what’s the area of the base

Answer:

4 only play piano

Step-by-step explanation:

12 + 16 = 28

32 - 28 = 4

Answer:

3200

Step-by-step explanation:

Simple interest = PRT/100

= (16000 × 5 × 4%\)/100

= 320000/100

= 3200

Answer:

280 drinks

Step-by-step explanation:

Answer:

280 drinks. We need to divide 1 2/5 by 1/200 in order to get this answer.

[tex]m_{\overline{AB}}=\frac{0-0}{1-5}=0\\m_{\overline{CD}}=\frac{2-2}{3-7}=0\\\\\therefore \overline{AB} \parallel \overline{CD} \text{ because } m_{\overline{AB}}=m_{\overline{CD}}[/tex]

[tex]m_{\overline{BC}}=\frac{2-0}{7-5}=1\\m_{\overline{AD}}=\frac{2-0}{3-1}=1\\\\\therefore \overline{BC} \parallel \overline{AD} \text{ because } m_{\overline{BC}}=m_{\overline{AD}}[/tex]

As ABCD has two pairs of opposite parallel sides, ABCD is a parallelogram.

Answer:

yes

Step-by-step explanation:

Yes.

The graph of y = 2x - 2 is a straight line sloping up to the right.

It passes the vertical line test, so it is a function.

Answer:

Random sampling

Step-by-step explanation:

Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.

Answers: sin(2∅) = 120/169,  cos(2∅) = 119/169, tan(2∅) = 120/119

Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.

Analysis:

If cos∅ = adjacent/hypotenuse =  12/13,

Then, opposite of the right angled triangle = [tex]\sqrt{13^{2} - 12^{2} }[/tex] = 5

sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12

sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169

cos(2∅) = [tex]cos^{2}[/tex]∅ - [tex]sin^{2}[/tex]∅ = [tex](\frac{12}{13}) ^{2}[/tex] - [tex](\frac{5}{13} )^{2}[/tex] = 144/169 - 25/169 = 119/169

tan(2∅) = sin(2∅) / cos(2∅)  = 120/169 ÷ 119/169 = 120/119

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Based on the result from the box plot, the number of blue marbles is equal to the median of the data set and this is equal to 40.

A boxplot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:

For this exercise, we would create a box plot (see attachment) for the marbles in a bag of 100 marbles. By critically observing the box plot, we can logically deduce that the number of blue marbles is equal to the median of the data set and this is given by:

Median = 4 × 10

Median = 40.

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Using proportions, it is found that the scale factor of the transformation is of 1/3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, during the transformation, each coordinate was divided by 3, hence, applying the proportion, the scale factor of the transformation is of 1/3.

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A type I error takes place if a given null hypothesis is rejected but is said to be true in the population such as the forecast shows it is snowing outside but actually it is isn't.

A type II error is known to be a statistical term that tells the error that takes place when one fails not to accept a null hypothesis that is said to be really false. A type II error create a false negative.

Note that:

The power of the test shows that:

See full question below

Suppose you have the following null and alternative hypothesis:

H o: it is snowing.

H a: It is not snowing

(A) in the context of this problem, describe a Type-1 error

(B) Describe Type II error

(C)Describe power of the test

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Answer:

The answer is [tex]\frac{3}{10}[/tex]

Step-by-step explanation:

Answer:

w=2  w = -9

Step-by-step explanation:

w^2 + 7w - 18 = 0

We can factor this equation

What 2 numbers multiply to -18 and add to 7

9*-2 = -18

9+-2 = 7

(w-2) (w+9) = 0

Using the zero product property

w-2 = 0    w+9 =0

w=2  w = -9

Answer:

[tex]w_1=2\\w_2=-9[/tex]

Step-by-step explanation:

This is going to be solved using the quadratic formula.

1. Determine the quadratic equation’s coefficient [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].

Use the standard form, [tex]ax^2+bx+c=0[/tex]  , to find the coefficients of our equation,

[tex]w^2+7w-18=0[/tex]:

a = 1

b = 7

c = -18

2. Plug these coefficients into the quadratic formula

The quadratic formula gives us the roots for  [tex]aw^2+bw+c=0[/tex] , in which [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are numbers (or coefficients), as follows:

[tex]w=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

7 additional steps:

a = 1

b = 7

c = -18

[tex]w=\frac{-7\pm\sqrt{7^2=4*1*-18} }{2*1}[/tex]

Simplify exponents and square roots

[tex]w=\frac{-7\pm\sqrt{49-4*1*-18} }{2*1}[/tex]

Perform any multiplication or division, from left to right:

[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2*1}\\w=\frac{-7\pm\sqrt{49--72}}{2*1}\\\\w=\frac{-7\pm\sqrt{49+72}}{2*1}\\w=\frac{-7\pm\sqrt{121}}{2*1}[/tex]

to get the result:

[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2}[/tex]

3. Simplify square root [tex]\sqrt{121}[/tex]

Simplify 121 by finding its prime factors:

121 ( 11 * 11)

The prime factorization of 121 is 11^2

Write the prime factors:

[tex]\sqrt{121}=\sqrt{11\cdot 11}[/tex]

Group the prime factors into pairs and rewrite them in exponent form:

'[tex]\sqrt{11\cdot 11}=\sqrt{11^2}[/tex]

Use the rule [tex]\sqrt{x^2=x}[/tex]  to simplify further:

[tex]\sqrt{11^2}=11[/tex]

4. Solve the equation for w

[tex]w=\frac{-7\pm11}{2}[/tex]

The ±  means two answers are possible.

Separate the equations:

[tex]w_1=\frac{(-7+11)}{2}[/tex] and [tex]w_2=\frac{-7-11}{2}[/tex]

[tex]w_1=\frac{-7+11}{2}[/tex]

[tex]w_1=\frac{4}{2}[/tex]

[tex]w_1=2[/tex]

[tex]w_2=\frac{-7-11}{2}[/tex]

[tex]w_2=\frac{-18}{2}[/tex]

[tex]w_2=-9[/tex]

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Terms and topics

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Learn more:

The weekday hours you purchased is 5 hours.

The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.

2a + 10b = 220 equation 1

a + b = 26 equation 2

Where:

Multiply equation 2 by 10

10a + 10b = 260 equation 3

Subtract equation 3 from equation 2

8a = 40

a = 5 hours

(5 x 3) + b = 26

15 + b = 26

b = 26 - 15

b = 11 hours

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Answer:

The value of x is 30 degrees.

Step-by-step explanation:

We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)

[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]

Reason:

Choices A, C and D have repeated x values. It allows us to rule them out.

Table A has x = 6 repeating. Table C has x = 3 and x = -3 repeated. Table D has x = 4 and x = 5 show up twice each.

Whenever we have repeated x values, it indicates we do not have a function. A function is only possible when each x value goes to exactly one y value only.

Table A has the input x = 6 lead to y = 2 and y = -2 at the same time. Table C and table D are a similar story. So this is another way to rule out choices A, C and D.

Luckily table B has no repeated x values. Each x input leads to exactly one and only one y output. Therefore, table B is a function.

Side Note: the y values can repeat, but the function won't be one-to-one.

Answer:

-2 =w

Step-by-step explanation:

9(w – 4) – 7w = 5(3w – 2)

The first step is to distribute

9w -36 - 7w = 15w -10

Combine like terms

2w -36 = 15w -10

Subtract 2w from each side

2w -36 -2w = 15w-10-2w

-36 = 13w -10

Add 10 to each side

-36+10 =13w-10+1-

-26 = 13w

Divide by 13

-26/13 =13w/13

-2 =w

Answer:

[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]

Step-by-step explanation:

Let's factorize the 1st option :

⇒ [tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]

⇒ [tex]f(x) = \frac{x^{2}+x-6x-6 }{(x+2)(x-2)}[/tex]

⇒ [tex]f(x) = \frac{(x+1)(x-6)}{(x+2)(x-2)}[/tex]

===============================================================

Finding the zeros :

⇒ Factors of numerator should be equated to 0

=============================================================

Solution :

[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]

Answer:

first option

Step-by-step explanation:

the zeros are determined by the numerator of the rational function.

given that the zeros are x = - 1 and x = 6 , then the corresponding factors are

(x + 1) and (x - 6) , that is

(x + 1)(x - 6) ← expand using FOIL

= x² - 5x - 6

the rational function is then

f(x) = [tex]\frac{x^2-5x-6}{x^2-4}[/tex]

The exact length of a which is equivalent to BC is 7units

A triangle is a shape with 3 sides and angles. In order to determine the sides BC, we will use the cosine rule

c² = a² + b² - 2abcosC

Given the following parameters

b = 2

c = 5√3

theta = 30 degrees

Substitute

c² = 2² + (5√3)² - 2abcos30
c² = 4 + 75 - 2(2)(5√3)*√3/2

c² = 79 - 30
c² = 49
c = 7 units

Hence the exact length of a which is equivalent to BC is 7units

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Answer:

r - 3

Step-by-step explanation:

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to write the verbal phrase "r decreased by 3" as an algebraic expression.

[tex]\triangle~\fbox{\bf{KEY:}}\star[/tex]

Here we decrease the variable "r" by 3.

Remember, variables always represent some number.

Let's think about it this way...

///\\\////\\\\////\\\///\\\///\\\///\\\///\\\///\\///\\///\\///\\///\//\\///\\\///\\\///\\\///\\///\\\///\

So we have a number r, and we decrease it by 3.

Now its value is less than the original value.

We subtracted 3 from the original value of r, and now its value is less than the original one.

Thus, "decreased by" is the same as "subtracted" in mathematics.

r decreased by 3 ⇒ [tex]\star\large\pmb{r-3}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Step-by-step explanation:

length = 2×width + 6

84 = 2×length + 2×width

now using the first in the second equation :

84 = 2×(2×width + 6) + 2×width = 4×width + 12 + 2×width

84 = 6×width + 12

72 = 6×width

width = 12 cm

length = 2×width + 6 = 2×12 + 6 = 24 + 6 = 30 cm

Answer:

(p + q) + r

is the correct answer

The measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

We have a  length of an arc of a circle of radius 7 is approximately 10.99 cm.

The radius r = 7 cm

The arc length l = 10.99 cm

We know,

l = rθ

θ is the central angle.

θ = l/r  = 10.99/7 = 1.57 radians

To convert 1.57 radians into the degree multiply it by 180/π

θ = 89.95 degree

Thus, the measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.

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Answer:

60%

Step-by-step explanation:

So, this question is saying the bowls can be between a diameter of 6.95 and 7.05

Box 1, 3 and 5 are in this margin.

Box 2 and 4 are not.

3/5 boxes can be included.

3/5 is 6/10

6/10 is 60%

Answer:

[tex]1\frac{1}{9}[/tex]

Step-by-step explanation:

Given the following question:

[tex]1\frac{2}{3} \times\frac{2}{3}[/tex]

In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.

[tex]1\frac{2}{3} =3\times1=3+2=\frac{5}{3}[/tex]
[tex]\frac{5}{3} \times\frac{2}{3}[/tex]
[tex]5\times2=10[/tex]
[tex]3\times3=9[/tex]
[tex]=\frac{10}{9}[/tex]

Convert the improper fraction into a mixed number:

[tex]\frac{10}{9}[/tex]
[tex]\frac{10}{9} =10\div9=1\frac{1}{9}[/tex]
[tex]=1\frac{1}{9}[/tex]

Your answer is "1 1/9."

Hope this helps.

The probability that he would have done at least this well if he had no ESP is 0.99979

To determine the probability, we need to first find the probability of doing well with ESP.

The probability of having 20 correct answers out of 23 coin flips is:

[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]

Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:

[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]

There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.

Therefore, the probability of doing well with ESP is:

[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]

= 0.00021

The probability that he would have at least done well if he had no ESP is:

= 1 - 0.00021

= 0.99979

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The probability that the student selected at random is a freshman is; 29%

From the given table;

Total number of male students = 4 + 6 + 2 + 2 = 14

Number of freshmen students = 4 students

Thus;

Probability that the student selected at random is a freshman is;

P(Freshman | Male) = 4/14 * 100% = 28.57% ≈ 29%

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A percentage is a way to describe a part of a whole. The percentage decrease is 20%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

One year, the population of a city was 358,000. Several years later it was 286,400. Therefore, the percentage decrease is,

Percentage decrease = (358,000-286,400)/(358,000) × 100% = 20%

Hence, the percentage decrease is 20%.

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Answer:

600(1+1)^3 with future amount being 4800

Step-by-step explanation:

The amount of the money after 27 years will be $4800.

The quantity of money anyone has is termed as the amount. The solution to the question is given as follows:-

Given that investments double every 9 years and you start with a $600 investment. how much money would you have after 27 years?

We know that the amount is getting double in every 9 years so the number of times the amount will get doubled will be = 27 / 9 = 3

Future amount = 600(1+1)³

Future amount  = 600 ( 2 )³

Future amount = 600 ( 8 ) = $4800

Therefore the amount of the money after 27 years will be $4800.

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Answer:

$156.96

Step-by-step explanation:

10% off of $160.00 would be $16.00 so minus that by $160.00. Which then equals $144.00. Sales tax should be reduced to the sale price. So that would make it 144 times 0.09 for the 9% which equals $12.96 then add the $144.00 which then makes it $156.96. Hope it helps and I'm not wrong about sales tax:)