A casino only has red playing chips for $10 each and blue playing chips for $5 each. Jack paid $400 to purchase 50 playing chips at the cashier's window. How many red playing chips were given to him?

The blanks in this two-column proof should be completed (filled) as follows:

Statements                              Reasons_______________

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.

In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent i.e AD ≅ CD.

Additionally, HL is an acronym for hypotenuse leg and it states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.

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Answer:

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

Step-by-step explanation:

or what the  guy said on top :D

The probability that a deck to guarantee that you have 4 of a kind is 40.

Probability:

In math probability refers the possibility of event.

Given,

Here we need to find the minimum number of cards you would have to pull from a deck to guarantee that you have 4 of a kind.

As we know that the total number of cards in the deck is 52.

So, the number of ways of choosing 4 cards from a pack of 52 playing cards is calculated as,

=> ⁵²C₄ = 52!/4!48!

=> ⁵²C₄ = 270725

Similarly, the number of ways of choosing 4 cards of same suit

=> ¹³C₄ = 13!/4!9!

=> ¹³C₄ = 715

So, the number of ways of choosing 4 cards of different suit is calculated as,

=> 715/17 = 40

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The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

On Subtracting 1 from your sample size, we get

150 – 1 = 149.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 149 and α = 0.025

from the table at df = 149 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(150) = 2.28

Now, 2.262 × 2.28 = 5.17

So, the confidence interval be,

(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)

Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

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Answer: $84 i think

Step-by-step explanation:

The volume of the composite shape is 38mm³(nearest whole number)

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.

The volume of a the composite solid above = volume of cone + volume of cylinder

volume of cone = 1/3πr²h

=1/3×3.14×2²×3

= 12.56mm³

volume of the cylinder = πr²h

= 3.14×2²×2

= 25.12mm³

therefore the volume of the shape = 12.56+25.12

= 37.68mm³

= 38mm³( nearest whole number)

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Answer:

Step-by-step explanation:

Answer:

[tex]\boxed{\tt 2c-4}[/tex]

Step-by-step explanation:

[tex]\tt 2\left(c-2\right)[/tex]

Apply the distributive property:-

[tex]\tt 2\left(c-2\right)=2c-2\times \:2[/tex]

[tex]\bf 2\times\:2=4[/tex]

[tex]\tt 2c-4[/tex]

___________________

Hope this helps!

Have a great day!

Answer:

7%

Step-by-step explanation:

When trying to figure out percentages, we can try to use a proportional relationship. Percent means out of a hundred, and since we don't know the percentage on top,  we can mark it as ?.

21/300 = ?/100

To figure this out quickly, we can try figuring out how many times we need to multiply or divide to get to the next number. Between 21 and ?, we can't do anything because we are unsure of what ? is.

Between 300 and 100, we can notice that to get to 100, we must divide by 3. 300/3 = 100

This means that the first ratio is three times the amount of the second ratio, which means that the second ratio is 1/3 of the first.

We can multiply 21 by 1/3 (or divide by 3), which will get us to 7.

7/100 = 0.07 = 7%

For the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that, the equation of the line is

y – 5 = 2(x + 9)

Compare the equation with the standard equation as

y-y₁=m(x-x₁)

y – 5 = 2(x + 9).

y-5=2(x-(-9)

Where x₁ and y₁ are the points on which the line lies.

Thus, for the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).

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Answer:

(x + 7)(x² - 8)

Step-by-step explanation:

x³ + 7x² - 8x - 56 =

let's put the total multiplier x² out of brackets

x²(x + 7) - 8x - 56 =

let's put the total multiplier -8 out of brackets

x²(x + 7) - 8(x + 7) =

let's put the total multiplier (x + 7) out of brackets

(x + 7)(x² - 8)

The point estimate of the population standard deviation is Select one is 5.4558.

Given data

9,13,15,15,21,24

We have to find first mean

Here n=6

[tex]$\begin{aligned} \text { mean } \bar{x} & =\frac{\sum x_i}{n} \\ & =\frac{9+13+15+15+21+24}{6} \\ & =\frac{97}{6} \\ & =16.166\end{aligned}$[/tex]

[tex]$\therefore$[/tex] Standard deviation

[tex]S=\sqrt{\frac{\sum\left(x_i-x\right)^2}{n-1}}$$[/tex]

S= root (9-16.(66)^2+(13-16.166)^2+(15-16.166)^2+(15-16.166)^2+(21-16.166)^2+(25- 16.166)^2/(6-1)

[tex]\begin{aligned}& =\sqrt{\frac{148.833336}{5}} \\& =\sqrt{29.7666} \\& =5.4558\end{aligned}[/tex]

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Answer:

Step-by-step explanation:

b) 7.688 The point estimate of the population standard deviation is 7.688. The point estimate of a population parameter is the estimate of the population parameter based on a single sample. In this case, the point estimate of the population standard deviation is the sample standard deviation, which is a measure of the spread or variability of the sample data. To calculate the sample standard deviation, we need to first calculate the sample mean, which is the average of the values in the sample. In this case, the sample mean is (9 + 13 + 15 + 15 + 21 + 24)/6 = 14.5. We can then use this value to calculate the sample standard deviation, which is √(((9-14.5)² + (13-14.5)² + (15-14.5)² + (15-14.5)² + (21-14.5)² + (24-14.5)²)/6) = 7.688. This is the point estimate of the population standard deviation. The other answer choices are not the sample standard deviation.

Answer:

Step-by-step explanation:

for this one you need to solve for x and x=42

Answer:

Step-by-step explanation:

Divide both sides by 2. Divide 24 by 2 to get 12.

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

Use the elimination method to get rid of one of the variables.

Find the value of one variable.

Find the value of the remaining variables using substitution.

Clearly state the final answer.

Check your answer by substituting both values into either of the original equations.

Answer:

50,000

Step-by-step explanation:

1,750 x 2 = 3,500

25,000 x 2 = 50,000

Each corner of a triangle can form an exterior angle of the triangle by extending one side of the triangle. As we can see in above picture, where 'w' is exterior angle of angle 'z'.

The measure of the exterior angle to ∠d is 126°. So, the correct option is option (D).

We have given that,

A ∆DEF such that m∠d = (2x + 19)°,

m∠e = (3x + 24)°, and m∠f = 87°.

we have to find out the degree measure of the exterior angle to ∠d.

As we know that sum of angles of triangle is equal to 180° .

so, m∠d + m∠e + m∠f = 180°

=> (3x + 24)° + (2x + 19)° + 87° = 180°

=> (5x + 24 + 19 + 87)° = 180°

=> 5x + 130° = 180°

=> 5x = 50°

=> x = 10°

plug this value in angle d , angle e we get ,

m∠d = (3 ×10 + 24 )° = 54°

We can see that adding the angle measurement d and the exterior angle measurement gives d = 180 degrees. This is because they are a pair of adjacent angles and both lie on a straight line.

measure of Exterior angle of ∠d + measure of ∠d = 180°

Measure of exterior angle of ∠d

= 180° - m∠d

= 180° - 54° = 126°

Hence, the measure of exterior angle of d is 126°.

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Answer:

Step-by-step explanation:

In order to calculate the correlation between two variables related to the same sample you need to calculate first the mean of each variable.

Before determining the correlation, the covariance of the two variables in the issue must always be computed. The standard deviation of each variable is then needed. The correlation analysis is calculated by dividing the covariance even by combination of a standard deviations of two or more variables.

A correlation is a statistical measurement of the two-variable connection. The measure works best with parameters that have a linear connection with one another.

The degree of the relationship between two variables is examined using correlation. To get the correlation between two variables, divided the covariance value by the standard deviation of both variables. Correlation analysis for two variables in the same sample should be performed. If you run a survey with two factors, a responder should be able to answer both variables at a glance. Furthermore, other participants' replies to the parameter might be evaluated for a correlation test.

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An equation for the nth term of the arithmetic sequence: an =  n - 6.

ad 10th term a10 = 4.

The formula for the nth term of the

an = a + (n -1)d

In which,

The arithmetic sequence is given as-

−5,−4,−3,−2, ...

Then, the equation will be

d = a2 - a1

d = -4 - (-5) = 1

an = a + (n -1)d

an = -5 + n - 1

Put n = 10 in the equation.

a10 = 10 - 6

a10 = 4

Thus, the 10th term of the sequence is 4.

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The correct question is-

Write an equation for the nth term of the arithmetic sequence. Then find a10.

−5,−4,−3,−2, ...

She may thus combine 21 pounds of tea priced at $3 and 14 pounds of tea priced at $2 to create tea that costs $2.6 per pound.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

Let 3x be the pounds of tea for $3 and 2x be the pounds of tea for $2.

Total required pounds=35

3x+2x=35

x=35/5

x=7

So, She can add 21 pounds of tea for $3 and 14 pounds of tea for $2 to make the tea that is $2.6 per pound.

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If a right triangle's height is 5 times the length of its base and the area of the triangle is 160, then the height of the triangle is 40 units

A right triangle's height is 5 times the length of its base

Consider the length of the base as b and the height as h

h = 5b

The area of the triangle = 160 square units

The area of the triangle = 1/2 × b × h

Where b is the base of the triangle

h is the height of the triangle

Substitute the values in the equation

1/2 × b × h = 160

1/2 × b × 5b = 160

1/2 ×5b^2 = 160

5b^2 = 320

b^2 = 320/5

b^2 = 64

b = [tex]\sqrt{64}[/tex]

b = 8 units

Then the height of the triangle h = 5b

= 5 × 8

= 40 units

Therefore, the height of the triangle is 40 units

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Answer: 3.6

Step-by-step explanation:

Step 1:  30/100 = x/12

Step 2: Multiply 12x30 and then divide it by 100

The true proportion of adults is in the interval 0.4026< P< 0.4594.

Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.

Data provided:

selected (x) = 329

Total(n) = 763

Sample proportion (p') = x/n

                                       = 329/ 763

                                       = 0.431

Critical z-value = 1.59

margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]

                             = 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]

                             = 1.59 × 0.0179

                             = 0.0284

88% confidence interval is:

(p' ± E) = ( 0.431 ± 0.0284)

          = 0.4594 and 0.4026

Therefore the estimate is 0.4026< P< 0.4594.

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The value of the other leg of the right angled triangle is found as 4√14 cm.

For the given question, the values for the right angled triangle are-

Hypotenuse (H)  - 15 cm

Side (B) = 1 cm

Let the other side be (P).

Then,

H² = P² + B²

P²  = H² - B²

Put the values-

P²  = 15² - 1²

P²  = 225 - 1

P²  = 224

P = 4√14

Thus, the value of the other leg of the right angled triangle is found as 4√14 cm.

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Answer:

Is it 53?

Step-by-step explanation:

3 tens means 30, and adding 23 ones would be 53

Using the secant-secant theorem,

[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ \\ \\ \angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]

The required simplified solution of the given expression is -40.

Given that,
To determine the simplified solution of the given expression 10c - cd + d³ at c = -6 and d = 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= 10c - cd + d³

Substitute the values,
= -60 + 12 + 8
= -40

Thus, the required simplified solution of the given expression is -40.

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Answer:

C ≈ 241.9 cm

Step-by-step explanation:

the circumference (C) of the circle is calculated as

C = πd ( d is the diameter )

here d = 77 , then

C = π × 77 ≈ 241.9 cm ( to 1 dec. point )

The correct boxes to the complete pairs are,

12 - 1/2r        →      (-8 - r) + (2r - 4)

r - 13/6         →       (7r - 3/2) - (2/3 + 6r)

13r + 20       →       (6r + 7) + (13 + 7r)

-12 + r          →        (-8 - r) + (2r - 4)

What is simplified expression?

Writing a similar expression devoid of similar terms is what is meant by the expression "simplify." In other words, we will rewrite the expression using the fewest number of terms.

Consider, the given expressions

(1)  (6r + 7) + (13 + 7r)

Simplifying this,

6r + 7 + 13 + 7r

13r + 20

(2) (13 - 3/2r) - (1 - r)

Simplifying this,

13 - 3/2r - 1 + r

12 - 1/2r

(3) (-8 - r) + (2r - 4)

Simplifying this,

-8 - r + 2r - 4

-12 + r

(4) (7r - 3/2) - (2/3 + 6r)

Simplifying this,

7r - 3/2 - 2/3 - 6r

r - 13/6

Hence, the correct boxes to the complete pairs are,

12 - 1/2r        →      (-8 - r) + (2r - 4)

r - 13/6         →       (7r - 3/2) - (2/3 + 6r)

13r + 20       →       (6r + 7) + (13 + 7r)

-12 + r          →        (-8 - r) + (2r - 4)

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Complete question:

Complete question is attached below,

The social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots

Main body:

Cumulative Earnings before this pay period = $128,300

pay amount this period = $3000

tax rate of 6.2% on social security = 6.2%

effective earning = 128300 = 3000

                            = 125300

social security deduction = 6.2 % of 125300

⇒ 6.2 *125300 /100

⇒$7768

Medicare deductions = 1.45%

⇒ 1.45*125300/100

⇒$1816

Hence , the social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

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The number of ways 3 courses can be selected is 3654.

How to calculate combination?

Total no. of courses available = 29

Courses needed to graduate = 3

No of ways these courses can be selected:

= ²⁹C₃

= 29!/ [(29-3)! - 3!]

= 29! / 26! 3!

= 29 * 28 * 27 * 26!/ 26! 3*2

= 29* 14* 9

=3654

So, the number of ways 3 courses can be selected is 3654.

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