A plan for a house includes a rectangular room with an area of 80 square feet and a perimeter of 36 feet. What are the length and width of the room

Answer:

Yes, Josh has enough information to find how far he is from the picnic table.  Josh is 90.1 ft from the picnic table (to the nearest tenth).

Step-by-step explanation:

Yes, Josh has enough information to find how far he is from the picnic table.

From the given information, we can model this as a right triangle where the angle is 54°, the side opposite the angle is the distance between the picnic table and the tree, and the side adjacent the angle is the distance between Josh and the picnic table. (See attached diagram).

To calculate the distance between Josh and the picnic table (labelled "x" on the attached diagram), use the tangent trigonometric ratio.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

Substitute the values into the tan ratio:

[tex]\implies \tan 54^{\circ}=\dfrac{124}{x}[/tex]

[tex]\implies x=\dfrac{124}{\tan 54^{\circ}}[/tex]

[tex]\implies x=90.09127...[/tex]

[tex]\implies x=90.1\; \sf ft\;(nearest\;tenth)[/tex]

Therefore, Josh is 90.1 ft from the picnic table (to the nearest tenth).

Monthly payment is $973.52, difference is $349,000 and monthly payment for a fully amortizing mortgage would be $3,331.87.

percentage, a relative value indicating hundredth parts of any quantity.

To find the total number of monthly payments, we need to multiply the number of years by 12 (the number of months in a year) and subtract 1 (for the final balloon payment).

So the total number of monthly payments is:

12 x 12 - 1 = 143

b. To find the amount of each monthly payment, we can use the formula

First, we need to convert the APR to a monthly interest rate by dividing by 12:

Monthly Interest Rate = 0.0335 / 12 = 0.002792

Monthly Payment = (350000 x 0.002792) / (1 - (1 + 0.002792)⁻¹⁴³)

= $973.52

The monthly payment is $973.52.

c. The balloon payment is simply the full principal amount of $350,000. The difference between the regular monthly payment and the balloon payment is:

Balloon Payment - Monthly Payment = $350,000 - $973.52 = $349,026.48

The difference is $349,000.

d. To find the monthly payment for a 12-year, fully amortizing mortgage, we can use the same formula as in part b, but with a different Total Number of Payments:

Total Number of Payments = 12 x 12 = 144

Monthly Payment = (350000 x 0.002792) / (1 - (1 + 0.002792)⁻¹⁴⁴) = $3,331.87

The monthly payment for a fully amortizing mortgage would be $3,331.87.

Hence, monthly payment is $973.52, difference is $349,000 and monthly payment for a fully amortizing mortgage would be $3,331.87.

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Answer:

Part 1:

Range = 98 - 23 = 75

Part 2:

First, find the sample mean:

Mean = (23 + 53 + 67 + 61 + 66 + 91 + 27 + 85 + 98 + 44 + 73)/11 = 61.9

Then, find the sum of the squared differences between each jersey number and the mean:

(23-61.9)^2 + (53-61.9)^2 + (67-61.9)^2 + (61-61.9)^2 + (66-61.9)^2 + (91-61.9)^2 + (27-61.9)^2 + (85-61.9)^2 + (98-61.9)^2 + (44-61.9)^2 + (73-61.9)^2 = 12388.4

Sample variance = 12388.4/10 = 1238.84

Sample standard deviation = √1238.84 = 35.17

Part 3:

Sample variance = 1238.84

Part 4:

The results tell us that there is a relatively large range in jersey numbers, with a difference of 75 between the highest and lowest numbers. The sample variance and standard deviation also indicate that there is a considerable amount of variability in the data, with jersey numbers varying significantly from the mean. This suggests that there is no pattern or structure to the jersey numbers on the football team, and that they are assigned somewhat randomly.

Step-by-step explanation:

The equation 2 2/3 × 2/3 = 2 4/9 is true.

A fraction represents a part of a whole or a ratio between two quantities. It is written as a/b, where "a" is the numerator and "b" is the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or the ratio.

The equation that is true is:

C. 2 2/3 × 2/3 = 2 4/9

To solve the problem, we can convert the mixed numbers to improper fractions, and then multiply:

2 2/3 = 8/3

2/3 = 2/3

8/3 × 2/3 = 16/9

We can then convert the improper fraction back to a mixed number:

16/9 = 1 7/9

Therefore, the equation 2 2/3 × 2/3 = 2 4/9 is true.

