Solve the following systems of inequalities and select the correct graph: 2x − y < 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

When h = 4, j = 5, and k = -1, the expression jkh + hj - jk equals 5.

To solve the expression we have to substitute the value of each variable in the expression. Then simplify the expression according to mathematic rule. After solving we get the solution of the expression.

An expression is a combination of numbers, variables, and/or operations that can be evaluated or simplified to obtain a numerical or algebraic result.

The given expression is:

jkh + hj - jk

Substituting the given values of h, j, and k, we get:

jkh + hj - jk = (5 x (-1) x 4) + (5 x 4) - (5 x (-1))

Now simplify the expression

jkh + hj - jk = (-20) + 20 + 5

jkh + hj - jk = 5

Therefore, the value of  jkh + hj - jk equals 5.

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The total area of the path is 296 square feet, and the value of x is,

⇒ 64.2 feet.

Now, We know that;

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

Based on the screenshot provided, the rectangular vegetable garden has dimensions of (x+2) feet by (x+10) feet, and there is a stone path around the garden that is 3 feet wide on all sides.

To find the value of x, we need to set up an equation using the information given.

Hence, The total area of the garden and the path is equal to the area of the outer rectangle minus the area of the inner rectangle, which is:

(x+2+2) × (x+10+2) = (x+2) × (x+10) + 296

Simplifying and solving for x, we get:

x² + 16x + 48 = x² + 12x + 20 + 296

4x = 268

x = 67

Therefore, the value of x is, 67 feet.

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Answer:

D

Step-by-step explanation:

The probability of guessing the correct answer to a true-false question is 1/2.

The probability of guessing the correct answer to all 8 questions is:

(1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/256

Therefore, the probability of guessing the correct answers to all 8 questions is 1/256.

The answer is D.

I hope this helps!

The delineation of A as a subset of B, and also the differentiation in assertion that A is not equivalent to B, can be attributed to A containing merely three elements (a, b, along with c) as opposed to B's countenance of five elements (including a, b, c, d, subsequently e).

As all components of A coincidentally exist within B, one may ascertrain that A is indeed a subset of B.

However, due to B enclosing two additional elements (d, then e) which are not replete within A, we can conclusively deny that A is comparable to B.

Symbolically:

A ⊆ B (A constitutes a subset of B)

A ≠ B (A isn't analogous to B)

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Applying the Pythagorean theorem, the length of the unknown side in the right triangle is: a ≈ 13.2.

The Pythagorean theorem is expressed as:

c² = a² + b², given that a and b are small legs of the right triangle and c is the longest leg or hypotenuse facing the right angle in the triangle.

Given the following:

c = 16

b = 9

a = ?

Plug in the values:

16² = a² + 9²

a² = 16² - 9²

a = √(16² - 9²)

a ≈ 13.2

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Answer:

The correct statement is: ΔJDC ≅ ΔYAM.

This is because the given statement ΔJCD ΣΔMAY tells us that ΔJCD is congruent to ΔMAY by the SAS (side-angle-side) postulate.

We can use this information to conclude that ΔJDC is congruent to ΔYAM by the CPCTC (corresponding parts of congruent triangles are congruent) theorem. Specifically, the corresponding parts that are congruent are:

Therefore, the correct congruency statement is ΔJDC ≅ ΔYAM. The other statements are not correct.

The evaluation of the equation by expressing the terms as improper fractions indicates that the value of y is 14 2/3

A fraction is an expression of a part of a whole, using two numbers, one located in the numerator, and the other in the denominator in the expression of the fraction separated by a line, known as the fraction bar.

The equation can be expressed as follows;

4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9

The above equation comprising of fractions can be expressed using improper fractions as follows;

4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9

38/9 + (149/9 - y) = 136/9 - 79/9 = 57/9

38/9 + 149/9 - 57/9 = y

130/9 = y

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The median of the data set is 24 and the mean is 23.

To find the median of the data set, we need to first put the values in order from least to greatest:

3, 8, 24, 24, 31, 33, 38

There are 7 values in the data set, so the median is the middle value. Since there are an odd number of values, the median is the fourth value, which is 24.

To find the mean of the data set, we add up all the values and divide by the number of values:

Mean = (3 + 8 + 24 + 24 + 31 + 33 + 38) / 7

Mean = 161 / 7

Mean = 23

Therefore, the median of the data set is 24 and the mean is 23.

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The p-value for this hypothesis test for a proportion is 0.9319.

We are given that;

Number of employees=700

Percent=400%

Now,

Plugging these values into the formula, we get:

Z=7000.40(1−0.40)​​0.4357−0.40​≈1.49

Since the alternative hypothesis is p<0.40, this is a left-tailed test. The p-value is the area to the left of 1.49 under the standard normal curve1. Using a normal table or a calculator, we find that:

p-value=P(Z<1.49)≈0.9319

Therefore, by percentage the answer will be 0.9319.

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Answer:80

Step-by-step explanation: 3x+8=5x-40 so 2x=48 so x=24. 24*3+8=80 so our answer is 80.

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

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The measure of the angle m∠4 which forms a straight line angle with the angles 60° and 61° along the line Q is equal to 59°

When a transversal line cuts a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

m∠4 + 60° + 61° = 180° {supplementary angles}

m∠4 + 121° = 180°

m∠4 = 180° - 121° {subtract 121° from both sides}

m∠4 = 59°.

Therefore, the measure of the angle m∠4 which forms a straight line angle with the angles 60° and 61° along the line Q is equal to 59°

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Answer:

C

Step-by-step explanation:

Answer:

B  x ≤ 0

Step-by-step explanation:

A solid dot on zero means that zero is included.

The line to the left of zero with an arrowhead means that all numbers less than zero are all included.

The graph represents zero and all numbers less than zero.

The correct inequality is

B  x ≤ 0

The required, in a reflection of triangle AB ≡ A'B' and ΔABC ≡ ΔABC are true.

AB ≡ A'B': True, because a reflection conserves length, so corresponding segments are congruent.

BC < B'C': False, in general, the length of conserves is preserved under a reflection, so BC = B'C'.

Triangle BACE = triangle B'A'C': True, because a reflection also conserves shape and size, so corresponding angles and sides are congruent.

∠BCA > ∠B'C'A': False, because the measure of an angle is not preserved under a reflection.

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The value of x is 20.

Given that a rectangle PQRS has diagonals PR = 4x - 15, and QS = 3x + 5, we need to find the value of x,
Since, we know that the diagonals of a rectangle are equal,

So,

PR = QS

4x-15 = 3x+5

x = 20

Hence the value of x is 20.

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The area of the rectangle is 10 in².

We have,

Given,

Length = 5 inches

Width = 2 inches

Now,

Area of a rectangle.

= length x width

= 5 x 2

= 10 in²

Thus,

The area of the rectangle is 10 in².

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If at the soccer game, Sue bought a pack of gum for 25¢ and a candy bar for $1.00, the average cost of the items Sue and her brother bought is 67 cents.

To find the average cost of the items, we need to add up the total cost and divide by the number of items. In this case, there are three items: gum, candy bar, and hot dog.

The total cost is 25¢ + $1.00 + 75¢ = $2.00

The number of items is 3.

So, the average cost is $2.00 / 3 = $0.67 (rounded to the nearest penny).

This means that on average, each item costs 67 cents.

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The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

We have,

We can simplify the given expression as follows:

(X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y)

= (5X - 5Y) ÷ 8 - 1 ÷ (4X + 4Y)

[distributing the factors]

= (5X - 5Y) /8 - 1/(4X + 4Y)

[finding a common denominator]

= ((5X - 5Y)(4X + 4Y) - 1)/(4X + 4Y)

= (20X² + 20XY - 20XY - 20Y² - 1) / (4X + 4Y)

= (20X² - 20Y² - 1) / (4X + 4Y)

Therefore,

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

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The interest is $293.88 in interest

The remaining balance is approximately $2793.88.

Monthly Interest Rate = 0.2 / 12

Monthly Interest Rate ≈ 0.01667 (rounded)

Month 1:

Interest: $4000 * 0.01667 ≈ $66.68 (rounded)

New Balance: $4000 + $66.68 = $4066.68

Payment: $300

Remaining Balance: $4066.68 - $300 = $3766.68

Month 2:

Interest: $3766.68 * 0.01667 ≈ $62.82 (rounded)

New Balance: $3766.68 + $62.82 = $3829.50

Payment: $300

Remaining Balance: $3829.50 - $300 = $3529.50

Month 3:

Interest: $3529.50 * 0.01667 ≈ $58.86 (rounded)

New Balance: $3529.50 + $58.86 = $3588.36

Payment: $300

Remaining Balance: $3588.36 - $300 = $3288.36

Month 4:

Interest: $3288.36 * 0.01667 ≈ $54.80 (rounded)

New Balance: $3288.36 + $54.80 = $3343.16

Payment: $300

Remaining Balance: $3343.16 - $300 = $3043.16

Interest: $3043.16 * 0.01667 ≈ $50.72 (rounded)

New Balance: $3043.16 + $50.72 = $3093.88

Payment: $300

Remaining Balance: $3093.88 - $300 = $2793.88

Total = $66.68 + $62.82 + $58.86 + $54.80 + $50.72

≈ $293.88 in interest

The remaining balance is approximately $2793.88.

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The value of the height of the​ cylinder is,

⇒ h = 19 inches

We have to given that;

The volume of a cylinder is 171 pi cubic inches and the radius of the cylinder is 3 inches.

