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The difference between 3 times a number x and 2 is 19. What is the value of x?

A. 7

B. 6

C. 5

D. 1

Answer:

the length of the opposite side of the triangle is approximately 21.8594 miles                    

Step-by-step explanation:

tan(theta) = opposite/hypotenuse

opposite = tan(theta) x hypotenuse

Substituting the given values, we get:

opposite = 0.7536 x 29

opposite = 21.8594 miles (rounded to four decimal places)

The expression to simplify is:

We use the distributive property, shown below, to simplify further:

Distributive Property

So, we have:

We can now add like terms, just adding up the numbers we have:

Answer:

The answer would be "j"

Step-by-step explanation:

First, you would want to find the value of the original equation:

5(y + 2) + 4

Use order of operations and distribute the five.

5y + 10 + 4

5y +14

This is the value of the original equation

Now we can work through the other options, but because we already know the answer, lets see about that one.

5 x y + 5 x 2 + 4

Again, use order of operations.

Multiply first

5y + 10 + 4

and complete the equation

5y + 14, which equals our original equation.

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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Answer:

2

Step-by-step explanation:

To find the interquartile range, subtract the lower quartile from the upper quartile.

The upper quartile is 7.

The lower quartile is 5.

Subtract.7–5=2

The interquartile range for Mike's teammates' shoe sizes is 2 sizes.

The interquartile range for Mike's teammates' shoe sizes is R = 2

The distance between the upper and lower quartiles is known as the interquartile range. Half of the interquartile range corresponds to the semi-interquartile range. Finding the values of the quartiles in a small data set is straightforward.

The spread of the data, or statistical dispersion, is measured by the interquartile range. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the spread between the data's 75th and 25th percentiles.

Given data ,

Let the interquartile range be represented as R

Now , the equation will be

Let the shoe sizes be represented as set A

A = { 2 , 4 , 6 , 8 , 10 }

Now , the upper range of the quartile is = 7

The lower range of the quartile is = 5

And , the interquartile range R = upper quartile - lower quartile

On simplifying , we get

The interquartile range R = 7 - 5 = 2

Hence , the interquartile range R = 2

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Answer:

1095.

Step-by-step explanation:

The increase per night is 545 - 435 = 110.

So on 6th night we can expect 435 + 6(110)

= 1095.

The area covered by the face of the building which has the shape of a parallelogram would be = 2,464m².

The parallelogram is defined as a type of quadrilateral that has two sides that are parallel which are opposite each other.

To calculate the area of one face of the building, the formula that needs to be used is the formula for the area of a parallelogram.

That is;

Area of parallelogram = base × height.

where;

height = 28 meters.

Base = 88 meters.

Therefore the area of the parallelogram = 28×88 = 2,464m²

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The answer is a+b+c≡7(mod13).

In modular arithmetic, the integers coprime (relatively prime) to n from the set of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n.

Given:  ca=−2ab−bc substituting this value to the other two equations we get b(a−c)=2b²(2a+c) & b(3a+c)=8b²(2a+c)

We know that  b≠0  (because  b  is a positive integer less than  13 ), so we can simplify it off. If  2a+c=0 , then also  a−c=0 , but this implies  a=c=0 , which is excluded. Thus we obtain

2b=a−c/ 2a+c

8b=3a+c/ 2a+c

Thus we need

4(a−c) / 2a+c=c+3a / 2a+c

and therefore  4a−4c=c+3a , that is,  a=5c .

Now we can substitute in  2ab+bc+ca=0  to get

10bc+bc+5c²=0

Since c≠0 we obtain 11b+5c=0, so 2b=5c Multiplying by 7 yields 14b=35c and so b=9c

Now we can substitute in

ab+2bc+ca=2abc

to get 45c²+18c²+5c²=90c³

Thus

3c²=12c³

and so −c=3, that is, c=10. Hence a=5c=11 and b=9c=12

Thus, a=11,b=12,c=10 and so a+b+c≡7(mod13).

Hence, the answer is a+b+c≡7(mod13).

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Answer:

The cost per ounce of the small cup is $0.269

Step-by-step explanation:

To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.

