Find the measure of

Answer:

Step-by-step explanation:

300

in sequare

Answer: 3060 in³

Step-by-step explanation:

Volume is how much a shape can hold.  It's a 3 dimensional measurement so you need to multiply 3 dimensions

V= length x width x height

Sometimes students get confused with which is which side but it really doesn't matter because multiplication is commutative meaning you can switch it and it doesn't matter.  Like  5x2 is the same thing as 2x5  both will still be 10

length=15

width=12

height= 17

If Volume = length x width x height

=15 x 12 x 17 =  =3060

Because it's 3 dimensional, units are are cubed as well. but questions says no units

The measure of the other acute angle to the nearest degree is 34°, since the trigonometric tangent ratio of one acute angle is 3/2.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

we shall call the acute angles X and Y such that;

tan X = 3/2 {opposite/adjacent}

X = tan⁻¹(3/2) {cross multiplication}

X = 56° approximately to the nearest degree

Y = 180° - (56 + 90)° {sum of interior angles of a triangle}

Y = 180° - 146°

Y = 34°

Therefore, the measure of the other acute angle to the nearest degree is 34°, since the trigonometric tangent ratio of one acute angle is 3/2.

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The equation for the relationship would be y = 0.25x - 2 and the unknown value would be 2. 5.

To find the equation, you first need to find the slope of the line by picking two points and applying the slope formula. The two points are (4, -1) and (12, 1).

The slope is:

= (y2 - y1) / (x2 - x1)

= ( 1 - ( - 1 ) ) / ( 12 - 4)

= 2 / 8

= 0. 25

We can then find the full equation :

y - ( - 1 ) = 0.25 (x - 4)

y = 0.25x - 2

The unknown y value when x is 18 is:

y = 0.25 ( 18 ) - 2

y = 2. 5

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The MLE of λ = 1/p is:

â = 1/0.6364 = 1.5714 (rounded to four decimal places).

Let Y be the number of components that survive 24 hours. Then Y ~ Bin(22, p), where p is the probability that a component survives 24 hours. The maximum likelihood estimator (MLE) of p is the sample proportion of components that survive 24 hours, which is y/n = 14/22 = 0.6364.

Now, let X be the lifetime of a component, which is exponentially distributed with parameter λ = 1. Then the probability that a component survives 24 hours is P(X > 24) = e^(-24λ). Substituting λ = 1, we get p = e^(-24).

The likelihood function L(p) is then given by:

L(p) = (22 choose 14) * p^14 * (1-p)^8

Taking the natural logarithm of L(p), we get:

ln L(p) = ln(22 choose 14) + 14 ln p + 8 ln(1-p)

To find the MLE of p, we differentiate ln L(p) with respect to p and set the result to zero:

d/dp ln L(p) = 14/p - 8/(1-p) = 0

Solving for p, we get:

p = 14/22 = 0.6364

This is the same as the MLE of p we obtained earlier, which makes sense since p = e^(-24) is a function of the MLE of p.

Therefore, the MLE of λ = 1/p is:

â = 1/0.6364 = 1.5714 (rounded to four decimal places).

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The randomly select 500 students and observe that 85 of them smoke. Estimate the probability that a randomly selected student smokes , the correct answer is 27.
To estimate the probability that a randomly selected student smokes, we use the proportion of students who smoke in our sample of 500. We observed that 85 out of 500 students smoke, so the proportion is: 85/500 = 0.17
To convert this proportion to a probability, we simply round to two decimal places: 0.17 ≈ 0.27
Therefore, the estimated probability that a randomly selected student smokes is approximately 0.27, which is answer choice a.

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|| (3,3) - (1,1) || < 2 + r

Simplifying this inequality, we get:

2√2 < 2 + r

r > 2√2 - 2

So, any value of r such that r > 2√2 - 2 will satisfy the condition B2(1,1)∩Br(3,3)≠0.

For the first question, we need to find an r such that the open ball centered at (0,0) with radius 1 (denoted as Br(0,1)) intersects with the open ball centered at (2,0) with radius t (denoted as Bt(2,1)). Since the usual norm is the Euclidean norm, the distance between (0,0) and (2,0) is 2. Thus, we have the inequality:

|| (2,0) - (0,0) || < 1 + t

Simplifying this inequality, we get:

2 < 1 + t

t > 1

So, any value of r such that 1 < r < 3 will satisfy the condition Br(0,1) ∩ Bt(2,1)≠0.

For the second question, we need to find an r such that the open ball centered at (1,1) with radius 2 (denoted as B2(1,1)) intersects with the open ball centered at (3,3) with radius r (denoted as Br(3,3)). Using the Euclidean norm, we have:

|| (3,3) - (1,1) || < 2 + r

Simplifying this inequality, we get:

2√2 < 2 + r

r > 2√2 - 2

So, any value of r such that r > 2√2 - 2 will satisfy the condition B2(1,1)∩Br(3,3)≠0.

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To determine which of the following systems of equations have nonzero solutions, we need to solve each system and see if there are any non-trivial solutions (i.e., solutions where not all variables are zero). If there are non-trivial solutions, then the system has nonzero solutions. Otherwise, the system has only the trivial solution of all variables being zero.

Let's take each system one at a time:

1) x + y = 0, 2x + 2y = 0
This system can be simplified to x + y = 0. Solving for y, we get y = -x. This system has infinitely many solutions, all of which are of the form (x, -x) for any real value of x except zero. Therefore, this system has nonzero solutions.

2) x + y = 0, 2x + 2y = 1
This system can be simplified to x + y = 0. Solving for y, we get y = -x. Substituting this into the second equation, we get 2x + 2(-x) = 1, which simplifies to 0 = 1, which is impossible. Therefore, this system has no solutions.

3) x + y = 1, 2x + 2y = 2
This system can be simplified to x + y = 1. Solving for y, we get y = 1 - x. Substituting this into the second equation, we get 2x + 2(1 - x) = 2, which simplifies to 0 = 0. This is always true, regardless of the value of x. Therefore, this system has infinitely many solutions, all of which are of the form (x, 1 - x) for any real value of x. Therefore, this system has nonzero solutions.

In summary, the first and third systems have nonzero solutions, while the second system has no solutions. The first system has infinitely many solutions, while the third system also has infinitely many solutions.

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The equation of line g is y = (3/10)x + 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line f is y - 7 = (3/10)(x - 4).

Since line g is parallel to line f, it will have the same slope as line f, which is 3/10.

Hence, the equation of line g can be written in the form:

y - y1 = m(x - x1)

Where (x1, y1) is the given point (10, 4) and m is the slope of line f, which is 3/10.

Substituting the values, we get:

y - y1 = m(x - x1)

y - 4 = (3/10)(x - 10)

y - 4 = (3/10)x - 3

y = (3/10)x + 1

Therefore, y = (3/10)x + 1 is the equation of line g.

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the answer is  -2 (6 x + 7)

Mike works 39 hours per week at Job A and 20 hours per week at Job B.

We need to formulate some expressions here.

Let:

Hours Mike works at Job A = x

Hours Mike works at Job B = y

We know that:

x + y = 59 ---------- equation 1

We also know that he makes $6 per hour at Job A, and $7 per hour at Job B, and his total pay is $374. So we can set up another equation based on his total pay:

6x + 7y = 374 --------- equation 2

Now we have two equations with two unknowns, which we can solve simultaneously.

Using substitution method:

solve for x in terms of y:

x = 59 - y

We can substitute this expression for x into equation 2:

6(59 - y) + 7y = 374

Simplifying and solving for y:

354 - 6y + 7y = 374

y = 20

So Mike works 20 hours per week at Job B. We can substitute this value for y into equation 1 to find x:

x + 20 = 59

x = 39

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The probability of randomly selecting a park that neither allows camping nor has a playground is 31/77.

We have,

We know that there are 59 parks that allow camping, 76 parks that have playgrounds, and a total of 154 parks.

Number of parks that allow camping only = 59 - 14 = 45

Number of parks that have playgrounds only = 76 - 14 = 62

Number of parks that have both camping and playgrounds = 14

The number of parks that neither allow camping nor have a playground.

= Total number of parks - (number of parks that allow camping only + number of parks that have playgrounds only - number of parks that have both camping and playgrounds)

= 154 - (45 + 62 - 14)

= 61

Now,

The probability of randomly selecting a park that neither allows camping nor has a playground.

= 61/154

= 31/77

Thus,

The probability of randomly selecting a park that neither allows camping nor has a playground is 31/77.

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We cannot conclude that the new beta-blocker medicine is effective at treating high blood pressure at a significance level of αα = 0.01.  

We can perform a chi-squared test to determine if there is a significant difference between the number of subjects in the treatment group who had their high blood pressure successfully treated and the number of subjects in the control group who had their high blood pressure successfully treated.

First, we need to calculate the expected counts for each group. Since we know that the treatment group had 114 successful outcomes, and the control group had 100 successful outcomes, we can calculate the expected counts as follows:

Expected counts for treatment group: (114 * 180) / 210 = 146.7

Expected counts for control group: (100 * 180) / 210 = 187.3

Next, we can calculate the chi-squared value using the formula:

chi-squared = sum(([tex]observed - expected)^2[/tex]/ expected)

where observed and expected are the actual counts and expected counts, respectively.

For the treatment group, the observed count is 114, and the expected count is 146.7. Therefore, we calculate the chi-squared value as:

chi-squared = [tex](114 - 146.7)^2[/tex] / 146.7 = 12.2

For the control group, the observed count is 187.3, and the expected count is 187.3. Therefore, we calculate the chi-squared value as:

chi-squared = (187.3 - [tex]187.3)^2[/tex] / 187.3 = 0

We can then calculate the p-value using the formula:

p-value = 2 * (chi-squared / degrees of freedom)

where degrees of freedom is the number of categories minus 1 for each cell. In this case, we have two cells, one for the treatment group and one for the control group, so the degrees of freedom is 2 - 1 = 1.

Substituting the values into the formula, we get:

p-value = 2 * (12.2 / 1) = 2.44

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Answer:

(−∞,∞)

Step-by-step explanation:

y = x² - 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

So, the domain of this quadratic function is: (−∞,∞)

The given set of ordered pairs represents a function because each output has exactly one corresponding input. So, the correct answer is A) Yes, because for each output there is exactly one input.

A relation between two variables is a set of ordered pairs, where the first element in each pair corresponds to the input or independent variable (usually denoted by x), and the second element corresponds to the output or dependent variable (usually denoted by y).

In the given set of ordered pairs, each output has exactly one corresponding input, and therefore the relation satisfies the definition of a function. For example, the input of 3/4 is associated with only one output of -2, and the output of -7 is associated with only one input of -2. Hence, the relation represents a function.

So, the correct answer is A).

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The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2.

b = 1, ≥

From the diagram, the solution to the inequality is x ≥ 1 and x ≤ -3

Hence:

|x + b| ≥ 2

x + b ≥ 2 or -(x + b) ≥ 2

x ≥ 2 - b or x ≤ -2 - b

2 - b = 1 and -2 - b = -3

b = 1

Hence |x + 1| ≥ 2

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2. b = 1, ≥

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Answer:Domain is all real numbers

Step-by-step explanation:

f(x)=x^2

it is a parabola and all parabola’s domains are all real numbers

Answer:

2y92+83(n83-5)+12

Step-by-step explanation:

well if you carry the 4 and move the decimal over 3 places and divide by a hamsterball & justin biebers nipple, you get the answer

The sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is 37 for k= 18.

The cubic equation is given as,

p(x) = x³ - x² - 18x +k

To find the real roots of the cubic equation p(x) we can equate p(x) =0 , we get,

x³ - x² - 18x +k = 0

⇒ x² (x -1) - 18(x - k/18) = 0

For factoring the equation we can equate  (x -1) = (x - k/18) by comparing it with solving of general equations.

That is by arranging the cubic equation after equating (x -1) = (x - k/18)  we will get,

(x-1)(x² -18) =0

Thus we get,

(x -1) = (x - k/18)

⇒ k/18 =1

⇒ k =18

The cubic equation which will give us real roots will become,

p(x) = x³ - x² - 18x +18

By factoring we can find the real roots as,

x³ - x² - 18x +18 =0

⇒ (x² -18)(x -1) =0

⇒x= 1 , x = 3√2 and x= -3√2

Let us say, a = 1 , b = 3√2 and c = -3√2 are the required real roots.

The square of real roots are as follows,

a² = 1

b² = 18

c² = 18

Thus, the sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is

= a² + b²+ c²

= 1 + 18 + 18

= 37

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If Sheila’s test had a z-score of 2.2 then her test score was 89.6%.

We can use the formula for calculating the z-score of a value,

z = (x - μ) / σ, value we want to convert to a z-score is x, mean of the distribution is μ,  standard deviation of the distribution is σ and z score is z. In this case, we know that the average mark on the test was 72%, which means μ = 72. We also know that the standard deviation was 8%, which means σ = 8. We know that Sheila's z-score was 2.2,

We can rearrange the formula to solve for x,

x = μ + zσ

Substituting in the values we know,

x = 72 + 2.2 * 8

x = 72 + 17.6

x = 89.6

Therefore, Sheila's test score was 89.6%.

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Answer: m∠CBD = 98°

Step-by-step explanation:

The price should you sell the bracelets at is given by the term of the amount is $64.

The increase in income that comes from selling one more unit of output is known as marginal revenue. Although marginal revenue can remain constant above a certain level of output, it will eventually start to decline as the output level rises due to the law of diminishing returns. According to economic theory, companies that are completely competitive keep on producing goods until marginal revenue and marginal cost are equal.

Price, the sum of money required to purchase a specific good. Price is also a measure of value insofar as it reflects what consumers are willing to pay for a product's worth.

Overall marginal cost (MC) = Explicit (stated) marginal cost + Profit per unit given up = $2 + $6 = $8

Profit is maximized when Marginal revenue (MR) equals Overall MC.

P = 120 - 2Q

Total revenue (TR) = P x Q = 120Q - 2Q2

MR = dTR/dQ = 120 - 4Q

Equating with Overall MC,

120 - 4Q = 8

4Q = 112

Q = 28

P = 120 - (2 x 28) = 120 - 56 = $64.

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The price should you sell the bracelets at is given by the term of the amount is $64.

The term "marginal revenue" refers to the additional income generated by selling one additional unit of output. Although marginal income can remain constant above a particular output level, it will ultimately start to decrease as the output level increases owing to the law of diminishing returns.

Companies that are entirely competitive continue to produce items until marginal income and marginal cost are equal, according to economic theory. A certain good's price is the amount of money needed to buy it. Insofar as it represents what customers are prepared to pay for a product's worth, price is likewise a measure of value.

Overall marginal cost (MC) = Explicit (stated) marginal cost + Profit per unit given up = $2 + $6 = $8

Profit is maximized when Marginal revenue (MR) equals Overall MC.

P = 120 - 2Q

Total revenue (TR) = P x Q = 120Q - 2Q2

MR = dTR/dQ = 120 - 4Q

Equating with Overall MC,

120 - 4Q = 8

4Q = 112

Q = 28

P = 120 - (2 x 28)

= 120 - 56

= $64.

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1. The modal number of pairs of shoes owned by the children will be; 3.

2. The median number of pairs of shoes owned by the children  will be;3.

3. The Mean is 3.

1. The modal number of pairs of shoes owned by the children would be 3.

2. The median number of pairs of shoes owned by the children are;

= 14/2 th term

= 7 th term

= 3

3. The Mean would be

= (1 x 2+ 2 x 3+ 3 x 5+ 4 x 2 + 5 x 1+ 6x 1)/ (2 +3 +5 +2 + 1 +1)

= 42/14

= 3

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The total area of the garden is 36 ft2.

To find the area of the rectangular piece that the gardener wants to add to the existing garden, we need to find the length and width of the rectangle.

The length of the rectangle is the distance between the points (-17, 15) and (-20, 15), which is 3 units.

The width of the rectangle is the distance between the points (-17, 15) and (-17, 11), which is 4 units.

Therefore, the area of the rectangular piece that the gardener wants to add is 3 x 4 = 12 square feet.

To find the total area of the garden, we need to add the area of the existing garden to the area of the rectangular piece that the gardener wants to add:

24 + 12 = 36

Therefore, the total area of the garden will be 36 square feet.

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Answer:

-1

Step-by-step explanation:

4x + 13 = 9

4x + 13 - 13 = 9 -13

4x = -4

-4/4 = -1

X = -1

Answer:

-1.

Step-by-step explanation:

4x + 13 = 9

4x =  9 -13

4x = -4

x = -4/4

X = -1

Based on the information, there is not sufficient evidence to conclude that tablets contain the right amount of active ingredients.

H0: µ = 320 versus Ha: µ ≠ 320

This is a two tailed test.

The test statistic formula is given as below:

t = (x - µ)/[S/✓(n)]

n = Sample size = 36 n = Population mean = 320 x = Sample mean = 319 S = Sample Standard deviation = 3

We have = Level of significance = 0.09 from the given data.

df = n - 1 = 35

1.7436 is the critical value.

[Using a t-table, we can determine this value.]

The P-value is 0.0533.

P-value = 0.09.

So, we reject the null hypothesis. There is not sufficient evidence to conclude that tablets contain the right amount of active ingredients.

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The correct answer is:
a. V1, V2 form the basis; V3 = 4V1 + V2, V4 = -4V1 + V2

To find a subset of the vectors that forms a basis for the space spanned by the vectors and express each vector that is not in the basis as a linear combination of the basis vectors, follow these steps:

1. Write the given vectors as rows of a matrix:
  A = | 1   0  1  1 |
      |-7   7 -4  1 |
      |-3   7  0  5 |
      |-11  7 -8 -3 |

2. Perform Gaussian elimination to find the row-reduced echelon form (RREF) of the matrix A.

3. The RREF of matrix A is:
  RREF(A) = | 1  0  1  1 |
            | 0  1 -2  3 |
            | 0  0  0  0 |
            | 0  0  0  0 |

4. Identify the pivot columns in the RREF matrix. In this case, the first and second columns have pivots.

5. The pivot columns correspond to the original vectors that form a basis. In this case, V1 and V2 form the basis.

6. Express each vector that is not in the basis as a linear combination of the basis vectors. For V3 and V4, we can see that:
  V3 = 4V1 + V2
  V4 = -4V1 + V2

So, the correct answer is:
a. V1, V2 form the basis; V3 = 4V1 + V2, V4 = -4V1 + V2

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The transformations that move the pentagon FGHIJ onto the pentagon F'G'H'I'J' includes a rotation and a reflection. The correct option therefore is the option C.

C. Rotation, reflection

A rotation transformation is one in which a geometric figure is rotated about a fixed point or location, known as the center of rotation.

The coordinates of the image are; I(-5, 4), H(-2, 4), G(-1. 3), F(-2, 0), and J(-4, 1)

The coordinates of a point, (x, y), following a 90 degrees clockwise rotation are; (y, -x)

Therefore, the coordinates of the image of the after a 90 degrees rotation are; I'(4, 5), H'(4, 2), G'(3, 1), F'(0, 2), J'(1, 4)

The coordinates of the point on the preimage, (x, y), following a reflection over the y-axis is the point (x, -y), therefore;

The coordinates of the image of the figure F'G'H'I'J' after a reflection over the x-axis are;
I''(4, -5), H''(4, -2), G''(3, -1), F''(0, -2), and J''(1, -4)

The above points corresponds to the coordinates of the figure, F'G'H'I'J' in the diagram, therefore;

The series of transformations that maps the pentagon FGHIJ onto the pentagon F'G'H'I'J' is a 90 degrees clockwise rotation and a reflection over the y-axis. Option C is the correct option

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Therefore, the length of a side of the square is x/4 inches by the equation.

In this context, we have a wire that we need to bend into a square. A square has four equal sides, so if we let s be the length of one side of the square, then the total length of the wire must be 4s.

The equation 4s = x represents this relationship, where x is the total length of the wire.

To solve for s, we can isolate s on one side of the equation by dividing both sides by 4. This gives us:

4s / 4 = x / 4

Simplifying, we get:

s = x / 4

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There are indeed 48 triangles that can be chosen from the rectangular array shown .

To find the 48 triangles, you should use the Combination formula which will show you the number of ways to pick 3 points when given 8 points.

C ( n, k ) = n! / ( k ! x ( n - k ) ! )

C ( 8 , 3 ) = 8 ! / (3 ! x ( 8 - 3 ) ! )

C ( 8, 3 ) = 336 / 6

C ( 8, 3) = 56

Now, there are technically 56 ways to pick the points but some of these ways are collinear and these cannot form triangles. Each row will have 4 such points so the number of ways to pick triangles is:

= 56 - ( 4 x 2 )

= 48 triangles

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