We know that;

Volume of cylinder = πr²h

Hence, We get;

⇒ 171π = π × 3² × h

⇒ 171 = 9h

⇒ h = 171 / 9

⇒ h = 19 inches

Thus,

The value of the height of the​ cylinder is,

⇒ h = 19 inches

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Answer:

y = − 1.3x + 10

Step-by-step explanation:

The slope-intercept form is y = mx + b

2.00x + 1.50y = 15

1.50y = -2x + 15

y = − 1.3x + 10

So, the answer to this is y = − 1.3x + 10

Answer: y= -4/3 +10

Step-by-step explanation:

given the equation 2.00x+1.50y=15

subtract 2.00x from both sides

1.50y = -2.00x +15

then divide both sides by 1.50 to isolate y

then you get your answer

y = -4/3 + 10

The correct box plot would have a box extending from 15 to 21, with a median line at 19, and whiskers extending from 12 to 24. So, correct option is A.

To create a box plot, we need to first find the five-number summary, which includes the minimum value, first quartile (Q₁), median, third quartile (Q₃), and maximum value.

The minimum value in the given data set is 12 and the maximum value is 24. To find the median, we need to find the middle number of the set. Since there are nine numbers in the set, the median would be the average of the fifth and sixth numbers, which is 19.

To find the first quartile (Q₁) and third quartile (Q₃), we can find the medians of the lower and upper halves of the data set, respectively. The lower half of the data set includes the numbers 12, 15, 15, 17, and 19. The median of this set is 15. The upper half of the data set includes the numbers 19, 20, 22, and 24. The median of this set is 21.

Using these values, we can create a box plot with a box extending from Q₁ to Q₃, a line in the box indicating the median, and whiskers extending from the box to the minimum and maximum values.

So, correct option is A.

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Complete question is:

The data below represents the number of runners on each cross country team in the Northern Conference. 12, 15, 15, 17, 19, 19, 20, 22, 24.

Which box plot correctly summarizes the data?

The experimental  probability is 1/5, or 0.20. The theoretical probability is 0.206.

Probability is represented as the number of ways for an event to happen over all possible outcomes.

a.     For the theoretical probability, there is 1 black spot and 5 total options. Therefore, the probability is 1/5, or 0.20.

b.     For experimental probability, there were 103 times it landed on black out of 500 spins. The probability is 103/500, or 0.206.

c.   Lastly, the multiple choice. The larger sample size you take, assuming a fair spinner, the more likely you are to see results similar to the theoretical probability. This is because the larger sample size taken, the less each individual spin effects the outcome.

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Answer:

Step-by-step explanation:

18

18 is a mulitple of both 6 and 18

The equation that describes the point estimate of the population mean is x = 35.5

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

As a general rule

The point estimate of the mean equals the sample mean

This means that

Point estimate = 35.5

Hence, the equation is x = 35.5

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The solution is, she have in her retirement account 25 years from now is $261172.09.

Here, we have,

given data

contribute principal P = $250

employer = 50 %

employer add = $125

interest rate = 0.5 % = 0.005

time = 25 year = 300 months

to find out

how much will she have in her retirement account 25 years from now

solution

here monthly payment = 250 + 125 = $375

we will apply here amount formula that is

amount = P × (1+r)^t -1 /r × ( 1 + rate )

put here value

amount = 375 × (1+0.05)^300 -1 /0.05 × ( 1 + 0.005 )

amount = 261172.09

Hence, she have in her retirement account 25 years from now is $261172.09.

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complete question:

Stephanie is going to contribute $250 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will add $125 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .5 percent, how much will she have in her retirement account 25 years from now?

Answer: 2.4

Step-by-step explanation: obviously not anywhere close to 3 trust

Answer:

55,500 cm².

Given:

To find the surface area of the solid figure represented by the given net, we first have to identify the shape of the figure. By analyzing the net, we can see that the figure is a rectangular prism with a length of 65 cm, a width of 40 cm and a height of 250 cm. To find the surface area of a rectangular prism, we use the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values, we get:

Steps:

2(65)(40) + 2(65)(250) + 2(40)(250) = 13,000 + 32,500 + 10,000 = 55,500 cm²

Get:

Therefore, the surface area of the solid figure represented by the given net is 55,500 cm².

Answer:

600 cm².

Step-by-step explanation:

The net provided represents a three-dimensional solid figure. The surface area of this figure can be calculated by finding the area of each individual face and adding them together. The net includes six faces, each of which have different dimensions. The areas of these faces are: 65 cm², 250 cm², 40 cm², 90 cm², 90 cm², and 65 cm². Adding them together, we get a total surface area of 600 cm². Therefore, the surface area of the solid figure represented by the given net is 600 cm².

There are 3/20  pink tulips in the garden

By determining the percentage of the garden that is made up of pink tulips.

If 3/10 of the tulips are pink and tulips account for half of the garden, the percentage of the garden that is pink tulips is:

(3/10) x (1/2) = 3/20

So, 3/20 of the garden is pink tulips.

Hence, the answer is 3/20.

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