What is the solution to the inequality?

4 ( 2x + 5 ) − 2x ≥ 10

135 + 162.5 + 180 + 235 + 185 + 167.5 = 1065

1065/6 = 177.5

 average height is 177.5 cm

Answer:

Average height of sunflowers is:

177.5 cm

Step-by-step explanation:

Average is calculated as sum of all observations divided by number of observations

The heights of six sunflowers are 135.0 cm, 162.5 cm, 180.0 cm, 235.0 cm, 185.0 cm, and 167.5 cm.

Average= [tex]\dfrac{135+162.5+180+235+185+167.5}{6}[/tex]

Average= [tex]\dfrac{1065}{6}[/tex]

Average= 177.5

Hence, Average height of sunflowers is:

177.5 cm

Answer:

-5, 6i

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of this circle is:

(x - 1)² + (y - 1)² = 5²

Just supposing we choose x = 2.  What's the corresponding y-value?

Actually, there are two unique y-values for each x value.

Let x = 2 in (x - 1)² + (y - 1)² = 5².  Then:

(2 - 1)² + (y - 1)² = 5², or

   1²      + (y - 1)² = 25

Solving for (y - 1)², we get  (y - 1)² = 25 - 4, or 24.

Taking the square root of both sides:

y - 1 = ±√24, so that y = 1 ±√24,

This simplifies to y = 1 ± 2√6.

Therefore, if x = 2, y has two values:

(2, 1+2√6) and

(2, 1-2√6

Answer:

A. $336.16

Step-by-step explanation:

The payment per $100 can be set up as a ratio:  

[tex]\frac{3.52}{100}[/tex]

Let the unknown payment be x. Now setting up the ratio over the full value:  

[tex]\frac{x}{9550}[/tex]

Set them equal and solve for x:  

[tex]\frac{3.52}{100}=\frac{x}{9550}[/tex]

1[tex]100x=33616[/tex]

This gives x = $336.16

Therefore, the answer is option A.

they receive 25 per entry but 5 goes towards the cost of the race

 so 25-5 = 20 per entry is for the charity

 so 20x + 5000 = 25000

subtract 5000 from each side

20x= 20000

 divide both sides by 20

 x = 20000/ 20  

x = 1000

 they need at least 1000 entries to make 25000

 so to make more than 25000, they need 1001 entries

we know that

Vertical angles are a pair of opposite and congruent angles formed by intersecting lines

In this problem

[tex](7x-8)=(6x+11)[/tex] --------> by vertical angles

Solve for x

Combine like terms

[tex](7x-6x)=(11+8)[/tex]

[tex]x=19\ degrees[/tex]

therefore

the answer is

the value of x is [tex]19\ degrees[/tex]

The student's problem involves the use of the trapezoid rule to approximate total distance traveled by a race car, finding the speed at a particular time point (Sv(6)), and calculating the car's average speed to see if it meets the qualifying speed.

To solve this problem, we need to conduct several mathematical operations. Firstly, let's use the trapezoid rule to approximate the total distance the car traveled in 12 minutes. Then we'll find an approximation for Sv(6) and explain its meaning. Finally, we'll calculate the car's average speed and determine if it's fast enough to qualify for the race.

https://brainly.com/question/33247395

#SPJ3

Final answer:

Elga's age is determined by setting up an equation E + 3E = 32 and solving for E. After simplifying, we find that Elga is 8 years old.

Explanation:

To solve this problem, we can use algebra to set up two equations based on the information given that Alvin's age is three times Elga's age and the sum of their ages is 32.

Let's let E represent Elga's age. According to the problem, Alvin's age will be 3E because it is three times Elga's age. We can write the following equation to represent the sum of their ages:

E + 3E = 32

Combining like terms, we have:

4E = 32

Dividing both sides by 4 to solve for E, we get:

E = 32 / 4

Therefore, Elga's age is:

E = 8

Elga is 8 years old.

Answer:

His answer will have a very large value.

Step-by-step explanation:

Lets take an example:

Let the item price be = $50

John is calculating 6% tax on an item. This becomes:

[tex]0.06\times50=3[/tex] dollars

But he accidentally divides by 0.06. This becomes: [tex]\frac{50}{0.06}= 833.33[/tex] dollars

We can see that the answer is completely wrong and the value is very large.

Final answer:

The least number of hours Ammon could have worked is 13 hours, and Nakia worked 16 hours since Nakia worked 3 hours more than Ammon, and together they worked more than 27 hours.

Explanation:

Let's denote the number of hours that Ammon worked as A and the number of hours that Nakia worked as N. According to the question, Nakia worked 3 more hours than Ammon, which can be written as N = A + 3. It's also given that together they worked more than 27 hours, so we can write this as A + N > 27. Substituting the first equation into the second, we get A + (A + 3) > 27, which simplifies to 2A + 3 > 27. By subtracting 3 from both sides, we get 2A > 24. Dividing by 2 gives us A > 12. Since A must be a whole number, the smallest whole number greater than 12 is 13.

Now that we know A is at least 13, we can find the minimum number of hours Nakia worked, which is A + 3. That gives us N = 13 + 3 = 16. Therefore, the least number of hours Ammon worked is 13 hours and Nakia worked 16 hours.

Answer:

N - 8 = 22

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of her lawn=64.15 feet.

Width of her lawn=22.70 meters.

we are given that:

1 foot=0.3048 meters.

