Heather's statement shows a previous balance
of $1413.92, a payment of $40, and new
transactions totaling $381.51. What is her
new balance if her APR is 16.2%?

The correct representation of the inequality –3(2x – 5) < 5(2 – x) are :

-6x + 15 < 10 - 5x

x < 5

Given an inequality,

–3(2x – 5) < 5(2 – x)

We have to find the equivalent representation of the inequality.

(-3)(2x) - (-3)(5) < (5)(2) - (5)(x)

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

x < 5

Hence the correct options are -6x + 15 < 10 - 5x and x < 5.

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Answer: C. 96

Step-by-step explanation:

I took 8×3×4=96

Since the height is 5 in and it already took up one inch, that means just 4 more inches to go hence the 4 in the multiplication.

The value of z with a p-value of 0.262 is given as follows:

z = -0.64.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, we want the z-score with a p-value of 0.262, hence, looking at the z-table, we have that it is:

z = -0.64.

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the domain and range of the inequality are,

x ≥ 1 and y ≥ - 4

The inequality is:

⇒ y ≤ √(x - 1) - 4

Now, To find:

The domain and range of the given inequality.

Solution:

We have,

⇒ y ≤ √(x - 1) - 4

The related equation is:

⇒ y ≤ √(x - 1) - 4

This equation is defined if:

√x - 1 ≥ 0

x ≥ 1

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set.

So, the domain of the given inequality is, x ≥ 1

We know that,

√(x - 1)  ≥ 0

√(x - 1) - 4 ≥ - 4

y ≥ - 4

So, the range of the given inequality is, y ≥ - 4

Therefore, the correct option is C.

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The probability of a random point which is located on  AK  will be present on BE is equal to 0.3.

From the attached figure we have,

On the number line point A is located at -10.

And on the same number line point K is at 10.

Distance between AK = ( 10 ) - ( -10 )

⇒ Distance between AK = 10 + 10

⇒ Distance between AK = 20

Now, on the same number line location of point B is -8.

And location of point E is -2.

Length of BE = ( -2 ) - ( -8 )

⇒ Length of BE = -2 + 8

⇒ Length of BE = 6

Probability of random point on AK will be on BE

= Favorable outcomes / total number of outcomes

= Length of BE / Length of AK

= 6 / 20

= 3 / 10

= 0.3

Therefore, the probability of a random point located on AK will be on BE is equal to 0.3.

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The above question is incomplete , the complete question is:

What is the probability that a random point on AK will be on BE?

Attached figure.

The fish tank requires 7900 square cm of glass.

First, choose three fish for our tank. Let's choose a neon tetra, a guppy, and a corydoras catfish.

According to the guideline given, each fish requires 4,000 cubic centimeters of water for every inch of a fish's length. Determine the total length of the three fish to calculate the required water volume.

Assuming the neon tetra is 1 inch long, the guppy is 2 inches long, and the corydoras catfish is 3 inches long, the total length of the fish is 1+2+3=6 inches.

To accommodate these three fish, we need 6 inches x 4,000 cubic centimeters of water per inch = 24,000 cubic centimeters of water.

To design the fish tank. Make it a rectangular prism shape with the dimensions of 50 cm x 30 cm x 40 cm (length x width x height).

To calculate the amount of glass necessary to build the tank, to find the surface area of the glass required. There are five sides to the tank (four sides and the base), find the area of each and add them up.

The front and back sides each have an area of 50 cm x 40 cm = 2000 square cm.

The two side walls each have an area of 30 cm x 40 cm = 1200 square cm.

The base has an area of 50 cm x 30 cm = 1500 square cm.

So, the total surface area of glass required is:

2(2000 square cm) + 2(1200 square cm) + 1500 square cm = 7900 square cm.

Therefore, 7900 square cm of glass is needed to build our fish tank.

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The slope of a linear function of the table of values given above is calculated as: m = 3.

The slope of a linear function is calculated as change in y over change in x. Note that f(x) is also the same as variable "y".

To calculate the slope, pick any two pairs of values from the table given, i.e. (2, 3) and (3, 6):

Slope of the linear function (m) = change in y / change in x = 6 - 3 / 3 - 2

Slope (m) = 3/1

Slope (m) = 3.

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Factorization is a mathematical process of breaking down a number or an expression into smaller numbers or simpler expressions that can be multiplied together to get the original number or expression.

Expressions, which are essentially mathematical statements containing numbers and letters, can be factorized in algebra. For illustration, consider the phrase 2x + 4. Finding the expressions or numbers that are common to each term allows us to factorize the expression. Since 2 appears in both terms, we can remove it by factoring to get 2(x + 2).

Given equation =  [tex]2x^{2} + 7x + 6[/tex]
                         ⇒   [tex]2x^{2} + 4x + 3x + 6[/tex]

                         ⇒ [tex]2x ( x+2) +3(x+2)[/tex]

                         ⇒[tex](2x + 3) (x+2)[/tex]

Therefore the factors of the expression [tex]2x^{2} + 7x + 6[/tex] are [tex](2x + 3) (x+2)[/tex].

