POSSIBLE POINTS: 20
A prestigious program accepts 2 out of every 9 applicants per yer. If the program accepted 360 applicants, how many applicants were NOT accepted?
A.1260
B.1620
C.2520
D.3240
E.3600

Answer:

-8 + 3 + x =  x - 5

Step-by-step explanation:

This is because X does not have a value & both 8 & 3 are constants making them computable

Answer:

Below

Step-by-step explanation:

s = small box number         volume =  6s

L = large box number         volume   = 15L

6s + 15 L =243    

  AND      s = L +2  

We will use certain constraints to imitate the repetition of the process as mentioned below

To simulate one repetition of the procedure using random digits, we shall perform as follows:

from a line of the random digits table, ten one and two-digit numbers could be selected with the following conditions;

1. skipping repeated numbers

2. skipping numbers from 77    to 99  

here the numbers 01   to 12   i.e. first-class passengers in the group of selected random numbers are to be counted.

As we know, numbers represent first-class passengers while numbers to represent coach-class people.

Hence, using this we can use random digits

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2. 2x-7=3 Addition Property

3. 2x=10  Division Property

4. x = 5

Answer:

I hope I helped

I have not been taught on this topic yet but I manage to answer the question if the answer is wrong it isn't my fault I haven't been taught yet.

I wish you a happy day

Step-by-step explanation:

1.)4x – 7 = 2x + 3

4x – 2x – 7 = 2x – 2x + 3 (subtraction property)

2x – 7 = 3

2x – 7 +7 = 3 + 7(addition property)

2x = 10(division property)

x = 5(reflexive property)

Answer:

-76

each term is being subtracted from the preceding the next odd number

The solution of the system of equation are;

⇒ x = 6

⇒ y = - 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equations are,

4x + 2y = 10

x = y + 13

Now,

Since, The system of equations are,

⇒ 4x + 2y = 10  ..(i)

⇒ x = y + 13  

⇒ x - y = 13    ..(ii)

Multiply by 2 in equation (ii) and add with (i);

⇒ 2x - 2y + 4x + 2y = 26 + 10

⇒ 6x = 36

⇒ x = 6

And, x - y = 13

⇒ 6 - y = 13

⇒ 6 - 13 = y

⇒ y = - 7

Thus, The solution of the system of equation are;

⇒ x = 6

⇒ y = - 7

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z = -2.51 is the required test statistic.

A statistic employed in statistical hypothesis testing is known as a test statistic.

A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

The probability value, or p-value, indicates the likelihood that your data could have been true under the null hypothesis.

This is accomplished by estimating the probability of your test statistic, which is the figure obtained from a statistical analysis of your data.

So, we have to use: Ha: pB < pNY

This implies that the alternative thesis is revised as follows:

Ha: pB - pNY < 0

In contrast to the null hypothesis:

H₀: pB - pNY = 0

This is the test statistic:

z = X - μ/a

Now, pB = 0.581, pNY = 0.832.

It follows that: X = 0.581 - 0.832 = -0.251

The test for the null hypothesis is 0.

This follows to: μ = 0

Standard deviation: 0.1

This follows to: s = 0.1

Test statistic:

z = X - μ/a

z = -0.251-0/0.1

z = -2.51

Therefore, z = -2.51 is the required test statistic.

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Complete question:
A study was conducted to compare the proportion of drivers in Boston and New York who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in Boston was 0.581 and the proportion wearing seat belts in New York was 0.832. Due to local laws at the time the study was conducted, it was suspected that a smaller proportion of drivers wear seat belts in Boston than New York.

Find the test statistic for this test using Ha: pB < pNY. (Use standard error = 0.1.)

The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.

Here,

All the calculations attached in image.

z= 1.96

p = 0.5

q = 1-p = 0.5

E = 0.05

sample size =

(z^2).(pq)=(1.96^2).(0.5)(.0.5)

384.16,

round up

n for study =385

Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.

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The value of x=11 and the value of an angle ∠RDB=45°.

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to the measurement of an angle or a rotation. This measurement is the ratio of the length of a circular arc to its radius.

By using the secant-secant theorem,

(13x+7-60)/2=5x-10

13x-53=10x-20

3x-53=-20

3x=33

x=11

m ∠RDB=5(11)-10

=45°

Hence, the value of x=11 and the value of an angle ∠RDB=45°.

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Answer:

Step-by-step explanation:

1. is .4444444 or 4/9

All you do for this is enter -2 as x for 4(3)^x

2.  is x^24 or answer (4)

this is because you will multiply the exponents starting with -4 till you get 24.  

-4 x -1 = 4

4 x 6 = 24

3. sorry I have to go for this one, plug in any number into x and experiment with the 4 answers till one of them gives you the same solution

A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

Given,

We must determine the kind of variable needed in the given problem to build a confidence interval for a population proportion.

Considering that;

The percentage of the entire population that possesses a specific quality is known as the population proportion (which is qualitative in nature). Therefore, a qualitative variable with two alternative outcomes must be used to generate the confidence interval for the population proportion.

Therefore, the nature of the various types of variables is used to choose the correct option. A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

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Question is incomplete. Completed question is given below;

What type of variable is required to construct a confidence interval for a population proportion?

A. Quantitative

B. Qualitative with any number of possible outcomes

C. Continuous

D. Qualitative with 2 possible outcomes

E. Discrete

F. Qualitative with 3 or more possible outcomes

The balanced equation is Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄).

An equation is a combination of different variables, in which two expressions are equal to each other.

The given equation is,

Ba(C₂O₄) + K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)

Since, there are 2 atom of potassium on right side and also (IO₃) is two times.

To balance the equation, Coefficient of K(IO₃) should be 2.

The equation can be represented as,

Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)

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If Amanda stays on her current course, she will go 72,000 km in three years.

Given data,

In the first four months after purchasing a new car, Amanda Chicopee covered 8,000 kilometers. How many miles will Amanda log in three years if she continues on her path?

Here,

She drove 8000 km in 4 months.

⇒ In 1 month = 8000/4 = 2000 km

To find how many miles in 3 years,

⇒ In 36 months = 2000 * 36

                          = 72000 km

Hence, 72000 km will Amanda log in three years if she continues on her path.

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Step-by-step explanation:

4x+12=0

4x= -12

x = -3

.........

The proportion is not equal to 0.04.

The test statistic

Z =  1.149

What is the random sample?

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

Since the calculated value of Z =  1.149 is less than 1.96 at 5% (0.05) level of significance.

The null hypothesis is accepted

Hence the proportion is not equal to 0.04

Given data a random sample of 300 circuits is tested, revealing 17 defectives.

The proportion of success

P = 17 / 300 = 0.056                                    

Null hypothesis:- H₀ = P ≠0.04

Alternative hypothesis:- H₁ = P =0.04

Q = 1-P = 1-0.04=0.96

Level of significance ∝ =0.05

The test statistic

[tex]z = \frac{p -P}{\sqrt{PQ/n} }[/tex]

now substitute all values, and we get

on calculation, Z =  1.149

Since the calculated value of Z =  1.149 is less than 1.96 at a 5% (0.05) level of significance.

The null hypothesis is accepted.

Hence the proportion is not equal to 0.04.

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For maximum area the wire should be bent in the form of circle  and for minimum area the wire should bent into equilateral triangle.

What is the area of any geometrical shape?

The area of a shape is the “space enclosed within the perimeter or within the boundary” of the given shape. We calculate the area for different shapes using math formulas.

Given that a piece of wire 10m long is cut into two pieces so now we have two wires with lengths of 5m and 5m.

One wire is bent into an equilateral so the perimeter of that triangle would be 3 m.

Perimeter = 3 m

3*side = 3 m

side = 1 m

Now the area of the equilateral triangle = [tex]A=\frac{\sqrt{3}}{4}\times (side)^2[/tex]

                                                                    A = 0.4330 m² -----(I)

Now the circumference of the circle = 5 m

                      2π×r = 5

                          r = 5/2π

                          r = 0.7957 m.

Now the area of the circle = π×r²

                                            = 3.14 × (0.7957)²

                                            = 1.988 m² --------(II)

From (I) and (II), we can say that

Area of the equilateral triangle < Area of the circle

Hence, for maximum area the wire should be bent in the form of circle  and for minimum area the wire should bent into equilateral triangle.

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The angle measures in this problem are given as follows:

The sides of the mountains are parallel, which means that the angles of these sides have the same measures, as follows:

Then the measure of x is obtained considering that angles x, y and z form a ray, that is, the sum of their measures is of 180º, hence:

x + y + z = 180

x + 55 + 37 = 180

x = 180 - (55 + 37)

x = 88º.

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Answer:

Solution = (2, 1.5)

Step-by-step explanation:

Step 1: Solve for y in 6x - 4y = 18

    1. 6x - 4y = 18 → -4y = -6x + 18 → y = 1.5x - 4.5

Step 2: Substitute 1.5x - 4.5 for y in -x - 6y = 7

    2. -x - 6(1.5x - 4.5) = 7

Step 3: Solve for x

    3. -x - 9x + 27 = 7 → -10x + 27 = -20 → -10x = -20 → x = 2

Step 4: Substitute 2 for x in -x - 6y = 7

    4. -(2) - 6y = 7

Step 5: Solve for y

    5. -2 - 6y = 7 → -6y = 9 → y = -1.5

Hope this helps you out :)

Answer:

y = x × 3, 12

Step-by-step explanation:

If a recipe for cheesecake requires 3 cups of sugar per batch, we can use this equation:

y = x × 3

Using this, we can determine how many cups are needed when we need to make 4 batches.

y = 4 × 3 = 12

You need 12 cups of sugar for 4 batches.

The surface area of the given pyramid 126 m².

What do you mean by surface area?

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

According to data in the given question,

We have the given information:

A pyramid has a square base with edges that measure 6 meters, and a slant height of 7.5 meters.

Now, we need to determine the surface area of given pyramid,

The formula for a pyramid's surface area with a square base is:

[tex]SA=b^{2}+2*(bs)[/tex]

Where b is the base length and s is the slant height.

We have the following information for the stated situation,

b= 6 m

s= 7.5 m

Then, we will putting the given values in the above formula,

[tex]SA=b^{2}+2*(bs)[/tex]

[tex]SA=6^{2}+2*(6*7.5)\\SA=36+90\\SA=126m^{2}[/tex]

Therefore, the surface area is 126m².

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The probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.

Given that.

The percentage of customers who will disclose a food allergy is 0.08

At Ying Ying's bakery, 121 people place orders on a single day.

We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.

Formula for Binomial probability distribution:

P(X=x)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ

Where P(x)= probability of getting success in x trials,

n= sample size ,

p represents the probability that each event will succeed.

As stated, we have n=12

p=0.08

Let x signify that the client will disclose a food allergy.

Following that, the probability that at least one client will disclose a food allergy will be:

P(x≥1)=1-P(x<1)

=1-P(x=0)

=1-¹²C₀(0.08)⁰(1-0.08)¹²⁻⁰

=1-(1)(0.12)¹²

=1-0.3677

=0.6323

Therefore, the probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.

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Answer:

∠RPQ = 105

∠R = 45

Step-by-step explanation:

Question 1

By intersecting chord theorem ? = (175 + 35) / 2

? = (175 + 35) / 2

? = 210 / 2

? = 105

(See image below)

Question 2

By intersecting secant theorem ∠R = (140 - 50)/2

∠R = (140 - 50)/2

∠R = 90/2

∠R = 45

(See image below)

Intersecting chord theorem : Corresponding angle equals sum of corresponding arcs divided by two

Intersecting secant theorem : The inscribed angle equals major arc minus minor arc divided by two

Answer:

21

Step-by-step explanation:

The amount added to each of the 3 sides is a rectangle 6.25 m by 1.5 m.

Then there are two square corners added that each one is 1.5 m by 1.5 m.

Total added area = 3 × 6.25 m × 1.5 m + 2 × 1.5 m × 1.5 m

Total added area = 28.125 m² + 4.5 m²

Total added area = 32.625 m²

The area of each tile is:

0.25 m × 0.25 m = 0.0625 m²

A box of tiles has 25 tiles. The total area covered by a box of tiles is:

25 × 0.0625 m² = 1.5625 m²

The number of boxes need is:

32.625 m² / 1.5625 m² = 20.88

Since 20.88 boxes are needed, but she needs to buy full boxes, she needs 21 boxes of tiles.

Answer: 21

The slope of the two points passing through points  (​12,10​) and ​(30​,25​) will be 5 / 6.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. the slope is defined as the ratio of the rise to the run.

Given that points ​(​12,10​) and ​(30​,25​) form a proportional relationship.

The slope of the line passing through the two points will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 25-10 ) / ( 30-12 )

Slope = 15 / 18

Slope = 5 / 6

Therefore, the slope of the two points passing through points  (​12,10​) and ​(30​,25​) will be 5 / 6.

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Answer:

It's -10 degrees

The laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].

Given,

[tex]f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}[/tex]

applying laplace transform on both sides,

[tex]L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex]

The range for values of s for which F(s) exists is when F(s)≥0

[tex]\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0[/tex]

using formula to find roots,

[tex]s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi[/tex]

Thus,  the laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].

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Answer:

30 I think but I'm not positive

Step-by-step explanation:

Answer:

21%

Step-by-step explanation:

Approximate number = 75 

exact number = 95error

approximate number - exact number| ÷ exact number error = |(75-95)| / 95 = |20| / 95 = 0.21percentage of error = 0.21 x 100% = 21%

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