Cost per ounce = Cost of the cup ÷ Number of ounces in the cup

Cost of the cup = $2.69

Number of ounces in the cup = 10 oz

So,

Cost per ounce = $2.69 ÷ 10 oz

Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)

Therefore, the cost per ounce of the small cup is $0.269.

Answer:

I believe the answer is 6.6

Step-by-step explanation:

If you multiply 6 by 10 you get 60. Divide 60 by 9 you get 6.6

A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer: Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the following formula:

average rate of change = (y2 - y1)/(x2 - x1)

Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.

In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.

For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (g(3) - g(-1))/(3 - (-1))

= (9 + 18 - (1 - 6))/(4)

= 27/4

= 6.75

For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (f(3) - f(-1))/(3 - (-1))

= (2 - 2)/(4)

= 0

Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.

I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

Step-by-step explanation:

There are total cadies in the bag:

Probability of pulling a coffee candy is:

So each 5th candy should be coffee candy

Then you need to pull at least:

Note:

To ensure 3 coffee candies you would need to pull 25 - 2 = 23 candies

Answer:

(1, -4), (4, -1)

Step-by-step explanation:

A solution to a system of equations is when the two lines intersect. In this case, we have two intersections, which means two solutions.

From left to right, we first see an intersection at (1, -4).

Continuing to the right, we see another intersection at (4, -1)

These are our two solutions.

(1, -4), (4, -1)

Hope this helps!

The odds of getting a total of 15¢ is 1/36

Probability is the likelihood of a desired event happening.

George has the following coins to pick from 5¢, 2, 10¢, 3, 20¢, 2. That's six coins all together

To find the odd (or probability) of getting a total of 15¢ if he can only select two contains at random, we will need to look at the two possible combinations out of the six coins.

The combination that will give 15¢ is 10¢ and 5¢. Therefore, the odds is:

Probability(total of 15¢) = Probability(10¢) x Probability(5¢)

Pr(total of 15¢)  = 1/6 x 1/6 = 1/36     (Note: 5¢ and 10¢ appear once)

Therefore, the odds of him getting a total of 15¢ is 1/36

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Answer:

The Area of the composite figure would be 76.26 in^2

Step-by-step explanation:

According to the Figure Given:

Total Horizontal Distance = 14 in

Length = 6 in

To Find :

The Area of the composite figure

Solution:

Firstly we need to find the area of Rectangular part.

So We know that,

\(\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}\)

Here, Length is 6 in but the breadth is unknown.

To Find out the breadth, we’ll use this formula:

\( \boxed{\rm \: Breadth = total \: distance - Radius}\)

According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,

\( \longrightarrow\rm \: Length \: of \: the \: circle = Radius\)

\(\longrightarrow \rm \: 6 \: in = radius\)

Hence Radius is 6 in.

So Substitute the value of Total distance and Radius:

\( \longrightarrow\rm \: Breadth = 14-6\)

\( \longrightarrow\rm \: Breadth = 8 \: in\)

Hence, the Breadth is 8 in.

Then, Substitute the values of Length and Breadth in the formula of Rectangle :

\( \longrightarrow\rm \: Area \: of \: Rectangle = 6 \times 8\)

\(\longrightarrow \rm \: Area \: of \: Rectangle = 48 \: in {}^{2} \)

Then, We need to find the area of Quarter circle :

We know that,

\(\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}} \)

Now Substitute their values:

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4} \)

Solve it.

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4} \)

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4} \)

\(\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9\)

\(\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2} \)

Now we can Find out the total Area of composite figure:

We know that,

\(\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}\)

So Substitute their values:

\(\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26\)

Solve it.

\(\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}} \)

Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.

\( \rule{225pt}{2pt}\)

I hope this helps!

The radius of a circle with circumference of 4π/3 is equal to 2/3

The circumference of a circle is the same as the total length of the circle boundary. It can also be called the perimeter of a circle.

The circle in question have its circumference as

4π/3.

circumference of circle = 2πr

4π/3 = 2πr

divide through by π

4/3 = 2r

r = 4/(3×2) {by cross multiplication}

r = 4/6

radius = 2/3.

