Find the area of each of the figures

when T = 0, L = 150 (the original number of pages  to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).

A chart can be defined as a pictorial representation or  diagram that presents data or values ​​in an organized manner. Points on a graph often represent a relationship between two or more things.

We can use a linear equation of the form to describe a function that relates the number of pages read to the time elapsed since the start of reading:

L = mT + b

where L is the number of pages remaining, T is the elapsed time  in hours, m is the page read rate  in pages per hour, and b is the original number of pages remaining when T = 0.  

In this case, we know that Ray is reading at a constant rate of 25 pages per hour, so m = -25 (since we are counting  the remaining pages). We also know that when T = 0 (start of  reading),  150 pages remain unread, so b = 150. Combining everything we get:

L = -25T + 150

This formula describes a function that combines the number of pages being read with the time elapsed since the start of  reading. Note that when T = 0, L = 150 (the original number of pages  to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).

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Answer:

$2,631.55

Step-by-step explanation:

To find the total amount in the account after 6 years, we can use the compound interest formula.

[tex]\boxed{\sf A=P\left(1+\dfrac{r}{n}\right)^{nt}}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2000\left(1+\dfrac{0.046}{4}\right)^{4 \cdot 6}[/tex]

[tex]\implies \sf A=2000\left(1+0.0115\right)^{24}[/tex]

[tex]\implies \sf A=2000\left(1.0115\right)^{24}[/tex]

[tex]\implies \sf A=2000\left(1.3157739...\right)[/tex]

[tex]\implies \sf A=2631.54794...[/tex]

Therefore, the total amount after 6 years is $2,631.55 rounded to the nearest cent.

Answer:

r=4

center: (-2,4)

Step-by-step explanation:

The equation of a circle is:

(x-h)²+(y-k)²=r²

(h,k) would be the center of the circle and r would be length of the radius

To find r, we simply take the square root of 16, which would be 4

And the center is given in the equation

In the given diagram, the volume of the composite shape is 12,672 ft³

From the question, we are to calculate the volume of the given composite shape

The composite shape is made up of a pyramid and a cuboid

Thus,

Volume of the shape = Volume of pyramid + Volume of cuboid

Volume of pyramid = 1/3 × base area × height

Volume of cuboid = Length × Width × Height

Calculating the volume of the pyramid

Volume of pyramid = 1/3 × 24² ×15

Volume of pyramid = 1/3 × 576 ×15

Volume of pyramid = 576 × 5

Volume of pyramid = 2880 ft³

Calculating the volume of the cuboid

Volume of the cuboid = 24² × 17

Volume of the cuboid = 9792 ft³

Thus,

Volume of the shape = 2880 ft³ + 9792 ft³

Volume of the shape = 12,672 ft³

Hence, the volume of the shape is 12,672 ft³

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It will take 15.03 years for Bentley's money to triple.

For Bentley:

We have

Principal (P) = $670

Interest rate (r) = 6 7/8% = 0.06875 (compounded quarterly)

Time (t) = unknown

Amount after t years (A) = [tex]P(1 + r/4)^{4t}[/tex]

For Camden:

We have

Principal (P) = $670

Interest rate (r) = 7 3/8% = 0.07375 (compounded annually)

Time (t) = unknown

Amount after t years (A) = [tex]P(1 + r)^t[/tex]

We have to find t such that 3P_Bentley = Camden.

[tex]2010 = 2010(1 + r/4)^{4t} / (1 + r)^t[/tex]

Simplifying, we get:

[tex](1 + r/4)^{4t} / (1 + r)^t = 1/3[/tex]

Taking natural logarithm:

4t ln(1 + r/4) - t ln(1 + r) = ln(1/3)

4 ln(1 + r/4) - ln(1 + r) = ln(1/3) / t

t = (4 ln(3.88356) - 4 ln(16)) / ln(3)

Solving for t, we get:

t = 15.034752564

t = 15.03 years.

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In order to do a comparison for percents, you must convert them to decimal form and then juxtapose the decimal values side by side to see which is greater or less.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent sign is commonly used, however the acronyms pct., pct, and sometimes pc are also used. A % is a number with no dimensions; it has no unit of measurement.

To calculate the percentage, divide the amount by the total value and multiply the result by 100.

Divide a percentage by 100 to get a decimal. So 25% is equal to 25/100, or 0.25. Multiply a decimal by 100 (simply shift the decimal point two places to the right) to convert it to a percentage. For example, 0.065 equals 6.5% and 3.75 equals 375%.

