How many solutions for the equation, 8x - 19 = -4 -7x

Answer:

32.5 ft^2

Step-by-step explanation:

All sides of a square have the same length.  Area would therefore be:

 (5.7 ft)(5.7 ft) = 32.5 ft^2

The values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

The expression p(- x ≤ t22 ≤ x) represents the probability of a t-distribution with 22 degrees of freedom lying between - x and x.

We want to find the values of x such that this probability is 0.98.

We can use a table of t-distribution probabilities or a calculator to find the value of t for which the probability of a t-distribution with 22 degrees of freedom lying between −t and t is 0.98.

This value is , 2.518.

Therefore, we need to solve the inequalities:

-2.518 ≤ -x ≤ 2.518

Solving for x, we get:

-2.518 ≤ -x x ≤ 2.518

Therefore, the values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

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Answer:

1=4

Step-by-step explanation:

I don't want to do it all but I gave you one of them!

Answer The picture shows you where to place your line

Step-by-step explanation:

Answer:

B).  x= 2i

Step-by-step explanation:

Answer:

36 prices

Step-by-step explanation:

Given the following :

Dentist bought 9 bags of prizes for his patients

Each bag had 12 prizes, and prices were divided equally among three boxes: The each box will. Have :

Total number of prices :

Number of bags × number of prices per bag

9 × 12 = 108 prices

Number of boxes in which prices were equally distributed = 3

Hence, each box will have :

Total prices / number of boxes

= 108 / 3

= 36 prices per box

Answer:

2y

Step-by-step explanation:

Answer:

\(2y\)

Step-by-step explanation:

\((x+y)-(x-y)\)

\((x+y)-x+y\) <-- Remember to distribute -1 in the parentheses!

\(x+y-x+y\)

\(2y\)

Answer:

32

Step-by-step explanation:

Just 16 x 2

Answer:

Wednesday

Step-by-step explanation:

Averages

Wednesday-5.5

Monday-7.5

Friday-6.5

The solutions to the quadratic equation 4x² + 9 = 94 are x = √(85)/2 and x = -√(85)/2.

A second-degree polynomial equation is a quadratic equation. Depending on the discriminant (b square - 4ac) of the equation, quadratic equations might have zero, one, or two real solutions. If the discriminant is positive, there are two unique real solutions to the problem. There is only one actual solution to the equation if the discriminant is zero (called a double root). The equation may have two complex conjugate solutions (using the fictitious unit). if the discriminant is negative rather than having any real solutions. Several fields, including science, engineering, economics, and others, use quadratic equations.

The given equation is 4x² + 9 = 94

Simplifying the equation we have:

4x² = 85

x = ±√(85/4) = ±(√(85)/2)

Hence, the solutions to the quadratic equation 4x² + 9 = 94 are x = √(85)/2 and x = -√(85)/2.

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Given the n™ term of a number sequence, the first three terms of the sequence are 0, 2 and 6

The sequence is given as:

n^2 - n​

To write down the first three terms of the sequence, we set n =1, 2 and 3

So, we have:

When n = 1

n^2 - n​ = 1^2 - 1

Evaluate

n^2 - n​ = 0

When n = 2

n^2 - n​ = 2^2 - 2

Evaluate

n^2 - n​ = 2

When n = 3

n^2 - n​ = 3^2 - 3

Evaluate

n^2 - n​ = 6

Hence, the first three terms of the sequence are 0, 2 and 6

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The value of the function g(2x - 5) = 3x + 9 will be at g(1) equal to 18

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Here we have the function:-

g(2x - 5) = 3x + 9

At g(1) it means that the value of (2x - 5)=1

(2x - 5)=1

x=6/2

x=3

So the value of the function at g(1) will be:-

g(1) = 3x + 9

g(1) = 3x3 + 9

g(1)=18

Hence the value of the function g(2x - 5) = 3x + 9 will be at g(1) equal to 18

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Answer:

$630

Step-by-step explanation:

week 1 : $336

week 2 : $294

gross pay : $630

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer:

4,3

Step-by-step explanation:

Rearrange the equation :

\( \sqrt{x - 3} = x - 3\)

Then, we must square both sides:

x-3 = x²-6x+9

x²-6x+9-x+3=0

x²-7x+12=0

(x-4)(x-3) =0

So x =4,3

Answer:

x = 3, x = 4

Step-by-step explanation:

Given

\(\sqrt{x-3}\) + 3 = x ( subtract 3 from both sides )

\(\sqrt{x-3}\) = x - 3 ( square both sides )

x - 3 = (x - 3)²

x - 3 = x² - 6x + 9 ( subtract x - 3 from both sides )

0 = x² - 7x + 12 ← in standard form

0 = (x - 3)(x - 4) ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

As a check

Substitute these values into the equation and if both sides are equal then they are solutions

x = 3 : \(\sqrt{3-3}\) + 3 = \(\sqrt{0}\) + 3 = 3  = 3 = right side

x = 4 : \(\sqrt{4-3}\) + 3 = \(\sqrt{1}\) + 3 = 1 + 3 = 4 = right side

solutions are x = 3, x = 4

Answer:

8,846 units at $6.50

Step-by-step explanation:

Demand = X/5.75

10,000 = X/5.75

X = 57500

Demand at $6.50 would be:  Demand = 57500/6.50

Demand (at $6.50) = 8846

Answer:

7/13 is closest to 1/2

Since 1/26 is closest to zero, 7/13 is closest to 1/2.

Answer:

x = 2 so y = 7

x = 4 so y = 11

Step-by-step explanation:

y = 2x + 3

x = 0 so y = 2(0) + 3 | y = 3

x = 2 so y = 2(2) + 3 | y = 7

x = 4 so y = 2(4) + 3 | y = 11

x = 6 so y = 2(6) + 3 | y = 15

Answer:

x=120

y=180

Step-by-step explanation:

x=300-y

12x+15y=4140

12(300-y)+15=4140

y=180

substitute

x=300-180

x=120

The value of sin(θ) is approximately 0.921 and the value of cos(θ) is approximately 0.391.

To find the value of each variable using sine and cosine, we need to set up a right triangle with the given information. Let's label the sides of the triangle as follows:

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h2 = s2 + t2

h2 = 31.32 + 13.32

h2 = 979.69 + 176.89

h2 = 1156.58

h = √1156.58

h ≈ 34.0

Now that we know the length of the hypotenuse, we can use sine and cosine to find the values of the variables:

sin(θ) = s / h

sin(θ) = 31.3 / 34.0

sin(θ) ≈ 0.921

cos(θ) = t / h

cos(θ) = 13.3 / 34.0

cos(θ) ≈ 0.391

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Answer: 270

Step-by-step explanation: 20% of 225 = 45

225 + 45 - 270 therefore Toby's bookstore sold 270 books in Feburary.

It will take 10 days for 1023 students to know the secret.

We can start by using the formula for exponential growth: n = 2^k

where n is the number of students who know the secret and k is the number of days.

On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.

We want to find k when n = 1023, so we can solve for k:

1023 = 2^k

log2 1023 = k

k = 10

So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.

Therefore, It will take 10 days for 1023 students to know the secret.

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It will take 10 days for 1023 students to know the secret.

We can start by using the formula for exponential growth: n = 2^k

where n is the number of students who know the secret and k is the number of days.

On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.

We want to find k when n = 1023, so we can solve for k:

1023 = 2^k

log2 (1023) = k

k = 10

So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.

Therefore, It will take 10 days for 1023 students to know the secret.

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The appropriate hypothesis test methods for this data set are:

B. Paired t-test

D. Nonparametric paired test

We have,

Since the agency is measuring the weight of the same individuals before and after the program, a paired test is suitable.

The paired t-test is appropriate if the data follows a normal distribution and the differences between the paired observations are approximately normally distributed.

If the assumptions for the paired t-test are not met, a nonparametric paired test (such as the Wilcoxon signed-rank test) can be used as an alternative.

ANOVA and independent t-tests are not appropriate for this data set since they involve comparing independent groups, which is not the case here.

Thus,

The appropriate hypothesis test methods for this data set are:

B. Paired t-test

D. Nonparametric paired test

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Answer:

\(x=\dfrac{\pi}{2},\quad x=\dfrac{3\pi}{2}\)

Step-by-step explanation:

Given trigonometric equation:

\(\boxed{2\cos^2(x) \csc(x)-\cos^2(x)=0}\)

To solve the equation, begin by factoring out cos²(x) from the left side of the equation:

\(\cos^2(x) \left(2\csc(x)-1\right)=0\)

Apply the zero-product property to create two equations to solve:

\(\cos^2(x)=0\quad \textsf{and} \quad 2\csc(x)-1=0\)

\(\hrulefill\)

Solve cos²(x) = 0:

\(\begin{aligned}\cos^2(x)&=0\\\\\sqrt{\cos^2(x)}&=\sqrt{0}\\\\\cos(x)&=0\\\\x&=\dfrac{\pi}{2}+2\pi n, \dfrac{3\pi}{2}+2\pi n\end{aligned}\)

[To find the solutions using a unit circle, locate the points where the x-coordinate is zero, since each (x, y) point on the unit circle is equal to (cos θ, sin θ).]

Therefore, the solutions on the interval [0, 2π] are:

\(x=\dfrac{\pi}{2},\; \dfrac{3\pi}{2}\)

\(\hrulefill\)

Solve 2csc(x) - 1 = 0:

\(\begin{aligned}2 \csc(x)-1&=0\\\\2\csc(x)&=1\\\\\csc(x)&=\dfrac{1}{2}\\\\\dfrac{1}{\sin(x)}&=\dfrac{1}{2}\\\\\sin(x)&=2\end{aligned}\)

As the range of the sine function is  -1 ≤ sin(x) ≤ 1, there is no solution for x ∈ R.

\(\hrulefill\)

Therefore, the solutions to the given trigonometric equation on the interval [0, 2π] are:

\(\boxed{x=\dfrac{\pi}{2},\quad x=\dfrac{3\pi}{2}}\)

Answer:

360 miles

Step-by-step explanation:

if 90 miles per hour and a half then

1 1/5 x 4= 6

90 x 4 = 360

It will take approximately 33.09 days until only 2 ounces of Element X remain. Rounded to 2 decimal places, the answer is 33.09 days.

The decay of Element X can be modeled by the exponential decay formula:

N = N₀ * (1/2)^(t/T)

where:

N₀ = initial quantity of Element X

N = remaining quantity of Element X

t = time elapsed

T = half-life of Element X

In this problem, we know that:

N₀ = 27 ounces

N = 2 ounces

T = 12 days

Substituting these values into the formula, we get:

2 = 27 * (1/2)^(t/12)

Dividing both sides by 27, we get:

1/2^(t/12) = 2/27

Taking the logarithm of both sides (with base 2), we get:

t/12 = log₂(2/27)

Solving for t, we get:

t = 12 * log₂(2/27)

t ≈ 33.09

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