The area of a rectangular garden is 7980m2 If the width of the garden is 84 what is its length?

The value of the model expression when simplified is (d)

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

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

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Answer:

31

Step-by-step explanation:

if the lenght is 10(×2), the width is 3 and the height is 4(×2). The sum of 20, 3,and 8 will be 31. That is the answer

Answer:

what is the question...

Step-by-step explanation:

The point-slope form equation y - 2 = -3/4(x - 6) has been plotted in the graph shown in the image attached below.

In Mathematics, the point-slope form simply refers to a standard equation which can only be used when the slope of a straight line and one of the points on this line are known.

Mathematically, the point-slope form of a straight line is represented by this equation:

y - y₁ = m(x - x₁)

Where:

The point-slope form equation is given as follows:

y - 2 = -3/4(x - 6)

From the information above, we can logically deduce the following parameters:

Point at y = 2.

Point at x = 6.

Slope, m = -3/4

For this exercise, you should input the x-value, y-value, and slope (m) into your point-slope form graph as shown in the image attached below.

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Answer: 60 square inches

Step-by-step explanation:

Answer:

66 square inches

Step-by-step explanation:

10 times 6 equals 60 and 60 plus 6 is 66. You add the six because that is the area of the triangle and you get 60 from multiplying 10 and 6 because that is the area of the rectangle.

f(x) = 4 * 3^x

To find the formula for the exponential function that passes through the points (0, 4) and (3, 108), we need to follow these steps:

Step 1: Write the general exponential function
The general exponential function is of the form f(x) = ab^x, where a and b are constants.

Step 2: Plug in the first point (0, 4)
Using the point (0, 4), substitute x=0 and y=4 into the equation and solve for a:
4 = a * b^0
Since any number raised to the power of 0 is 1, we have:
4 = a * 1
So, a = 4.

Step 3: Plug in the second point (3, 108) and solve for b
Now we have the function f(x) = 4 * b^x. Using the point (3, 108), substitute x=3 and y=108 into the equation and solve for b:
108 = 4 * b^3

Divide by 4:
27 = b^3

Now take the cube root of both sides:
b = 3

Step 4: Write the final formula
Now that we have found a and b, we can write the final formula for the exponential function that passes through the two points (0, 4) and (3, 108):
Therefore, f(x) = 4 * 3^x

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25463 grams radioactive kind of americium will be left after 2160 years.

We know that Half Life Formula will be,

\(N=I(\frac{1}{2})^{\frac{t}{T}}\)

where N is the quantity left after time 't'; 'T' is the half life of the substance and 'I' is the initial quantity of the substance.

Given that the initial quantity of the substance (I) = 814816 grams

Half life of the radioactive kind of americium is (T) = 432 years

The time elapsed (t) = 2160 years

Now we have to find the quantity left that is the value of N for the given values.

N = \(814816\times(\frac{1}{2})^{\frac{2160}{432}}=814816\times(\frac{1}{2})^5\) = 814816/32 = 25463 grams.

Hence 25463 grams radioactive kind of americium will be left after 2160 years.

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The quadratic equation 7 · x · (2 ·x + 5) = 0 have the points x₁ = 0 and x₂ = - 5 / 2 as its x-intercepts.

In this problem we must determine the the x-intecerpts of a quadratic equation, that is, the values of x such that A · x² + B · x + C = 0. This question can be resolved by means of algebra properties. First, write the quadratic equation:

7 · x · (2 ·x + 5) = 0

Second, expand the expression and simplify until standard form is found:

7 · x · (2 ·x + 5) = 0

14 · x² + 35 · x = 0

Third, complete the square:

x² + (35 / 14) · x + 25 / 16 = 25 / 16

(x + 35 / 28)² = 25 / 16

Fourth, clear the variable x:

x + 35 / 28 = ± 5 / 4

x = - 35 / 28 ± 5 / 4

x = - 5 / 4 ± 5 / 4

The points x₁ = 0 and x₂ = - 5 / 2 are the x-intercepts of the quadratic equation 7 · x · (2 ·x + 5) = 0.

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The time William would arrive in town B IS 1 : 47 pm.

The first step is to determine the distance and the time of Dennis's travel.

Time = 14 hours (2 pm + 12) - 10 hours = 4 hours

Distance = time x average speed

4 x 52 = 208 miles

The second step is to determine the time of William's travel:

Distance / average speed = time

208 / 40 = 5.20 = 5 hours 12 minutes

Time William left for the trip = 10 am - 1 hour 25 minutes = 8 :35am

Time he would reach town B = 8 : 35am + 5 hours 12 minutes = 13 hours 47 minutes = 1 : 47 pm

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The more coins that are tossed for both gamblers, the less advantageous Gambler A is. But when a few coins are tossed, Gambler A will continue to hold a significant edge.

The binomial distribution;

In probability theory and statistics, the binomial distribution with parameters n and p is used to describe the discrete probability distribution of the number of successes in a set of n independent experiments.

Let X be the number of wins in the first n flips by A, Y be the signal that the last flip by A also wins, and Z be the number of wins in the n flips by B.

As Y is unrelated to X and Z, the following follows:

P(X + Y > Z) = P(Y = 1) P(X ≥ Z) + P(Y = 0) P(X > Z)

= 1/2(P(X = Z) + 2P(X > Z))

P(X > Z) = P(Z > X)

Here,

The less favorable Gambler A is, the more coins are tossed for both players. However, Gambler A will continue to have a sizable advantage even after a few coins are tossed.

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A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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The correct answer is the Additive rate of change.

We have given that,

A data set contains an independent and a dependent variable.

Let x be the independent variable and y be the dependent variable.

To write the  relationship we will have :

y = kx + c

Where k and c are constants.

In the case of a line, the constant k is the gradient.

A multiplicative change is a log form and it is given by :

Y = Ck^x

The relationship is not linear but exponential.

The correct answer is the Additive rate of change.

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Answer:

x - 1 < n < 3x + 5

Step-by-step explanation:

If you have two sides of a triangle, the length of the third side is at least the difference between the other two sides, and at most the sum of the other two sides.

Answer:

The equation of the circle is (x-2)^2+(y-1)^2=13

Step-by-step explanation:

a. False. The sample is 46%. We are 95% that the proportion of the population is between 43% and 49%.

b. True, this is the correct interpretation of a confidence interval of proportions.

c. False. The confidence interval does not say anything about the proportion of samples, just about the population.

d. False. As the confidence level decreases, so does z, which means that the margin of error decreases.

In a sample with a number n of people surveyed with a probability of success of, and a confidence level of, we have the following confidence interval of proportions.

In which

z is the score that has a p-value of.

The margin of error is:

So the confidence interval can be written as:

Interpreting a confidence interval:

x% confidence interval between (a,b) means that we are 95% sure that the true proportion of the population is between a and b.

In this problem, we have that:

95% confidence interval between (43%, 49%).

a. We are 95% confident that between 43% and 49% of Americans in this sample support the decision of the U.S. Supreme Court on the 2010 healthcare law.

False. The sample is 46%. We are 95% that the proportion of the population is between 43% and 49%.

b. We are 95% confident that between 43% and 49% of Americans support the decision of the U.S. Supreme Court on the 2010 healthcare law.

True, this is the correct interpretation of a confidence interval of proportions.

c. If we considered many random samples of 1,012 Americans, and we calculated the sample proportions of those who support the decision of the U.S. Supreme Court, 95% of those sample proportions will be between 43% and 49%.

False. The confidence interval does not say anything about the proportion of samples, just about the population.

d. The margin of error at a 90% confidence level would be higher than 3%.

False

As the confidence level decreases, so does z, which means that the margin of error decreases.

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Answer:

x=10

Step-by-step explanation:

If we subtract 2 from 52 we get 50 and ten mutiplys into 50.

The result of the expression is 60.

The given expression can be solved by applying the principle of BODMAS.

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression.

This indicates that numerous operator expressions must only be spelled out in this order, from left to right. We begin by resolving the brackets, then move on to powers or roots, division or multiplication (depending on which comes first from the left side of the expression), and lastly subtraction or addition (depending on which comes on the left side).

Given, 50+20/10*5 = 50+2*5=50+10=60

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Answer:

phones = $9

accessories = $2

explanation:

x=phones

y=accessories

18x+21y=204

6x+14y=82

The Ratios are equivalent to 2:3 ,Therefore, the correct answer is:

6 to 9 ,8 to 12,4/6

The ratios are equivalent to 2:3, we need to simplify each ratio and check if it equals 2:3.

Let's simplify each ratio:

12 to 36: Divide both numbers by their greatest common divisor (GCD), which is 12.

Simplified ratio: 1 to 3

6 to 9: Divide both numbers by their GCD, which is 3.

Simplified ratio: 2 to 3

10/18: Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2.

Simplified ratio: 5/9

8 to 12: Divide both numbers by their GCD, which is 4.

Simplified ratio: 2 to 3

16 to 20: Divide both numbers by their GCD, which is 4.

Simplified ratio: 4 to 5

4/6: Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2.

Simplified ratio: 2/3

From the simplified ratios, we can see that 6 to 9, 8 to 12, and 4/6 are all equivalent to 2:3. Therefore, the correct answer is:

6 to 9

8 to 12

4/6

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Answer:

d)

Step-by-step explanation:

turn 9x + y = 8 to slope intercept form

9x + y = 8

-9x         -9x

y = -9x + 8

m = -9

y intercept = 8

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-XxDeathshotxX

The angle between sides GM and MT is ∠M.

The 2 sides that include ∠T are MT and GT.

The angle between sides GT and MG is ∠G.

There's not much to say about this, but I can answer questions if you have any.

Hello there!

When we are given the graph of a line and two points on the graph, we can calculate the slope of the line using Rise/Run.

Rise=How many units we move up (here, the rise is 3)

Run=How many units we move left or right (Here, the run is 5)

So the slope of this line is \(\frac{3}{5}\)

Hope this helps you!

~Just a joyful teen

\(SilentNature(GraceRosalia)\)

Answer:

Step-by-step explanation:

Set up a ratio.

3 bags/1 day = 2/3 bag/x day

Cross multiply to solve.

3x=2/3

So x=2/3(1/3)=2/9 of a day

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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After matching each set of values of a function to the pair of points that satisfy the function, we get

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Given the set of data

(4,3) and (6.7) rate of change = 2, and initial value = -5

k= 7-3/6-4 = 2, y=2x-5

(2,10) and (5, 19) rate of change=3, and initial value = 4

k= 19-10/5-2 = 9/3 = 3, y=3x+4

(2,5) and (5.2)→ rate of change = -1, and initial value = 7.

k= 2-5/5-2 =  -3/3 = -1, y= -x+7

(2.4) and (4,3) →→ rate of change = -0.5, and initial value =5

k= 3-4/4-2 = -1/2 =-0.5, y=-0.5x+5

A function has two sets of values: the set of input values and the set of output values. The set of input values makes up the function's domain. The set of output values makes up the function's range.

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Drag the tiles to the correct boxes to complete the pairs. Match each set of values of a function to the pair of points that satisfy the function. rate of change = -1, and initial value = 7 rate of change = 2, and initial value = -5 rate of change = -0.5, and initial value = 5 rate of change = 3, and initial value = 4 (4, 3) and (6, 7) arrowRight (2, 10) and (5, 19) arrowRight (2, 5) and (5, 2) arrowRight (2, 4) and (4, 3) arrowRight

If a storage facility charges $1 per cubic yard and the storage space is 32 ft. The storage charge is $1999.97.

What is mathematical conversions?

Mathematical conversions refer to the process of changing one unit of measurement to another unit of measurement that is equivalent in value.

First, we need to convert the dimensions from feet to yards, since the rate is given per cubic yard.

32 feet = 10.6667 yards (dividing by 3)

160 feet = 53.3333 yards (dividing by 3)

10 feet = 3.3333 yards (dividing by 3)

Next, we can calculate the volume of the storage space in cubic yards by multiplying the three dimensions:

Volume = 10.6667 yards x 53.3333 yards x 3.3333 yards

Volume = 1999.97 cubic yards (rounded to two decimal places)

Finally, we can calculate the storage charge by multiplying the volume by the rate:

Charge = 1999.97 cubic yards x $1/cubic yard

Charge = $1999.97

Therefore, the storage charge is $1999.97.

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Answer:

The correct option is;

c.

Step-by-step explanation:

The given translation given is that of a reflection across a line ST

Whereby we take the line ST to represent the x-axis, then a reflection across ST will be of the form;

Coordinates of point of primage before reflection = (x, y)

Coordinates of point of image after reflection = (x, -y)

Therefore, the coordinates of the point of the reflected image of U will be the same as the coordinate of the point J and the image of U coincides with the point J

Therefore, the image of U and J are the same distance along the same ray from the T.

When a triangle is reflected, it must be reflected across a line.

The true statement about the reflection is (b) the image of U and J are the same distance along the same ray from T

From the question, we understand that:

Triangle STU is reflected across line ST

This means that, triangle STU will be flipped over line ST, such that point U and point J will coincide

This is so because, the distance from point J to line ST is the same as the distance from point U to line ST

Hence, the valid reason is (b)

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Answer:

6. x° is approximately 21.04°

7. x° is approximately 39.56°

8. x° is approximately 58.03°

9. x° is approximately 72.85°

Step-by-step explanation:

6. In the given right triangle (a triangle with the measure of one of the interior angles equal to 90°, indicated by the small square between two sides) , we have;

The hypotenuse side length = 15

The adjacent side to the given reference angle, x° = 14

By trigonometric ratio, we have;

\(cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}\)

\(\therefore cos(x^{\circ}) = \dfrac{14}{15}\)

To find the value of x°, we make use of the inverse cosine function, arccos found on a scientific calculator, as follows;

x° = arccos(14/15) ≈ 21.04°

x° ≈ 21.04°

7. In the given right triangle, we have;

The length of the opposite side to the given reference angle, x° = 19

The length of the adjacent side to the given reference angle, x° = 23

By trigonometric ratios, we have;

\(Tan(\angle X) = \dfrac{Opposite \, side \ length}{Adjacent\, side \ length}\)

\(\therefore tan(x^{\circ}) = \dfrac{19}{23}\)

Therefore;

x° = arctan(19/23) ≈ 39.56°

x° ≈ 39.56°

8. In the given right triangle, the adjacent side to the reference angle, x° and the hypotenuse side are given, therefore, we have;

x° = arccos(9/17) ≈ 58.03°

x° ≈ 58.03°

9. The opposite side to the reference angle and the hypotenuse side are given

By trigonometric ratio, we have;

\(sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}\)

\(\therefore sin(x^{\circ}) = \dfrac{43}{45}\)

x° = arcsin(43/45) ≈ 72.85°

x° ≈ 72.85°.

Answer:

Y = 10/7X + 4

Y intercept = 4

Slope = 10/7

X intercept = -40/7

Step-by-step explanation:

Incase you are asked the equation of the line

The slope intercept equation is as follows -

(1)....Y = mx + b

where m - Slope

b - Y - intercept

the standard formula of slope which is commonly referred to as "the rate of change" is -

(2) .....m= Y2 - Y1 / X2 - X1

in this case you can refer to the final and initial X and Y values directly from the small points on the line.

and so(3)..... - X1 = -6 X2 = 6

- Y2 = 9 Y1 = -1

the y intercept is defined as the value we get whenever X id zero. and X has a value of zero when a line crosses the y axis.

thus, X = 0 & Y = 4 ( 0 , 4 )

now lets substitute our values(3) into the slope formula (equation 2)

m = 9 - - 1 / 6 - - 1 = 10/7

now that we found the line's slope, let's simply plug the y intercept

into the slope intercept formula (1)

Y = 10/7X + 4