Write down the inequality described by "negative three groups of x is less than two", and solve for x

If the angles are ∠1 = 2x + 4 and ∠2 = 3x - 3, then m∠TRS =  36°.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of ∠1 = 2x + 4

The measure of ∠2 = 3x - 3

The measure of ∠TRS is -

∠TRS = ∠1 + ∠2

Since, PR is a bisector then ∠1 = ∠2.

The equation is -

2x + 4 = 3x - 3

2x - 3x = - 3 - 4

-x = -7

x = 7

Substitute the value of x in the angles -

∠1 = 2(7) + 4

∠1 = 14 + 4

∠1 = 18°

∠2 = 3(7) - 3

∠2 = 21 - 3

∠2 = 18°

So, the value of ∠TRS is -

∠1 + ∠2

18° + 18°

36°

Therefore, the measure of ∠TRS is 36°.

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Answer:

B

Step-by-step explanation:

the scale factor of 2 means the sides of Δ DEF are twice those of Δ ABC.

However, corresponding angles remain congruent , then

largest angle in Δ DEF is also 82°

Answer:

1,2,3,

Step-by-step explanation:

I GOT THE ANSWER WRONG AND IT TOLD ME THE CORRECT ANSWER

Answer:

5

Step-by-step explanation:

Answer:

y-int. is (0,1)

Step-by-step explanation:

Answer:

can you provide the table?

Step-by-step explanation:

Answer:

8y+9

Step-by-step explanation:

Answer:

6y + 44

Step-by-step explanation:

y + 4 + 5(y + 8)

y + 4 + 5y + 40

6y + 44

The probability of getting a subject who is not diabetic, given that the test result is negative, is approximately 0.1786.

To find the probability of getting a subject who is not diabetic, given that the test result is negative, we can use the data provided in the table. From the table, we can see that out of the total subjects tested, 5 are not diabetic and have a negative test result. The total number of subjects with a negative test result is 28.

To calculate the probability, we divide the number of subjects who are not diabetic and have a negative test result (5) by the total number of subjects with a negative test result (28).

Probability = Number of subjects who are not diabetic and have a negative test result / Total number of subjects with a negative test result

Probability = 5 / 28

Simplifying this fraction, we get:

Probability ≈ 0.1786

Therefore, the probability of getting a subject who is not diabetic, given that the test result is negative, is approximately 0.1786.

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The process involves finding the complementary solution x_c(t) by solving the homogeneous equation, determining the particular solution x_p(t) using the method of variation of parameters, and combining them to obtain the general solution x(t).

1. The method of variation of parameters can be used to solve the initial value problem x' = axf(t), x(a) = xa, where a and f(t) are given functions. In this case, we have the values a = 4 - 2t and f(t) = 16t^2. We need to find the solution x(t) using the initial condition x(0) = 2.

2. To solve the initial value problem using the method of variation of parameters, we first find the complementary solution x_c(t) by solving the homogeneous equation x' = ax.

3. For the given a = 4 - 2t, the homogeneous equation becomes x' = (4 - 2t)x. By separation of variables and integration, we find the complementary solution x_c(t) = Ce^(2t - t^2).

4. Next, we find the particular solution x_p(t) by assuming a particular solution of the form x_p(t) = u(t)e^(2t - t^2), where u(t) is a function to be determined.

5. Differentiating x_p(t) and substituting it into the original differential equation, we can solve for u'(t) and determine the form of u(t). After finding u(t), we substitute it back into x_p(t).

6. Finally, the general solution is given by x(t) = x_c(t) + x_p(t). By substituting the values and integrating, we can obtain the specific solution x(t) for the given initial condition.

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Answer:

Vvvgfffff

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 9.4 \ units}\)

Step-by-step explanation:

Coordinates are (0,5) and (8,0)

\(\sf Distance\ Formula = \sqrt{(x2-x1)^2 + (y2-y1)^2} \\\\D = \sqrt{(8-0)^2 + (0-5)^2} \\\\D = \sqrt{8^2 + (-5)^2} \\\\D = \sqrt{64+25} \\\\D = \sqrt{89} \\\\D = 9.4\ units\)

There is only one free variable (z), this system has infinitely many solutions. The answer is (F) Infinitely many.

Now, Let's write the system in matrix form:

|-9  12  0  -12 |

|15  -18  0  12 |

|0   8   - 6  -8 |

|2   -4   0   4|

And, [w = [72

         x    - 114

          y      18

          z] = - 20}

We want to use row operations to put the matrix into row echelon form:

-9  12 0  -12  

0  2  0  -14

0  0  -6  44

0  0  0  0

Now the matrix is in row echelon form. To solve for the variables, we can use back substitution. Starting with the last row, we see that $0z = 0$, so we don't have any information about $z$. Moving up to the third row, we have:

-6y+44z=0

Solving for y, we get:

y = 22/3z

Moving up to the second row, we have:

2x-14z=0

Solving for x, we get:

x = 7z

Finally, moving up to the first row, we have:

-9w+12x-12z=72

Substituting in our expressions for x and z, we get:

-9w+12(7z)-12z=72

Simplifying:

-9w+72z=72

Dividing by -9, we get:

w-8z=-8

So our solutions are of the form:

w  = - 8z

x      7z

y     22/3z

z     z

Since, there is only one free variable (z), this system has infinitely many solutions. The answer is (F) Infinitely many

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The approximate length of a side of the rhombus is 10.67 cm.

A rhombus is a quadrilateral with all sides of equal length.

The diagonals of a rhombus bisect each other at right angles.

Let's label the length of one diagonal as d1 and the other diagonal as d2.

In the given rugby-shaped figure, the length of d1 is 14 cm, and the length of d2 is 12 cm.

Since the diagonals of a rhombus bisect each other at right angles, we can divide the figure into four right-angled triangles.

Using the Pythagorean theorem, we can find the length of the sides of these triangles.

In one of the triangles, the hypotenuse is d1/2 (half of the diagonal) and one of the legs is x (the length of a side of the rhombus).

Applying the Pythagorean theorem, we have \((x/2)^2 + (x/2)^2 = (d1/2)^2\).

Simplifying the equation, we get \(x^{2/4} + x^{2/4} = 14^{2/4\).

Combining like terms, we have \(2x^{2/4} = 14^{2/4\).

Further simplifying, we get \(x^2 = (14^{2/4)\) * 4/2.

\(x^2 = 14^2\).

Taking the square root of both sides, we have x = √(\(14^2\)).

Evaluating the square root, we find x ≈ 10.67 cm.

Therefore, the approximate length of a side of the rhombus is 10.67 cm.

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Answer:

8

Step-by-step explanation:

A lurking variable is an explanatory variable that was not examined in a study but has an effect on the value of the study's response variable.

A concealed variable affects both the dependent and independent variables, resulting in an incorrect connection. Confounding is a causal concept that cannot be expressed using correlations or linkages. Confounders have a significant quantitative role in explaining why correlation does not imply causation.

In the case of risk assessments assessing the degree and form of threat to human health, it is critical to account for confounding in order to isolate the impact of a specific hazard such as a food additive, pesticide, or new drug. It is difficult to recruit and screen volunteers with the same background (age, diet, education, geography, etc.) for prospective studies, and historical investigations can have similar variability.

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Statement 1, "The cost of printing 2 invitations is $4.50," is not true, as the correct cost is $1.50.

To determine which statement is not true regarding the function c = 2.50(n - 2) + 1.50, we can evaluate each statement using the given function.

The function c = 2.50(n - 2) + 1.50 represents the cost in dollars of printing n invitations. We need to analyze each statement and determine if it aligns with the properties of the function.

Let's evaluate each statement one by one:

1. The cost of printing 2 invitations is $4.50.

To verify this statement, we substitute n = 2 into the function:

c = 2.50(2 - 2) + 1.50

c = 2.50(0) + 1.50

c = 0 + 1.50

c = 1.50

This statement is false since the cost of printing 2 invitations is $1.50, not $4.50.

2. The cost of printing 4 invitations is $7.50.

Substituting n = 4 into the function:

c = 2.50(4 - 2) + 1.50

c = 2.50(2) + 1.50

c = 5.00 + 1.50

c = 6.50

This statement is false since the cost of printing 4 invitations is $6.50, not $7.50.

3. The cost of printing 6 invitations is $10.50.

Substituting n = 6 into the function:

c = 2.50(6 - 2) + 1.50

c = 2.50(4) + 1.50

c = 10.00 + 1.50

c = 11.50

This statement is true since the cost of printing 6 invitations is indeed $11.50.

4. The cost of printing 8 invitations is $13.50.

Substituting n = 8 into the function:

c = 2.50(8 - 2) + 1.50

c = 2.50(6) + 1.50

c = 15.00 + 1.50

c = 16.50

This statement is true since the cost of printing 8 invitations is indeed $16.50.

In conclusion, statement 1, "The cost of printing 2 invitations is $4.50," is not true, as the correct cost is $1.50.


