Josh is at a park. He knows that the distance from the picnic table to a tree is 124 feet. Josh also knows the angle formed by a segment from his location to the picnic table and a segment from his position to the tree is 54 degrees and that triangle formed by his position, the picnic table, and the tree is a right triangle, with a right angle at the picnic table. Does josh have enough to find how far he is from the picnic table.

The required, two expressions are not equivalent, and Pat's claim is false.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
a) To show that Pat is wrong, we can substitute p = 3 into both expressions and compare the results:

4 - (p + p + p) = 4 - (3 + 3 + 3) = 4 - 9 = -5

4 - p + p + p = 4 - 3 + 3 + 3 = 7

Since the two expressions have different values when p = 3, Pat's claim is false.

b) Simplifying each expression algebraically, we have:

4 - (p + p + p) = 4 - 3p

4 - p + p + p = 4 + p

Therefore, the two expressions are not equivalent, and Pat's claim is false.

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The values of the unknown in the figures are a = 40, b = 32 and c = 275

Figure (a)

A quadrilateral has a total angle measure of 360 degrees.

So, we have

90 - a + 92 + 128 + 90 = 360

Evaluate the like terms

-a = 360 - 400

So, we have

a = 40

Figure (b)

The total measure of angles on a line is 180 degrees.

So, we have the following

4b - 10 + 2b - 2 = 180

Evaluate the like terms

6b = 192

So, we have

b = 32

Figure (c)

The total measure of angles at a point is 360 degrees

So, we have the following

c + 19 + (94 - 28) = 360

Evaluate the like terms

c = 275

Hence, the value of c is 275 degrees

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Horizontal cross-sections of the prisms at the same height have the same area.

Option D.

A right rectangular prism is a three-dimensional shape with six faces which are all rectangles. It has twelve edges and eight vertices.

An oblique triangular prism is a prism with 2 congruent triangular faces and 3 rectangular faces at an angle to the triangular faces.

This is the volume of solid figures concept.

The volume of a prism is obtained by multiplying the area of its base to its height. If the two given solid figures have the same volume and the same height then, the areas of their bases are also equal.

In this case, the height of the right rectangular prism and the oblique triangular prism are 12 cm and both prisms have the same volume, we can conclude that:

Horizontal cross-sections of the prisms at the same height have the same area.

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Answer:

Step-by-step explanation:

i assume you mean that the mat is 11 feet on each side so

area = s*s(or S^2)

so 11*11=121feet sq

Answer: 8.2 weeks.

Step-by-step explanation: If y = 4*3^t, then 600 = 4*3^t. Therefore, t = log3 (600/4), which is approximately 8.2 weeks.

Answer:

Step-by-step explanation:

90 degrees is the answer because there is no movement

Step-by-step explanation:

here,

so the correct answer is this

The total surface area of the given solid is 256 inch²

Surface area is the measure of the total area that the surface of an object occupies. It is usually expressed in square units, such as square meters, square centimeters, or square feet.

Here in this problem take the surface of the solid as the number of faces and calculate the area of each face as shown below.

Here we have

Solid box with dimensions 4 in, 5 in, and 8 in

The surface of the given solid can be divided as given in the picture

The surface area of the shape = Sum of areas of [ 1 to 12 faces ]

Area of (1, 2, 3, 7, 8, 9 faces ) = 6 (4 × 4 )= 96 inch²  

Area of (4, 5, 6, 10, 11, 12 faces ) = 6 (5 × 4) = 120 inch²    

Area of bottom = (8 × 5) = 40 inch²  

Total Surface area = [ 96 + 120 + 40 ] = 256 inch²

Therefore,

The total surface area of the given solid is 256 inch²

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Answer:

(4,2)

Step-by-step explanation:

Based on the information in the graph, we can infer that the length of Main St between 5th Ave. and 6th Ave. is 0.24km.