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Answer:

well...it depends how much ice cream ia in the cone...if its 3 or more it Will definently overflow.

Answer:

c step 3

Step-by-step explanation:

from the correct x^(2/5) do we suddenly get to

x^(5/2).

1/x³ = x^(-3) is a correct identity, and using it has no impact on x^(2/5). that should still stay x^(2/5).

the correct step 3 is then

x^(2/5)x^(-3)

step 4 is then

x^(2/5 - 3) = x^(2/5 - 15/5) = x^(-13)/5

The true mean amount of money spent on lunch per week for all students falls within the range of $20.12 to $23.88.

Margin of error is a statistical term that refers to the amount of random sampling error that is present in a survey or statistical estimate. In other words, it is the amount of uncertainty or variation that is inherent in any statistical measurement or survey result.

To construct a 98% confidence interval for the mean amount of money spent on lunch per week for all students, we need to use the formula:

Confidence interval = sample mean ± (z-score)(standard error)

Here, the sample mean is $22, the margin of error is 2, and the sample size is 273. To find the z-score for a 98% confidence interval, we can use a standard normal distribution table or calculator. The z-score for a 98% confidence interval is approximately 2.33.

To calculate the standard error, we need to use the formula:

[tex]Standard Error = \frac{standard Deviation}{\sqrt{sample Size} }[/tex]

Since the standard deviation is not given, we can estimate it using the sample standard deviation. Let's assume that the sample standard deviation is $8. The Standard Error calculated as:

[tex]Standard Error = \frac{8}{\sqrt{273} }[/tex]  ≈ 0.48

Substituting the values into the formula for the confidence interval, we get:

Confidence interval = $22 ± 2.33(0.48) ≈ $20.12 to $23.88

Therefore, we can be 98% confident that the true mean amount of money spent on lunch per week for all students falls within the range of $20.12 to $23.88.

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Answer: 71km/h

Step-by-step explanation:

He traveled 260km according to what you gave and 100 km using 60 km/h and 160km using 80km/h Also is this man has rocket since he walked 60km/h. His whole journey take 3h40m. Just take 260 divide by 3h40m so you got the final answer about 71km/h

Answer:

8,192

Step-by-step explanation:

20/100*80 =16 apply tjis in every step as they asked 4 times

a + 8. This expression represents the total number of almonds that Daniel snacked on in all.

What is the difference between expression and equation?

An expression is a mathematical phrase that contains numbers, variables, and operations. It can be evaluated to produce a single numerical value or another expression. Expressions do not contain an equal sign (=), and they do not represent a statement that is either true or false.

An equation, on the other hand, is a mathematical statement that shows the equality between two expressions. It contains an equal sign (=) and represents a statement that is either true or false. Equations typically contain variables that can take on different values, and they can be used to solve for an unknown variable by manipulating the equation using algebraic operations.

To summarize, expressions are mathematical phrases that do not contain an equal sign and can be evaluated to produce a value, while equations are mathematical statements that do contain an equal sign and represent a relationship between two expressions that is either true or false.

We can use addition to represent the total number of almonds that Daniel snacked on. If Daniel snacked on an initial amount of almonds, say "a", and then snacked on an additional 8 almonds, we can write the expression:

a + 8

This expression represents the total number of almonds that Daniel snacked on in all.

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Answer:

25.12cm²

Step-by-step explanation:

Hope it helps. Have a nice week.

Answer:

2

Step-by-step explanation:

you first follow the BODMAS law then you divide 1/3÷2/3 It will give you 1/2 so you 3/2-1/2 +1 it will give you 2

Answer:

the value of b is 10 +151620 but we have; to check

The value of b in the equation is 13/12

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

x^2/24 - y^2/b^2 = 1

The equation of a hyperbola with center at the origin and semi-axes lengths a and b can be written as:

x^2/a^2 - y^2/b^2 = 1

Comparing this equation with the given equation, we have:

a^2 = 24.

The directrix of the hyperbola is given as

x = 576/26

For a hyperbola with center at the origin, the distance between the center and the directrix is a^2/b.

So, we have:

a^2/b = 576/26

Substituting the value of a^2, we get:

24/b = 576/26

So, we have

b = 13/12

Hence, the value of b is 13/12

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Comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for less principal amount.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

Given,

Interest earned by Tommy SI = $140

Time t = 5 years

Principal amount P = $400

Interest earned by Jane SI = $132

Time t = 4 years

Principal amount P = $600

Simple interest SI = (P × r × t)/100

where r = interest rate

For Tommy,

140 = ( 400 × r × 5) /100

r = 7%

For Jane,

132 = ( 600 × r × 4) / 100

r = 5.5%

Therefore comparing the interest rates of Jane and Tommy, we can say that Tommy's bank is better because he earns more amount of money for the less principal amount.

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Answer:

the frequency of the recessive allele in the population is 0.5 or 50%.

Step-by-step explanation:

In a population in Hardy-Weinberg equilibrium, the frequency of alleles remains constant from generation to generation. According to the Hardy-Weinberg law, if p is the frequency of the dominant allele and q is the frequency of the recessive allele, then:

p + q = 1

and

p^2 + 2pq + q^2 = 1

where p^2 represents the frequency of homozygous dominant individuals, 2pq represents the frequency of heterozygous individuals, and q^2 represents the frequency of homozygous recessive individuals.

Given that the frequency of dominant yellow-flowered plants is 50%, or 0.5, we can assume that p = 0.5. Substituting into the first equation, we get:

0.5 + q = 1

Solving for q, we get:

q = 1 - 0.5

q = 0.5

Therefore, the frequency of the recessive allele in the population is 0.5 or 50%.

Answer:

64 people

Step-by-step explanation:

I'm not so sure but I think its right.

Here's how I figured it out:

60x2=120

42x2=84

120-20=100%

84-20=64

The triangles JTK and KSL are not congruent. So we cannot complete a similarity statement.

what is congruent ?

In geometry, two figures are said to be congruent if they have the same shape and size. In other words, if all corresponding angles are congruent and all corresponding sides are of equal length, then the two figures are congruent.

For example, two triangles are congruent if all three pairs of corresponding angles are congruent and all three pairs of corresponding sides are of equal length. Similarly, two circles are congruent if they have the same radius.

According to the question:
To determine if the triangles JTK and KSL are similar, we need to check if their corresponding angles are congruent and their corresponding sides are in proportion.

First, we can see that angle JTK and angle KSL are congruent because they are both right angles.

Next, we can use the Pythagorean theorem to find the length of side TK:

[tex]TK^2 = JK^2 - JT^2[/tex]

[tex]TK^2 = 14^2 - 2^2[/tex]

[tex]TK^2 = 192[/tex]

TK = sqrt(192)

TK = 8*sqrt(3)

Now, we can compare the ratios of the corresponding sides to see if they are equal:

JT : JK : TK = 2 : 14 : 8*sqrt(3)

KS : KL : SL = 32 : 22.4 : 15.2

We can simplify these ratios by dividing by the greatest common factor, which is 2:

JT : JK : TK = 1 : 7 : 4*sqrt(3)

KS : KL : SL = 8 : 5.6 : 3.8

We can see that these ratios are not equal. Therefore, the triangles JTK and KSL are not similar.

Since the triangles are not similar, we cannot complete a similarity statement.

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1. The volume of a cone is  8π cubic inches.

2. The volume of a sphere is  8π cubic inches.

3. The volume of a cube is  8π cubic inches.

4. The volume of a cylinder is  8π cubic inches.

5. The volume of a rectangular prism is  8π cubic inches.

The volume of a thing is the area that it occupies in three dimensions. Space is what a thing occupies, to put it simply.

1. The volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height. Substituting the given values, we get V = (1/3)π(2²)(6) = (4/3)π(6) = 8π cubic inches.

2. The volume of a sphere is given by V = (4/3)πr³, where r is the radius. Substituting the given value, we get V = (4/3)π(24³) = 18432π cubic inches.

3. The volume of a cube is given by V = s³, where s is the side length. Substituting the given value, we get V = 6³ = 216 cubic inches.

4. The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. Substituting the given values, we get V = π(4²)(5) = 80π cubic inches.

5. The volume of a rectangular prism is given by V = lwh, where l, w, and h are the length, width, and height, respectively. Substituting the given values, we get V = (9)(5)(5) = 225 cubic inches.

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The vertex of the equation (x - 1)^2 - 9 = 0 is (1. 9)

The vertex of a quadratic equation is the point at which the graph of the equation reaches its maximum or minimum value.

For a quadratic equation in standard form, y = ax^2 + bx + c, the vertex is located at the point (-b/2a, f(-b/2a))

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

(x - 1)^2 - 9 = 0

A quadratic equation is represented as

a(x - h)^2 + k = 0

Where the vertex is

Vertex = (h, k)

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

Vertex = (h, k) = (1, 9)

Hence, the vertex is (1, 9)

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Complete question

How do I find the vertex of the equation

(x - 1)^2 - 9 = 0

Answer:

11,100

Step-by-step explanation:

1% of 30,000 is 300 so if we times 300 by 37 we get 11,100

there is 11,100 sheep in 37%.

hope this helps :)

The distance from the island to Gatsby's dock is 1.3 miles.

A Pythagoras theorem is a principle that can be used to determine the unknown side of a right angled triangle when the other two sides are known.

Applying the Pythagoras theorem to the given question, let the distance from island to Gatsby's dock be represented by s. Then;

/Hyp/^2 = /Opp/^2 + /Adj/^2

s^2 = 1.2^2 + 0.5^2

      = 1.44 + 0.25

      = 1.69

s = 1.69^1/2

  = 1.3

Thus, the straight-line distance from the island to Gatsby's dock is 1.3 miles.

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In 1990, 19 billion dollars worth of books were sold.

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]

We know a function is called an exponential function when the independent variable is the exponent.

An example of an exponential function is, aˣ.

Given, The equation y = 19(1.057) represents book sales in billions of dollars since 1990.

The equation is, y = 19(1.057)ˣ, Where x = the number of years.

Therefore, At x = 0 or in 1990,

y = 19(1.057)⁰.

y = 19(1).

y = 19 billion dollars

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Answer:

Step-by-step explanatio

A. To complete the table, we need to plug in different values of "x" into the equation y = 2x + 66 and solve for "y". We can choose any values of "x", but it's usually helpful to choose values that are easy to calculate. Here's the table with "x" values ranging from 0 to 7:

x y

0 66

1 68

2 70

3 72

4 74

5 76

6 78

7 80

B. To graph the equation, we can plot the points from the table on a coordinate plane. We can use the x-axis to represent the number of hours after the storm enters the Gulf of Mexico (x), and the y-axis to represent the wind speed in miles per hour (y). The points should fall on a straight line with a slope of 2 and a y-intercept of 66. We can plot the points and draw the line as follows:

C. The wind speed of a tropical storm becomes a hurricane when it reaches or exceeds 74 miles per hour. Looking at the graph, we can see that the wind speed reaches 74 miles per hour when x = 4. Therefore, the storm becomes a hurricane 4 hours after entering the Gulf of Mexico.

Answer:

Values from the set = 1, 2, 3, 4.

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The inequation is,

→ 4x - 2 < 15

Then the value of x will be,

→ 4x - 2 < 15

→ 4x < 15 + 2

→ 4x < 17

→ x < 17/4

→ [ x < 4.25 ]

Hence, the answer is x < 4.25.

The piecewise function that models model the water level L (x) (in inches) as a function of the number of days x since the beginning of the drought is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which;

A piecewise function is a function with different definitions, based on the input of the function.

For the first 14 days, the parameters are given as follows:

Hence:

L(x) = 60 - 2x, 0 ≤ x ≤ 14.

For the last 5 days, the parameters are obtained as follows:

Hence:

L(x) = 30 + 5x, 15 ≤ x ≤ 19.

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Answer:

41

Step-by-step explanation:

we can get this answer because:

3(3)=9

4(8)=32

and u add 32 and 9 together and get 41

$54.28 rounded to the nearest 10 dollars is $50.00

Answer:

1200ml or 1.2l of water

Step-by-step explanation:

concentrate:water

1:3

400:x

3×400=1200

400:1200

1200ml or 1.2l of water

bonjours

oui sa est égale au volume

Answer:

34 Foot

Step-by-step explanation:

You're basically just doing the pythagorean theory: a^2+b^2=c^2

You just are not directly being given a or b and instead you have to find them which you do by subtracting how big the garden is from the total length: 50-20=30(a) 30-14=16(b). After that you just do the normal theory getting 30^2+16^2=c^2 which leads to 900+256=c^2 then 1156=c^2 so you take the square root of both sides in order to turn c^2 into plain c or the length of the walk way which will get you 34 feet.