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answear 12x

Step-by-step explanation:

6.5x-3.6x=

30x-18x=

12x

Answer:

A(4;-1)

B(4;-5)

S=yB-yA/ xB-xA

= -5+1/ 4-4

=-4/0

impossible

The requried 3 1/2 cups of chocolate chips would be needed for 7 dozen cookies, so the answer is (c).

The ratio of chocolate chips to cookies is 1 1/2 cups for every 3 dozen cookies. To find how much chocolate chips are needed for 7 dozen cookies, we can use the following proportion:

1 1/2 cups / 3 dozen cookies = x cups / 7 dozen cookies

where x is the unknown amount of chocolate chips needed for 7 dozen cookies.

To solve for x, we can cross-multiply and simplify:

(1 1/2 cups) * (7 dozen cookies) = (3 dozen cookies) * x

21/2 cups = 3x

x = 3.5

Therefore, 3 1/2 cups of chocolate chips would be needed for 7 dozen cookies, so the answer is (c).

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Answer:

215

Step-by-step explanation:

To solve this expression, we must first use the order of operations. We begin with the parentheses and evaluate 23-11, giving us 12. Then, we divide 48 by 12, which equals 4. Finally, we multiply 4 by 38, resulting in 152. We add this to 63, giving us a final answer of 215. Thus, the solution to 63+48÷(23-11)×38 is 215.

The answers are explained in the solution.

Given are lines drawn in a coordinate plane, we need to identify the equations,

So, we have,

y = 2x – 4 = r

y = 2x + 4 = p

This is because these lines are parallel and have same slope, also the y-intercept is -4 and 4,

y = x = n

y = -x = s

This is also because, the line of y = x passes from origin.

b) We can use a translation to map the line p or r onto the line r or p.

c) We can use an axial symmetry in the y-axis to map the line n or s onto the line s or n.

d) The line s or n is mapped onto itself under central symmetry in the point (0, 0).

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The edge length of one cube-shaped box used to store canned goods is 2 feet.

The surface area of a cube-shaped box is given as 24 square feet. Let's assume that the length of each edge of the cube is 'a'.

The surface area of the cube is given as 6a² since a cube has 6 faces, each with an area of 'a²'.

We are given that the surface area of one box is 24 square feet. Therefore,

6a² = 24

Dividing both sides by 6, we get

a² = 4

Taking the square root of both sides, we get:

a = 2

Therefore, the edge length of one box is 2 feet.

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The solution is given below.

The result of the mixed digits given when expressed as improper fractions are as follows;

3 1/2 = ((2×3)+1)/2 = 7/2

7 4/5 = ((5×7)+4)/5 = 39/5

5 3/4 = ((4×5)+3)/4 = 23/4

4 1/3 = ((3×4)+1)/3 = 13/3

4 2/3 = ((3×4)+2)/3 = 14/3

5 1/5 = ((5×5)+1)/5 = 26/5

8 2/3 = ((3×8)+2)/3 = 26/3

2 3/5 = ((5×2)+3)/5 = 13/5

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complete question:

3 1/2 as a improper fraction7 and 4/5 as an improper fraction5 3/4 as an improper fraction4 1/3 as an improper fraction4 + 2/3 as an improper fraction5 1/5 as an improper fraction8 2/3 as an improper fraction 2 3/5 as an improper fraction

Answer: 17/29 As A Fraction! (58.6%)

Step-by-step explanation: Just Divide 17 (Amount Won) By Amount Played (29)

When about 60.2 liters of fuel are added to each car, the two vehicles will have the same mass.

Let x be the number of liters of fuel needed for the two vehicles to have the same mass.

The first vehicle's total mass with fuel is: 1295 + 0.737x

The total weight of the second vehicle with gasoline is: 1290 + 0.820x

We want the two masses to be equal so that we may equalize the two expressions and solve for x:

295 + 0.737x = 1290 + 0.820x

0.083x = 5

x = 60.24

Therefore, the two vehicles will have the same mass when approximately 60.2 liters of fuel have been added to each vehicle.

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Answer: 46

Step-by-step explanation:

368/8 = 46

36/8 = 4R4

48/8 = 6

46

The equation to calculate an object's speed is Speed = Distance ÷ Time.

Option A is the correct answer.

We have,

Speed is the ratio of distance and time.

Mathematically,

It can be written as,

Speed = Distance / Time

Speed = Distance ÷ Time

Thus,

The equation to calculate an object's speed is Speed = Distance ÷ Time.

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Answer: 18º

Step-by-step explanation:

a + 126º = 180º (adj.  ∠s on st. line)

a = 54º

Let the adjacent angle next to b be c.

a + c = 180º (int. ∠, AB//CD)

54º + c = 180º

c = 126º

108º + x = 126º (ext. ∠ of Δ)

x = 18º

Answer:

1 730.1504 bytes^3

Step-by-step explanation:

6.6 x 6.4 x 6.4 x 6.4 x B x B x B

can be written as:

(6.6 x 6.4 x 6.4 x 6.4) x B^3

where B^3 represents B cubed or B raised to the power of 3.

Therefore, the product using exponents is:

1684.032 x B^3

Hello!

To find the equation of the line that passes through the points (0, -8) and (4, -3), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

First, we can find the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, -8) and (x2, y2) = (4, -3). Substituting these values, we get:

m = (-3 - (-8)) / (4 - 0) = 5/4

So the slope of the line is 5/4. Now we can use the point-slope form of the equation with either of the given points. Let's use the point (0, -8):

y - (-8) = 5/4(x - 0)

Simplifying this equation, we get:

y + 8 = 5/4x

Subtracting 8 from both sides, we get the final equation:

y = 5/4x - 8

So the equation of the line that passes through the points (0, -8) and (4, -3) is y = 5/4x - 8.

Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,

μ ≤ 4

Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.

We have,

The null and alternative hypotheses to determine if the females who read the "great sense of humor" description gave the potential partner an average attractiveness rating that was higher than neutral (μ = 4) can be written as:

Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,

μ ≤ 4

Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.

Thus,

The null hypothesis states that the mean attractiveness rating of males who are described positively and with a great sense of humor is not significantly different from a neutral rating of 4.

The alternative hypothesis states that the mean attractiveness rating of such males is significantly higher than a neutral rating of 4.

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Answer:

Step-by-step explanation:

We can start by drawing a diagram of the situation:

markdown

Copy code

                     *

                    / \

                   /   \

                  /     \

                 /       \

         _______/_________\_______

              4ft         4ft

               |          |

              1ft        h ft

We can see that the distance from the center of the wheel to the white plank is also 4 feet (since the radius of the wheel is 4 feet).

Next, we need to find the height of the white plank after the wheel is rolled forward through an angle of π/3 radians.

To do this, we can use trigonometry. Let's call the height of the white plank after the motion "h". We can use the sine function to relate the angle through which the wheel is rolled and the height of the plank:

sin(π/3) = h/4

Simplifying this equation, we get:

h = 4sin(π/3)

h = 4(√3/2)

h = 2√3

Therefore, the height of the white plank after the motion is 2√3 feet from the ground.

Applying the right triangle altitude theorem, the value of x in the given right triangle is: x = 4.

According to the right triangle altitude theorem, we have the following from the theorem as:

h = √(xy), where h is the altitude of the triangle and x and y are the segments divided on the hypotenuse.

Therefore, we have:

2√6 = √(x*3)

(2√6)² = x*3

12 = 3x

x = 12/3

x = 4

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Answer:

120/30*29*28*27

Step-by-step explanation:

Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.

We have,

The amount of tax applied to the bill is 6% of the subtotal, or 0.06x.

The total bill (including tax) is.

x + 0.06x = 1.06x

To find the amount of tip Wyatt left on the total bill, we need to multiply the total bill by 17% (or 0.17):

0.17(1.06x) = 0.1802x

The expression in terms of xx that represents the total amount that Wyatt paid is:

= x + 0.06x + 0.1802x

Simplifying the expression by combining like terms.

Total amount = 1.2422x

Thus,

Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.

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The prism is a right hexagonal prism.

The lateral area of the right hexagonal prism is 1008 square centimeters.

The sum of the area of a regular hexagon is 187.06 cm².

The surface area of the prism is 1196.06 cm².

We have,

7)

The prism is a right hexagonal prism.

8)

Perimeter = 6 x side length = 6 x 12 cm = 72 cm

Each rectangular face of the prism has a height of 14 cm and a width equal to one of the sides of the hexagon, which is 12 cm.

The area of each face.

= height x width

= 14 cm x 12 cm

= 168 cm²

And,

Lateral Area

= 6 x Area

= 6 x 168 cm²

= 1008 cm^2

9)

The formula for the area of a regular hexagon is given by:

Area = (3 x sqrt(3) / 2) x side length^2

Side length = 12 cm

Area = (3 x √(3) / 2) x 12²

Area = (3 x √(3) / 2) x 144

Area = 54 x √(3)

Area ≈ 93.53 cm² (rounded to two decimal places)

Now,

The sum of the area of a regular hexagon.

= 2 x 93.53

= 187.06 cm²

10)

There are 6 surfaces.

Each surface is in rectangular shape.

So,

Surface area

= 6 x (12 x 14)

= 1008 cm²

And,

The surface area of the prism.

= 1008 + 187.06

= 1196.06 cm²

Therefore,

The prism is a right hexagonal prism.

The lateral area of the right hexagonal prism is 1008 square centimeters.

The sum of the area of a regular hexagon is 187.06 cm².

The surface area of the prism is 1196.06 cm².

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