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Answer:

$162.01

Step-by-step explanation:

amount of money she earns: 12($18.50) = $222

spends $59.99

amount of money after her purchase: $222-$59.99=$162.01

The measures of center for this data set are the mean and median. The mean is 5.1 and median is 6.

The measure of variability is the range. The range is 10.

The measures of center describe the typical or central value of the data. For this data set, we can use the mean or the median as measures of center. The mean is the average of all the quiz scores, while the median is the middle value when the scores are arranged in order.

Mean = (0x1 + 1x0 + 2x0 + 3x0 + 4x0 + 5x2 + 6x4 + 7x2 + 8x2 + 9x1 + 10x0) / (1+0+0+0+0+2+4+2+2+1+0) = 5.1

Median = 6 (the middle score)

The measures of variability describe the spread or dispersion of the data. For this data set, we can use the range. The range will be:

= Highest score - Lowest score

= 10 - 0

= 10

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The line plot shows a student's quiz scores.

Quiz Scores

0 = 1

1,2,3,4 = 0

5 = 2

6 = 4

7 = 2

8 = 2

9 = 1

10 = 0

Which measures of center and variability should be used to describe the data?

we know that

discriminant of quadratic is [tex]b^{2}[/tex]-4ac

putting values we get

81-32

= 49

hence the discriminant is 49

The tangent function for the given terminal point is undefined.

The given terminal point of Θ is (0,-1). The tangent of an angle is defined as the quotient between the y-component and the x- component of the terminal point.

So, according to the question, tan Θ = -1/0. Hence, tan Θ is undefined as -1/0 is not defined.

Hence, tan Θ for the given function is not defined.

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The solutions of the inequalities are shown below

x [tex]\geq[/tex] 5

x< 13

x[tex]\geq[/tex]1

x> 1

Solving inequalities involves finding all possible values of a variable that make the inequality true. The process for solving an inequality depends on the type of inequality and the operations involved.

[tex]6^x + 4 \leq 6^{2x - 1} \\x + 4 \leq 2x - 1\\x - 2x\leq -1 - 4\\-x \leq -5\\x \geq 5[/tex]

[tex]2^{x + 3} > 4x^{x - 5} \\2^{x + 3} > 2^{2x - 10}\\x + 3 > 2x - 10\\x - 2x > - 10 - 3\\-x > - 13\\x < 13[/tex]

[tex]9^x \leq 9^{2x - 1}\\ x \leq 2x - 1\\x - 2x \leq -1\\-x \leq -1\\x \geq 1[/tex]

[tex]5^4 > 25^{2x} \\5^4 > 5^{4x} \\4 > 4x\\x > 1[/tex]

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The inequality to represent the situation is 11x + 18 ≤  40.

The rental car company charges $22 per day to rent a car at 0.08 for every mile driven. Samuel wants to rent a car knowing that he plans to drive 450 miles he has at most to spend $80.

Therefore, the inequality to represent the situation of Samuel when x is the number of days can be represented as follows:

Hence,

22x + 0.08 × 450 ≤ 80

22x + 36 ≤  80

Divided both sides of the inequality by 2

11x + 18 ≤  40

Hence, the required inequality expression is 11x + 18 ≤  40

where

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Answer: C: 5/8

Step-by-step explanation:

Simply 5/8 of the bar is filled in

Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.

Here, we have,

Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.

Positive Outcomes/Total Results = x/n = Probability(Event)

Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.

Here in the question,

Total region = 8.

Shaded region = 5

So, probability of falling in the shaded region = 5/8

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The 90% confidence interval based on the data provided will be (0.6152, 0.7848)

It should be noted that standard error = ✓[(p * q) / n]

p = population proportion

q = 1 - p

n = sample size

sample proportion = x / n = 105 / 150 = 0.7

standard error = ✓(p * q) / n] = sqrt[(0.7 * 0.3) / 150] = 0.0516

margin of error = 1.645 * 0.0516 = 0.0848

Confidence interval = sample proportion ± margin of error

                 = 0.7 ± 0.0848

                 = (0.6152, 0.7848)

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Answer:

See explanation.

Step-by-step explanation:

Let's analyze each solution to determine if it's viable or non-viable based on the given constraints: Johnnie and Amy have $38.50, and they cannot buy more than 7 lunches.

1. 8 slices of pizza and 0 hamburgers

This solution is non-viable because they are not allowed to buy more than 7 lunches. In this case, they would be buying 8 lunches.

2. 5 slices of pizza and 2 hamburgers

Cost: 5×4.75+2×5.55=23.75+11.10=34.85

This solution is viable because the total cost is within their budget, and they are buying 7 lunches.

