1. Linda says the two expressions (12x+16) - 6x and -4(x + 2) are equivalent
Is she correct Explain how you know by showing your work.

The height of the building in the scale drawing will be 5 inches.

The scale ratio must be used to determine the height of the building in the scale drawing.

The scale ratio is:

1 inch = 170 feet

We can devise a ratio:

1 inch / 170 feet = x inches / 850 feet

In the scale drawing, x represents the height of the building in inches.

To find x, we can cross-multiply and simplify:

1 inch * 850 feet = 170 feet * x inches

850 inches = 170 feet * x

Dividing both sides by 170 yields:

x = 850 inches / 170 = 5 inches

As a result, the building's height will be 5 inches in the scale drawing.

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The t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (df) is 1.753050356.

We have to determine the t-value.

The area in the right tail is 0.10 with 32 degrees of freedom(df).

The t-test is a test that is used as an alternative to the z-test in statistics. If the data are normally distributed but the sample size is small and the population standard deviation is unknown, the t-test is utilized.

A value that appears on the t distribution is the critical t value. The area under the curve and the degrees of freedom can be used to determine the t statistic value.

Using Excel Formula,

The t-value = (=TINV(0.1,15))  

The t-value = 1.753050356

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The angles for the given parallel lines are estimated.

m(∠DGF ) = 92; m(∠HGF ) = 88; m(∠AGD ) = 88; m(∠BDG ) = 92; m(∠BDC ) = 88; m(∠CDE ) = 92 ; m(∠EDG ) = 88.

A line that cuts over two parallel lines is referred to as a transversal line.

Each pair of internal angles located on the exact side of a transversal that meets two parallel lines is supplementary, or they add up to 180°.

The opposing angles created by the junction of two lines are known as vertical angles but rather vertically opposite angles.

m(∠AGH ) = m(∠BDG ) (corresponding angles)

3x +  2 = 2x + 32

x = 30

m(∠AGH ) = 3(30) +  2 = 92

m(∠BDG ) = 2(30) + 32 = 92

m(∠DGF ) = m(∠AGH ) = 92 (vertically opposite angles)

m(∠HGF ) = 180 - m(∠AGH ) = 180 - 92 = 88 (linear pair).

m(∠AGD ) = m(∠HGF ) = 88 (vertically opposite angles)

m(∠BDG ) = 92 (calculated earlier)

m(∠BDC ) = m(∠AGD ) =  88 (corresponding angles)

m(∠CDE ) = m(∠BDG ) = 92  (vertically opposite angles)

m(∠EDG ) = m(∠BDC ) =  88  (vertically opposite angles).

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The probability of one event given the known outcome of a (possibly) related event is known as conditional probability.

Conditional probability is the measure of the probability of an event occurring given that the another event will already occurred. It is denoted by P(A | B), which represents the probability of event A given that event B has occurred. The conditional probability of A given B can be calculated using the formula:

P(A | B)=P(A and B)/P(B)

where P(A and B) represents the probability of both events A and B occurring, and P(B) represents the probability of event B occurring.

For example, consider a deck of 52 playing cards. The probability of drawing a king from the deck is 4/52, or 1/13. If one card is drawn from the deck and it is revealed to be a heart, then the probability of drawing a king from the remaining cards in the deck that are not hearts is:

P(king | heart) = P(king and heart) / P(heart)

P(king and heart) = 1/52 (there is only one king of hearts in the deck)

P(heart) = 13/52 (there are 13 hearts in the deck)

P(king | heart) = (1/52) / (13/52) = 1/13

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The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.

The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.

Using this theorem, we can write:

y = hypotenuse

Opposite of 30° angle = 5 = hypotenuse/2

Opposite of 60° angle = x = hypotenuse × (√(3)/2)

Solving for the hypotenuse in terms of y from the first equation, we get:

hypotenuse = 5×2 = 10

Substituting this value into the third equation, we get:

x = 10 × (√(3)/2) = 5 × √(3)

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In response to the stated question, we may state that According to the inequality facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is: B. g > 1.5

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

We know that h > 3 and h - 2g = 0.

When we plug h = 2g into the first inequality, we get:

2g > 3

g > 1.5

As a result, we know that g must be bigger than 1.5, ruling out alternatives C and D.

Option A is not certainly true since we don't know if the value of g is bigger than 2.5.

Option E is also not certainly true, because we only know that g is more than 1.5, but not if it is bigger than 2.

According to the facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is:

B. g > 1.5

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Answer:To simplify the expression, you need to combine the like terms, which are the terms that have the same variable and power. In this case, the like terms are -3a and 5a:

(-3a + 56) + (5a + 40)

= (-3a + 5a) + (56 + 40)

= 2a + 96

Therefore, the simplified expression is 2a + 96.

Enjoy (:

Step-by-step explanation:

By finding the derivative and evaluating it in x = -2, we will see that the slope is 12.

To find the slope of the tangent line at a given point, we need to take the derivative and evaluate it in the x-value of the given point.

Here we have the function:

f(x) = 3x² + 7

If we differentiate it with respect to x, we will get:

f'(x) = 2·3x

f'(x) = 6x

That is the derivative, now we want to find the slope at (-2, 19), to find the slope at that point we need to get:

f'(-2) = 6·-2

f'(-2) = -12

That is the slope of the graph.

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Answer: Beth Blauer

Step-by-step explanation:

According to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]

Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric shapes using algebraic principles. It involves the use of coordinates to represent points, lines, curves, and other geometric figures on a plane or in space.

we need to know the coordinates of its foci, co-vertices, and the center. We can start by finding the center of the ellipse, which is the midpoint of the line segment joining the foci:

Center = ( (-8 + (-8))/2 , (14 + (-16))/2 ) = (-8,-1)

Next, we can find the distance between the foci, which is given by:

[tex]distance between foci = 2c = sqrt[(14 - (-16))^2 + (-8 - (-8))^2] = 30[/tex]

where c is the distance from the center to either focus.

We also know that the distance between the co-vertices is given by:

distance between co-vertices = 2a = |-16 - 0| = 16

where a is the distance from the center to either co-vertex.

Finally, we can use the standard form equation for an ellipse centered at the origin:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

where b is the distance from the center to either vertex.

To find b, we can use the Pythagorean theorem:

[tex]b^2 = c^2 - a^2 \\b^2 = 30^2 - 16^2\\b^2 = 784\\b = 28[/tex]

Now we have all the information we need to write the equation of the ellipse:

[tex](x+8)^2/16^2 + (y+1)^2/28^2 = 1[/tex]

Therefore, according to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]

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In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.

Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.

Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:

P(accurate order) = 1246 / 1300 = 0.958 for McDonald's

P(accurate order) = 1020 / 1100 = 0.927 Taco Bell

P(accurate order) = 708 / 800 = 0.885 for Burger King

P(accurate order) = 940 / 1000 = 0.94 for Wendy's

P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929

As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.

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From the given probability distribution, the probability of x being 4 in the given probability distribution is 0.15,

According to the given probability distribution in Table 1, the probability of x being 4 is 0.15. This means that out of all the possible values of x (0 to 6), there is a 15% chance that x will be equal to 4.

To understand the probability distribution better, we can visualize it using a graph. The x-axis represents the possible values of x, while the y-axis represents the probability of each value. We can plot the values from Table 1 to create a histogram or a bar graph.

From the graph, we can see that the probability distribution is skewed to the right, with the highest probability being at x=2. This means that there is a higher chance that x will be closer to 2 than to 0 or 6.

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Answer:

76(/783/)-468

Step-by-step explanation:

Answer:

Step-by-step explanation:

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The player should be willing to pay up to $12 to play this game and not lose money in the long run.

First we need to multiply the probability of winning by the amount won and subtract the probability of losing by the amount lost.

The probability of rolling a 1 on a 6-sided die is 1/6, and the probability of rolling any other number is 5/6.

So, the expected value of the game is:

(1/6) x $4 - (5/6) x $2

= ($4/6) - ($10/6)

= -$1/3

This means that on average, for every game played, the player can expect to lose $1/3.

To find out how much the player should be willing to pay to play this game and not lose money in the long run, we can set the expected value equal to zero:

(1/6) x $4 - (5/6) x $2 = $0

Simplifying the equation, we get:

$4/6 = $10/6

Multiplying both sides by x, we get:

(1/6) x - $2 = 0

Solving for x, we get:

x = $12

Therefore, the player should be willing to pay up to $12 to play this game and not lose money in the long run.

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In linear equation, 28  pieces of cake did Mrs Devi buy.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.  

                                   Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Cost of M cake = $3.5

For every 3 M cakes she bought 7 B cakes.

Let 1 unit be 3 M cakes and 7 B cakes. 1 unit costs= 3(3.5) + 7(2.5)= $28

She bought $112 / $28 = 4 units of cakes.

Which means 12 M cakes and 28 B cakes.

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Answer:

[tex](x-4)^2+(y+1)^2=162[/tex]

Step-by-step explanation:

Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):

[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]

Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]

The percentages of the area under curve are 50%, 68%, and 99.7%.

Assuming a standard normal distribution with mean m = 0 and standard deviation s = 1, the percentage of the area under the curve can be determined as follows

To the left of m: This is equivalent to finding the area to the left of the z-score corresponding to m = 0. This is 50%, as the normal distribution is symmetric around the mean.

Between m s and m 1 s: This is equivalent to finding the area between the z-scores corresponding to z = -1 and z = 1. Using a standard normal distribution table or calculator, this is approximately 68% (which is also known as the 68-95-99.7 rule).

Between m 3s and m 1 3s: This is equivalent to finding the area between the z-scores corresponding to z = -3 and z = 3. Using a standard normal distribution table or calculator, this is approximately 99.7% (which is also known as the 68-95-99.7 rule).

Therefore, the percentages of the area under the normal curve are: (a) 50%, (b) 68%, and (c) 99.7%.

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The length distance of ab between the points  (-4,-6) and b (3,2) is   10.6 units.

Now to find the distance between points A(-4,6) and B(3,2), we  can use the distance formula which is :

d = sqrt((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁)=(-4,-6) and (x₂,y₂)=(3,2), now we substituting the  values into the formula  after which we get :

d = sqrt((3 - (-4))² + (2 - (-6))²) = sqrt((7)² + (8)²) = sqrt(49 + 64) = sqrt(113) ≈ 10.6

it comes out  that the distance between points A and B is approximately 10.6  units  which are rounded to the nearest tenth.

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The value of height (h)  will be 6 cm.

What is Parallelogram?

A parallelogram is a four-sided polygon in which both pairs of opposite sides are parallel and equal in length. It is a special case of a quadrilateral, which means a polygon with four sides. The opposite angles in a parallelogram are also equal in measure, and the adjacent angles are supplementary, which means they add up to 180 degrees.

Given : height (H) = 5 cm

            base (B) = 12 cm

Similarly, height (h) = 5 cm

               base (h) = 12 cm

Now, we know that area of parallelogram will be same whether we use different method.

So, area of given parallelogram  =  base × height

                                         B × H    =  b × h

                                        12 × 5    =  10 × h

                                            60     =  10 h

So,   h = 60/10 = 6 cm.

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Answer:

m = -5/8

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-1, -7) (-9, -2)

We see the y increase by 5 and the x decrease by 8, so the slope is

m = -5/8

Answer:

Step-by-step explanation:

To find the temperature corresponding to the 67th percentile, we need to find the z-score that has an area of 0.67 to the left of it in the standard normal distribution. We can use a table or a calculator to find this z-score.

Using a standard normal distribution table, we can look up the value that corresponds to an area of 0.67 to the left of the mean, which is 0.44. This means that P(Z ≤ 0.44) = 0.67, where Z is the standard normal random variable.

Next, we can use the formula for standardizing a normal random variable to convert this z-score to the corresponding temperature on the thermometer scale:

z = (x - μ) / σ

where μ is the mean, σ is the standard deviation, and x is the temperature we want to find.

Rearranging this formula, we get:

x = μ + z * σ

Plugging in the values, we get:

x = 0 + 0.44 * 1.00

x = 0.44

Therefore, the temperature corresponding to the 67th percentile is 0.44°C.

Answer:

(a) y = 0.80x + 50

(b) Plugging x = 5 into the equation from part (a), we get y = 0.80(5) + 50 = 54, so the ordered pair associated with x = 5 is (5, 54). This means that if the car is driven for 5 miles, the total charge to the renter is $54.

(c) Let y be the total charge and solve for x:

y = 0.80x + 50

187.60 = 0.80x + 50

137.60 = 0.80x

x ≈ 172

Therefore, the car must have been driven approximately 172 miles

Answer:

(a) y = 0.8x + 50

(b)  D. The ordered pair associated with the equation x = 5 is (5, 54) and it means that the charge for driving the car for 5 miles is $54.

(c) If the renter paid $187.60, the car must have been driven for 172 miles.

Step-by-step explanation:

In the given problem, we are told that the rental car costs a flat fee of $50 plus an additional charge of $0.80 per mile driven.

Let x be the number of miles driven.

Let y be the total charge to the renter (in dollars).

We know that the total charge y will depend on the number of miles driven x, and we can express this relationship using a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the value of y when x = 0).

In this case, we know that the cost per mile is $0.80 so the slope of the line is m = 0.8, and the flat fee is $50 so the y-intercept is b = 50.

Substitute these values into the equation to get:

[tex]y = 0.8x + 50[/tex]

[tex]\hrulefill[/tex]

To find the ordered pair associated with x = 5, substitute x = 5 into the equation:

[tex]\begin{aligned}x=5\implies y &= 0.8(5) + 50\\&=4+54\\&=54\end{aligned}[/tex]

The ordered pair associated with the equation x = 5 is (5, 54) and it means that the charge for driving the car for 5 miles is $54.

[tex]\hrulefill[/tex]

To find how many miles the car was driven if the renter paid $187.60, set y = 187.60 and solve for x:

[tex]\begin{aligned}\implies 0.8x + 50&=187.60\\0.8x + 50-50&=187.60-50\\0.8x&=137.60\\\dfrac{0.8x}{0.8}&=\dfrac{137.60}{0.8}\\x &= 172\end{aligned}[/tex]

Therefore, if the renter paid $187.60, the car must have been driven for 172 miles.

From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.

A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.

The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.

A line is a collection of points that extends in two opposing directions and is endlessly long and thin.

From the given figure we observe that,

1. Two line segments are LA and EP.

2. Two rays are EC and AH.

3. Two lines are b and AP.

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Answer:

To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.

F1 × F2 can be expanded using the distributive property:

F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3

= 36y^2 + 12y - 54y - 18

= 36y^2 - 42y - 18

Now we can subtract F3 from the result:

F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)

= 36y^2 - 42y - 18 + y + 8

= 36y^2 - 41y - 10

Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.

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Answer:

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

In this case, we know that P = $5500, r = 4.5% = 0.045, and we want to find t when A = $6700. We also know that the interest is compounded annually, so n = 1.

Substituting these values into the formula, we get:

$6700 = $5500(1 + 0.045/1)^(1t)

Dividing both sides by $5500, we get:

1.218181818 = (1.045)^t

Taking the natural logarithm of both sides, we get:

ln(1.218181818) = ln(1.045)^t

Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:

ln(1.218181818) = t ln(1.045)

Dividing both sides by ln(1.045), we get:

t = ln(1.218181818)/ln(1.045) ≈ 4.2

Therefore, the person must leave the money in the bank for about 4.2 years to reach $6700. To the nearest tenth of a year, the answer is 4.2 years.

Answer:

Let's start by expressing "Z increased by 16%" using algebra.

Let Z be the original value of some quantity.

To increase Z by 16%, we need to add 16% of Z to Z:

Z + 0.16Z

Simplifying this expression by factoring out Z, we get:

Z(1 + 0.16)

Combining like terms, we have:

Z(1.16)

Therefore, "Z increased by 16%" can be expressed algebraically as:

Z increased by 16% = Z(1.16)

Answer:

z(1.16)

Step-by-step explanation: