Miguel and Kala each opened a savings account today. Miguel opened his account with a starting amount of $ 320 , and he is going to put in $ 85 per month. Kala opened her account with a starting amount of $ 820 , and she is going to put in $ 35 per month. Let x be the number of months after today.
a)
For each account, write an expression for the amount of money in the account after months.

(b)
Write an equation to show when the two accounts would have the same amount of money.

The exponential function in the given table is:

y = 0.02*(1/2)^x

This seems to be an exponential function of the form:

y = a*b^x

Using the points in the table we can try to find the values of a and b.

for the first point we can write:

0.02 = a*b^0

0.02 = a

Then the function is:

y = 0.02*b^x

Now the second point, (1, 0.01), replacing that we will get:

0.01 = 0.02*b^1

0.01 = 0.02*b

0.01/0.02 = b

1/2 = b

The function is:

y = 0.02*(1/2)^x

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The expanded form that can be used to factor the function is 12x² - 18x + 10x - 15.

option C,

To factor 12x² - 8x - 15 by grouping, we need to split the middle term -8x into two terms whose sum is -8x and whose product is -180 (the product of 12 and -15).

We can do this by splitting -8x into -18x and +10x:

12x² - 18x + 10x - 15

Now, we can group the first two terms together and the last two terms together, and factor out the greatest common factor from each group:

6x(2x - 3) + 5(2x - 3)

Notice that we have a common factor of (2x - 3) in both groups, so we can factor it out:

(2x - 3)(6x + 5)

Therefore, the factored form of 12x² - 8x - 15 by grouping is (2x - 3)(6x + 5).

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If the boxes are all stacked on top of each other, what is their combined height is 11/8

Height of large box = 7/8m

Height of medium box = 2/6m shorter than large box

Height of small box = 1/4m shorter than the medium box

Calculating the height of the medium and small boxes.

Medium box height x large box height

= 2/6 × 7/8

= 7/24

Since, the small box is 1/4 of a meter shorter than the medium box, therefore its height -

= 7/24 - 1/4

= 5/24

Calculating the height of three boxes -

7/8 + 7/24 + 5/24

= 21/24 + 7/24 + 5/24

= 33/24

= 11/8

Correct Question:

Lupe measured the height of three rectangular prisms she was using to pack up some clothing. The large box was 7/8 of a meter tall. The medium box was 2/6 shorter than the large box. The small box was 1/4 of a meter shorter than the medium box. If the boxes are all stacked on top of each other, what is their combined height?

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Answer : The probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).

The probability of an accident being caused by aggressive driving is 56%, or 0.56. Therefore, the probability of an accident NOT being caused by aggressive driving is 1 - 0.56 = 0.44. Since the accidents are chosen at random, we can assume that they are independent events. Therefore, we can multiply the probabilities together to find the overall probability.

For part 1, we want to find the probability that none of the 3 accidents are caused by aggressive driving. This means we want the probability of an accident not being caused by aggressive driving (0.44) to happen 3 times in a row:

P(none are caused by aggressive driving) = 0.44 * 0.44 * 0.44 = 0.085184

Round to 3 decimal places:

P(none are caused by aggressive driving) = 0.085

Therefore, the probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).

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Therefore , the solution of the given problem of expressions comes out to be Sebastian strolled his dog for 4/5 of the allotted time today.

Calculations like arbitrary division, joining, multiplication variable , and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.

Here,

You can calculate how much of the allotted time Sebastian spent walking his dog today by dividing the time he spent walking him (20 minutes) by the time he was meant to walk him (25 minutes).

Therefore, the division formula that represents this portion is:

=> 20 ÷ 25

The short form of this phrase is:

=>  4/5

As a result, Sebastian strolled his dog for 4/5 of the allotted time today.