3. 4 slices of pizza and 3 hamburgers

Cost: 4×4.75+3×5.55=19.00+16.65=35.65

This solution is viable because the total cost is within their budget, and they are buying 7 lunches.

4. 3 slices of pizza and 2 hamburgers

Cost: 3×4.75+2×5.55=14.25+11.10=25.35

This solution is non-viable because they are only buying 5 lunches, which is less than the maximum allowed. But if it is acceptable to only buy below 7 lunches, then this solution can be viable.

5. 2 slices of pizza and 6 hamburgers

Cost: 2×4.75+6×5.55=9.50+33.30=42.80

This solution is non-viable because the total cost exceeds their budget.

6. 0 slices of pizza and 7 hamburgers

Cost: 7×5.55=38.85

This solution is non-viable because the total cost exceeds their budget.

In conclusion, the viable solutions are:

5 slices of pizza and 2 hamburgers

4 slices of pizza and 3 hamburgers

Possible in being viable:

3 slices of pizza and 2 hamburgers

The length of the rectangle with the above information is calculated as: 7 feet.

Let the length of the rectangle be l and the width be w. Then, we know that:

Perimeter = 2(l + w) = 18 feet

Area = lw = 14 square feet

We can use the first equation to solve for one of the variables in terms of the other:

l + w = 9

l = 9 - w

Substituting l = 9 - w into the equation for the area, we get:

(9 - w)w = 14

w² - 9w + 14 = 0

Factorize

(w - 2)(w - 7) = 0

Therefore, w = 2 or w = 7. Since the length of the rectangle must be larger than its width, we choose w = 2 and l = 9 - w = 7.

Thus, the length of the rectangle is 7 feet.

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1) The amount is php 340,060

2) The rate is 13%

3) The amount is  php 137,622

Compound interest is commonly used in many types of financial products, such as savings accounts, CDs, and loans.

1)

[tex]A = P(1 + r/n)^nt\\A = 80000( 1 + 0.16)^9.75\\A = php 340,060[/tex]

2)

[tex]12300 = 9750(1 + r)^2\\12300/9750 = (1 + r)^21.26 = (1 + r)^2\\ln 1.26 = 2 ln1 + r\\ln 1.26/2 = ln1 + r\\0.12 = ln1 + r\\e^{0.12} = 1 + r\\r = e^{0.12} - 1\\r = 0.13\\r = 13%[/tex]

3)

[tex]A = 50000(1 + 0.15/2)^2 * 7\\A = php 137,622[/tex]

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If function "h" is one-to-one function which is having values h(-9) = 5, and h(3) = -4, then the inverse statement is (d) h⁻¹(-4) = 3.

We know that the function "h" is a one-to-one function, so, it has an inverse function (h⁻¹). To find the inverse function, we need to exchange  roles of "x" and "y" and solve for y. This gives:

x = h(y)

y = h⁻¹(x)

The given values of function "h" are h(-9) = 5 and h(3) = -4, we find the values of h⁻¹(5) and h⁻¹(-4):

h(-9) = 5

So, h⁻¹(5) = -9 (by exchanging roles of x and y)

and h(3) = -4

So, h⁻¹(-4) = 3 (exchanging the roles of x and y)

The function "h⁻¹(-4) = 3" is represented in option (d).

Therefore, the correct option is (d).

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Answer:

Triangle A = scalene

Triangle B = scalene

Triangle C = equilateral

Step-by-step explanation:

scalene triangle = all lengths are different

isosceles triangle = 2 side lengths are the same

equilateral triangle = all 3 side lengths are the same

The resulting matrix after row 1 is multiplied by 2 is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

The first row is given as follows:

7, -4 and 8.

Multiplying the first row by two, we have that:

(when we multiply a matrix by a constant, each element of the matrix is multiplied by the constant).

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

(the second row was kept constant, while the first row was multiplied by 2).

The matrix is:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

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Let's assume that the number of Android phones sold is x and the number of iOS phones sold is y. Then we can write two equations based on the given information:

x + y = 110    (equation 1)

400x + 650y = 54000   (equation 2)

To solve for x and y, we can use any method of solving systems of equations. Here, we will use the substitution method:

From equation 1, we can solve for x in terms of y: x = 110 - y

Substitute x = 110 - y into equation 2 and solve for y:

400(110 - y) + 650y = 54000

44000 - 400y + 650y = 54000

250y = 10000

y = 40

Substitute y = 40 into equation 1 and solve for x:

x + 40 = 110

x = 70

Therefore, the phone store sold 70 Android phones and 40 iOS phones.

Note that in the proof stated above, there is no incorrect statement.

The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.

The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.

The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.

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Step-by-step explanation:

m=y1-y2/x1-x2

m=2-8/5-8

m=-6/-3

m=2

y=m(x-x1)+y1

y=m(x-8)+8

y=2x-16+8

y=2x-22

Answer: Y=mx+c

Step-by-step explanation:

The Slope-Intercept Form can be written in the form: y = mx + c Where “m” is the slope of the line “c” is the y-intercept of the equation of the line

Answer:

Step-by-step explanation:

a

The missing part of the attached proof:

a) definition of angle congruence

b) ∠CPA ≅ ∠CPB

c) CP ≅ CP

The complete paragraph proof would be,

Because CP is perpendicular bisector of AB, CP is perpendicular to AB and point P is the midpoint of AB.

By definition of midpoint,

AP = BP

and by the definition of perpendicuar lines,

m∠CPA = m∠CPB = 90°

Then by definition of segment congruence,

AP ≅ BP

and by definition of angle congruence,

∠CPA ≅ ∠CPB

By the reflexive property of segment congruene,

CP ≅ CP

So, ΔCPA ≅ ΔCPB         ........by SAS congruence theorem

and CA ≅ CB because corresponding parts of congruent triangles are congruent.

So, CA = CB by the definition of segment congruence.

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Answer: We can solve this problem by finding the total weight of the meat and then dividing by the weight of each patty to see if we can make the desired number of patties.

Let's add the weights of the two packages of meat:

10 + 11.5 = 21.5

For option A, we need 87 1/4-pound patties.

Each pound of meat will yield 4 patties of this size, so 21.5 pounds of meat will yield:

21.5 x 4 = 86 patties

Since we need 87 patties, Claude does not have enough meat for option A.

For option B, we need 45 1/2-pound patties.

Each pound of meat will yield 2 patties of this size, so 21.5 pounds of meat will yield:

21.5 x 2 = 43 patties

Since we need 45 patties, Claude does not have enough meat for option B.

For option C, we need 30 1/2-pound patties and 2 74-pound patties.

Each pound of meat will yield 2 patties of the smaller size and 1 patty of the larger size, so 21.5 pounds of meat will yield:

(21.5 x 2) + (2 x 1) = 43 + 2 = 45 patties

Since Claude only has 21.5 pounds of meat, he does not have enough for option C.

For option D, we need 29 3/4-pound patties.

Each pound of meat will yield 1.5 patties of this size, so 21.5 pounds of meat will yield:

21.5 x 1.5 = 32.25 patties

Since we only need 29.75 patties, Claude has enough meat for option D.

Therefore, the answer is Yes, Claude can make 29 3/4-pound hamburger patties.

Gabriela walks 1 mile distance on her way home from school as she is running part of the way.

The distance between two things is measured in distance units like miles, kilometres, or metres. Given that it only possesses magnitude and not direction, distance is a scalar number.

We must ascertain Gabriela's total trip distance before we can respond to this query.

We can get the overall distance by adding the distance she runs to the distance she walks because she runs a portion of the route and walks the other.  

Gabriela commutes two miles to school, so

She needs to travel a total of 2 miles.

We need to figure out how far she runs because she is running a portion of the way.

Since running is typically faster than walking, we can infer that she covers the distance in one mile by running half of it.

She will therefore need to walk the additional mile.  

Gabriela walks a mile on her way home from school, which is the answer to the question.

This is because she walks the remaining mile and runs the first mile.

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The class mark of the modal class is: 25

From the given histogram, the following Frequency Distribution is obtained:

Class Interval Mid point Frequency

625-675 650 3

676-726 701 5

727 - 777 752 7

778 - 828 803 8

829 - 879 854 6

880 - 930 905 2

931 - 981 956 0

982 - 1032 1007 1

b. To find the lower class limit of the first class:

First class: 625

c. The upper limit of the first class is:

First class: 676

The class mark of the modal class is:

The modal class is: 803

The class mark is upper limit + lower limit/2

Thus, 828-778/2

=> 50/2

The class mark of the modal class is: 25

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Answer:

Set your calculator to degree mode.

cos(37°) = 52/x

x cos(37°) = 52

x = 52/cos(37°) = 65.1

The amount of water in the basement is V = 22,500 gallons

Given data ,

To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.

First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:

50 feet x 40 feet x 1.5 feet = 3,000 cubic feet

There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:

3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons

Hence , there are 22,500 gallons of water in the basement

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