If 9 is added to twice a number and this sum is multiplied by 6 the result is the same as if the number is multiplied by 7 and 14 is added to the product. What is the number?

Answer:

2

Step-by-step explanation:

The greatest common factor of whole numbers is the largest number that is a factor of all numbers. That is, it is the largest number that can divide all numbers.

In this case, the largest number that divide all the numbers is 2, who can divide 4, 18 and 12.

So:

[tex](4k, 18k^{4} ,12)= 2(2k,9k^{4} , 6)[/tex]

Answer: [tex][Q - R] + [S - T]=10m+7n-14[/tex]

Step-by-step explanation:

Given : [tex]Q = 7m + 3n[/tex],

[tex]R = 11 -2m[/tex],

[tex]S = n + 5[/tex], and

[tex]T = -m - 3n + 8[/tex]

Now  , [tex]Q-R= 7m + 3n-(11 - 2m)[/tex]

[tex]Q-R= 7m +3n-11+2m[/tex]    [ ∵ (-)(+)=(-) and (-)(-)=(+)]

[Note : when -1 is outside the parenthesis it indicates that -1 should be multiplied with each of the terms present inside the parenthesis .]

[tex]Q-R= 9m +3n-11[/tex]  [Combine like terms.]

[tex]S-T=n + 5-(-m - 3n + 8)[/tex]

[tex]S-T=n + 5+m+3n-8[/tex]    [ ∵ (-)(+)=(-) and (-)(-)=(+)]

[tex]S-T=4n +m-3[/tex]    [Combine like terms.]

Now, [tex][Q - R] + [S - T]=[9m +3n-11]+[4n +m-3][/tex]

[tex]=9m +3n-11+4n+m-3[/tex]

[tex]=10m+7n-14[/tex]  [combine like terms]

Hence, [tex][Q - R] + [S - T]=10m+7n-14[/tex]

The answer is 140, you just add them up and it goes by 2.

Answer:

i will say bullet proof vest there are my reason

1. your teacher is suppose to keep you safe

2.bullet proof vest would keep you safe from gun shootings

3. school guards should check everyone's pockets before interning the school building

i hope this helps you -pandamathhelper  

Answer:

9

Step-by-step explanation:

15 divided by 1.75 equals 9.

And in order to double check, we multiply 9 and 1.75 together which equals 15.75.

Answer:

m=8

Step-by-step explanation:

on imagine 2021

The expressions describing the area of the shaded region is 1/2 × 1/4

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, a rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles.

We need to find the expressions for the area of the shaded region,

So, we have,

The height is 6 and the length is 12

The shaded part is 3 boxes by 3 boxes

Therefore, we can write =

3/6 × 3/12 = 1/2 × 1/4

Hence, the expressions describing the area of the shaded region is 1/2 × 1/4

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The probability Bill hits a higher percentage than Wilt in free throws is approximately 0.0085, or 0.85%.

To find the probability that Bill hits a higher percentage of his shots than Wilt, we can use the concept of binomial distributions.

Let's denote:

- [tex]\( W \)[/tex] as the number of successful shots Wilt makes out of 50,

- [tex]\( B \)[/tex] as the number of successful shots Bill makes out of 50.

Since Wilt makes 75% of his free throws and Bill makes 85% of his free throws, we can calculate the expected number of successful shots for each:

- For Wilt: [tex]\( E(W) = 50 \times 0.75 = 37.5 \)[/tex]

- For Bill: [tex]\( E(B) = 50 \times 0.85 = 42.5 \)[/tex]

Now, we can use the normal approximation to the binomial distribution to calculate the probability that Bill hits a higher percentage of his shots than Wilt. We'll assume that both distributions are approximately normal due to the central limit theorem.

The standard deviation for each player's distribution can be calculated as:

- For Wilt: [tex]\( \sigma_W = \sqrt{n \times p_W \times (1-p_W)} = \sqrt{50 \times 0.75 \times 0.25} \)[/tex]

- For Bill: [tex]\( \sigma_B = \sqrt{n \times p_B \times (1-p_B)} = \sqrt{50 \times 0.85 \times 0.15} \)[/tex]

Now, we can calculate the probability using a normal distribution:

[tex]\[ P(B > W) = P\left(Z > \frac{{E(B) - E(W)}}{{\sqrt{\sigma_B^2 + \sigma_W^2}}}\right) \][/tex]

Where [tex]\( Z \)[/tex] is a standard normal random variable.

Calculating:

[tex]\[ P(B > W) = P\left(Z > \frac{{42.5 - 37.5}}{{\sqrt{50 \times 0.85 \times 0.15 + 50 \times 0.75 \times 0.25}}}\right) \][/tex]

[tex]\[ P(B > W) = P(Z > 2.3717) \][/tex]

Using a standard normal distribution table or calculator, we find that  [tex]P(Z > 2.3717) \approx 0.0085 \).[/tex]

So, the probability that Bill hits a higher percentage of his shots than Wilt is approximately 0.0085, or 0.85%.

The required graph of the quadratic function is the parabola shown in the attachment.

Given that,
To determine the graph to the best match of the graphed quadratic equation. F(x) = x² + 4x.

A parabola is a cross-section cut out of the cone and represented by an equation.

What is a graph?

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The given equation represents the parabola with vertex at (-2, - 5).
and a graph of the parabola is attached below.

Thus, the required graph of the quadratic function is the parabola shown in the attachment.

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Answer:

the x-intercepts are (-1,0) and (-11,0), the y-intercept is (0,11).

To determine equations with no real solutions, assess for a negative discriminant or no x-intercepts in quadratic equations. Steps include identifying unknowns, choosing appropriate equations, simplifying terms, and checking for reasonableness.

To select each equation that has NO real solution, we must assess the equations provided, looking for specific characteristics that indicate the absence of real solutions. One of the hallmarks of such equations is when they represent a quadratic equation with no x-intercepts or the discriminant (b^2 - 4ac) in the quadratic formula is negative, which means the roots are complex numbers.

When working on problems like these, it's crucial to go through several steps: Identify the unknown, identify the knowns, choose an equation, eliminate terms to simplify the algebra, and then check the answer to see if it is reasonable.

Let's use an example equation: x^2 + 4 = 0. To determine if this has real solutions, we can identify the unknown (x), the knowns (coefficients of x), solve the equation or calculate the discriminant (4^2 - 4*1*-4 = 16 +16 = 32, which is positive), and confirm whether the solutions are real or not. In this case, because the discriminant is positive, this equation does have real solutions, and therefore would not be included in a list of equations with no real solutions.

The equations 2x² - 4x + 5 = -3, x² - 12x + 60 = 12, and x² + 3x + 6 = 0 have no real solutions, based on their negative discriminants.

We need to determine the discriminant (b² - 4ac) of each equation to check for real solutions. A negative discriminant indicates no real solutions.

Equations Analysis

Equations with No Real Solutions

Complete Question - Select each equation that has no real solution.

Answer: 2,3,5

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

i just know

Answer:

c = 23.3

Step-by-step explanation:

Answer:

[tex]23.3 \pi[/tex] cm

Step-by-step explanation:

Circumference of circle = [tex]2 \pi r[/tex]

The circumference of a circle is 60π cm.

So,  [tex]2 \pi r=60 \pi[/tex]

[tex]2r=60[/tex]

[tex]r=30[/tex]

Formula of length of arc = [tex]2 \pi r \times \frac{\theta}{360}[/tex]

Length of arc = [tex]2 \pi \times 30 \times \frac{140}{360}[/tex]

Length of arc = [tex]23.3 \pi[/tex]

So, Option C is true

Hence Length of arc is [tex]23.3 \pi[/tex] cm

The expression in the simplest form that represents the expected population next year will be 1.065p.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The ongoing populace of a city can be addressed by p. the populace is supposed to increment by 6.5% one year from now.

The expression in the simplest form that represents the expected population next year will be given as,

⇒ p(1 + 0.065)

⇒ 1.065p

The expression in the simplest form that represents the expected population next year will be 1.065p.

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Final answer:

To calculate the number of times a hummingbird flaps its wings per minute, you multiply the number of flaps per second by 60. In this case, hummingbirds flap their wings approximately 4800 times per minute.

Explanation:

To calculate how many times a hummingbird flaps its wings per minute, you can start by determining how many times it flaps its wings per second. Given that some species of hummingbirds flap their wings 80 times per second, you can simply multiply this by 60 to find the number of times per minute:

80 flaps/second x 60 seconds/minute = 4800 flaps/minute

Therefore, hummingbirds flap their wings approximately 4800 times per minute.

Answer: 2.32 seconds.

Step-by-step explanation:

Knowing that:

You can calculate how much longer it takes to her to swim the second half than the first half, by subtracting 30.12 seconds and 27.8 seconds.

Then:

[tex]30.12\ seconds-27.8\ seconds=2.32\ seconds[/tex]

Therefore, it took her 2.32 seconds longer to swim the second half on the race than the first half.

Answer:

2.32 seconds.

Step-by-step explanation:

We have been given that Lily swims a 100 meter race. She swims the first half 27.8 seconds and she swims the second half in 30.12 seconds.

To find how much longer it took Lily to swim the second half on the race than the first half, we need to subtract the time taken by Lily on first half from the time taken by Lily on second half.

[tex]\text{Difference of time}=30.12\text{ seconds}-\text{27.8 seconds}[/tex]

[tex]\text{Difference of time}=2.32\text{ seconds}[/tex]

Therefore, it took Lily 2.32 seconds more to swim the second half on the race than the first half.