.

We know that,

First we write the co-ordinates of the triangle in the given graph.

P is (-3,3)

Q is (2,1)

R is (-4,-2)

The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.

Midpoint Formula is

(x₁+x₂/2, y₁+y₂/2)

So,

The midpoint of the side PR is

(-3+(-4)/2, 3+(-2)/2)

(-3-4/2, 3-2/2)

(-7/2,1/2)

So, S point is (-3.5, 0.5)

The midpoint of the side QR is

(2+(-4)/2, 1+(-2)/2)

(2-4/2, 1-2/2)

(-2/2,-1/2)

So, T point is (-1, -0.5)

Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

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Answer:

Step-by-step explanation:

Five students reported the amount of time (in minutes) they spent studying for an AP Statistics test the night be the test.

Mean of time is:

Deviation >> Square of deviation:

Sum of squares:

Standard deviation:

The geometric mean for the above set of data given is: 1.1475 (Option B). See the explanation below.

The geometric mean can be defined as the average rate of return of a set of values obtained by multiplying the terms together.

Geometric mean is best suited for series with serial correlation, which is notably true for investment portfolios.

The formula for geometric mean is given as:

\(\left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}\)

Hence,

The geometric Mean =

1.0147506490423

\(\approx\) 1.1475


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Answer:

Step-by-step explanation:

1-3/5>4x+1/5-3x

2/5>4x+1/5-3x

2/5>x+1/5

1/5>x

Answer:

x<1/5

Step-by-step explanation:

(assuming you are solving for x)

1-3/5>4x+1/5-3x

move everything to the left side.

4x+1/5-3x-1+3/5<0

x+4/5-1<0

x-1/5<0

x<1/5

Answer:

false

Step-by-step explanation:

Answer:

5400

Step-by-step explanation:

10% of 6000 is 600 meaning you're left with 5400 to pay.

Answer:

It is 2 π r

Step-by-step explanation:

Hope this helps you!!!1

Answer:

  13 refrigerators and 7 pianos will NOT overload the truck

Step-by-step explanation:

For x refrigerators, their total weight is 300x.

For y pianos, their total weight is 525y.

The total weight of both of these together must not exceed 7600, so the inequality is ...

  300x +525y ≤ 7600

__

The point (x, y) = (13, 7) lies in the solution area. The truck will not be overloaded.

__

Check

  300(13) +525(7) = 7575 . . . this is less than 7600

Answer:

Step-by-step explanation:

Represent the number of refrigerators by r and that of pianos by p.

Then the total weight in the truck bed is calculated and we determine whether or not this total is less than the truck capacity.

Find the total weight of the load consisting of 13 refrigerators and 7 pianos.   The inequality given above becomes:

w(r, p) = (300 lb)r + (525 lb)p ≤ 7600 lb

w(13, 7) = (300 lb)13 + (525 lb)7 ≤ 7600 lb becomes:

w(13, 7) = 3900 lb + 3675 lb = 7575 lb

Since 7575 lb is just under the truck's capacity (7600 lb), the truck will not be overloaded.