To find the value of Main St. between 5th Ave. and 6th Ave we must perform the following mathematical procedure:

In accordance with the above, what we did was a relationship between the fractions that represent the length of each street. In this case we had to clear the x that represented Main St. between 5th Ave. and 6th Ave.

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The height of the water in the tank after 5 minutes is approximately 732.6 inches.

V = πr²h, where V is a cylinder's volume, r is its radius, and h is its height, is the formula for calculating a cylinder's volume. The formula is created by first determining the area of the cylinder's base, which equals r2, and then multiplying that area by the cylinder's height to determine the volume. The volume of tanks, pipelines, and other cylindrical objects may be calculated using this formula, among many other uses.

The volume of a cylinder, which is:

V = πr²h

Given that, diameter is 15 feet, so the radius is 7.5 feet.

Also,

2 feet per second = 2 * 12 * 60 inches per minute = 1440 inches per minute

V = πr²h

Substituting the values:

V = π(7.5)^2(14405)

Here, 14405 is the amount of water that flows into the tank in 5 minutes.

Divide the volume of water by the area of the base of the cylinder

V/A = h

2,044,123/(π(7.5)^2) ≈ 732.6 inches

Hence, the height of the water in the tank after 5 minutes is approximately 732.6 inches.

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The statistical significance does not necessarily imply practical significance. In this case, while the IQ score of 160 is statistically significant, it may not necessarily be practically

To assess whether any of the IQ scores are statistically significantly high or low, we need to calculate the z-score for each score. The formula for calculating the z-score is:

z = (x - μ) / σ

Where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

First, we need to calculate the mean and standard deviation of the IQ scores:

Mean = (100 + 90 + 110 + 160 + 90 + 85 + 65 + 100 + 95 + 98) / 10 = 99.3

Standard deviation = √[((100-99.3)² + (90-99.3)² + (110-99.3)² + (160-99.3)² + (90-99.3)² + (85-99.3)² + (65-99.3)² + (100-99.3)² + (95-99.3)² + (98-99.3)²) / 10] = 39.77

Now we can calculate the z-score for each IQ score:

z1 = (100 - 99.3) / 39.77 = 0.018

z2 = (90 - 99.3) / 39.77 = -0.233

z3 = (110 - 99.3) / 39.77 = 0.27

z4 = (160 - 99.3) / 39.77 = 1.53

z5 = (90 - 99.3) / 39.77 = -0.23

z6 = (85 - 99.3) / 39.77 = -0.36

z7 = (65 - 99.3) / 39.77 = -0.86

z8 = (100 - 99.3) / 39.77 = 0.017

z9 = (95 - 99.3) / 39.77 = -0.108

z10 = (98 - 99.3) / 39.77 = 0.032

Using the z-table, we can find the percent of scores below each z-score:

z1 =  0.018 or 70.01%

z2 = -0.233 or 34.67%

z3 = 0.27 or 75.01%

z4 = 1.53 or 83.68%

z5 = -0.23 or 34.67%

z6 = -0.36 or 37.47%

z7 = -0.86 or 45.16%

z8 =  0.017 or 70.01%

z9 = -0.108 or 31.80%

z10 =  0.032 or 69.15%

To determine whether each z-score is statistically significant, we need to compare it to a predetermined level of significance, typically α = 0.05. If the probability associated with the z-score (i.e., the percent of scores below it) is less than or equal to α, we consider the score statistically significant.

Based on this criterion, the only score that is statistically significant is the IQ score of 160 (z-score = 2.29, percent of scores below = 83.68%). All other scores have a probability greater than α, and therefore are not statistically significant.

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For the equation 75x+30y=1500,  x is (100 - 2y) / 5 and y is (100 - 5x) / 2.

An equation is a mathematical statement that uses symbols and numbers to express a relationship between two or more variables. It states that two expressions are equal to each other.

We can solve for x and y in the equation 75x + 30y = 1500 by using algebraic manipulation.