Therefore, the radius of a circle with circumference of 4π/3 is equal to 2/3

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The radius of a circle with a circumference of 4π/3 is equal to 2/3 units.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, we have the following;

Circumference of circle, C = 2πr

4π/3 = 2πr

4π = 6πr

Radius, r = 4/6 = 2/3 units.

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Answer:

y=1/2x+11

Step-by-step explanation:

use the slope of one half and the point and put them into point slope form.

y-y1 = m(x-x1) or y-16 = 1/2(x-10), distribute 1/2

y-16=1/2x - 5, add 16 to both sides

y = 1/2x + 11

The multiplicative rate of change for the function  is approximately.

To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.

The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.

Using the chain rule, the derivative of is:

Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is

The value of ln(2/5) is approximately -0.916.

It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.

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Answer:

The pvalue of Z when X = 104.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

What is the probability that, for an adult after a 12-hour fast, x is less than 104?

This is the pvalue of Z when X = 104.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{104 - \mu}{\sigma}\)

\(\mu\) and \(\sigma\) are the values of the mean and of the standard deviation, respectively.

The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = \(\dfrac{360^{\circ}}{6}\) = 60°

Therefore;

b. Area of circular pie = π·r²

Where;

\(r = \mathbf{\dfrac{d}{2}}\)

Therefore;

\(r = \dfrac{9}{2} = \mathbf{ 4.5}\)

\(The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}\)

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.

d. Let the arc length of the pie piece = 7 inches

\(\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8\)

\(The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}\)

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A) The probability that a piece of toast lands butter side down when dropped from a 2.5-foot high table is 0.81 means that out of all possible outcomes of dropping a piece of toast from that height, 81% of the time it will land with the butter side facing down.

B) No, it does not mean that exactly 81 out of 100 pieces of toast will land butter side down. The probability of a single piece of toast landing butter-side down is 0.81, so when 100 pieces of toast are dropped, we can expect around 81 of them to land butter-side down on average, but the actual number may vary due to randomness.

C) Maria may or may not be surprised, depending on her expectations and the level of significance she sets for her test. To carry out a simulation, we can use a random number generator to simulate dropping 10 pieces of toast with a probability of 0.81 of landing butter side down. We can repeat this simulation multiple times, say 1000 times, and count the number of times the simulation yields 4 or fewer pieces of toast landing butter side down. If this rarely happens (e.g., less than 5% of the time), we can say that Maria should be surprised.

D) The dot plot displaying the results of 50 simulated trials of dropping 10 pieces of toast can provide some information about the variability of the outcomes. If most of the dots are clustered around 8 or 9 (which would correspond to 80% or 90% of the pieces of toast landing butter side down), then Maria's result of only 4 out of 10 pieces landing butter side down would be considered unusual, and she should be surprised. However, if the dots are spread over a wide range, it would suggest that getting 4 out of 10 is not that uncommon, and Maria should not be surprised.

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Answer:

Translation

Step-by-step explanation:

You're moving down 5 units, and left 1 unit, so therefore it's a translation 5 units down and 1 unit to the left.

Answer:

option number 2

Step-by-step explanation:

you can see inital and final co ordinate

Answer:

y > -2

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph:

Therefore, the most appropriate range from the given answer options is:

Note:  The graph appears to be the exponential function  \(y=2^x-2\)  with a horizontal asymptote at y = -2.  This means that the curve will get closer and closer to y = -2 as x approaches negative infinity, but it will never touch it.  The function approaches infinity as x approaches infinity.  Therefore, the range for this function is y > -2

The inverse of matrix A, if it exists, is:

A^(-1) = [7/43, 2/43; 10/43, 9/43]

To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.

Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:

det(A) = (9 * 7) - (-2 * -10)

= 63 - 20

= 43

Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.

The formula to calculate the inverse of a 2x2 matrix is:

A^(-1) = (1/det(A)) * [d, -b; -c, a]

Plugging in the values from matrix A and the determinant, we have:

A^(-1) = (1/43) * [7, 2; 10, 9]

Simplifying further, we get:

A^(-1) = [7/43, 2/43; 10/43, 9/43].

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Answer:

the answer should be 36