The length of a rectangle is 5m longer than its width. If the perimeter of the rectangle is 54m, find its length and width.

According to the question, we are given a triangle XYZ

where,

Angle sum property states that sum of all the angles of triangle is 180°. So by adding all the three angles we will get the required value of a.

∠X + ∠Y + ∠Z = 180°

30° + 20° + 2a° = 180°

50° + 2a° = 180°

2a° = 180° - 50°

2a° = 130°

a° = 130/2

a° = 65°

Therefore, required value of a is 65°

Answer:

B

Step-by-step explanation:

remember : the sum of all angles in a triangle is always 180°.

are you sure the third angle is called ZZ ?

I am rather sure it would be called XY !

so,

180 = ZX + ZY + XY = 30 + 20 + 2a

130 = 2a

a = 130/2 = 65°

A concave hexagon with 2 pairs of congruent sides is a shape that has six sides and two pairs of sides that are of equal length, but the shape curves inward at one or more angles, creating a concave indentation.

A hexagon is a six-sided polygon, and when two pairs of its sides are congruent,

it means that four of its sides have the same length, if the shape curves inward at one or more angles,

it creates a concave hexagon, which means that the indentation on the shape is facing inward, rather than outward, a concave hexagon with 2 pairs of congruent sides is a six-sided polygon with four sides of equal length, but with a curvature that creates an inward indentation.

Hence, a concave hexagon with 2 pairs of congruent sides is a six-sided figure with an indentation and two sets of sides with equal lengths.

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Answer:

x = 12

m(∠B) = 45°

Step-by-step explanation:

Given question is incomplete; find the complete question in the attachment.

In the figure attached two lines 'l' and 'm' are the parallel lines and line 'n' is a transverse.

Angles A and B are the "Alternate exterior angles" which will equal in measure.

m(∠A) = m(∠B)

(5x - 15) = (2x + 21)

5x - 2x = 15 + 21

3x = 36

x = 12

Since, m(∠B) = (2x + 21)

                     = (2×12) + 21

                     = 24 + 21

                     = 45°

Therefore, x = 12 and measure of angle B will be 45°.

Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.

A mathematical equation resembles a formula connecting two assertions when the equals letter (=) is employed to denote equality. An equation in algebra is a statement of fact that demonstrates the equality of numerous mathematical variables. For example, the equation obd + 6 = 12 has an equal sign separating the numbers doc d + 6 and 12. You can mathematically expression how many syllables correspond per each side of every letter. Often, a symbol's message is its exact opposite.

Here,

Given :

Equation : y =57x for the distance travelled by  alisha.

Thus,

To find the equation is correct or not.

By comparing it with distance/time = speed equation we get to know

that the equation represented by alisha is wrong.

The correct equation can be => y/x =57 .

Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.

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Answer:

b= 8

Step-by-step explanation:

you use Pythagorean theorem to solve this problem

a² + b² = c²

since you already have a and c and you're missing b you rearrange the formula to:

\(c^{2}\)-\(a^{2}\) = b²

17² - 15² = b²

64² = b²

\(\sqrt{64}\) = b

8 = b

Step-by-step explanation:

To find side b use Pythagoras theorem:

Hypotenuse²=Base²+Height ²

17²=B²+15²

289-225=B²

64=B²

√8=B²

So,

8 yards is Side B

Now,

We can use Heron's Formula

√S(S-A) (S-B) (S-C)

Let's find semi perimeter

17+15+8/2

40/2=20

So, S=20

Let A=8,B=15,C=17

√20(20-8) (20-15) (20-17)

√20×12×5×3

√2×2×5×5×2×2×3×3 (Factorising the numbers)

2×5×2×2×3

120 yards Answer

hope it helps...

Stronger evidence against the null hypothesis is indicated by: smaller p-values.

A statistical conjecture known as a null hypothesis asserts that certain features of a population or data-generating process are not different from one another.

A mechanism to reject the null hypothesis with a predetermined level of confidence is provided by hypothesis testing.

The alternative hypothesis is supported if the null hypothesis can be rejected.

The foundation of the scientific falsification principle is null hypothesis testing. The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.

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The amount of soil needed to fill the garden box is given as follows:

1728 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

V = 19 x 12 x 6 + 10 x 3 x 12

V = 1728 ft³.

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Solution:

Given:

A 52-card deck

There are four suits in a standard deck of cards, Clubs, Hearts, Spades, and Diamonds.

There are 13 diamond cards.

Hence,

Probability is calculated by;

Thus, the probability of drawing a diamond on the first draw is;

Since two draws are made with replacement, the cards are completed back again before the next draw.