First, we can simplify the equation by dividing both sides by the greatest common factor of 75 and 30, which is 15:

(75x + 30y) / 15 = 1500 / 15

Simplifying the left side gives:

5x + 2y = 100

Next, we can isolate one of the variables. Let's isolate y by subtracting 5x from both sides:

5x + 2y - 5x = 100 - 5x

Simplifying the left side gives:

2y = 100 - 5x

by dividing both sides by 2:

y = (100 - 5x) / 2

This is the equation for y in terms of x. We can use this equation to solve for y given a value of x, or we can substitute it back into the original equation to solve for x in terms of y.

Let's solve for x in terms of y by isolating x in the equation 5x + 2y = 100:

5x = 100 - 2y

Dividing both sides by 5 gives:

x = (100 - 2y) / 5

This is the equation for x in terms of y. We can use this equation to solve for x given a value of y, or we can substitute it back into the original equation to solve for y in terms of x.

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b. The distance between points K and L is 10 units.

c. ΔJKL is not an equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

Given points as:

J (-5,-3)

K (1,5),

L (7,-3)

b. To determine the distance between points K and L, we can use the distance formula:

distance = √(x₂ – x₁)² + (y₂ – y₁)²

Substituting the coordinates of K and L, we get:

distance = √((7 - 1)² + (-3 - 5)²)

distance = √(36 + 64)

distance = √(100)

distance = 10

Therefore, the distance between points K and L is 10 units.

c. To determine if JKL is an equilateral triangle, we need to check if all three sides have the same length.

We can find the lengths of each side using the distance formula:

JK = √((1 - (-5))² + (5 - (-3))²) = √(6^2 + 8²) = 10

KL = 10 (as we found in part b)

LJ = √((-5 - 7)² + (-3 - (-3))²) = √((-12)²) = 12

Since all three sides have different lengths (JK and KL are 10 units, while LJ is 12 units), JKL is not an equilateral triangle.

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The number of players the team can bring to the tournament is 20.

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0.

In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.

Here, we have

Given: Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals.

we have to determine the number of players the team can bring to the tournament.

So to make an equation, the bus charge would be the y-intercept (If no member went, they still paid for the bus fee) and the meals would be the slope (since it is dependent on how many members ride the bus.)

The total would add up to be 2412.50, so the equation would be:

2412.50 = 67x+1072.50

where x = the number of players the team can bring to the tournament without going outside of their budget.

After solving this, we get

2412.50 = 67x+1072.50

2412.50 - 1072.50 = 67x

1340 = 67x

x = 20

Hence, the number of players the team can bring to the tournament is 20.

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The sale price per sheet in this example is $12.60.

What is the discount?

A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. It is a form of incentive that is used to encourage customers to purchase goods or services, often by making them more affordable or attractive.

To compare the two deals, we need to calculate the sale price per sheet for each deal.

In the previous example, the sale price per sheet was $15.00 after a 20% discount off the regular price of $18.00.

In this example, the sale price per sheet is 30% off the regular price of $18.00, so we can calculate the sale price per sheet as:

Sale price per sheet = Regular price per sheet - Discount amount

Sale price per sheet = $18.00 - (30% x $18.00)

Sale price per sheet = $18.00 - $5.40

Sale price per sheet = $12.60

Comparing the two deals, we can see that the sale price per sheet in this example is lower than the sale price per sheet in the previous example. Therefore, the better deal is the 30% discount off the regular price of $18.00, which results in a sale price per sheet of $12.60.

Therefore, the sale price per sheet in this example is $12.60.

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Answer:

I think is D

Step-by-step explanation:

because

R:622 and Y:410

The measurement that, in inches, comes closest toward the length equal of a square tile is: 11 in.

A square is a shape that we frequently encounter in our daily lives. Illustrations of square shapes that are frequently used include chess pieces, clock hands, picture frames, pizza boxes, coasters, computer keys, etc.

In the bathroom, Robert is paving the floor.

The area of each square-shaped tile is 120.5 square inches.

Area = side²

side = √Area

side = √120.5

side = 10.97 in

side = 11 in (approx)

The measurement that, in inches, comes closest toward the length equal of a square tile is: 11 in.

