QUICK, which graph is proportional ?

Answer:

We can solve this problem by:-

Here,

X=38°(Being vertically opposite angle)

So, X=38°

Vertical angles are congruent

The value of x = 38 degrees.

Given :

We are given with two lines that intersects .

we need to find out the vertical angle for the given angle.

When two lines intersects then the opposite angles are equal .

Opposite angles we call it as vertical angles .

Vertical angles are equal when two line intersects.

From the given diagram , vertical angles x  and 38  are congruent .

so \(x=38\)

The value of x is 38 degrees.

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A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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The probability of the train from Le Havre having to wait at Garde du Nord for the train from Troyes to arrive on any given day is equal to the probability that the latter train is late.

This probability can be calculated using the following formula: P = (1-A)^B, where A is the average arrival time of the train from Troyes and B is the average time it takes for the train from Le Havre to depart after the first train is scheduled to arrive. The expected value of the probability can then be calculated by taking the average of this formula over the long run. For example, if the train from Troyes is typically 5 minutes late and the train from Le Havre leaves 10 minutes after it is due to arrive, the expected probability of a delay is (1-5/60)^(10/60) = 0.7355. Therefore, over the long run, the train from Le Havre will have to wait for the train from Troyes to arrive 73.55% of the time.

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The probability of event A is 5/18.

The probability of event B is 29/36.

Probability is used to determine how likely it is that a random event would happen. The probability that the random event would happen would lie between 0 and 1.

The probability that the sum is greater than 8 = sample space that have a sum greater than 8 / total number of sample space

sample space that have a sum greater than 8 = (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6, 4) (6,5) (6,6) = 10

Total number of sample space = 36

The probability that the sum is greater than 8 = 10 / 36 = 5/18

The probability that the number is not divisible by 5 = sample spaces that is not divisible by 5 / total number of sample spaces

= 29 / 36

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Here is the rest of the question:

Write your answers as exact fractions.

P(a)

P(b)

Answer:

there is no possible slope for this equation. if it asks for a number it is 0

Step-by-step explanation:

There are approximately 720 blue balls, 1080 red balls, 360 green balls, 540 orange balls, and 900 yellow balls in the bin.

To predict how many of each color are in the bin, we can assume that the ratio of each color in the bin is the same as the ratio in the sample of 20 balls.

First, we calculate the total number of each color in the sample:

Blue: 4 balls

Red: 6 balls

Green: 2 balls

Orange: 3 balls

Yellow: 5 balls

Next, we calculate the total number of balls in the sample:

4 + 6 + 2 + 3 + 5 = 20

Now, we can set up proportions to estimate the number of each color in the bin:

Blue: (4/20) * 3600 = 720

Red: (6/20) * 3600 = 1080

Green: (2/20) * 3600 = 360

Orange: (3/20) * 3600 = 540

Yellow: (5/20) * 3600 = 900

Therefore, we predict that there are approximately 720 blue balls in the bin.

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The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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The association in the graph is classified as follows:

C. Nonlinear.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

m represents the gradient of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.

The concept of the gradient means that in a linear association, the output changes by a fixed amount relative to the input.

From the image, we have that the increase does not follow a constant amount, hence we have nonlinear association.

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w (x) = x2 + 3x + 8

w (4) =?

we know that

W(4) is the value of the function w(x) when the value of x is equal to 4

so

substitute

For x=4

therefore

w(4)=36

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Answer:

NO.

Step-by-step explanation:

The Professor's hypothesis:

An introductory course in Logic will affect college students with their other studies (will affect their Great Point Average - GPA).

25 students are used as the experimental group while the rest of the class are the control group.

The mean GPA in a sample size (SS) of 6 is = 2.58

The mean GPA in the full sample size of 25 would be = 10.75 by crossmultiplying.

This makes me believe the question was written wrongly. I assume SD (standard deviation) of 0.6 instead of SS (sample size) of 6.

Going by this, if standard deviation is 0.6 then the interval within which the GPA of the experimental group (the 25 students) falls is:

[2.58 - 0.6] to [2.58 + 0.6]

= 1.98 to 3.18

The rest of the graduating class (the control group) had a mean GPA of 2.33

Can the professor conclude that the GPA for the sample is significantly different from that of the control group?

The answer is NO because the GPA of the control group falls within the GPA interval of the experimental group!

