Multiply 12. 462 by 13.

At the end of the first round, the total time is 648 seconds ( option E )

An average is the result that you get when you add two or more numbers together and divide the total by the number of numbers you added together.

For example, if there are 10 students in a class with ages 10, 11, 12, 10, 10,12,12,10,11,12 their average age will be( 10+ 11+12+10+10+12+12+10+11+12)/10

for Mariam her average time is 76 which means her total time is 76× 2= 152

for Jake and Rafael their average time is 84 which means their total time is 84×4= 336

for Sam,his average time is 80 which means is total time is 80×2= 160

therefore the total time spent by the 4 students is 152+336+160=648seconds

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For the given values of the arithmetic sequence d = -2 , a₂₁ = 18,then the value of a₁ = 58.

As given in the question,

Given values of the arithmetic sequence :

Common difference 'd' = -2

Twenty first term a₂₁ = 18

Formula for the nth term of arithmetic sequence with common difference 'd' and first term a₁ is given by:

aₙ = a₁ + (n -1) d

Substitute the value n =21 , a₂₁ =18 and d = -2 in the above equation we get,

⇒a₂₁ = a₁ + (21 -1)(-2)

⇒18 = a₁ + 20(-2)

⇒ a₁ = 18 +40

⇒a₁ = 58

Therefore, for the given values of the arithmetic sequence d = -2 ,

a₂₁ = 18,then the value of a₁ = 58.

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The smallest positive integer is 267 that should be multiply with given series.

What is meaning of series?

A series in mathematics is the total of a given set of terms. Real or complex numbers are typically used in these terms, but considerably more generality is conceivable.

Given series is 3, 6, 9, .... , 2400.

Assume that n should be multiply with the given series.

The series becomes 3n, 6n, 9n, .... , 2400n.

Now add the series:

(3n + 6n + 9n + ....+ 2400n)

Taking common 3n:

= 3n( 1 + 2 + 3 + ...+ 800)

Apply the formula the sum of the first n positive integers is n(n+1)/2

= 3n ×{800(800+1)}/2

=3n × 400 × 801

= 3n  × 4 × 100 × 3 × 3 × 89

= (4 × 100 × 3 × 3) × (3 × 89) × n

The product of (4 × 100 × 3 × 3)  is a perfect square. But 3 × 89 is not a perfect square. Thus n = 3 × 89 = 267.

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Answer:

Step-by-step explanation:

Given a car's cost of operation is $485 for 500 miles, you want an equation relating cost for m miles, and solutions to that equation for 1200 miles, and for a cost of $820.

The cost per mile is found by dividing the cost by the associated number of miles:

  $485/(500 mi) = $0.97 /mi

The equation for the cost will show the cost as the cost per mile multiplied by the number of miles:

  C = 0.97m . . . . . where C is cost in dollars for m miles driven

The cost for driving $1200 miles will be ...

  C = 0.97(1200) = $1164

The cost of driving 1200 miles is $1164.

The number of miles that can be driven for a cost of $820 is ...

  820 = 0.97m

  m = 820/0.97 = 845.36

About 845 miles are driven for a cost of $820.

The expected value of a player's winnings on each roll is equal to: D. $30.00

In order to determine the expected value of a player's winnings on each roll, we would list all of the outcomes that are associated with rolling a fair six-sided die.

By rolling a fair six-sided die, we would obtain the following outcomes:

Outcomes = 1, 2, 3, 4, 5, and 6.

Generally speaking, there are only two (2) numbers that are multiples of three (3) in a fair six-sided die and these include the following:

Multiples of three (3) = 3 and 6

When a player rolls a three (3), the player's possible winning is giving by:

Player's winning = 3 × 20 = $60

When a player rolls a three (3), the player's possible winning is giving by:

Player's winning = 6 × 20 = $120

Total winnings = $60 + $120

Total winnings = $180

Now, we can determine the expected value of a player's winnings on each roll:

Expected value = 1/6 × 180

Expected value = $30.

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Complete Question:

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?

A. $3.33

B. $6.66

C. $8.50

D. $30.00

E. $40.00

Answer:

Step-by-step explanation:

It would be D.

The value of the algebraic expression 2/5g + 3h - 6 if evaluated when g = 10 and h = 6 is 16.

2/5g + 3h - 6

When g = 10 and h = 6

2/5g + 3h - 6

2/5(10) + 3(6) - 6

20/5 + 18 - 6

4 + 18 - 6

16

In conclusion, the value of the expression 2/5g + 3h - 6 when evaluated is given by 16

Complete question:

Evaluate 2/5g + 2h - 6 start fraction, 2, divided by, 5, end fraction, g, plus, 3, h, minus, 6 when g=10 g, equals, 10 and h=6 h, equals, 6

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Hello!

If Brad had a small gathering at a local steakhouse where they ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters. After adding an 18% gratuity their total before sales tax should have been $130.45

Step-by-step explanation:

[tex]4[/tex] x [tex]9.95=39.80[/tex]

[tex]3[/tex] x [tex]12.95=38.85[/tex]

[tex]2[/tex] x [tex]15.95=31.90[/tex]

[tex]31.90+[/tex][tex]38.85+[/tex][tex]39.80=[/tex][tex]110.55[/tex]

[tex]110.55[/tex] x [tex]0.18[/tex] [tex]=19.899[/tex]

[tex]110.55+19.90[/tex][tex]=130.45[/tex]

The constant of proportionality is 1/7

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The the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3

The quadratic function is given by

f(x) = [tex]-3(x+2)^2[/tex] + 1

The vertex form of the quadratic function is

f(x) = [tex]a(x-h)^2[/tex] + k

Where (h, k)  is the coordinates of the vertex

x =  h is the axis of symmetry

Compare the given function and the vertex form of the quadratic function and find the value of the each term

The value of h = -2

The value of k = 1

The coordinates of the vertex = (-2, 1)

The axis of symmetry is at x = h

h = -2

Draw the graph using the details

Hence, the the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3

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Answer:

19.47

Step-by-step explanation:

Answer:

[tex]m\angle A \approx 19.47 \textdegree[/tex]

Step-by-step explanation:

Utilize the trigonometric ratio sine.

[tex]\sin(m\angle A) = \dfrac{2}{6}[/tex]

[tex]\sin(m\angle A) = \dfrac{1}{3}[/tex]

[tex]m\angle A = \sin^{-1}\left( \dfrac{1}{3} \right)[/tex]

[tex]m\angle A \approx 19.47 \textdegree[/tex]

The probability of the value of  (0.21) distribution using the normal distribution table is: 0.3166

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

In the question, we have

Probability of (0.21 < z <1.28)

= P(z < 1.28) - P(z < 0.21)

Probability of value for z

= 1.28 using z table is 0.8997

=> P(z < 1.28)

= 0.8997

probability of value for z = 0.21

Now, find the value of the probability using the normal distribution table:

using the z table of 0.21; we get:

The value of z is: 0.5832

=> P(z < 0.21) = 0.5832;

The value of  Probability of (0.21 < z <1.28)

= Probability of (z < 1.28) - Probability of (z < 0.21)

= 0.8997 - 0.5832

= 0.3165

~ 0.3166

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The slope of the line that passes through (1, 1)  and (7, 5) is 2/3

From the question, the points are given as

a. (1, 1) and (7,5)

Rewrite the above points properly

So, we have the following ordered pairs

(1, 1) and (7,5)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (1, 1) and (7,5)

Substitute the known values in the above equation

So, we have the following equation

Slope = (5 - 1)/(7 - 1)

Evaluate

Slope = 2/3

Hence, the slope of the line is 2/3

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Possible question

Find the slope of the line that passes through a. (1, 1) and (7,5)

Answer: x=43

Step-by-step explanation:

3x-19=110

3x-19+19=110+19

3x=129

3x/3=129/3

x=43

D( x ) function and also a rule for the set of points (5, 10), (6, 12), and (-2, -4). Both the statment is true.

Given that,
Among the options which statment best represents the expression D(x) = 2x is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
D(x) = 2x

As from the observation D(x) is a function of the independent variable x.
Also,
At x = 5, 6, -2
D(x) = 10, 12, -4
So it is also a rule for the set of points (5, 10), (6, 12), and (-2, -4).

Thus, the D( x ) function and also a rule for the set of points (5, 10), (6, 12), and (-2, -4). Both the statment is true.

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P(-4,-1) are the coordinates of circumcentre of the triangle

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.

Let A(-5,-4), B(3,-4), C(-1,6) be the vertices of the given △ABC.

Let P(x,y) be the circumcentre of △ABC. Then,

PA = PB = PC

Also, PA² = PB² = PC²

PA² = PB²

(x-(-5))² + (y-(-4))² = (x-3)² + (y-(-4))²

(x+5)² + (y+4)² = (x-3)² + (y+4)²

x²+10x+25 + y²+8y+16 = x²-6x+9 + y²+8y+16

10x-6x = 9-25

4x = -16

x = -16/4 = -4

Also, PB² = PC²

(x-3)² + (y+4)² = (x+1)² + (y-6)²

x²-6x+9 + y²+8y+16 = x²+2x+1 + y²-12y+36

-6x-2x+8y+12y = 37-9-16

-8y+20y = 12

-2x+5y = 3 .......(1)

put x= -4 into (1):

-2(-4)+5y = 3

8+5y = 3

5y = 3-8

5y = -5

y = -1

Therefore, the coordinates of circumcentre of △ABC are P(-4,-1)

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If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your working memory.

A cognitive apparatus known as working memory has a finite capacity and can only temporarily store information. It is crucial for reasoning, decision-making, and behaviour direction. When working on a long-division problem, kids use their working memory abilities to retain the long-division steps. Other instances include keeping track of complicated instructions, taking notes in class, recalling an argument while someone else is speaking, or performing mental calculations. In contrast to long-term memory, which stores a large amount of knowledge over a lifetime, working memory is the little amount of information that may be kept in mind and used to carry out cognitive tasks. One of the most often used concepts in psychology is working memory.

Given,

If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your:

d) Working memory

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Answer: 0.8

Step-by-step explanation:

The z-observed value for the test of average number of times that a typical american says a word that is considered to be profane is -0.41.

The formula for calculating the z-score is-

z = (x - μ)/s

in which,

n = sample size (= 15)

μ = mean (= 4)

σ = standard deviation (= 5.6)

s = σ/√n

s = 5.6/√15

s = 1.44

Put the value in z score;

z = (3.4 - 4)/1.44

z = -0.41

Because of how near to zero this test statistic is, we will not be able to rule out the null hypothesis. Seven.

There isn't enough proof to claim that there is a mean difference or that it exists in your circumstance.

Thus, they're basically arguing that we can't rule out the null hypothesis.

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The price of the share 3 years later, given the increase in value, can be found to be $43.29

The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.

This means that the price of the share 3 years later would be:

= Share price currently x ( 1 + increase in value)

= 37 x ( 1 + 17 % )

= 37 x 1. 17

= $ 43. 29

The price is  $43.29

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meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow

A) The matrix equation that represents the given information is;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) The cost of a banana is; $0.05

The cost of an orange is; $0.12

A matrix equation is defined as an equation where a variable stands for a matrix .

Let x represent cost of oranges

Let y represent cost of bananas

5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas

cost me $1.41. Thus, the equations are;

5x + 14y = 1.30  ----(1)

8x + 9y = 1.41   -----(2)

A) Now, the matrix form of the simultaneous equation above will be;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) Multiply the first equation by 8 and the second one by 5 to get;

40x + 112y = 10.4

40x +   45y = 7.05   Subtract to get;

            67y = 3.35

Divide both sides by 67 to get;

y = $0.05 per banana

Plug in 0.05 for y into eq 1 to get;

5x + 14(0.05) = 1.30

5x + 0.7 = 1.3

5x = 1.3 - 0.7

5x = 0.6

x = 0.6/5

x = $0.12

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Answer:

Step-by-step explanation:

a find the interpret the slope and the y-intercept of the graph

A 99% confidence interval of what the actual average mileage is for a car before it is junked is;  (153589, 174411)

The formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

s is standard deviation

n is sample size

z is critical value at confidence level

We are given;

x' = 164000

n = 48

s = 28000

CL = 99%

z-score at confidence level of 99% is 2.576

Thus;

CI = 164000 ± 2.576(28000/√48)

CI = 164000 ± 10410.78

CI = (164000 - 10410.78), (164000 + 10410.78)

CI = (153589, 174411)

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Answer:

x = 1

Step-by-step explanation:

Given equation,

→ -31 - 4x = -5 - 5(1 + 5x)

Now the value of x will be,

→ -31 - 4x = -5 - 5(1 + 5x)

→ -31 - 4x = -5 - 5 - 25x

→ -4x + 25x = -10 + 31

→ 21x = 21

→ x = 21/21

→ [ x = 1 ]

Hence, the value of x is 1.

The value of the variable x in the equation -31 -4x = -5- 5(1+ 5x) will be 1.

The given algebraic expression with the variable x is,

-31 - 4x = -5 -5(1+ 5x)

By further solving it, we get,

- 31 - 4x = -5 -5 -25x

To simplify the equation, we have to first separate the constants and variables,

=> 25x - 4x = -5 -5 + 31

=> 21x = 31 - 5 -5

=> 21x = 31- 10

=> 21x = 21

=> x = 21/21

=> x= 1.

Hence, the value of the variable x in the algebraic expression, -31 - 4x = -5 -5(1+ 5x), is found to be 1.

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Answer:

b

Step-by-step explanation:

b

Answer: Amelia 5, Keturah 10, Jordan 6, Bryce 18

Step-by-step explanation:

If Amelia scored 5 and Keturah scored 2 times of Amelia's score, then 5 x 2 is 10, so Keturah scored 10. If Keturah scored 10 and Jordan scored 4 points fewer than Jordan's score, then 10 - 4 is 6, so Jordan scored 6. If Jordan scored 6 and Bryce scored 3 times of Jordan's score, then 6 x 3 is 18, so Bryce scored 18. So C is the correct answer.

Answer:

b. y + 5 = -2(x + 3) or

    y = - 2x - 11

Step-by-step explanation:

Point-slope equation:

Convert this to slope-intercept form:

Correct choice is b.

The quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.

For the stated values,

Sum of zeroes is 3 and product is -40​

Use formula,

x² - x (sum of zeros) + (product of zeros) = 0.

Put the values.

x² - x (3) + (-40) = 0.

x² - 3x + -40 = 0.

Thus, the quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.

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Answer: During the Russian war, The Russians and Germans were at war with each other, Beating them brutally.

Step-by-step explanation: