The
• The top of a second mattress has 1½ times as much area as
the first mattress. What is the area of the top of the second
mattress? Write an equation to model the problem.

Any sequence of five spins that consists only of numbers 1 and 2 would be an outcome of Event A.

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

Event A = the spinner lands on numbers all less than 3

An outcome of Event A would be a sequence of five spins on the spinner that result in numbers all less than 3,

For example: 1, 2, 1, 2, 1.

See that each number in the above sequence is less than 3

Hence, the event A represents outcomes less than 3

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Answer:

a) $40.05

b) $161.99

c) C(x) = 6.45 + 0.93x, if x ≤ 20

C(x) = 6.45 + 0.84x, if x > 20 and x ≤ 50

C(x) = 6.45 + 0.77x if x > 50

Note that the angle labeled ∠PQR is given as 70°

First, note that the Lengths of tangents drawn from external points to a circle are equal in length. This means that:

Length of PT = Lenght of TR

This makes Δ TPR and Isosceles Triangle.

This also makes ∠P = ∠R..............................1

Thus:

∠P + ∠R + ∠T = 180°

Given expression 1 above,

we can say:

x + x + 38° = 180°

Thatis 2x = 180 - 40

2x = 140°

x = 140/2

x = 70°

Note that Line TP is parallel to Line QR and Line PQ is a transversal line. Thus, ∠P and ∠Q are co-interior angles. This means that:

∠P + ∠Q = 180°

Recall that:

70 + 40 + ∠Q = 180°
∠Q = 180 -70 -40

∠Q = 70°

Thus: ∠ PQR = 70°

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Full Question:

See attached image.

Answer: Matt completes his homework faster than Jill by 14 minutes

Step-by-step explanation:

5*12= 60 so if I multiply 3 by 12 I get how many minutes it took Matt to finish her homework. (which was 36 minutes)

6*10=60 so if I multiply 5 by 10 I get how many minutes it took Jill to finish her homework (which was 50 minutes)

50 minus 36 is a difference of 14

The temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.

What is the temperature?

Temperature is a physical property of matter that measures the degree of hotness or coldness of an object. It is a scalar quantity that is expressed in units such as Celsius, Fahrenheit, or Kelvin.

The statement "f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M."f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.

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the simplified Answer to the given expression 36 x 5 +59 x(234)(51) will be 7,04,286.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given, an expression 36 x 5 +59 x(234)(51)

Simplifying using PEMDAS

=> 36 x 5 +59 x(234)(51)

First, we will open a bracket

=> 36 * 5 + 59 * 11934

Now multiple of the given terms:

=> 180 + 704106

Addition of the last two-term

=> 7,04,286

Therefore, the simplified Answer to the given expression will be 7,04,286.

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The measure of angle D, m∠D, found using the specified lengths of the three sides of the triangle and the law of cosines is; m∠D = 75.7°

The law of cosines specifies the relationship between the measures of an angle, and the lengths of the three sides of a triangle. Specifically, the law of cosines states that the square of the length of a (reference) side of a triangle, is equivalent to the sum of the squares of the lengths of the other two sides, less the product of 2, the lengths of the other two sides and the cosine of the angle opposite to the reference side.

Mathematically, the law of cosines can be presented as follows;

Where;

a, b, and c are the lengths of the three sides of the triangle

Angle A, ∠A, is the opposite angle to side a.

Therefore, according to the law of cosines, we get;

38² = 36² + 24² - 2 × 36 × 24 × cos(∠D)

2 × 36 × 24 × cos(∠D) = 36² + 24² - 38² = 428

2 × 36 × 24 × cos(∠D) = 428

cos(∠D) = 428/(2 × 36 × 24) = 428/1728 = 107/432

cos(∠D) = 107/432

m∠D = arccos(107/432) ≈ 75.7°

The measure of angle D, m∠D ≈ 75.7°

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The minimum = (-11, -2)

And the maximum = (2, 5).

Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

Given:

The function,

f(x) = ∛(x + 3).

The graph of the function is given in the attached image.

f'(x) = d/dx{∛(x + 3)}

     = 1/{3(x + 3[tex])^{2/3}[/tex]}

The critical point = (-3, 0)

The minimum = (-11, -2)

And the maximum = (2, 5).

Therefore, all the required values are given above.

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Answer:

f(x) = 2[tex](\frac{1}{2}) ^{x}[/tex]

Step-by-step explanation:

The y intercept is 2 where in the parent function it is 1.  In the parent function, as x is increasing y is increasing.  In this function as the x is increasing the y is decreasing.