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Answer:

95ft²

Step-by-step explanation:

2πr = 11π

πr = 11π/2

r = 11/2 = 5.5ft

area = πr²

area = π(5.5)² = 95.0331... ≈ 95ft²

Therefore , the solution of the given problem of rectangle comes out to be  DE ≅ BF | Corresponding parts of congruent triangles are congruent

A rectangle is a cube with four perpendicular sides in the Euclidean plane. It is also known as an equal-sided rectangle or an equiangular trapezoid. Additionally, the trapezoid may have a straight border. A square has four edges that are the same length. Quadrilaterals that are rectangular have four identical sides but instead four 90° edges. As a result, it is sometimes referred to as a "rectangular trapezoid".

Here,

ABCD is a rectangle | Given

=> AE ≅ CF | Given

AEFC is a parallelogram | Definition of parallelogram

=> AC ≅ EF | Opposite sides of a parallelogram are congruent

=> ∠EAF ≅ ∠ACF | Opposite angles of a parallelogram are congruent

=> ∠EAF ≅ ∠CAD | Diagonals of a rectangle bisect each other

=> ∠ACF ≅ ∠CAD | Transitive property of congruence

=> ∆ACF ≅ ∆CAD | ASA (angle-side-angle) congruence

=> DF ≅ DF | Reflexive property of congruence

=> ∆DFC ≅ ∆DFE | SSS (side-side-side) congruence

=> ∠BCF ≅ ∠ADE | Corresponding angles of congruent triangles are congruent

=> ∠BCF ≅ ∠BDF | Diagonals of a rectangle bisect each other

=> ∠ADE ≅ ∠BDF | Transitive property of congruence

=>∆ADE ≅ ∆BDF | ASA congruence

=> DE ≅ BF | Corresponding parts of congruent triangles are congruent

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Answer:

Step-by-step explanation:

12% of 77 is 10.24 or 10.

Step-by-step explanation:

12/100 * 77

12*77=824

824/100

divide by 2

206/25

use long division method

8.24

The inequality used for number line will be $12 < price < $20.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Hence, on a number line, we can say that the value of numbers grows as we move to the right. This indicates that there are more numbers on the right than on the left. For instance, 3 comes after 1, hence 3 > 1.

The price will lie in the following inequality -

$12 < price < $20

Below is the number line for the same -

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Answer:

To solve the equation 3x + 5y = 500 for x, we need to isolate x on one side of the equation. First, we can subtract 5y from both sides to get 3x = 500 - 5y. Then, we can divide both sides by 3 to get x = (500 - 5y) / 3.

It might be helpful to rewrite the equation in terms of one variable if we want to solve for one unknown quantity in terms of another. In this case, rewriting the equation in terms of x allows us to see how many child tickets the school needs to sell to raise exactly $500, given any number of adult tickets sold. This can be useful in planning and budgeting for the carnival.

Step-by-step explanation:

By answering the presented question, we may conclude that When x equals 7, the equation holds true. As a result, "True" is the correct response.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.

The image's equation is:

2x + 4 = 18

We must solve for x to discover if the equation is true or untrue.

When we subtract 4 from both sides, we get:

2x = 14

When we divide both sides by 2, we get:

x = 7

When x equals 7, the equation holds true. As a result, "True" is the correct response.

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Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

The two solutions to the given quadratic equation are x = (a+b + √(a2 - 6ab + 8b2))/(2(a-b)) and x = (a+b - √(a2 - 6ab + 8b2))/(2(a-b)).

The general form of a quadratic equation is ax2 + bx + c = 0. To solve this equation, we need to use the Quadratic Formula. The Quadratic Formula is [tex]x = [-b ± √(b2 - 4ac)]/ 2a[/tex].

We can plug the values for a, b, and c into this equation. For this equation, a = (a-b), b = -(a+b), and c = 2b.

Therefore, using the Quadratic Formula, we get [tex]x = [-(-(a+b)) ± √((-(a+b))2 - 4(a-b)(2b))]/ 2(a-b)[/tex].

Simplifying this, we get [tex]x = [a+b ± √(a2 + 2ab - 4ab - 8b2)]/(2(a-b))[/tex].