Hence,

64.15 feet=21.86232 meters.

Hence, length of lawn=21.86232 meters.

Hence, width of the lawn is greater than the length of the lawn.

( since 22.70 meters> 21.862332 meters)

Also 1 meter=1.0936 yards.

so, width of lawn in yards is:

22.70×1.0936=24.82472 yards.

length of lawn is: 23.9086462752 yards.

Hence, width of lawn is 0.9160737 yards more than the length of lawn.

The surface area of the triangular prism is 468 (square cm).

The surface area A of a triangular prism is given by the formula:

[tex]\[ A = 2A_{\text{base}} + P_{\text{base}} \times h \][/tex]

where:

- [tex]\( A_{\text{base}} \)[/tex] is the area of one of the triangular bases,

- [tex]\( P_{\text{base}} \)[/tex] is the perimeter of one of the triangular bases,

- h is the distance between the bases.

The area of a right triangle is given by:

[tex]\[ A_{\text{base}} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

And the perimeter of a right triangle is the sum of the lengths of its three sides.

Given that the legs of the right triangles forming the bases are 9 cm and 12 cm, and the distance between the bases is 10 cm, we can calculate the surface area.

1. Area of the triangular base [tex](\(A_{\text{base}})\)[/tex]:

[tex]\[ A_{\text{base}} = \frac{1}{2} \times 9 \times 12 \][/tex]

2. Perimeter of the triangular base [tex](\(P_{\text{base}})\)[/tex]:

[tex]\[ P_{\text{base}} = 9 + 12 + \sqrt{9^2 + 12^2} \][/tex]

3. Surface area of the triangular prism A:

[tex]\[ A = 2 \times A_{\text{base}} + P_{\text{base}} \times 10 \][/tex]

Calculate each part and find the total surface area.

[tex]\[ A_{\text{base}} = \frac{1}{2} \times 9 \times 12 = 54 \, \text{cm}^2 \][/tex]

[tex]\[ P_{\text{base}} = 9 + 12 + \sqrt{9^2 + 12^2} = 9 + 12 + 15 = 36 \, \text{cm} \][/tex]

[tex]\[ A = 2 \times 54 + 36 \times 10 = 108 + 360 = 468 \, \text{cm}^2 \][/tex]

So, the surface area of the triangular prism is [tex]\(468 \, \text{cm}^2\)[/tex].

The probability of losing money in this scenario is 23.89%.

Probability of Losing Money in Roulette (200 spins, red bet)

Step-by-Step Calculation:

1) Probability of winning on one spin:

Red covers 18 out of 38 numbers (European roulette).

P(win) = 18/38 ≈ 0.474.

2) Number of wins needed to break even:

Divide total spins by 2 due to 1:1 payout on red.

200 spins / 2 = 100 wins needed.

3) Binomial distribution:

200 trials (spins), each with 2 outcomes (win/loss).

Success probability = P(win) = 0.474.

Failure probability = P(loss) = 1 - P(win) = 0.526.

4) Normal approximation:

Check conditions for normal approximation:

np > 5 (200 × 0.474 ≈ 95 > 5)

nq > 5 (200 ×0.526 ≈ 105 > 5)

Both conditions met, so normal approximation is valid.

5) Calculate mean and standard deviation:

Mean (μ) = np = 200 × 0.474 ≈ 94.8.

Standard deviation (σ) = sqrt(npq) = sqrt(200 * 0.474 * 0.526) ≈ 7.4.

6) Find probability of losing money:

We need wins < 100, which translates to losses ≥ 100.

Convert losses to z-scores:

z = (x - μ) / σ = (100 - 94.8) / 7.4 ≈ 0.71.

Look up probability of z ≥ 0.71 in standard normal distribution table:

P(z ≥ 0.71) ≈ 0.2389.

7) Generalization:

For any number of spins (n) and break-even win threshold (k), the steps are similar. Use the binomial distribution or its normal approximation to calculate the probability of winning k or fewer times.

we have that

[tex]PR = 4x - 2\\RS = 3x - 5[/tex]

we know that

[tex]PS=PR+RS[/tex]

substitute the values of PR and RS in the formula above

[tex]PS=(4x-2)+(3x-5)[/tex]

Combine like terms

[tex]PS=(7x-7)[/tex]

therefore

the answer is

[tex]PS=(7x-7)[/tex]

The expression which represents PS is; 7x -7

According to the question;

From observation;

Read more on addition of algebraic expressions;

https://brainly.com/question/2164351

the correct answer is - 1/2

Answer: The value of the scale factor is [tex]-\frac{1}{2}[/tex].

Explanation:

It is given that the △E′F′G′ is the image of △EFG under a dilation through point C.

We know that the length of sides of image are in the proportion of length of sides of preimage. That proportion factor is also known as scale factor.

It is given that the length of FG is 8 cm and the length of F'G' is 4 cm.

[tex]k=\frac{F'G'}{FG} =\frac{4}{8} =\frac{1}{2}[/tex]

Therefore the side of image and preimage are in proportion of [tex]\frac{1}{2}[/tex].

Since the image and preimage are not on the same side of the center of dilation it means the factor must be negative. So,

[tex]k=-\frac{1}{2}[/tex].

Therefore, [tex]-\frac{1}{2}[/tex] is the scale factor of dilation.

Answer: A. 15 over 31

I took a the test and got it right, thank you!