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Discount is 0.354838, Discount percentage is 35.4838 %.

According to the question

A shop item is marked down from r 6.20 to r 4.

A discount is an amount that is subtracted from the regular price of an item.

Based on the given conditions

= \(\frac{6.2-4}{6.2}\)

Solving 6.2 - 4, we get 2.2

= 2.2/6.2

Discount = 11/31 = 0.354838

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred. For example, a percentage discount of 20% would mean that an item that originally cost $100 would now cost $80.

Discount percentage = \(\frac{11}{31}\) × 100

= 35.4838 %

Hence,

Discount is 0.354838, Discount percentage is 35.4838 %.

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Answer:  c or d

Step-by-step explanation:

The domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as: (-∞, -49) U (-49, ∞)

In mathematics, the domain of a function is the set of all possible input values (usually represented by the variable x) for which the function is defined. It is the set of all values that can be substituted for the independent variable in a function to produce a valid output. The domain of a function is often restricted by the context in which it is being used, such as the type of problem or the natural limitations of the situation.

The given expression is (x-12)/(x+49).

The denominator of the expression is x + 49. The denominator cannot be equal to 0, as division by 0 is undefined. Therefore, x + 49 ≠ 0.

Solving for x, we get:

x ≠ -49

Therefore, the domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as:

(-∞, -49) U (-49, ∞)

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The probability of students passing the exam is 0.036.

The counted probability of 8 people being present in museum is 0.375

Probability refers to the occurrence of an event taking place.

using formula,

P = (X = k) = ( n take k )*\(p^{k}\)*\((1-p)^{(n-k)}\)

staging the values

P = (X=6) = (10 take 6)\(*(1/5)^{6}* (4/5)^{4}\)

≈ 0.026

probability when 7 questions are correct

P = (X =7) = ( 10 take 7)\(*(1/5)^{7}*(4/5)^{3}\)

≈ 0.008

probability when 8 questions are correct

P = (X =8) = ( 10 take8)\(*(1/5)^{8}*(4/5)^{2}\)

≈ 0.001

probability when 9 questions are correct

P = (X =9) = ( 10 take 9)\(*(1/5)^{9}*(4/5)^{1}\)

≈ 0.00003

probability when 10 questions are correct

P = (X =10) = ( 10 take 10)\(*(1/5)^{10}*(4/5)^{0}\)

≈ 0.00001

the probability that the student will pass

P(pass) = P(X≥6)

=P(X=6)+P(X =7) +P(X =8)+P(X =9)+P(X =10)

≈0.036

The probability of students passing the exam is 0.036.

P(X≥8) =P(X =8)+P(X =9)+P(X =10)

≈ (10 take 8)\(*(0.85)^{8}*(0.15)^{2}\)+(10 take 9)\(*(0.85)^{9}*(0.15)^{1}\)

+(10 take 10)\(*(0.85)^{10}*(0.15)^{0}\)

≈  0.375

The counted probability of 8 people being present in museum is 0.375

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The statement is true. If S, U, and W are subspaces of V such that S+W=U+W, then S=U.

To prove the statement, we need to show that if S+W=U+W, then S=U.

Suppose S+W=U+W. Let x be an arbitrary element in S. Since x is in S, we know that x is in S+W. And since S+W=U+W, x must also be in U+W. This means that x can be expressed as a sum of vectors, where one vector is from U and the other vector is from W.

Now, let's consider the vector x as a sum of two vectors: x=u+w, where u is in U and w is in W. Since x is in U+W, it must also be in U. This implies that x=u, and since x was an arbitrary element in S, we can conclude that S is a subset of U.

Similarly, if we consider an arbitrary element y in U, we can express it as y=s+v, where s is in S and v is in W. Since y is in U+W, it must also be in S+W. Therefore, y=s, and since y was an arbitrary element in U, we can conclude that U is a subset of S.

Since S is a subset of U and U is a subset of S, we can conclude that S=U. Thus, the statement is proven, and if S+W=U+W, then S=U.

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Answer:

Hope the picture will help you

Answer:

here is my answer. check it out

Answer:

same side interior angles

Step-by-step explanation:

<4 and <6 are same side interior angles

Same  side interior angles are on the same side of the transversal and inbetween the two lines

A negatively skewed distribution, sometimes referred to as a left-skewed distribution, is a kind of distribution where more values are clustered on the right side (tail) of the scatterplot but the left tail of the distribution graph is longer.

The mean of positively skewed data will be lower than median in a distribution that has a negative skewness, which is the exact reverse of what would be expected. The distribution exhibits zero skewness if the data is graphed symmetrically, regardless of how long or thick the tails are.

More values are plotted on the graph's right side, the distribution's tail is longer on the left, and the distribution is said to be negatively skewed.

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Answer:

The answer is below

Step-by-step explanation:

In a certain​ year, the amount A of garbage in pounds produced after t days by an average household is given by A = 7.5t.

Plot a graph for t > 0

how many days it will take to get 200 pounds of garbage.

Solution:

a) Let the time in days (t) be on the x axis and the amount of garbage (A) in pounds be on the y axis. Therefore:

At t = 0; A = 7.5(0) = 0

At t = 10; A = 7.5(10) = 75

The graph was plotted using the geogebra online graphing tool.

b) number of days require to get 200 pounds of garbage can be gotten by finding the value t for which A = 200. Therefore:

A = 7.5t

t = A / 7.5 = 200 / 7.5

t = 26.67 days

Note that this prompt is designed to test ones knowledge on cosigners and loans. See the correct responses below.

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Answer:

x=30 because if you look across from x the angle is 30 degrees.

Step-by-step explanation:

The answer is (B) Null hypothesis: H0: μ1=μ2

The average tuitions of in-state graduate programs are the same in both school A and school B. Alternative hypothesis: H1: μ1≠μ2 .

The average tuitions of in-state graduate programs are different in both school A and school B.

a) Null hypothesis: The average tuitions of in-state graduate programs are the same in both school A and school B.

Alternative hypothesis: The average tuitions of in-state graduate programs are different in both school A and school B.

b) Null hypothesis: H0: μ1=μ2.

The average tuitions of in-state graduate programs are the same in both school A and school B.)

Alternative hypothesis: H1: μ1≠μ2 .

The average tuitions of in-state graduate programs are different in both school A and school B.

c) You should use a 2-SampTTest as we have two samples with unknown standard deviations.

d) Type I Error: Rejecting the null hypothesis when it is true.

Type II Error: Failing to reject the null hypothesis when it is false.

e) Given information, Sample 1 School

A): Sample size (n1) = 12 Mean (x1)

= $64,000

Standard Deviation (s1) = $8,000

Sample 2 (School B): Sample size (n2) = 16Mean (x2)

= $80,000

Standard Deviation (s2) = $6,000

Level of Significance (α) = 0.10

Calculation of test statistic is shown below:

\(t=\frac{(64,000-80,000)-(0)}{\sqrt{\frac{8,000^{2}}{12}+\frac{6,000^{2}}{16}}}= -2.95\)

Degrees of freedom for the test statistic

= (n1-1)+(n2-1) = 11+15

= 26

From the t-tables for a two-tailed test with α= 0.10 and 26 degrees of freedom, we get the value as 1.706.

So, we reject the null hypothesis as the calculated value of t is greater than the tabled value.

Thus, there is sufficient evidence to suggest that the mean tuitions are different for school A and school B.

The difference in average tuition is statistically significant.

Therefore, we accept the alternative hypothesis.

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The probability of seeing exactly 5 hearts out of 10 cards is\((13/52)^5 × (39/52)^5.\)

The probability of seeing exactly 5 hearts out of 10 cards can be calculated as follows: The total number of cards in a deck is 52. The number of hearts in a deck is 13. Since no card has been removed from the deck, the probability of seeing a heart is 13/52. The probability of seeing a non-heart is 39/52. Since we are looking at 10 cards, the probability of seeing exactly 5 hearts,

p(h)= 13/52

p(nh) = 39/52

hence, \((13/52)^5 × (39/52)^5\)

This means that the probability of seeing exactly 5 hearts out of 10 cards is \((13/52)^5 × (39/52)^5.\)

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arctan(4/7) + arctan(7/4) is 90 degrees

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the functions that describe those relationships. It has applications in fields such as engineering, physics, astronomy, and navigation.

We can use the following trigonometric identity to simplify the expression:

arctan(x) + arctan(1/x) = pi/2

where x is a positive number.

In this case, we can set x = 4/7, which is a positive number, and apply the identity to get:

arctan(4/7) + arctan(7/4) = pi/2

Therefore, the sum of the two arctan terms simplifies to pi/2.

So, the simplified expression is:

arctan(4/7) + arctan(7/4) = 90 degrees (rounded to the nearest degree).

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Answer:

5.083

Step-by-step explanation:

\(V=\frac{1}{3}Bh=(1/3)(1/2)(1.7)(3.9)(4.6)=5.083\)