The line representing the equation part of the constraint 7x1 + 4x2 s 28 goes through the following two points a. (4,0) and (7,0) b. (0, 4) and (7,0) c. (4,0) and (0,7) d. (0, 4) and (0,7) e. none of the above

The congruence postulates used for each triangle are as follows;

3) AAS

4) None

5) HL congruence

6) None

Some of the triangle congruence postulate in geometry are;

SAS; Side Angle Side Congruence Postulate

SSS; Side Side Side Congruence Postulate

ASA; Angle Side Angle Congruence Postulate

AAS; Angle Angle Side Congruence Postulate

HL; Hypotenuse Leg Congruence Postulate

3) W e can see that we are given two triangles with two corresponding congruent angles and corresponding non-included side. Thus, the congruence postulate used is AAS.

4) We are given two triangles with two corresponding congruent angles but the sides given are not congruent to each other and so the triangles are not congruent.

5) We are given two triangles with their corresponding hypotenuse and leg being congruent and so the HL congruence postulate is used.

6) The angles shown don't match each other. It is just two congruent sides and this is insufficient to conclude the triangles are congruent.

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The solutions of Ax=0 in parametric vector​ form:

[tex]x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

we have a matrix where A is the row equivalent to that matrix:

[tex]\left[\begin{array}{cccc}1&3&0&-4\\2&6&0&-8\\\end{array}\right][/tex]

The given matrix can be written in an Augmented form as:

[tex]\left[\begin{array}{ccccc}1&3&0&-4&0\\2&6&0&-8&0\\\end{array}\right][/tex]

Row Reduced Echelon Form can be obtained using the following steps.

Interchanging the rows R₁ and R₂

.[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\1&3&0&-4&0\\\end{array}\right][/tex]

Applying the operation R₂-->2R₂-R₁, to make the second.

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\1&3&0&-4&0\\\end{array}\right][/tex]  R₂-->2R₂-R₁,

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\0&0&0&0&0\\\end{array}\right][/tex]

Dividing the first row by 2 to generate 1 at the

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\0&0&0&0&0\\\end{array}\right][/tex]  R₁--->1/2R₁

[tex]\left[\begin{array}{ccccc}1&3&0&-4&0\\0&0&0&0&0\\\end{array}\right][/tex]

From here the following equation can be deducted:

x₁+3x₂-4x₄=0

Making the subject of the equation:

x₁=-3x₂+4x₄

Hence, the Ax=0 parametric vector form’s solutions can be written as:

[tex]X=\left[\begin{array}{c}-3x_2+4x_4&x_2&x_3&x_4\\\\\end{array}\right] \\\\\\=\left[\begin{array}{c}-3x_1&x_2&0&0\\\\\end{array}\right] +\left[\begin{array}{c}0&0&x_3&0\\\\\end{array}\right] +\left[\begin{array}{c}4x_4&0&0&x_4\\\\\end{array}\right] \\\\\\ =x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

Numerical Result:

[tex]x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

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The smallest positive integer that is neither prime nor square and that has no prime factor less than 50 is 3137.

This can be determined by using the prime factorization method. Prime factorization is a process of breaking down a number into its prime factors. The prime factors of a number are the factors that are only divisible by one and itself. For 3137, the prime factors are 3, 7, 17 and 37 since these are the only prime numbers that can divide 3137 evenly. Since none of the prime factors are less than 50, 3137 is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50.

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A) The total no. of students taking only maths is 220 students.

let's say the total no. of students taking only maths = M

M = 360 - (100 + 40) = 220 students.

B) The total no. of students in the survey is 960 students.

let's say the total no. of students in the survey = S

S = 360 + 280 + 300 - (100 + 120 + 110) + 40 = 960 students.

C) The total no. of students who are taking exactly two of the courses is 330 students.

let's say the total no. of students who are taking exactly two of the courses = T

T = 100 + 120 + 110 = 330 students.

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In the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.

To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.

Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

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In the number 652.12, the 2 in the hundredth place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.

To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.

Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

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Answer: (-1, 0)

not sure

Step-by-step explanation:

The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.

a. y'=cos(x): This differential equation describes the slope field shown in figure A. To calculate the slope of a given point (x,y), we can use the formula y'=cos(x). For example, if x=π/2 and y=1, the slope of the line at that point is y'=cos(π/2)=-1.

b. y'=sin(x): This differential equation describes the slope field shown in figure B. To calculate the slope of a given point (x,y), we can use the formula y'=sin(x). For example, if x=0 and y=1, the slope of the line at that point is y'=sin(0)=0

c. y'=4-y: This differential equation describes the slope field shown in figure C. To calculate the slope of a given point (x,y), we can use the formula y'=4-y. For example, if x=0 and y=2, the slope of the line at that point is y'=4-2=2.

d. y'=x: This differential equation describes the slope field shown in figure D. To calculate the slope of a given point (x,y), we can use the formula y'=x. For example, if x=3 and y=2, the slope of the line at that point is y'=3.

e. y'=y: This differential equation describes the slope field shown in figure E. To calculate the slope of a given point (x,y), we can use the formula y'=y. For example, if x=3 and y=4, the slope of the line at that point is y'=4.

f. y'=x-y: This differential equation describes the slope field shown in figure F. To calculate the slope of a given point (x,y), we can use the formula y'=x-y. For example, if x=2 and y=1, the slope of the line at that point is y'=2-1=1.

The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.

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Answer:

20 dollars will be deducted if the card is not used. I am not sure what your question is but this is what I understood sorry it it isn't what you are asking for

Answer:

surface of 3cm cube=l³

=3³

=27

Hyperbola is formed when two cones that touch at their vertices and a plane cutting through the left cone parallel to its base to form a curve

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.

We have to find the conic section which is formed by two cones that touch at their vertices and a plane cutting through the left cone parallel to its base to form a curve circle parabola ellipse hyperbola.

A hyperbola is formed when the interesting plane is parallel to the axis of the cone, and intersect with both the nappes of the double cone.

Hence, Hyperbola is formed when two cones that touch at their vertices and a plane cutting through the left cone parallel to its base to form a curve

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Answer:

ellipse.

Step by-step explanation:

Answer: x = -2

Step-by-step explanation:

"Every graph represents a function" - statement is false.

Correct option: D

The vertical line test is used to verify function. That is, a graph must have a unique y value for it to be referred to as a function for a certain (unique) value of x.

If for a particular x, and y values are coming it means it is not a function.

Hence, every graph is a function is false.

Because if it crosses y axis twice it means for a particular x value , two different value of y will exist. And that is not possible for a function

Hence option D is correct: The statement is false because a graph that crosses the y-axis two times does not represent a function.

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The expected value for the number on which the pointer lands is 21/8.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given the pointer shown to the right can land on every number, and

the respective probability that the pointer can land is

shown in the table below,

table for probability,

outcome        probability

1                           1/4

2                          1/4

3                           1/8    

4                           3/8

expected value is given by,

E(x) = ∑ [tex]x_i.p(x_i)[/tex]

  = 1(1/4) + 2(1/4)  + 3(1/8)  + 4(3/8)

 = 1/4 + 1/2 + 3/8 + 3/2

   =  (2 + 4 + 3 + 12)/8

 =  21/8 = 2.625

Hence expected value is 21/8 or 2.625.

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The value of P(D OR E) = 0.1 + 0.4 - 0.02 = 0.48, P(D AND E) = 0.1 * 0.2 = 0.02,P(E | D) = 0.02 / 0.1 = 0.2

a. P(D AND E) = P(D) * P(E | D)

P(D) = 0.1 (10% of students have taken a distance learning class)

P(E | D) = 0.2 (20% of part-time students have taken a distance learning class)

Therefore, P(D AND E) = 0.1 * 0.2 = 0.02

b. P(E | D) = P(D AND E) / P(D)

P(E | D) = 0.02 / 0.1 = 0.2

c. P(D OR E) = P(D) + P(E) - P(D AND E)

P(D) = 0.1 (10% of students have taken a distance learning class)

P(E) = 0.4 (40% of students are part-time students)

P(D AND E) = 0.02 (10% of students have taken a distance learning class and that 40% of students are part-time students)

Therefore, P(D OR E) = 0.1 + 0.4 - 0.02 = 0.48

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Answer:

  (c)  C(p) =.15 (p- 50) + 8.95

Step-by-step explanation:

You want an equation for the cost of prints that are $0.15 for each print over 50 plus an additional $8.95.

The number of prints over 50 will be (p -50). At $0.15 for each of these, their cost will be ...

  0.15(p -50)

When the $8.95 charge is added, the total comes to ...

  c(p) = 0.15(p -50) +8.95

__

Additional comment

The problem statement asks for the function to be written C(p). The answer choices use c(p) with the variable x in the equation where p should be. In effect, none of the answer choices is correct.

The value of k in the equations is 2/3

From the question, we have the following parameters that can be used in our computation:

y = 9kx - 1

kx + 4y = 12

This can be expressed as

y = 9kx - 1

y = -kx/4 + 3

The slopes of perpendicular lines are opposite reciprocal

This means that

9k * -k/4 = -1

So, we have

k^2 = 4/9

Evaluate

k = 2/3

Hence, the value of k is 2/3

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The income tax liability of Mr. X is 450,000 rupees.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

Mr X had income from salary of 200000.

Income from Capital Gain of, 150000 and income from other sources is 250000.

Contribution to PF is 40000, PPF 70000, and LIC is 40000.

Income Tax liability = total income - total deductions

= 600,000 - 150,000

= 450,000

Therefore, the tax liability is 450,000 rupees.

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Zachary' Diner old 28 milkshake with whipped cream on top and 72 milkshake without whipped cream,  percentage of the milkshake had whipped cream is 28%.

Zachary ordered 28 milkshake with whipped cream on top and 72 milkshake without whipped cream.

So total number of milkshake is 100

So percentage of milkshake had whipped cream will be,

28/100 x 100

=28%

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

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The area bounded by the graphs of y and y0 over the given interval is A = ∫y0 dy|2-∫y0 dy|0.

The area bounded by the graphs of the indicated equations y and y0 over the given interval can be calculated using the formula A=∫y0 dy. To calculate the area, we need to first find the antiderivative of y0, which is F(y0) = ∫y0 dy. Then, we need to evaluate the integral from the lower limit of the given interval to the upper limit of the given interval. For example, if the given interval is from x=0 to x=2, then the area bounded by the two graphs would be A=F(y0)|2-0 = ∫y0 dy|2-0. Once we have evaluated the integral, we can calculate the area of the graph by subtracting the lower limit result from the antiderivative In this example, A=F(y0)|2-0 = ∫y0 dy|2-0 = F(y0)|2-F(y0)|0 = ∫y0 dy|2-∫y0 dy|0. Thus, the area bounded by the graphs of y and y0 over the given interval is A = ∫y0 dy|2-∫y0 dy|0.

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When multiplying decimal numbers, you move the decimal point to the left of the amount of integers in the equation that are to the right of the decimals.25.5 x 0.81 = 20.655

When multiplying decimal numbers, you move the decimal point to the left of the amount of integers in the equation that are to the right of the decimals.

After multiplication, you would move the decimal three places to the left because there is one number after the decimal point in 25.5 and two numbers after the decimal point in 0.81.

25.5 x 0.81 = 20.655

( notice there are 3 numbers to the right of the decimal point) ( note there are 3 numbers to the right of the decimal point)

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Answer:

16.

Step-by-step explanation:

Let x be the number.

32% of x = (32/100)x = 0.32x.

Ten more than 32% of x = 0.32x + 10.

0.32x + 10 = 26.

0.32x = 16.

x = 50.

So the number is 50, and 32% of it is 0.32 * 50 = 16.

Answer:

B

Step-by-step explanation:

Matthew's monthly take-home pay is approximately $2,960.69 (47,530 / 12). To calculate the exact amount, we need to subtract the state income tax from his monthly salary:

$47,530 / 12 = $3,961.67

$3,961.67 * 0.0307 = $122.57

$3,961.67 - $122.57 = $3,839.10

Therefore, the correct answer is B) $3,839.24

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

What is null hypothesis ?

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.

If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

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Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.

If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

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The amount of chicken meat required by the lion to meet his protein diet is 6.66 ounces.

A 120-pound lion need 50 gram of protein a day.

The protein provided by the 4-ounce chicken is 30 grams.

By using unitary method,

We can write,

4 ounce chicken = 30 grams protein

4/30 ounce chicken = 1 grams protein

Now, the required amount of protein is 50 grams.

So, the chicken meat needed is,

50 grams = 4/30 x 50 ounces

50 grams protein = 6.66 ounces.

So, a total of 6.66 ounces of chicken meat is required.

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Answer:

The perimeter of triangle FGL is unknown.

The function that describes the scenario is y = 7.25 + 0.65x

From the question, we have the following parameters that can be used in our computation:

Initial = 7.25

Rate = 0.65

Represent the number of miles with x

So, we have the following representation

y = 7.25 + 0.65x

Where the total cost is y

Hence, the function is represented above

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Answer:

400

Step-by-step explanation:

percent means per one hundred so

p/100=5/8

p=500/8

p=62.5%

so, 62.5% have paid their yearly fees .

400(5/8) =200

250 member paid their fees .

Answer:

250

Step-by-step explanation:

If a group contains 400 members

Then the 5/8 of 400 who didn't pay the fees are as follows:-

=5/8*400

=5*50

=250 out of 400

So, the fees is only paid by 250 members out of 400.

40 minutes in decimal is 0.666.

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The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Jamie drove 61 miles Jamie's car used 4 gallons of gas.

The number of miles per gallon that Jamie's car get will be given as,

Rate = 61 / 4

Rate = 15.25 miles per gallon

The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.

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