We need to know about mixed fraction to solve this problem. Natasha used approximately 4 cups of ingredients.

A mixed fraction is a fraction that is represented with its quotient and remainder. For example there is a mixed fraction \(5\frac{2}{3}\) where 5 is the quotient and 2 is the remainder. To convert a mixed fraction to a simple fraction we multiply the denominator by the quotient and add the remainder to it to get the numerator of the simple fraction, the denominator remains the same. In this question we have to find the cups of ingredients that Natasha uses to make the sauce, we have to simplify all the mixed fractions and then add the fraction together to get the number of cups.

cups of cream=\(2\frac{3}{4}\)=11/4

teaspoon of salt =1/2

cups of chive=3/8

cups pf butter=\(1\frac{1}{4}\)=5/4

total cups of ingredients used= 11/4+3/8+5/4=(22+3+10)/8=35/8≈4 cups

Therefore we found out that the total number of cups natasha uses to make the sauce is 4.

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Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

\(\textsf{D.} \quad 5^9=x\)

Step-by-step explanation:

Given logarithmic equation:

\(\log_5x-\log_525=7\)

\(\textsf{Apply the quotient log law}: \quad log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)\)

\(\implies \log_5\left(\dfrac{x}{25}\right)=7\)

\(\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b\)

\(\implies 5^7=\dfrac{x}{25}\)

Multiply both sides by 25:

\(\implies 25 \cdot 5^7=x\)

Rewrite 5 as 5²:

\(\implies 5^2 \cdot 5^7=x\)

\(\textsf{Apply exponent rule}: \quad a^b \cdot a^c=a^{b+c}\)

\(\implies 5^{2+7}=x\)

\(\implies 5^9=x\)

Answer:

all real values of x where x < -1

The correct statement is all real values of x where x < -1.

Option A is the correct answer.

We have,

To determine the values for which the graph of the function

f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.

Let's consider the factors individually:

(x - 3): This factor is positive for x > 3 and negative for x < 3.

(x + 1): This factor is positive for x > -1 and negative for x < -1.

To determine the overall sign of the function, we need to consider the signs of both factors together.

When both factors are positive or both factors are negative, the function is positive.

When the factors have opposite signs, the function is negative.

From the above analysis, we can conclude the following:

When x > 3, both factors are positive, so the function is positive.

When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.

When x < -1, both factors are negative, so the function is positive again.

Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).

Thus,

The correct statement is all real values of x where x < -1.

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The inequalities which matches the graph are: x ≥ ₋1.5 and ₋1.5 ≤ x

Given, a number line is moving from ₋3 to ₊5 .

Next a mark is made at ₋1.5 and everything to its left is shaded which means not visible.

When we mark the point and shade the left part of it then we can start applying the inequality expressions.

And from that we can match the applicable inequalities while observing the graph.

Therefore the only inequalities the graph represents is  x ≥ ₋1.5 and ₋1.5 ≤ x

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The calculated number of plants the flower bed can contain is 120

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

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

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Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

Answer:

x = 9.6

Step-by-step explanation:

25x = 12 x 20

25x = 240

x = 9.6

Answer: 16 degrees

Step-by-step explanation:

(3x + 18) = 66

Because vertically opposite angles are equal

66 - 18 = 48

48 divided by 3

=16

Answer:

Step-by-step explanation:

We are to rank the options given in the question to correctly prove the theorem that: "If A & B are set, and A is a subset of B"

To arrange the steps in the correct order, we have:

(a) Assume that B is countable

(b) The elements of B can be listed as b1, b2, b3

(c) Since A is a subset of B, taking the subsequence of {bn} that contains the terms that are in A gives a listing of the elements of A.

(d) Therefore A is countable, contradicting the hypothesis.

(e)  Thus B is not countable

Answer:

(1,3) (B)

Step-by-step explanation:

A function cannot have 2 y values per x value.  The x value of 1 has 2 y values on it which are -2 and 3.  Therefore, you must remove one of them.  The only one that applies is (1,3)

I completed the vertical line test which shows that A, C, nor D had another point on their lines. So B is the answer.

Answer:

Step-by-step explanation:

10/3

18/5

6/4  or 3/2 or 1 1/2

18/20 or 9/10

9/16

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

Answer:

56"

Step-by-step explanation: