Mateo's old bedroom was a square with integer dimensions. His new bedroom is 3 feet wider and 2 feet deeper. The increase in area is 46 square feet. What were the dimensions of Mateo's old bedroom?

The surface area of a triangular prism can be found by adding the areas of all the faces. To do this, we need to identify the faces of the triangular prism.

A triangular prism has three rectangular faces and two triangular faces. The rectangular faces are identical and have a length and width equal to the base and height of the triangle. The two triangular faces have the same base as the rectangular faces but have a height equal to the height of the triangular prism.

To find the surface area, we can use the formula:

Surface area = (2 × area of the base) + (perimeter of the base × height)

Where the area of the base is equal to the area of the triangle, which can be found using the formula:

Area of a triangle = (base × height) ÷ 2

Therefore, the formula for the surface area of a triangular prism is:

Surface area = 2 × [(base × height) ÷ 2] + (perimeter of the base × height)

Simplifying this equation, we get:

Surface area = base × height + (perimeter of the base × height)

So, to find the surface area of a triangular prism, we need to know the base and height of the triangle and the height of the prism. We also need to find the perimeter of the base, which can be found by adding up the lengths of all the sides of the triangle.

Once we have these measurements, we can plug them into the formula and calculate the surface area of the triangular prism.

Step-by-step explanation:

Sure! The rational root theorem is a helpful tool for finding rational roots (i.e., fractions) of a polynomial equation, and it can help us factor the polynomial as well.

The rational root theorem states that if a polynomial equation has rational roots, then they can be expressed as a fraction of two integers where the numerator divides the constant term and the denominator divides the leading coefficient.

In this case, the constant term is -18 and the leading coefficient is 2, so the possible rational roots are of the form:

±1, ±2, ±3, ±6, ±9, ±18 / ±1, ±2

We can test these values by plugging them into the equation and seeing if they result in a zero. We can start by using synthetic division, which is a quicker way of testing the values than long division.

Here are the steps for synthetic division using x = 1 as an example:

1 | 2 2 -18 -18

2 4 -14

2 4 -14 -32

The remainder is not zero, so x = 1 is not a root. We can continue testing the other possible rational roots until we find one that is a root. After testing all the possible rational roots, we find that x = -3 is a root. We can verify this by performing the synthetic division:

-3 | 2 2 -18 -18

| -12 30 -12

|--------------

| 2 -10 12 -30

We see that the remainder is zero, so x = -3 is a root. Using this root, we can factor the polynomial as:

2x^3 + 2x^2 - 18x -18 = (x + 3)(2x^2 - 8x + 6)

We can then factor the quadratic expression using either factoring or the quadratic formula:

2x^2 - 8x + 6 = 2(x^2 - 4x + 3) = 2(x - 1)(x - 3)

Therefore, the factored form of the polynomial is:

2x^3 + 2x^2 - 18x -18 = (x + 3)(x - 1)(x - 3)

I hope this explanation helps!

Jules' scatter plot will help her to visualize the relationship between the number of years of education and the annual income of the respondents.

A scatter plot is a graph that consists of points plotted in two dimensions in which the position of each point is determined by the value of two variables. In Jules' case, the two variables are the number of years of education and the annual income of each respondent. The plot allows her to visualize the relationship between the two variables.

To plot the points, Jules would have to calculate the coordinates for each respondent. For example, if a respondent said that they have 12 years of education and an annual income of $60,000, Jules would calculate the coordinates for this point as (12, 60000). She would then plot the point at (12, 60000) on the graph. She would repeat this process for each respondent in the survey.

The scatter plot will show Jules how the number of years of education is related to the annual income. She will be able to see if there is a correlation between the two variables, and if there is a pattern of how the two variables are related. This will allow her to make conclusions about the relationship between the two variables.

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2.95 miles

The question involves radio direction finders placed at two points, A and B, which are 4.32 miles apart on an east-west line. The transmitter has bearings 10.1 degrees from A and 310.1 degrees from B. The task is to determine the distance from A.In order to determine the distance from A, the first step is to construct a diagram of the scenario to visualize the placement of the three points, A, B, and the transmitter. To do so, a coordinate system is used, with A being located at the origin (0,0).The bearing of the transmitter from A is 10.1 degrees, which can be plotted on the diagram as a straight line from the origin to an angle of 10.1 degrees to the east. Similarly, the bearing of the transmitter from B is 310.1 degrees, which can be plotted on the diagram as a straight line from point B to an angle of 49.9 degrees to the west.To determine the distance from A, the Law of Cosines can be applied, which states that c^2 = a^2 + b^2 − 2ab cos(C), where c is the unknown side, a and b are the known sides, and C is the angle opposite the unknown side. In this case, c is the distance from A, a is the distance from B, and b is the distance between A and B. The angle C is equal to the sum of the two bearings (10.1 + 49.9 = 60 degrees).Therefore, c^2 = a^2 + b^2 − 2ab cos(C) can be rewritten as:dA^2 = d^2 + 4.32^2 - 2d(4.32)cos(60)dA^2 = d^2 + 4.32^2 - 2d(4.32)(1/2)dA^2 = d^2 + 4.32^2 - 2.16dTo solve for dA, the equation can be rearranged and solved for d:0 = d^2 - 2.16d + dA^2 - 4.32^2d = 1.08 ± sqrt(1.08^2 - dA^2 + 4.32^2)The positive root of this equation can be used to determine dA:dA = 1.08 + sqrt(1.08^2 - d^2 + 4.32^2)dA = 1.08 + sqrt(1.08^2 - 4.32^2 cos^2(10.1))dA ≈ 2.95 milesTherefore, the distance from A is approximately 2.95 miles.

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A man with a bachelor's degree earns 34% more annually than a woman with a bachelor's degree. Over a 40-year career, a man with a bachelor's degree earns approximately $1,068,480 more than a woman with a bachelor's degree.

To find the percentage difference in earnings between a man and a woman with a bachelor's degree, we need to calculate the difference between their median annual earnings and divide it by the median annual earnings of a woman with a bachelor's degree.

Percentage difference = ((median annual earnings of a man with a bachelor's degree - median annual earnings of a woman with a bachelor's degree) / median annual earnings of a woman with a bachelor's degree)) x 100

= ((66,612 - 49,314) / 49,314) x 100

= 34%

Therefore, a man with a bachelor's degree earns 34% more annually than a woman with a bachelor's degree.

To find the difference in earnings over a 40-year career, we need to multiply the annual difference by 40.

Difference in earnings over 40 years = (66,612 - 49,314) x 40

= $657,480

Therefore, a man with a bachelor's degree earns approximately $657,480 more than a woman with a bachelor's degree over a 40-year career.

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The equatiοn that represents the area = 5.5x + 11. Optiοn C is the cοrrect οptiοn.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.

Given that the width οf tulips and lilies in a field 5. 5 meters.

The length οf the field οf tulips is 2 meters.

The length οf the field οf lilies is x meters.

The tοtal length οf the field is (x+2) meters.

The area οf a rectangle is the prοduct οf length and width.

The area οf the field is 5.5(x+2) square meters

The distributive prοperty:

Accοrding tο the distributive prοperty, it is mandatοry tο multiply each οf the twο numbers by the factοr befοre adding them tοgether when a factοr is multiplied by the sum οr additiοn οf twο terms. A (B+ C) = AB + AC is a symbοlic representatiοn οf this prοperty.

Apply the distributive prοperty:

= (5.5 × x) + (5.5×2)

= 5.5x + 11

The equatiοn is Area = 5.5x + 11

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Answer:

3

Step-by-step explanation:

To find the absolute deviation, we need to find the difference between each data point and the mean of the data set, take the absolute value of each difference, and then calculate the average of those absolute differences.

First, let's find the mean of the data set:

(10 + 2 + 6 + 12 + 6 + 10 + 4 + 12) / 8 = 8

The mean is 8.

Next, we find the difference between each data point and the mean:

|10 - 8| = 2

|2 - 8| = 6

|6 - 8| = 2

|12 - 8| = 4

|6 - 8| = 2

|10 - 8| = 2

|4 - 8| = 4

|12 - 8| = 4

Now we take the average of those absolute differences:

(2 + 6 + 2 + 4 + 2 + 2 + 4 + 4) / 8 = 3

The absolute deviation of the data set is 3.

According to the question the Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.

Coconut is a tropical fruit that grows on palm trees. It is a large, egg-shaped drupe with a hard outer shell and a white fleshy inner layer. The flesh of the coconut is rich in vitamins, minerals, and fiber, and it is also a source of healthy fats. Coconut can be eaten fresh, dried, or even in the form of coconut milk or oil.

First, we will calculate the total number of fruits Kate had at her stall. To do this, we need to solve for x in the equation [tex]$\frac{3}{4}x + \frac{1}{3}(\frac{3}{4}x - x) + (\frac{3}{4}x - \frac{1}{3}(\frac{3}{4}x - x)) = x$.[/tex]
Solving for x, we get [tex]$x = \frac{8}{7}$.[/tex]
Therefore, Kate had [tex]$\frac{8}{7}$[/tex]fruits at her stall.
Next, we need to calculate the number of coconuts she had at first. We know that she sold 1/4 of the fruits, or [tex]$\frac{2}{7}$[/tex] of the fruits. We also know that the ratio of mangosteens sold to apples sold to coconuts sold was 3:5:3.
Therefore, the number of coconuts sold was [tex]$\frac{2}{7} \times \frac{3}{13} = \frac{6}{91}$[/tex].
The total amount earned from the coconuts sold was [tex]$\frac{6}{91} \times 4.50 = \frac{27}{91}$[/tex].
Subtracting this from the total amount earned, 198, we get [tex]$198 - \frac{27}{91} = \frac{171}{91}$[/tex].
This is the amount earned from the mangosteens and apples sold. The amount earned from each mangosteen sold was 1.50, and the amount earned from each Fuji apple sold was 3.00.
Therefore, to get the total amount earned from mangosteens and apples, we need to solve for x in the equation [tex]$\frac{2}{7} \times x + \frac{2}{7} \times 3x = \frac{171}{91}$[/tex].
Solving for x, we get [tex]$x = \frac{171}{171}$[/tex].
This means that the total number of mangosteens and apples sold was $\frac{171}{171}$. Since the ratio of mangosteens sold to apples sold was 3:5, the number of mangosteens sold was [tex]$\frac{3}{8}$[/tex] and the number of apples sold was $\frac{5}{8}$.
Therefore, the number of coconuts at first was [tex]$\frac{8}{7} - \frac{3}{8} - \frac{5}{8} = \frac{4}{7}$[/tex].
Therefore, Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.

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68% of buyers paid between $21,000 and $23,000 for the car.The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution

The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution. The rule states that 68% of observations fall within one standard deviation of the mean, 95% of observations fall within two standard deviations of the mean, and 99.7% of observations fall within three standard deviations of the mean. In this case, the mean price paid is $23,000 and the standard deviation is $2000. Therefore, the range of prices between $21,000 and $23,000 is one standard deviation from the mean, and 68% of buyers paid between $21,000 and $23,000.Mathematically, this can be expressed as P(21,000<X<23,000) = P(μ- σ < X < μ + σ) = 0.68, where μ is the mean and σ is the standard deviation. By substituting the given values of μ and σ, this equation simplifies to P(21,000<X<23,000) = P(23,000 - 2000 < X < 23,000 + 2000) = 0.68. Therefore,68% of buyers paid between $21,000 and $23,000 for the car.

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Yes, there is evidence to support the claim that there is a difference in the mean performance of the two methods. To test this, we can perform a two-sample t-test. The p-value for the test is 0.034. This means that there is a 3.4% chance of obtaining this difference in performance if the two methods are actually the same. Since this is lower than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference in the mean performance of the two methods.

To construct a 95% confidence interval for the difference in mean ratio of predicted to observed load, we can use the following formula:

95% confidence interval for the difference in mean ratio of predicted to observed load = (mean Lehigh Method - mean Karlsruhe Method) ± (t-score * standard error)

Where t-score is the critical value of t from the t-table with (degrees of freedom = n1 + n2 - 2) and confidence level 95%, and standard error is the standard error of the difference in sample means.

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The number of fruits that Mrs Ong bought is 40.

The fraction of the fruits that are pears are 1/4.

The expression that represents the number of oranges is: 1/2f - 3

Where f is the number of fruits

The expression that represents the number of pears is: (1/2 x 1/2)f - 2

1/4f - 2

The expression that represents the number of apples is: 1/2[1 - (1/2 + 1/4)]f - 1

1/8f - 1

Fraction of mangoes remaining = 1 - (1/4 + 1/2 + 1/8)

1 - 7/8 = 1/8

Number of fruits bought altogether = 1/8f = 5

f = 5 x 8 = 40

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In this scenario, the two variables being considered are time and parking fee. Time represents the amount of time Alayna parks her car, while the parking fee represents the cost incurred for parking her car for that duration.

The independent variable in this case is time, as it is the variable being manipulated or changed by Alayna, and the dependent variable is the parking fee, as it is dependent on the amount of time Alayna parks her car.

To create a graph for this data, the time should be plotted on the x-axis (horizontal axis) and the parking fee should be plotted on the y-axis (vertical axis). This is because time is the input variable, and parking fee is the output variable, meaning that it is determined by the time value.

In conclusion, time is the independent variable and should be placed on the x-axis, while parking fee is the dependent variable and should be placed on the y-axis to create a graph that illustrates the relationship between these two variables.

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The value of unknown c in the given triangle is 16.57 cm.

The right-angled triangle's three sides are related according to Pythagoras' theorem, sometimes referred to as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a right-angled triangle equals the sum of the squares of the other two sides. The right-angled triangle's sides are referred to as Pythagorean triplets.

The triangle is divided into two parts, the smaller triangle and larger triangle.

Using the Pythagoras Theorem for the larger triangle we have:

c² = a² + b²

(24.9)² = (15.6)² + b²

b = 19.40

Now, the value of the base of the smaller triangle is:

base = 19.40 - 13.80

base = 5.6

Applying Pythagoras Theorem:

c² = (15.6)² + (5.6)²

c = 16.57 cm

Hence, the value of unknown c in the given triangle is 16.57 cm.

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a.) Jill has 6 pence less than jack, therefore Jill has x-6 pences.

b.) If one box weighs 60grams, b number of boxes will weigh 60*b grams.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The fact that the set of solutions to such an equation forms a straight line in the plane is where the word "linear" originates.

The three forms of linear equations are

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If Jack has x pence, then Jill has 6 pence less than Jack, which means Jill has (x - 6) pence.

Therefore, in terms of x, the number of pence that Jill has is (x - 6).

If one box weighs 60 stams, then the weight of b boxes can be expressed as:

Weight of b boxes =[tex] 60 × b[/tex]

Therefore, in terms of b, the weight of b boxes is 60b stams.

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Hence, in answering the stated question, we may say that We can travel slope intercept down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

The intersection point in mathematics is the point on the y-axis where the slope of the line intersects. a point on a line or curve where the y-axis intersects. The equation for the straight line is Y = mx+c, where m represents the slope and c represents the y-intercept. The intercept form of the equation emphasises the line's slope (m) and y-intercept (b). The slope of an equation with the intercept form (y=mx+b) is m, and the y-intercept is b. Several equations can be reformulated to seem to be slope intercepts. When y=x is represented as y=1x+0, the slope and y-intercept are both set to 1.

We must solve for y in order to find the slope-intercept form of the equation:

6x + 2y = 4

2y = -6x + 4

y = -3x + 2

As a result, the slope is -3 and the y-intercept is 2.

To graph the line, first plot the y-intercept at the point (0, 2). The slope can then be used to find another point on the line. We can travel down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

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After 20 years, the wetland will have decreased in area by 20/5 = 4 times.

If the area has decreased by a sixth every 5 years, it will decrease by 4/6 = 2/3 after 20 years.

Therefore, the percent of the total area that disappears after 20 years is 2/3 = 66.67%.

Rounding to two decimal places, the answer is 66.67%.

Answer: Can you please show a pic to help me figure it out

Step-by-step explanation:

Answer: Let the probability that hunter P hits the target be denoted by "p", and the probability that hunter Q hits the target be denoted by "q".

(a) The probability that they both miss the target is given by:

(1-p)*(1-q)

(b) If the target is hit, then there are three possible outcomes:

(i) Only hunter P hits it: The probability of this event is given by:

p*(1-q)

(ii) Only hunter Q hits it: The probability of this event is given by:

(1-p)*q

(iii) Both hunters hit the target: The probability of this event is given by:

p*q

Note that the sum of the probabilities in (i), (ii), and (iii) is equal to 1, since one of these three events must occur if the target is hit.

Brainliest is so much appreciated. (:

The value of the missing angles of the diagram are:

1) ∠ADC = 134°

2) ∠AEB = 84°

∠EBC = 92°

1) We are told that ABD is an Isosceles Triangle. Thus:

If ∠BAD = 32°, then we know that the two base angles are equal and as such if the sum of the angles of a triangle is 180 degrees, then we have:

∠ABD ≅ ∠ADB = (180 - 32)/2

= 74°

All equilateral triangles have each of their interior angles as 60°. Thus:

∠ADC = 74 + 60

= 134°

2) The two base angles of an Isosceles triangle are equal and as such:

∠BAE = ∠ABE = 48°

∠AEB = 180 - 2(48)

= 84°

By the concept of Alternate angles, we know that:

∠DEA = ∠BAE = 48°

Sum of angles on a straight line is 180 degrees. Thus:

∠BEC = 180 - (84 + 48)

∠BEC = 48°

∠EBC = 180 - (40 + 48) = 92°

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Jake had $1200 of money initially, and he gave $200 to his mother.

What is Algebraic expression ?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

Let's assume that Jake had M dollars of money initially.

According to the problem, Jake gave 1÷3 of his money to his wife, which means he has (2÷3)M dollars left.

Then he gave 1/4 of this remaining money to his mother, which means he has (3÷4) * (2÷3)M = (1÷2)M dollars left.

Since we are given that Jake had $600 left after giving the money to his wife and mother, we can set up the following equation:

(1÷2)M = 600

Solving for M, we get:

M = 2 * 600 = 1200

Therefore, Jake had $1200 of money initially, and he gave (1÷4) * (2÷3)M = (1÷4) * (2÷3) * 1200 = $200 to his mother.

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Answer:

4c) the answer is :-3y=-6

divide by -3 and your ans is y=2

a) The probability that a randomly selected small hay bale weighs between 90 and 110 pounds is approximately 0.9044.

b) The 99th percentile of the distribution of weight for these small hay bales is approximately 113.96 pounds.

(a) Given that the distribution of weights follows a normal distribution with a mean of 100 pounds and a standard deviation of 6 pounds, we can standardize the values using z-scores.

The z-score formula is given by:

z = (x - μ) / σ

For 90 pounds:

z₁ = (90 - 100) / 6 = -1.6667

For 110 pounds:

z₂ = (110 - 100) / 6 = 1.6667

Using a standard normal distribution table, we can find the cumulative probability associated with z₁ and z₂:

P(90 ≤ X ≤ 110) = P(-1.6667 ≤ Z ≤ 1.6667) ≈ 0.9044

(b)

Using a standard normal distribution table, we can find the z-score associated with a cumulative probability of 0.99:

z = 2.3263

Now, we can use the z-score formula to find the corresponding value, x:

x = μ + z × σ

x = 100 + 2.3263 × 6

x ≈ 113.96

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Answer:330%

Step-by-step explanation:

20-------100%

66-------x%

x=100*66/20=330%

Answer:

A. 6cm B. 10cm

Step-by-step explanation:

The rectangle

Lenght = 18cm and width = 2cm

Area = l x w

Area = 18 x 2 = 36

Ifna square has area of 36cm², all sides are equal

X² = 36

X = square root of 36

X = 6cm

If a square as a Perimeter as the rectangle

Perimeter = 18 +18+ 2+2 =40cm

If Perimeter of square is 40cm and all 4 sides are equal

X =40/ 4

X= 10cm

When the triangle ABC is similar to triangle DEF see in above figure. The measure of side length DE, is equals to the 53.1 .

Similar triangles are the triangles that looks similar to each other but their sizes may or may not be exactly the same. Two triangles will be similar if the angles are equal (corresponding angles) and sides are in the same ratio (corresponding sides). We have, triangle ABC and triangle DEF. From the above figure, in ∆ABC,

length of side BC = 8

length of side AB = 13.7

In ∆DEF, length of side, EF = 31

We have to measure the length of side DE. Now, it is specific that triangle ABC is similar to triangle DEF. Using the definition of similar triangles, ratio of corresponding sides of ∆ABC and ∆DEF are in the same ratio. That is, BC/EF = AB/DE

=> 8/31 = 13.7/DE

Cross multiplication

=> DE × 8 = 31× 13.7

=> DE = 31×13.7/8

=> DE = 53.0875

Hence, required rounded side length,DE is 53.1..

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Complete question:

Triangle ABC is similar to Triangle DEF ( see the above figure). Find the measure of side DE. Round Your answer to the nearest tenth if necessary.

Answer:

Below

Step-by-step explanation:

Correct price would be   $24  +    .25 * 24    = $30

 the manage posted the markup as the selling price ( 25% of 24 = $ 6)

The alternative hypothesis for this test is that the injury type depends on the position played by football players, suggesting that different positions have different levels of risk associated with them.

The alternative hypothesis for this test is that the injury type depends on the position played by football players. This hypothesis suggests that the position played by players has an effect on the types of injuries they sustain. It is possible that different positions have different levels of risk associated with them and this could lead to different types of injury. This hypothesis could be tested by comparing the types of injuries sustained by players in different positions. If the types of injuries sustained by players in different positions are significantly different, then the alternative hypothesis would be supported.

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On this map, City C and City D are 2.1 feet apart. There are 700 kilometers between city C and city D.

A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplying, division, exponents, and so forth.

City A and City B are separated by 500 kilometers. On a particular wall map, this distance is denoted by a length of 1.5 feet.

Hence:

Scale = 1.5 feet represents 500 miles

City C and City D are 2.1 feet apart on this map.

Therefore: Actual distance = 2.1 feet x  (500 miles / 1.5 feet) = 700 miles.

The actual distance between city C and D is 700 miles

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After considering the equation, inverse of y = [tex]9x^ {2}[/tex] - 4 is found as  [tex]f^{-1x}[/tex]= ±√[(x + 4)/9].

To find the inverse of the function y = [tex]9x^{2}[/tex] - 4, we can follow these steps:

x = [tex]9y^{2}[/tex] - 4

x + 4 = [tex]9y^{2}[/tex]

[tex]y^{2}[/tex] = (x + 4)/9

y = ±√[(x + 4)/9]

Note that since we are finding the inverse of a function, we need to include both the positive and negative square roots to ensure that the inverse is a function.

3. Switch the roles of x and y by replacing y with [tex]f^{-1x}[/tex] and x with f(y):

[tex]f^{-1x}[/tex] = ±√[(x + 4)/9]

Therefore, the inverse of y = 9x² - 4 is [tex]f^{-1x}[/tex] = ±√[(x + 4)/9].

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