Finally, we can solve for the two values of x by computing the two cases. In the first case, we add the square root, and in the second case, we subtract the square root. This gives us the two solutions [tex]x = [(a+b + √(a2 - 6ab + 8b2))/(2(a-b))][/tex] and [tex]x = [(a+b - √(a2 - 6ab + 8b2))/(2(a-b))][/tex].

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The amount budgeted for dances is approximately $380.00.

Assume that "x" is the budgeted sum for dances. The problem states that there is a 5:7 ratio between the budget for dances and the budget for charitable activities. Hence, we can write:

x/532 = 5/7

We can cross-multiply and simplify to find the answer for "x"

7x = 532 × 5

7x = 2660

x = 2660/7

x ≈ 380.00

The estimated $380.00 planned money for dances is the result.

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Answer:

x = 17

Step-by-step explanation:

We Know

(6x + 3) + (7x - 44) = 180°

Let's solve

6x + 3 + 7x - 44 = 180

13x - 41 = 180

13x = 221

x = 17°

So, x = 17°

The factor that f increases by when the exponent increases is :

When the exponent x increases by 1, the function value increases by a factor of 3. When the exponent x increases by 2, the function value increases by a factor of 9.

When the exponent x increases by 1/2, the function value increases by a factor of √3. We can see this by evaluating as follows :

= (3^ ( 1 / 2 ) )

= √3

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On solving the provided question we cans ay that function  In the auction, 180 carrots cost £18.00.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

The initial cost of 20 carrots was £2.80. Thus the cost per carrot is £2.80 20 = £0.14.

If the price is decreased by 30%, the new carrot price is: £0.14 - (30% £0.14) = £0.098 or £0.10 (rounded to the nearest penny)

As a result, 180 carrots at the current sale price will cost: 180 £0.10 = £18.00

In the auction, 180 carrots cost £18.00.

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According the given question the side οf the WY is 25.

Angle-Side-Angle cοngruence rule is referred tο as ASA. Twο triangles are said tο be cοngruent accοrding tο this rule if any twο angles and the side included between them οf οne triangle are equal tο the cοrrespοnding angles and the included side οf the οther triangle.

See if the twο triangles given, ABC and XYZ, are cοngruent accοrding tο the ASA rule by lοοking at the image prοvided belοw. Accοrding tο the ASA cοngruence rule, twο triangles are said tο be cοngruent if twο οf their respective sides and angles are equal tο thοse οf twο οther triangles and their respective sides and angles, respectively.

BC = BD

m< B=13x-35

m < C = 5x-19

m < D = 2x + 14

m< B=13*11 - 35

m< B=143-35

m< B = 108

m<C=5x-19

m<C=511 - 19

m < C = 55-19

m < C = 36

This is sο because the theοrem οf SAS (Side-Angle-Side)

Sο, we have:

9x117x - 3

WY = 7x-3

WY = 7*4-3

WY = 28-3

WY = 25

Hence the side οf the WY is 25.

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[tex]4.25[/tex]π cm is the width of an arcs with such a central [tex]45-[/tex]degree angle and a circle with a diameter of [tex]289 cm^{2}[/tex] .

It doesn't have any sides or corners either. A circle, then, is a full entity unto itself. Nothing else can be tacked on to complete the circle. Due of this, circles are used as symbols for wholeness, perfection, totality, and heavenly symmetry and equilibrium.

A circle is indeed a closed arc that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre.

[tex]A =[/tex] π[tex]r^2[/tex]

Given that the circle's area is [tex]289 cm^{2}[/tex], we can use the following formula to find the radius:

289π = π

[tex]r^{2} = 289[/tex]

[tex]r = 17 cm[/tex]

With the radius now known, we can apply the following formula to determine the length of an arc with a central angle of [tex]45[/tex] degrees:

[tex]L = (45^{0} / 360^{0} ) * 2pi(17)[/tex]

[tex]L = (1/8) * 34[/tex]π

[tex]L = 4.25[/tex]π cm

A circle with an area of [tex]289 cm^{2}[/tex], [tex]4.25[/tex]π cm is the length of an arc with a central angle of [tex]45[/tex]degrees.

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A greater distance if it hits any other part of the bat.

When a ball hits the sweet spot of a bat, it will travel a greater distance than if it hits any other part of the bat. This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.

This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.

If the ball hits any other part of the bat, the energy transfer is less efficient, resulting in a less powerful hit and a shorter distance travelled by the ball.

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Option D has the correct direction of the alternative hypothesis but uses the sample proportion in the null hypothesis.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The appropriate hypotheses for this test are:

H0: p = 0.28 (the proportion of all high school students who work a part-time job during the school year is 0.28)

Ha: p > 0.28 (the proportion of all high school students who work a part-time job during the school year is greater than 0.28)

This is because the guidance counselor is interested in whether the proportion of all high school students who work part-time jobs during the school year is greater than 0.28, which was the proportion a decade ago. The null hypothesis states that the proportion is 0.28, and the alternative hypothesis states that it is greater than 0.28. Since the alternative hypothesis is one-sided (greater than), this is a one-tailed test.

Option B correctly states the null and alternative hypotheses with the appropriate population proportion in the null hypothesis and the direction of the alternative hypothesis. Options A and C use the sample proportion instead of the population proportion in the null hypothesis. Therefore, Option D has the correct direction of the alternative hypothesis but uses the sample proportion in the null hypothesis.

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Answer: The Answer is B!

Step-by-step explanation:

EDGE 2023

One possible solution is Keshawn has 2 nickels and 12 dimes.

What is inequality equation?

An inequality equation is a mathematical expression that compares two values or expressions using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to)

To solve the system of inequalities graphically, we can plot the two inequalities on the coordinate plane and shade the region that satisfies both inequalities. Let x be the number of nickels and y be the number of dimes.

The first inequality represents the maximum number of coins:

x + y ≤ 14

The second inequality represents the minimum value of the coins:

0.05x + 0.1y ≥ 1

We can rewrite this inequality as:

x + 2y ≥ 20

Now we can plot these two inequalities on the coordinate plane:

Draw a horizontal line for x + y = 14.

Draw a diagonal line with negative slope for x + 2y = 20.

Shade the region below the diagonal line and to the left of the horizontal line.

The shaded region represents the feasible region that satisfies both inequalities. We also know that x ≤ 4 since a maximum of 4 coins are nickels.

One possible solution that lies in the shaded region and satisfies the constraint x ≤ 4 is (x, y) = (2, 12). This means Keshawn has 2 nickels and 12 dimes. We can check that this solution satisfies both inequalities:

2 + 12 = 14 (maximum number of coins)

0.05(2) + 0.1(12) = 1.2 ≥ 1 (minimum value of the coins)

Therefore, one possible solution is Keshawn has 2 nickels and 12 dimes.

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The total surface area of this figure is 94, rounded to the nearest hundredth.

The figure in question is a rectangular prism. To calculate the total surface area of a rectangular prism, we must use the following formula: Total Surface Area = 2(lw + wh + lh), where l is the length, w is the width, and h is the height.

For this figure, the length is 5, the width is 4, and the height is 3. Thus, we can calculate the total surface area of the figure as follows: 2(5*4 + 4*3 + 5*3) = 2(20 + 12 + 15) = 2(47) = 94. Therefore, the total surface area of this figure is 94, rounded to the nearest hundredth.

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P(female or grade 11) = 31/34

Given that a classroom has 23 grade twelves (13 females and 10 males) and 11 grade elevens (7 females and 4 males). The teacher randomly chooses a student at random, what is the probability that it is a female or a grade eleven?The sample space is the total number of students which is given by23 + 11 = 34.There are 13 females in the grade 12 and 7 females in the grade 11. So the total number of female students is 13 + 7 = 20.There are 11 grade 11 students. So the total number of grade 11 students is 11.The total number of students that are female or in grade 11 is obtained by adding the two:20 + 11 = 31.So the probability of choosing a female or grade 11 student is:P(female or grade 11) = 31/34

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Step-by-step explanation:

she has x money at the beginning.

(3/4)x = dictionary

the remainder is (1/4)x.

1/2 of that (1/4 × 1/2 = 1/8) is the calculator.

that means she has (1/4)x - (1/8)x = (1/8)x left.

the dictionary is $30 more than the calculator.

so,

(3/4)x = (1/8)x + 30

(6/8)x = (1/8)x + 30

(5/8)x = 30

5x = 240

x = 240/5 = $48

so, the dictionary cost

(3/4)x = (3/4)×48 = 3×12 = $36

Therefore, the measure of angle 1 is 40°.

Two rays (half-lines) that share a terminal are combined to form an angle. In contrast, the rays are variously referred to as the angle's legs and its arms, with the latter serving as the angle's vertex.

The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we can use this property to find the measure of angle 1.

If mAB = 80°, then arc AB is also 80° because an inscribed angle intercepts an arc with the same measure as the angle. Therefore, the measure of arc AB is 80°.

Since angle 1 is an inscribed angle that intercepts arc AB, its measure is half the measure of arc AB. Therefore, we can find the measure of angle 1 as follows:

m∠1 = (1/2) x m arc AB

m∠1 = (1/2) x 80°

m∠1 = 40°

Therefore, the measure of angle 1 is 40°.

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Answer:

  C. The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

You want to know the transformations needed to form g(x) = 1/2(x+4)^2 -3 from f(x) = x^2.

The transformations ...

  f(x) ⇒ g(x) = c·f(x -h) +k

represent vertical expansion by a factor of 'c', right shift by 'h' units, and an upward shift of 'k' units.

Here, we have c=1/2, h=-4, k=-3. These mean the function f(x) has been vertically compressed to 1/2 its original height, and shifted left 4 and down 3.

The vertical compression will cause the graph to appear to be wider for any given distance above the vertex.

Answer:

Vol = 120 cm^3

Step-by-step explanation:

The volume of a prism is:

Vol = BaseArea×height

Here, the base is the triangle.

Area_triangle

= 1/2bh

= 1/2•6•4

= 12 cm^2

The height is 10cm (and we don't even need the 5cm measurement given)

Volume

= BaseArea × height

= 12 × 10

= 120 cm^3

After solving the given numbers with (PEMDAS) 11 - 11 x 11 + 11 = we get the answer of -88.

To solve 11-11x11+11, we need to use the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using this order of operations, we can simplify the expression as follows:

11 - 11 x 11 + 11

= 11 - 121 + 11 (since multiplication should be done before addition and subtraction)

= -99 + 11

= -88

Therefore, the value of 11-11x11+11 is -88.

In general, when simplifying expressions, it is important to follow the order of operations to ensure that you get the correct answer. Additionally, it is always a good idea to check your work by plugging the answer back into the original expression and making sure that it is correct.

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It would take the apprentice alone 11 hours to complete a kitchen island, the same amount of time it took the cabinet maker and apprentice together.

When the cabinet maker and apprentice work together, they are able to complete the kitchen island in 8 hours. This implies that the apprentice is able to do their portion of the work in 3 hours, while the cabinet maker does their portion in 8 hours. Therefore, if the apprentice were to work on the kitchen island alone, it would take them 11 hours to complete it, the same amount of time it took the cabinet maker and apprentice together. This is because the apprentice does not have the same level of experience and expertise as the cabinet maker, so they are not able to complete the same amount of work in the same amount of time as the cabinet maker. The cabinet maker is able to work faster and more efficiently, which is why they are able to complete the kitchen island in 8 hours, while the apprentice would need 11 hours to complete the same task.

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