help pls pls pls pls pls pls pls pls

The solutions to the inequality word problem are:

2) a + $68.50 ≥ $175

3) A He needs to save at least $106.50 more.

2) We are told that  Marshall wants to save at least $175 for a new video game system and some games.

So far, he has saved $68.50.

If the amount of money he needs to save extra is a, then the inequality we have:

a + $68.50 ≥ $175

3) a + $68.50 ≥ $175

subtracting $68.50 from both sides gives:

a ≥ 175 - 68.5

a ≥ $106.5

He needs to save at least $106.50 more.

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The total cost of the art supplies without the coupon is:

2 paint brushes x $10.50 per brush = $21.00

1 dozen colored pencils x $7.88 per dozen = $7.88

1 sketch book x $16.12 per book = $16.12

Total cost without coupon = $21.00 + $7.88 + $16.12 = $45.00

With the $15.00 off coupon, the total cost becomes:

$45.00 - $15.00 = $30.00

The amount saved by using the coupon is:

$45.00 - $30.00 = $15.00

The percentage saved can be calculated as:

Percentage saved = (Amount saved / Total cost without coupon) x 100%

Percentage saved = ($15.00 / $45.00) x 100%

Percentage saved = 33.33%

Therefore, the customer saved 33.33% by using her coupon.

The correct statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(SAT score, GPA).

There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.

For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.

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This is an incomplete question, I think the question will be

A sandwich shop employee named Lucy takes 2.5 minutes to make a sandwich. If she continues at the same rate, how long will it take her to make 10 sandwiches? Write the answer in minutes.

it will take Lucy 25 minutes to make 10 sandwiches if she continues at the same rate.

If Lucy takes 2.5 minutes to make a sandwich, then to find out how much time it would take for her to make 10 sandwiches, we simply multiply the time taken for one sandwich (2.5 minutes) by the number of sandwiches required (10).

10 x 2.5 = 25 minutes

Therefore, if she continues to work at the same rate of making one sandwich in 2.5 minutes, she will be able to make 10 sandwiches in 25 minutes.

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The fraction of the cookies that are peanut butter cookies is 1/5

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

Total = 10

Peanut butter = 2

using the above as a guide, we have the following:

Fraction = Peanut butter /Total

So, we have

Fraction = 2/10

Evaluate

Fraction = 1/5

Hence, the fraction is 1/5

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The rate of car is 35 mph.

Given that engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car.

Let c be the rate of wind.

215 + c = rate of plane with wind

215 - c = rate of plane against wind

Therefore, the travel time =distance/rate

⇒ 750/(215+c) = 540/(215-c)

Cross multiplying we get,

540(215+c) = 750(215-c)

116100+540c = 161250-750c

1290c = 45150

c=35

Hence, the rate of car is 35 mph.

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1.) The scale factor = 4

The perimeter ratio = 1:3

The area ratio = 1:16

To calculate the scale factor of the given shapes, the formula that should be used would be ;

Scale factor = Bigger dimensions/ Smaller dimensions

Length of the bigger rectangle (B) = 16

Length of the smaller rectangle (A) = 4

The scale factor = 16/4 = 4

The perimeter = 2(l+w)

length B = 16

width B = 8

perimeter B = 2(16+8)

= 2(24) = 48

Length A = 4

width A = 2

perimeter A =2(4+2)

= 16

The perimeter ratio = A:B = 16:48 = 1:3

Area = length×width

length A = 4

width A = 2

Area A = 4×2 = 8

length B = 16

width B = 8

area B = 8×16= 128

Area ratio of A:B = 8:128 = 1:16

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The probability that Amie will select a large shirt is 0.25 or 25%.

Given information:

USA Spirit T-shirts are available for purchase in a shop.

The shirts are available in red, blue, and white, with sizes ranging from small to medium to large to extra-large.

Amie will choose one shirt at random from the shelf if the shelf includes an equal number of shirts in each color and size combination.

There are three colors and four sizes, so there are a total of 3 x 4 = 12 shirts on the shelf.

Since there are an equal number of shirts of each size and color, there are 12/4 = 3 large shirts.

The probability of selecting a large shirt is the number of large shirts divided by the total number of shirts, which is:

3/12 = 1/4 = 0.25.

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The requried future value of Katy's annuity after 6 years will be $5268.63.

We can start by calculating the number of compounding periods over 6 years. Since Katy is investing quarterly, there are 6 x 4 = 24 compounding periods.

Next, we can use the formula for the future value of an ordinary annuity:

[tex]FV = PMT \times ((1 + r)^n - 1) / r[/tex]

Where PMT is the periodic payment, r is the interest rate per period, and n is the total number of periods.

Plugging in the given values, we get:

[tex]FV = $200 \times ((1 + 0.032/4)^{24} - 1) / (0.032/4)[/tex]

FV = $200 x (1.23675 - 1) / 0.008

FV = $200 x 30.84375

FV = $5268.63

Therefore, the future value of Katy's annuity after 6 years will be $5268.63.

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If player gains 20 points If die shows "6" and loses 3 points if die does not show "6", then there will be a gain of 83 points, Option(c) is correct.

To find the expected total gain or loss for the player, we need to find the expected value of the points earned or lost on each roll of the die and then multiply that by "number-of-rolls".

Let X be the random-variable representing the points earned on a single roll of the die.

If "6" appears on die, then , X = 20,

If "6" does not appear on die, then X = -3,

The probability of getting "6" is = 1/6, and

The probability of not getting "6" is = 5/6.

So, the expected-value of X is : E(X) = (1/6) × 20 + (5/6) × (-3) = 0.83,

It means that, on average, the player can expect to earn about 0.83 points per roll of the die.

To find the expected total gain or loss for 100 rolls of the die, we multiply the expected value of X by 100;

⇒ E(total) = 100 × E(X) = 100 × 0.83 = 83,

The "Expected-Value" is positive, the player can expect to gain about 83 points over 100 rolls of the die.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?

(a) A gain of about 1,700 points

(b) A gain of about 583 points

(c) A gain of about 83 points

(d) A loss of about 250 points

(e) A loss of about 300 points

The approximate value of the median is 25

The median is the middle number in a sorted, ascending, or descending, list of numbers and can be more descriptive of that data set than the average.

The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.

To find the median, calculate the value mean by adding together the middle values and dividing them by two.

Hence, the approximate value of the median is Median

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What is the approximate value of the median?

A 18

B 20

C 25

D 27

The statements that are always true are:

i. m∠5 + m∠6 = 180°

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

A triangle is a shape which is bounded by just three sides, thus it has three internal angles whose measures add up to 180°. The internal angle of a triangle is the measure of the angle formed within the two lines forming the edge. While the exterior angles are angles that exist outside the boundary of the triangle when its sides are extended.

From the given question and information, the statements that are always true regarding the diagram are:

i. m∠5 + m∠6 =180°  

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

The required diagram is attached to this answer as a guide

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Simplifying the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), the solution we would get by combing like terms can be expressed as: 12x - 2y + 7xy + 6.

Given the expression, (3x - 2y + 7) - (x + 8xy - 1) + (10x - xy), to simplify it, follow the steps shown below:

(3x - 2y + 7) - (x + 8xy - 1) + (10x - xy) [given]

Open the bracket by applying the distributive property:

3x - 2y + 7 - x + 8xy - 1 + 10x - xy

Combine like terms together:

3x - x + 10x - 2y + 8xy - xy + 7 - 1

12x - 2y + 7xy + 6

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The numbers arranged from greatest to least based on their absolute value is; |-34|, |-25|, |0.5|, |0.35|

The absolute value of a number is the expression or value of the distance of the number from 0 on the number line.

The numbers are; |-25|, |0.5|, |-34|, |0.35|

The absolute value of a number is positive, which indicates;

|-25| = 25

|0.5| = 0.5

|-34| = 34

|0.35| = 0.35

The above numbers arranged from greatest to least is therefore;

34 > 25 > 0.5 > 0.35

The numbers arranged from greatest to least based on their absolute value is therefore;

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The probability of picking L and another A with replacement is: 2/49

Probability of picking A and then another A with replacement is:  1/49

We are given the letter DALLAS.

There are a total of 7 letters. Thus, the probability of picking L is:

2/7

Probability of picking A after that with replacement is: 1/7

Thus, probability of picking L and another A with replacement is:

(2/7) * (1/7) = 2/49

Probability of picking A and then another A with replacement is:

(1/7) * (1/7) = 1/49

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The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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The factorised forms of the Polynomials using difference of squares are;

a). (x - 6) (x + 6)

b). 3 (x - 2) (x + 2).

The factorised forms of the polynomials using the trinomial method are;

a). (x + 3)²

b). 4 (x -5) (x + 3)

Recall that from the difference of squares concept;

a² - b² = (a - b) (a + b) where a² and b² are perfect squares.

Therefore, if we have; x² - 36; we have; x² - 6²

x² - 36 = (x-6) (x + 6).

For, 3x² - 12; = 3 (x² - 4)

= 3 (x -2) (x + 2).

For the trinomials;

x² + 6x + 9;. x² + 3x + 3x + 9

= (x + 3) (x + 3) = (x+3)².

Also, for 4x² - 8x - 60; we have

4 (x² - 2x - 15)

= 4 (x - 5) (x + 3).

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Answer:g=g(9)

Step-by-step explanation:

Answer:

2x2+x+5

Step-by-step explanation:

The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43

Principal,P = $200

Time, t = 6%

Number of periods, n = 12

Interest rate, r = 6%

= 6/100

= 0.06 rate per year,

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

FV = 200.00(1 + 0.06/12)^(12)(2)

FV = 200.00(1 + 0.005)^(24)

FV = $225.43

Therefore,

Principal = $200.00

Interest = $25.43

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a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future is 0.57

b) At 90% confidence, the margin of error is 0.0324.

c) The 90% confidence interval is (0.5376, 0.6024).

d) The 95% confidence interval is (0.5314, 0.6086).

(a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future can be found by dividing the number of respondents who lack confidence (575) by the total number of respondents (1,007):

Point estimate = 575/1007 = 0.57 (rounded to two decimal places)

(b) The margin of error can be calculated using the formula:

Margin of error = z√(p'(1-p')/n)

where z is the z-score associated with the desired level of confidence, p' is the point estimate, and n is the sample size. For a 90% confidence level, the z-score is 1.645.

Margin of error = 1.645√(0.57*(1-0.57)/1007) ≈ 0.0324 (rounded to four decimal places)

(c) The 90% confidence interval can be calculated using the formula:

Point estimate ± Margin of error

Substituting the values:

0.57 ± 0.0324

The 90% confidence interval is (0.5376, 0.6024) (rounded to four decimal places).

(d) The 95% confidence interval can be calculated in the same way, but with a different z-score. For a 95% confidence level, the z-score is 1.96.

Margin of error = 1.96√(0.57(1-0.57)/1007) ≈ 0.0386 (rounded to four decimal places)

0.57 ± 0.0386

The 95% confidence interval is (0.5314, 0.6086) (rounded to four decimal places).

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Answer:

The areas R and S are equal.

Step-by-step explanation:

Since, the tangent line to the curve y = x³ at point A(a, a³) is given by y = 3a²(x - a) + a³. This line intersects the curve at point B(a, a³), and we can find the x-coordinate of point B by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point B.

The slope of the tangent line at point B is 3a², so the equation of the tangent line at point B is y = 3a²(x - a) + a³. This line intersects the curve at another point C, and we can find the x-coordinate of point C by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point C.

The region bounded by the curve and the tangent line at point A is a triangle with base a - (a - a) = 0 and height a³ - a³ = 0, so its area is 0. The region bounded by the curve and the tangent line at point B is a triangle with base a - a = 0 and height a³ - a³ = 0, so its area is also 0. Therefore, the areas R and S are both equal to 0, which means they are equal to each other.

The surface area of the triangular prisms is calculated to be equal to 132 square meters.

The figure can be observed to be two identical triangular prisms with square base, and the surface area can be calculated as follows:

the slant height of a triangle face is derived using Pythagoras;

√(2² + 8²) = √68 m

area of one triangle face = 1/2 × 4 m × √68 m

area of one triangle face = 16.4924 m²

surface area of the figure = 8 × 16.4924 m²

surface area of the figure = 131.9392.

Therefore, the surface area of the triangular prisms is calculated to be equal to 132 square meters.

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The line that has the slope with the greatest value is determined as the: A. Blue line.

The slope of a line is the change in y over the change in x, which can also be calculated as:

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

Also, the steeper the slope, the greater the value of the slope that you will get, while the more gentle the slope, the smaller the value of the slope of the line we would get.

Out of the three lines shown in the graph, the steepest is the blue line, this means that it has the greatest slope value.

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The probability of A and L is 0.25, rounded to two decimal places

To find the probability of A and L, we need to find the number of elements in the intersection of A and L and divide by the total number of elements in the set S.

A = {x ∈ S | x ≥ 21}

= {21, 23, 29, 30}

L = {x ∈ S | x < 25}

= {10, 11, 13, 19, 21, 23}

A ∩ L = {x ∈ S | x ≥ 21 and x < 25}

= {21, 23}

Therefore, the probability of A and L is:

P(A and L) = |A ∩ L|/|S|

= 2/8

= 0.25

Therefore, the required probability of A and L is 0.25, rounded to two decimal places

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True. The total interest expense on the bond over its eight-year life is $400,000.

The total interest expense on the bond is calculated as follows;

Annual interest payment = face value of bond x annual interest rate

= $500,000 x 10%

= $50,000

Semi-annual interest payment = Annual interest payment / 2

= $50,000 / 2

= $25,000

The total interest expense over the bond's life is then calculated as:

Total interest expense = Semi-annual interest payment x Number of semi-annual periods

= $25,000 x 16

= $400,000

Therefore, the statement is true.

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