Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=8.4 and x=7.3 and passes through the point (0,8.2).

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 equation would be 5(x + 3) = 45

To solve:

1) Distribute 5 to x and then 5 to 3

2) That gives you this equation: 5x + 15 = 45

3) Then subtract 15 from both sides

4) You should get this: 5x = 30

5) Then divide 5/5 and 30/5 to isolate the x

6) The answer should be: x = 6

Have a good day/night :)

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.

To know more about algebraic expressions:

https://brainly.com/question/19864285

As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.

The value of p=0.8 and n=20

The probability that exactly 12 flights are on time = 0.1772

The probability that exactly fewer than 12 flights are on time =  0.1049

The probability that at least 12 flights are on time = 0.8951

The probability that between 10 and 12 flights, are on time = 0.1795

(a) Binomial probability is the probability of exactly 'k' successes on 'n' repeated trials in an experiment which has two possible outcomes.

As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.

(b) As, the probability of success on an individual trial is p and here success means the flight is on-time so the value of p be,

p = 80% = 0.8

As, we made 20 trials and n is the total number of trials then,

the value of n be,

n = 20

(c) Now, if the probability of success on an individual trial is p ,

Then the binomial probability is C(n,x)⋅p^x⋅(1−p)^(n−x)

The probability that exactly 12 flights are on time, be

P(X=12) = C(20,12)⋅(0.8)^12⋅(1−0.8)^(20-12)

P(X=12) = C(20,12)⋅(0.8)^12⋅(0.2)^(8)

P(X=12) = 10,07,760×0.0687×0.00000256

P(X=12) = 0.1772

(d) Now, the probability that exactly fewer than 12 flights are on time, be

P(X<12) = 1 - P(X>12)

So, P(X>12) = P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)

So, P(X>12) = 0.0545 + 0.0364 + 0.1746 + 0.2182 + 0.2054 + 0.1369 + 0.0576 + 0.0115

P(X>12) = 0.8951

P(X<12) = 1 - 0.8951

P(X<12) = 0.1049

(e)  Now, the probability that at least 12 flights are on time, be

P(X>12)=0.8951

(f) The probability that between 10 and 12 flights, are on time, be

P(X=10)+P(X=11)+P(X=12) = 0.0020 + 0.0003 + 0.1772

P(X=10)+P(X=11)+P(X=12) = 0.1795

Learn more about Probability here https://brainly.com/question/13604758

#SPJ1

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

Read more about Matrix equation at; https://brainly.com/question/11989522

#SPJ1

The value for p is 30.

learn more about hypothesis click here:

brainly.com/question/606806

#SPJ4

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

To learn more about Probability, visit:

brainly.com/question/24188569

#SPJ13

Answer: 0.8

Step-by-step explanation:

The constant of proportionality is 1/7

To learn more about constant of proportionality, refer to https://brainly.com/question/26171814

#SPJ1

The most reasonable estimate of the correlation coefficient is 0.9

The correlation coefficient gives an estimate of how strong is the linear relationship between two variables.

The correlation coefficient, r, is given by the formula;

[tex]r = \dfrac{\sum(x_i-\overline x)\cdot (y_i-\overline y)}{\sqrt{\sum (x_i-\overline x)^2\sum(y_i-\overline y)^2} }[/tex]

Where;

[tex]x_i[/tex] = The ith x-value

[tex]\overline x[/tex] = The mean (average of the x-values)

[tex]y_i[/tex] = The ith y-value

[tex]\overline y[/tex] = The mean (average of the y-values)

The give points on the scatter plot graph are;

(8, 9), (6, 9), (6, 6), (5, 5), (4, 5), (3, 4), (3, 3), (2, 4), (1, 2), (1, 3)

Plotting the above points on MS Excel gives;

The equation of the regression line is; y = 0.9407·x + 1.3313

The square of the correlation coefficient, R² = 0.8322

Therefore, R = √(0.8322) ≈ 0.9122

The option that is the most reasonable estimate of the correlation coefficient is therefore; 0.9

Learn more about the correlation coefficient number in statistics here:

https://brainly.com/question/4219149

#SPJ1

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.

To know more about the z-score, here

https://brainly.com/question/25638875

#SPJ4

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)

Learn about the circumcenter of a triangle on:

https://brainly.com/question/21360684

#SPJ1

The factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.

We are given an algebraic expression:

18y^4 + 24y^3 + 6y^2

We need to factorize by factoring out the Greatest Common Factor.

In the given algebraic expression, we can see that;

6 is the Greatest Common Factor of 18, 24, and 6.

y^2 is the Greatest Common Factor of y^4, y^3 and y^2.

So, we will take the common 6y^2 from the given expression;

18y^4 + 24y^3 + 6y^2

= 6y^2 (3y^2 + 4y + 1)

So, option A is correct.

Thus, the factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.

To learn more about factorization by Greatest Common Factor visit:

https://brainly.com/question/24197766

#SPJ9

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

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

Read more on algebraic expression:

https://brainly.com/question/15280356

#SPJ1

The value of a=2 and b= 4.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

a + 1 / b-1 = 5/1 and a-1/ b+ 1 = 1/1

So, a + 1 / b-1 = 5/1

now, cross multiplying

a+ 1 = 5b - 5

a- 5b = -6............(1)

Also, a-1/ b+ 1 = 1/1

a-1 = b + 1

a - b = 2 ..............(2)

solving Equation (1) and (2) , we get

2+ b - 5b= -6

-4b = -8

b= 2

and, a = 2 + 2 = 4

Learn more about Equation here:

https://brainly.com/question/10413253

#SPJ1

Answer:

6

Step-by-step explanation:

-1^2-3(5)+20

1-15+20

1+5

6

hopes this helps

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

Step-by-step explanation:

The profit made from the business that receives an initial $100 investment are as follows;

1. The amount received from the investment is $15

2. The number of lawns that should be mowed to buy the switch is 23 lawns

3. The profit made from the business considering the cost and the initial investment of the parents is $170

An investment is the money directed towards an asset purchase to increase the valuation of the business and products within a time period.

The amount invested = $100

The amount desired as return = 10% of the amount made from the business

1. The amount charged per lawn = $15

The number of lawn mowed = 10

The revenue of the business = 10 × $15 = $150

The amount paid as return on investment = 10% × $150 = $15

2. The amount required to buy the switch = $300

The number of lawns to be mowed, n, is therefore;

300 = 15 × n - 10% × 15 × n = 15·n - 1.5·n = 13.5·n

300 = 13.5·n

n = 300/13.5 ≈ 23 ( rounding up to the nearest whole number)

The number of lawns to be mowed is 23 lawns

3. The revenue from mowing 20 lawns is 20 × $15 = $300

The amount received by the investing parents = 10% × $300 = $30

The amount received from the parents investment = $100

The profit made after 20 lawns = $300 - $30 - $100 = $170

Learn more about percentages here:

https://brainly.com/question/843074

#SPJ1

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

X2+Y2 =53

= 53 + (50-1)(-4)

= 53-196

= -143

To learn more about Equation refer to:

https://brainly.com/question/2972832

#SPJ13

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.

To learn more about Arithmetic series, you can visit below link:

https://brainly.com/question/11346378?

#SPJ1

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.

To know more about the quadratic polynomial, here

https://brainly.com/question/17489661

#SPJ4

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.

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]

A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.

Given that, a police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets.

A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.

Perpendicular bisector: A line that bisects a line segment in two equal parts.

Median: The middle number; found by ordering all data points and picking out the one in the middle.

Angle bisector: The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

An altitude: Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it.

Therefore, a police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.

Learn more about the perpendicular bisector here:

https://brainly.com/question/24753075.

#SPJ1

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

To learn more about working memory, visit:

https://brainly.com/question/6292992

#SPJ4

Answer:

-0.2

Step-by-step explanation:

14.9-15.1= -0.2

To do equations like this in the beginning I used to switch the terms and then add a negative symbol in front of it

I would solve it like this

15.1-14.9

.2

And now since I switched the terms I change the sign to negative

-0.2

Hopes this helps please mark brainliest