Hence, the probability of drawing a diamond on the second draw is;

Therefore, the probability of drawing a diamond each time;

Answer:

If you click on the link you find a picture which has black dots on a white background. This suggests that we color every point on the plane either white or black, making sure to use infinitely many of each color. With these constraints it is indeed the case that there must be a black point and a white point at unit distance. (In fact, "infinite" can be weakened to nonempty.)

Step-by-step explanation:

Hint: starting with a black point, we're done unless the entire unit circle around that point is black. Now repeat that argument for each point on that unit circle: we've already generated a sizable swathe of the plane colored totally black...

The graph of h(x) is the graph of g vertically shifted down 5 units. Then the correct option is C.

Functions are found all across mathematics and are required for the creation of complex relationships.

The function g(x) = x² is transformed to obtain function h:

h(x) = g(x) − 5

h(x) = x² − 5

The graph h(x) get shifted downward by 5 units.

Then the correct option is C.

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The functiοn that gives the number οf illiterate peοple in Sylvania is

\(\mathrm{P(t) = 9000(2/5)^t}\)

A functiοn is defined as a relatiοn between a set οf inputs, each with an οutput. Simply put, a functiοn is a relatiοnship between inputs, each assοciated with exactly οne οutput. Each functiοn has a dοmain and cοdοmain οr scοpe.

Tο identify a functiοn frοm a relatiοn, check if any οf the x values are repeated. If it's nοt repeated, it's a functiοn. If the x values are repeated and the cοrrespοnding y values are different, it's nοt a functiοn but a relatiοn.

Sοlutiοn accοrding tο the questiοn:

Given, Tοtal number οf illiterate peοple = 9000

          Amοunt = 3/5

Fοr the first year = 9000 × (1 - 3/5) = 9000(2/5)

Nοw, fοr "t years":

P(t) = 9000(2/5)

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Answer:

The answer is b.7

Step-by-step explanation:

Because i had the question and got it right

Answer:

54

Step-by-step explanation:

If the waitress's tip was 20% based on the $67.50 bill, then her tip was $13.5

 The percentage is a mathematical operation that is expressed with the symbol "%" is a relationship that allows us to know the portion of an initial value to represent a set.

  It could also be defined as a representation of an original value that lets us know a certain number of elements that we want from that original value or set.

The easiest way to solve this problem is with a rule of three implement, as follows:

x = (20% * $67.5 ) / 100%

x = $13.5

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Answer:

the width of a rectangular is 3 cm

Step-by-step explanation:

Length L = 10 cm

Perimeter P = 26 cm

Width W = ?

perimeter = 2L + 2W

26 = 2(10) + 2W

26 - 20 = 2W

6 = 2W

W = 6 / 2

W = 3 cm

therefore,  the width of a rectangular is 3 cm

Answer:

4x

Step-by-step explanation:

\(\sqrt{x} \cdot \sqrt{x} = \sqrt{x^2} = x^{ 2 \times \frac{1}{2}} = x\)

\(given :\\\\ \sqrt{x} \cdot 4\sqrt{x} = 4 \cdot\sqrt{x} \sqrt{x} = 4 \sqrt{x^2} = 4x\)

The combined weight of the lightest and heaviest salmon is \(\frac{7}{8}\) lb.

A line plot is a graph that is used to show the distribution of a data set. A line plot is made up of a number line and checkmarks above the numbers on the number line. The checkmarks represents the frequency of a data in the data set. For example, there is one salmon with a weight of 1/8.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/8.

The farthest weight from one has the lightest weight and the salmon closest to one has the heaviest weight.

The lightest salmon has a weight of 1/8.

The heaviest salmon has a weight of 3/4.

The combined weight can be determined by adding the heaviest weight and the lightest weight together.

\(\frac{1}{8} + \frac{7}{8}\)

\(\frac{1 + 6}{8}\) = \(\frac{7}{8}\) lb

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The filled van has a height of 4 feet, indicating the vertical dimension from the floor to the top of the crates inside.

To determine the height of the van that is filled with crates, we need to consider the volume of the crates and the total volume of the van.

Given that each crate has a volume of one cubic foot, and there are 30 crates covering the floor of the van, the total volume occupied by these crates is 30 cubic feet.

Now, to find the remaining volume inside the van, we subtract the volume of the crates from the total volume of the van. The van has a volume of 150 cubic feet, and we have already accounted for 30 cubic feet occupied by the crates.

Remaining volume inside the van = Total volume of the van - Volume occupied by the crates

Remaining volume = 150 cubic feet - 30 cubic feet

Remaining volume = 120 cubic feet

Since the van is shaped like a rectangular prism, the height of the van represents the vertical dimension.

To find the height of the van, we divide the remaining volume by the area of the van's base. The base area can be found by dividing the remaining volume by the length and width of the van.

Given that the van is completely filled with crates, the base area is equal to the area of 30 crates.

Base area = Volume occupied by the crates / Height

Base area = 30 cubic feet / Height

Now, we can solve for the height:

Height = Volume of the remaining space / Base area

Height = 120 cubic feet / 30 cubic feet

Height = 4 feet

Therefore, the height of the van that is filled with crates is 4 feet.

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In essence, a function is a rule that assigns to each value of the input set (also known as the domain), a unique value of the output set (also known as the range).

A function is a fundamental mathematical concept that is used to describe the relationship between two sets of values.

To understand the idea of a function, imagine a machine that takes in an input and produces an output. The input values are the domain of the function, and the output values are the range. A function can be represented as an equation, a graph, or a table. For example, the equation f(x) = x + 3 represents a function that takes in an input value x and produces an output value that is 3 greater than the input value.

One of the key features of a function is that each input value must have a unique output value. This means that if you input the same value into the function twice, you should get the same output value both times. In mathematical terms, we say that a function is well-defined if it has a unique output value for each input value.

Functions are used in a wide range of mathematical applications, from algebra and calculus to statistics and data analysis. They provide a powerful tool for describing and analyzing relationships between different sets of values.

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The function constructed is y = 90x + 60.

"Information available from the question"

Jahlil is saving money at a constant rate to buy a new TV. After saving for 3 months, After saving for 3 months, Jahlil has $330. After saving for 5 months, Jahlil has $510.

Let x represents the months

and y represents the dollars

To find the dollars/month and by finding the slope.

(3, 330), (5, 510)

\(\frac{510-330}{5-3}\) = 90

Since its a constant rate, the function will be in the form, y = mx+b, and since we found the slope we can plug m=90.

y=90x+b

To find b, we simply substitute one of the points.

330 = 90(3) + b

b = 60

Thus, plugging it in,

y = 90x + 60

Hence, The function constructed is y = 90x + 60.

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Answer:

No

Step-by-step explanation:

The only consecutive integers that satisfy the Pythagorean theorem are 3, 4, and 5.

___

4^2 ≠ 2^2 + 3^2

16 ≠ 4 + 9 . . . . . . . an attempt at applying the Pythagorean theorem to the given numbers fails.

The expected value of a distribution is the mean of the distribution

The number of tosses is 62

The expected value is given as:

E(x) = 35

The probability is given as:

p = 9/16

So, we  have:

E(x) = n * p

Substitute known values

\(35 = n * 9/16\)

Divide both sides by 9/16

n = 62

Hence, the number of tosses is 62

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"The median and the 50th percentile rank score will always have the same value". The statement is false, so the correct option is b.

The median and the 50th percentile rank score do not always have the same value. While they are related concepts, they are not identical.

The median is the middle value in a dataset when it is arranged in ascending or descending order. It divides the dataset into two equal halves, where 50% of the data points are below the median and 50% are above it. It is a specific value within the dataset.

On the other hand, the 50th percentile rank score represents the value below which 50% of the data falls. It is a measure of relative position within the dataset. The 50th percentile rank score can correspond to a value that is not necessarily the same as the median.

In cases where the dataset has repeated values, the 50th percentile rank score could refer to a value that lies between two data points, rather than an actual data point.

Therefore, the median and the 50th percentile rank score are not always equal, making the statement false.

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Answer:

4.2 units^3

Step-by-step explanation:

Volume of a cone 1/3(nr^2h)

n = 22/7

r = radius  

h = height

1/3 x (22/7) x (2^2) = 4.2

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies follows an approximately normal distribution with a mean and standard deviation that are not specified in the given information. We don't have the necessary information to calculate the percentile in this case.

However, we can still calculate the answer using the provided information. To find the number of chocolate chips more than 1225, we need to determine the z-score and find the corresponding area under the normal curve. The z-score formula is given by z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, we don't know the mean and standard deviation, so we cannot calculate the exact z-score. However, we can still provide an explanation of the process. To find the z-score, we would subtract the mean from 1225 (the value we want to find the probability for) and divide the result by the standard deviation. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the corresponding area. The area represents the probability of a random variable being less than or equal to the given value. Since we want the probability of having more than 1225 chocolate chips, we would subtract the obtained probability from 1. Regarding the second question, without knowing the mean and standard deviation, it is not possible to determine the exact percentile for a bag that contains 1000 chocolate chips. Percentiles represent the proportion of data points that fall below a certain value.

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Answer:

-62

Step-by-step explanation:

g(x)=2-x^2

Let x = -8

g(-8)=2-(-8)^2

       = 2- 64

       = -62

Solve for the function of g then use what you get for g to solve for f.

g(-8) = 2 - (-8)^2

g(-8) = 2 - 64

g(-8) = -2

f(-2) = 2(-2) - 1

f(-2) = -4 - 1

f(-2) = -5

Best of Luck!