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The piecewise function is defined as follows:

A piece-wise function is a function that has different definitions, based on values of the input x of the function.

For this problem, the intervals are given as follows:

For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence:

y = x² + 4, x < 2.

For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:

y = -x + 4, x ≥ 2.

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The area of the trapezoidal flower garden from the dimensions is 123.5 square meters

The trapezoidal flower garden represents the given parameter, where we have the following readings

Parallel sides = 9 m and 10 m

Height = 13 m

Using the above dimensions, we have the area to be

Area = 1/2 * Sum of parallel sides * Height

When the dimensions are substituted, we have

Area = 1/2 * (9 + 10) * 13

Evaluate the products

Area = 123.5

HEnce, the area is 123.5 square meters

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In respοnse tο the query, we can state that Therefοre, the simplified equatiοn expressiοn fοr f(x+h) - f(x)/h is: 10x + 5h + 3

In a math equatiοn, twο assertiοns are cοnnected by the equals sign (=), which denοtes equivalence. A mathematical assertiοn used in algebraic equatiοns establishes the equivalence οf twο mathematical statements. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. Tο cοmprehend the relatiοnship between the twο sentences written οn οppοsing sides οf a letter, utilise a mathematical fοrmula. The lοgο and the specific prοgramme typically cοrrespοnd. An illustratiοn wοuld be 2x - 4 = 2.

functiοn f(x) intο the fοrmula fοr f(x+h) - f(x)/h, and then simplify the resulting expressiοn algebraically.

f (x + h) — f (x)

= [5(x + h)² + 3(x + 10] — [5x² + 3x]

= [5(x² + 2xh + h²) + 3x + 314 — [5x² + ax]

= [5x² + 10xh + 5k² + 3x + 3h] — [5x² + 3x]

= 10xh + 5h² + 3h f(x+h) - 1(x) h

= 10x + 5k + 3

Therefοre, the simplified expressiοn fοr f(x+h) - f(x)/h is:

10x + 5h + 3

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We know that 50% of the data falls between the minimum value and the median (i.e., between 5 and 35). So the answer is: 50%.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses. In addition to the median, other measures of central tendency include the mean and mode. Each measure has its own strengths and weaknesses, and the appropriate measure to use depends on the nature of the dataset and the research question being asked.

To answer this question, we need to determine the position of the lower whisker and the vertical bar relative to the range of the data.

The lower whisker extends to 5, which is the minimum value in the dataset. The vertical bar inside the box is located at 35, which represents the median of the dataset.

Therefore, we know that 50% of the data falls between the minimum value and the median (i.e., between 5 and 35).

So the answer is: 50%.

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Answer:

Assuming "she" in the question is a typo and it should be "if", here's the solution:

If the population of a small town is 567, and it decreases at a rate of 1.5% per year, we can find the population after 20 years using the formula:

P = 567 * (1 - 0.015)^20

where P is the population after 20 years.

Simplifying this expression, we get:

P = 567 * 0.742 = 420.414

Rounding this to the nearest whole number, we get:

P ≈ 420

Therefore, after 20 years, the population of the small town would be approximately 420.

Answer:

x = 8

Step-by-step explanation:

[tex]15 + x = 23[/tex]

[tex]x = 23 - 15[/tex]

∴[tex]x = 8[/tex]

Answer: variable Y, coefficient 11, Constant 4.5

Step-by-step explanation:

variable: Y

coefficient: 11

Constant: 4.5

Option A is correct, 162 is the greatest number of caps she can buy.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let x be the number of caps.

We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.

We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges (6x+25).

Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000.

We can represent this information in an equation as:

6x+25≤1000

Let us solve for x

Subtract 25 from both sides

6x≤1000-25

6x≤975

Divide both sides by 6

x≤162.5

Hence, Option A is correct, 162 is the greatest number of caps she can buy.

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Answer:yes

Step-by-step explanation: