II. Find the solution / solution set in each equation / inequality : (3 pts each)

21. x +. 13 = 28
22. x - 10 = 24
23. 2x = 40
24. x + 8 > - 12
25. 3 x 4 < 8​

Answer:

A will be at -3.3 B will be at -4.1 C will be at 6.1 D will be at 1.3 hope this helps

The expression for the total cost of their trip is 7 + 2x + 3y.

As per the question, assuming the number of bottles to be x and number of bags to be y. The equation will have one time fee of admission, product of cost of bottles and number of bottles and product of cost of bags and number of chips bags.

The one time fee and two products will be added to form the expression. Forming the equation now -

Expression = 7 + 2x + 3y

Therefore, the expression of trip when x bottles of water were bought during the visit is 7 + 2x + 3y.

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Answer:

They are about 3.6 miles away from each other.

Step-by-step explanation:

2²+3² = C²

13=C²

√13 = C

C = 3.6

The distance between Josh and Ben is 3.6 miles

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that Josh and Ben spotted a bear in the woods while riding their bikes. Josh rode 3 miles north and Ben rode 2 miles east.

The formula of the Pythagorean theorem is given as,

C² = a² + b²

C² = 2²+3²

C² = 13

C = √13

C = 3.6

Therefore, the distance between Josh and Ben is 3.6 miles

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The possible dimensions of the rectangular sandbox cover that can protect an area of 72 square meters are 4 m by 18 m and 8 m by 9 m.

To find the possible dimensions, we need to determine the length and width combinations that result in an area of 72 square meters. We can calculate the area of each option to verify if it matches the given area.

Option: 2 m by 36 m

Area = 2 m × 36 m = 72 square meters (matches the given area)

Option: 8 m by 9 m

Area = 8 m × 9 m = 72 square meters (matches the given area)

Option: 8.5 m by 8.5 m

Area = 8.5 m × 8.5 m = 72.25 square meters (doesn't match the given area)

Option: 4 m by 18 m

Area = 4 m × 18 m = 72 square meters (matches the given area)

Option: 6 m by 12 m

Area = 6 m × 12 m = 72 square meters (matches the given area)

Option: 7.5 m by 9.5 m

Area = 7.5 m × 9.5 m = 71.25 square meters (doesn't match the given area)

Therefore, the possible dimensions of the cover that can protect an area of 72 square meters are 4 m by 18 m and 8 m by 9 m.

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Answer:

y = -1/2x + 8

Step-by-step explanation:

y = -1/2x + b

6 = -1/2(4) + b

6 = -2 + b

8 = b

The difference between F(8) and F(2) is 12

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given: Function of Warming Room = F(m) = 2m + 58

To Find: F(8) - F(2)

F(8) = 2*8 + 58 = 16+58 = 74

F(2) = 2*2 + 58 = 4+58 = 62

F(8) - F(2) = 74 - 62 = 12

The difference between F(8) and F(2) is 12

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The line segments PR and QR and PQ to form an equilateral triangle.
The three blue line segments are PQ, PR, and QR.


To construct an equilateral triangle with PQ as one side using a compass and straightedge:

1.  Draw a line segment PQ.

2. Place the compass at point P and draw a circle with radius PQ.

3. Without changing the radius of the compass, place the compass at                  
      point Q and draw another circle.

4. The intersection of the two circles is point R.

Draw line segments PR and QR to form an equilateral triangle.

The three blue line segments are PQ, PR, and QR.
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The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Answer:

x=2 y=9

slope intercept form

y= mx+ b

Answer:

4,      -1,         5,          -2

Step-by-step explanation:

The 95% confidence interval for the population mean SAT score is given as follows:

(1340, 1460).

The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.

The bounds are obtained according to the equation defined as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which the variables of the equation are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

\(\overline{x} = 1400, n = 64, s = 240\)

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.

Then the lower bound of the interval is of:

1400 - 1.998 x 240/sqrt(64) = 1340.

The upper bound of the interval is of:

1400 + 1.998 x 240/sqrt(64) = 1460.

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Answer:

A. Angle Y is a right angle.

B. The measure of angle Z is 45°.

E. The perpendicular bisector of creates two smaller isosceles triangles.

Step-by-step explanation:

Let x represent the measures of base angles X and Z. 2x is the measure of vertex angle Y.

x + x + 2x = 180°

x = 45°

2x = m∠Y = 90°

The triangle is an isosceles right triangle which has base angles of 45°.

The perpendicular bisector of line XZ creates two smaller isosceles triangles with acute angles of 45°

Answer:

The answers are A B E

Step-by-step explanation:

The leading coefficient of the polynomial is -2, and the degree of the polynomial is 3.

To identify the leading coefficient and degree of the polynomial, we need to consider the highest power of the variable in the polynomial expression.

In the given polynomial, -2y³ is the term with the highest power of y. The coefficient of this term, which is -2, is the leading coefficient of the polynomial. The degree of a polynomial is determined by the highest power of the variable. In this case, the highest power of y is 3 in the term -2y³. Therefore, the degree of the polynomial is 3.

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Answer:

Line 1 and 4

Step-by-step explanation:

Perpendicular lines are easy to see once you realize that their slopes, the numbers in front of the x, are inverses. Line 1 and 4 are inverses.

1/3 and 3

Boom.

Answer: yes

Step-by-step explanation:

vertical line test

The equation \(y\ =-2\log_{2}\left(x+2\right)+8\) has x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞). Thus Option A,B and C are correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

Given function,
= \(y\ =-2\log_{2}\left(x+2\right)+8\)
Domain of the above function is grater than -2 because at -2 system goes to infinity. Domain can be given as(-2, ∞).

Given function has x intercept at (14, 0) and y intercept at (0, 6).

Thus, the given function of log has following characteristic i.e.
x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞).

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Answer:a) r >= -20
             b) -10 <= x, or x >=-10
             c) q<= 5

Step-by-step explanation:
a)-11r >=220
 -11r/-11 >= 220/-11
  r>=-20

b) -8<=-7+x/10
   -8+7<=x/10
   -1 <=x/10
    -10 <=x

c) -1-6(5q-2)>=-139
  -1 -30q +12 >= -139
   -30q+12-1>=-139
   -30q+11>=-139
   -30q >= -139-11
   -30q>= -151
    -30q/-30 >= -151/-31
    q <= 5,

u will notice the sign has changed from >= to <= it is coz when the negative signs erase themselves.
   

Answer:

450

Step-by-step explanation:

find perimeter of bases and then the area. then find Lateral Surface area to get Surface area

Answer:

48

Step-by-step explanation:

natural even numbers have a difference of 2 between them

let n be the minimum number , then the next 3 are

n + 2, n + 4, n + 6

sum the 4 numbers and equate to 204

n + n + 2 + n + 4 + n + 6 = 204

4n + 12 = 204 ( subtract 12 from both sides )

4n = 192 ( divide both sides by 4 )

n = 48

the 4 numbers are then 48, 50, 52, 54

with the minimum being 48

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

678.32 feet

Step-by-step explanation:

Circumference=2π(radius)=2·π·50≈314.15927
314.15927·2=628.31854
628.31854+50=678.31854

Answer:

678 ft (nearest foot)

Step-by-step explanation:

The distance from the center of a circle its edge is its radius.

Given that the distance from the center of a circular tent to the tent’s edge is 50 ft then:

⇒ radius (r) = 50

The edge of a circle is its circumference

Circumference of a circle = \(2\pi r\) (where r is the radius)

Therefore, the circumference of the tent is:

\(\implies 2 \cdot \pi \cdot 50=100\pi\) ft

If Kelly walked around the edge of the tent twice, then walked straight to the center:

⇒ total distance walked = 2 × circumference + radius

                                        = 2 × \(100\pi\) + 50

                                       = 678.3185307...

                                       = 678 ft (nearest foot)

12

Step-by-step explanation:

1.25 x 12=15.00 so he can at least sell 12 minimum and still have a .25 (25 cents) left

The minimum number of ice pops Mark needs to sell to make at least enough money to cover the cost of his supplies is 12

From the question,

We are to determine the minimum number of ice pops Mark needs to sell

From the given information

Mark is charging $1.25 per ice pop

and

He needs to make at least $14.75

∴ The minimum number of ice pops he needs to sell = The amount he needs to make ÷ The rate he is charging per ice pop

That is,

The minimum number of ice pops he needs to sell = $14.75 ÷ $1.25

The minimum number of ice pops he needs to sell = 11.8

Round up the answer to the nearest whole number

The minimum number of ice pops he needs to sell = 12

Hence, the minimum number of ice pops Mark needs to sell to make at least enough money to cover the cost of his supplies is 12.

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Answer:

the correct answer is the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

When you are trying to find if they are equivalent, you only want to use one value. If they are both positive, it doesn't mean that they are quivalent. They would have to be the same.

Answer:

b=-7    or the y-intercept is -7

Step-by-step explanation:

-7= =3(0)+b

-7=b

Answer:

We conclude that the original triangle ΔDEF is dilated by a scale factor of 5/2 to get the image triangle ΔD'E'F'.

Therefore, 'Cárl' is correct. Hence, option 'a' is correct.

Step-by-step explanation:

Checking the location of the vertices of the original triangle ΔDEF

Checking the location of the dilated vertices of the image triangle ΔD'E'F'

Notice that if we multiply the vertices of the original triangle ΔDEF by 5/2, we get the correct image vertices of image triangleΔD'E'F'

i.e.

D(-2, 4) → D'(5/2 (-2), 5/2 (4))  → D'(-5, 10)

E(2, 4) → E'(5/2 (2), 5/2(4))  → D'(5, 10)

F(0, 2) → E'(5/2 (0), 5/2(2))  → F'(0, 5)

Thus, we conclude that the original triangle ΔDEF is dilated by a scale factor of 5/2 to get the image triangle ΔD'E'F'.

Therefore, 'Cárl' is correct. Hence, option 'a' is correct.

Answer: Writing an equation in function form. You want to remove the x term from the side y is on and move it to the other side of the equal sign. To do this either add or subtract the x term from both sides. Next divide by the coefficient of the y term. Now your equation is in function form.

explanation: like 57 * Y =142500

what is the number for Y if u don't know u could divided 142500 by 57 and it equals? 2500;) hope I helped

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

Answer:

0

Step-by-step explanation:

Answer:

Midpoint of the line segment

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Step-by-step explanation:

Answer:

\( x = 4 \sqrt{3} \)

Step-by-step explanation:

By Pythagoras Theorem:

\( {x}^{2} = {( \sqrt{8 \times 4}) }^{2} + {(4)}^{2} \\ \\ {x}^{2} = {( \sqrt{32}) }^{2} + {(4)}^{2} \\ \\ {x}^{2} = 32 + 16 \\ \\ {x}^{2} = 48 \\ \\ x = \sqrt{48} \\ \\ x = \sqrt{ {4}^{2} \times 3} \\ \\ x = 4 \sqrt{3} \)