The given function

g(x)  = [x² - 3x -10][x²+ 2x² -5x +4  ]

is continuous at  x = -1,

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  [x² - 3x -10][x²+ 2x² -5x +4  ]

To check whether it is continuous at x = -2

First taking LHL,

[tex]\lim_{h \to \00}[/tex]  [(-1-h)² - 3(-1-h) -10][(-1-h)²+ 2(-1-h)² -5(-1-h) +4  ]

[tex]\lim_{h \to \00}[/tex]  [(-1-0)² - 3(-1-0) -10][(-1-0)²+ 2(-1-0)² -5(-1-0) +4  ]

⇒   -6 x 12

⇒     -72

Now, taking RHL

[tex]\lim_{h \to \00}[/tex]  [(-1+h)² - 3(-1+h) -10][(-1+h)²+ 2(-1+h)² -5(-1+h) +4  ]

[tex]\lim_{h \to \00}[/tex]  [(-1+0)² - 3(-1+0) -10][(-1+0)²+ 2(-1+0)² -5(-1+0) +4  ]

⇒   -6 x 12

⇒     -72

The value at x = -1

F(-1)  =  [(-1)² - 3(-1) -10][(-1)²+ 2(-1)² -5(-1) +4  ]

⇒ -6 x 12

⇒   -72

RHL = LHL =  F(-1)

Hence Proved,  the function is continuous at x = -1

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The total number of shaded squares will be equal to the product of 4 x 2/3.

A. For the problem 4 x 2/3, you can draw a model using rectangular arrays or area models. Draw four columns, each representing one of the four groups, and two rows to represent the two-thirds. Shade in two-thirds of the first column, then repeat for the next three columns. The total number of shaded squares will be equal to the product of 4 x 2/3.

B. For the problem 3 x 2/5, you can also draw a model using rectangular arrays or area models. Draw three columns, each representing one of the three groups, and two rows to represent the two-fifths. Shade in two-fifths of the first column, then repeat for the next two columns. The total number of shaded squares will be equal to the product of 3 x 2/5.

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He has 5hrs  to drive and 275 miles to drive to cover to arrive at the university.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

His college is 330 miles away.

After an hour of driving, he still has 275 miles to go.

If the roads are clear, he'll be able to keep up that pace for the whole drive.

If he drives 55 miles in 1 hr

he would drive 330 miles in

=6hrs.

his total travel time is 6 hr

He has 5hrs  to drive and 275 miles to drive.

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The number of square centimeters of icing that would be needed for one cake is equal to: C. 1,755 cm².

Since everything but the circular bottom of the cake was iced, the number of square centimeters of icing that would be needed for one cake can be calculated by using this mathematical expression:

Total surface area of cake = Curved surface area of cake + area of the top

Total surface area of cake = 2πrh + πr²

Where:

By substituting the given parameters into the total surface area of cake formula, we have;

Total surface area of cake = (2 × 3.14 × 13 × 15) + (3.14 × 13²)

Total surface area of cake = 1224.6 + 530.66

Total surface area of cake = 1755.26 ≈ 1755 square centimeter.

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Answer: C. 1,755 cm2

Hope this helps

the answer is -13. And this is why, because the negative sign is bigger so same sign add keep the same sign that’s why I got -13

Answer: The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven is 75° and it will increase at a rate of 25° per minute after being turned on.

The equation to model the temperature of the oven t minutes after being turned on is:

Temp = 75 + 25t

Where Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.

For example, if we want to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:

Temp = 75 + 25 * 17 = 75 + 425 = 500°

So, the temperature of the oven 17 minutes after being turned on is 500°.

In general, the temperature of the oven t minutes after being turned on can be found by substituting the value of t into the equation:

Temp = 75 + 25t.

Step-by-step explanation:

The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven will be;  75° and it will increase at a rate of 25° per minute after being turned on.

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation to model the temperature of the oven t minutes is:

Temp = 75 + 25t

Where, Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.

For example, if we need to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:

Temp = 75 + 25 * 17 = 75 + 425

Temp = 500°

Thus, the temperature of the oven 17 minutes after being turned on is 500°.

In general, the temperature of the oven t minutes after being turned on can be find by substituting the value of t into the equation:

Temp = 75 + 25t.

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1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.

The statistic is said to be in its simplest form is divided into its smallest equivalent fraction. What to do to find the most basic form. Look for common factors in the denominator and numerators. Confirm a fractional integer to verify if it qualifies as a prime number. A statement having two equal sides and an equaled sign in the middle is called an equation in mathematics. The general form of any equation contains the diplomas of all the variables in descending order. The conventional form of an equation is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). An identification holds true no matter what value is given to the variables.

given

equation 1 ) X2 +6x +3=0

by discriminant method

x =(6+√48)/2

=3+2√ 3

= 6.464.

equation 2) 5^2 + 2s - 6 = 0

= 25 + 2s - 6 = 0

= 19 = - 2s

s = 9.5

1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.

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Answer:

527.52 ft²

Step-by-step explanation:

The surface area of a cylinder is:

[tex]\displaystyle{2\pi r^2 + 2\pi r h}[/tex]

where r is radius and h is height.

From the attachment, we know that the radius (r) is 7 ft and the height is 5 ft. Therefore:

[tex]\displaystyle{\text{Surface Area} = 2 \cdot 3.14 \cdot (7)^2 + 2\cdot 3.14 \cdot 7 \cdot 5}\\\\\displaystyle{\text{Surface Area} = 6.28 \cdot 49 + 6.28 \cdot 35}\\\\\displaystyle{\text{Surface Area} = 307.72 + 219.80}\\\\\displaystyle{\text{Surface Area} = 527.52 \ \: \text{ft}^2}[/tex]

Therefore, the surface area of the cylinder is 527.52 ft²

The length of the UW of the triangle is 18. The correct option is D.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The length UW will b calculated as:-

First, in ΔTWU apply the Pythagorean theorem,

TU² = UW² + 12²

TU² = UW² + 144

In ΔTWV apply the Pythagorean theorem,

VT² = 12² + 8²

VT² = 208

Apply Pythagorean theorem in ΔVTU,

( 8 + UW)² = VT² + TU²

Substitute the value of TU² in the above equation,

( 8 + UW)² = 208 + UW² + 144

UW² + 16UW + 64 = UW² + 208 + 144

16UW = 288

UW = 288 / 16 = 18

Therefore, the length of UW is 18.

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Refer to the given image

Kevin's solution is incorrect because he used wrong formula.

Correct area of triangle = 20 square inches.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height,

i.e. A = 1/2 × b × h

Given,

Height of triangle h = 8 inches

Base of the triangle b = 5 inches

Formula for area of triangle A = 1/2(b h)

A = 1/2 (8 × 5)

A = 40/2

A = 20 square inches.

Area by given formula for area of the triangle A = b h

A = 8 × 5

A = 40

Since actual area of the triangle is 20 square inch, Kevin found the area with wrong formula.

Actual area of triangle is 20 square inches.

Hence, Kevin's solution is incorrect, as the formula used is wrong.

20 square inches is correct area of the triangle.

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We can conclude, the number -7/5 is less than the number 1 1/5.

One of the ways to know how a fraction compares to another is by simplifying the fraction, which can be done by dividing the numerator by the denominator.

Let's simplify the fractions given:

-7/5 = -1.4

-1 1/5 = 1 + 0.2 = -1.2

Moreover, in the case of negative numbers those that are closer to 0 are greater. Based on this, -1.2 is greater than -1.4, which means -7/5 is less than the number 1 1/5.

Note: This question is incomplete; here is the missing section:

The number -7/5 is less or greater than the number 1 1/5.

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Answer:

To find the account balance after 5 years, we need to calculate the compound interest earned during this period. The formula for compound interest is:

A = P × (1 + r/n)^(nt)

where:

A = the final amount of the investment

P = the principal investment amount ($1000)

r = the annual interest rate (7.2%)

n = the number of times that interest is compounded per year (1)

t = the number of years the investment is held (5)

So, plugging in the values into the formula, we get:

A = 1000 * (1 + 0.072/1)^(1 * 5)

A = 1000 * (1.072)^5

A = 1000 * 1.44444444

A = $1444.44

So, the account balance after 5 years would be $1444.44.

Answer:

Step-by-step explanation: I could mostly say $36,000. How I did it was:

1000x7.2x5=36,000

Could you find this helpful???

Answer:

Step-by-step explanation:

The monthly compound interest formula.

Future Value = monthly deposit x (1 + r) - 1/r

r = .07/12 = .00583

n = total number of time for compound = 35 years x 12 months/1 year = 420 months

PMT = monthly deposit = $200

Future Value = $200 x (1 + .00583)⁴²⁰ - 1/.00583

Future Value = $394,001.64 in 35 years

Total money you put into the account.

$200 x 420 months = $84,000

Total interest earned.

$394,001.64 - $84,000 = $310,001.64

The solution of the system of equations -6x -12= (1/2)x -4 include the following: D. x = -4 and x = -2.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-axis, which is given by  x = -4 and x = -2.

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The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If x and y are in direct proportion. Then the equation is given as,

y ∝ = x

y = kx

At x = 12 and y = 6, then the value of 'k' is given as,

6 = 12k

k = 1/2

Then the equation is given as,

y = (1/2)x

If the value of the variable 'x' is 2. Then the value of y is given as,

y = (1/2) 2

y = 1

The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.

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The mass of the sample after 4 days is 1.54 kg.

Exponential decay can be defined as the process in which a quantity decreases over time with the rate of decrease becoming proportionally smaller as the quantity gets smaller.

The formula for exponential decay is given by:

m(t) = m0 * e^(-kt)

where m(t) is the mass of the substance after time t

M0 is the initial mass

k is the decay rate parameter

E is the base of natural logarithms

Plugging in the values:

m(4) = 2.05 * e^(-0.04 * 4)

m(4) = 1.54 kg

Therefore, The mass of the sample after 4 days is 1.54 kg.

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