In an election between two candidates one got 52% of the total valid votes. 25% of the total votes were invalid.The total number of
votes was 7,200. The number of valid votes that the other candidate got was:

The median value in the data set is the average of the two middle values which is: 23.

In an ordered data set, the median is the middle value or average of the two middle values in the data set.

List out each data point in the data set given:

20, 20, 20, 22, 22, 24, 26, 26, 26, 26

The middle values in the data set are, 22 and 24.

Median = (22 + 24)/2

Median = 23

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Answer:

3.280

Step-by-step explanation:

You just add a 0

Answer:

0

Step-by-step explanation:

1. Substitute the values in: \(2^0 - (-1)^2\)

2. Evaluate the expression:  \(2^0 = 1\), \((-1)^2 = 1\), which means that 1 - 1 is 0

Therefore, 0 is the answer.

The Equation of parabola with focus (3,1) and directrix y = 3 is \(10x^2 + 9y^2-60x -14y+91 =0\)

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Here, focus (3,1) and directrix y=3

Let the locus of parabola be (x, y)

We know that, in Parabola

Distance between locus to focus = Distance between locus to directrix line

\(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\) = \(\frac{Ax_{1}+By_{1}+C }{\sqrt{A^2 + B^2 + C^2} }\)

\(\sqrt{(x-3)^2+(y-1)^2} = \frac{0.x+1.y-3}{\sqrt{0^2+1^2+(-3)^2} }\)

On squaring both sides, we get

\((x-3)^2 + (y-1)^2 = (\frac{y-3}{\sqrt{10} } )^2\)

\(x^2 -6x + 9 + y^2 -2y + 1 = \frac{y^2 -6y +9}{10}\)

\(10x^2 + 9y^2-60x -14y+91 =0\)

Thus, The Equation of parabola with focus (3,1) and directrix y = 3 is \(10x^2 + 9y^2-60x -14y+91 =0\)

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Based on the maximum taxable amount for social security in 2009, and the social security tax rate, the social security tax that Larry paid was $7,347.

The total amount paid by Larry as Social security tax can be found as;

= Maximum amount allowable for social security tax x Social security tax rate

The social security tax rate was 6.2% not 62.2%.

The social security tax was therefore:

= 118,500 x 6.2%

= $7,347

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

It is the distance that –5 is from 5 on the number line.

Step-by-step explanation:

It is the distance that –5 is from 5 on the number line.

Answer:

5 to 5 on the number line!

Step-by-step explanation:

Have a jolly weekend!^_^

Using it's concept, it is found that the probability that a resident is male and in the age group 60-79 is given by:

C. 0.29.

A probability is given by the number of desired outcomes divided by the number of total outcomes. A probability can also be interpreted as a relative frequency.

From the relative frequencies, we have that:

Hence, the probability that a resident is male and in the age group 60-79 is given by:

p = 0.19 + 0.1 = 0.29.

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Answer:

The answer is a^n+2n+8a^2n-a^2n-14a^n-48.

Step-by-step explanation:

1. Use the distributive property.

2. Remove the parenthesis.

3. Collect like terms.

Hope this helps and if you could mark me as brainliest. Thanks!

The factored form of  (a²ⁿ - aⁿ - 6) is divided by (aⁿ + 8) is

(a²ⁿ - aⁿ - 6) = (aⁿ + 7)(aⁿ + 8) - 62/(aⁿ + 8).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, (a²ⁿ - aⁿ - 6) is divided by (aⁿ + 8).

In case of long division in the quotient well multiply the first term of the divisor 'aⁿ' with such a number that it becomes equal to the first term of the dividend, Now aⁿ×aⁿ is a²ⁿ.

∴  (a²ⁿ - aⁿ - 6)/(aⁿ + 8) is,

(a²ⁿ - aⁿ - 6) = (aⁿ + 7)(aⁿ + 8) - 62/(aⁿ + 8).

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Answer:

1.) A

2.) D

3.) A

Step-by-step explanation:

Answer:

1) \(v=4.5\)

2)\(c=6.3\)

3)\(g=0.4\)

4)\(a=17.4\)

For those who have images blocked:

1) v = 4.5

2) c = 6.3

3) g = 0.4

4) a = 17.4

Interest earned on first investment in year 1 is $6,183.13

Interest earned on second  investment in year 1 is $6,167.68

Annual yield on first investment is 6.18%

Annual yield on second investment is 6.17%

What is daily compounding?

Daily compounding means that the interest on the investment is computed on daily basis, 365 days a year.

In a bid to determine the total interest earned in one year on the investment whose interest is compounded daily, we can make use of the future value below to determine its worth after 1 year, from which the initial investment can be deducted to determine the interest in year 1.

FV=PV*(1+r/n)^(n*t)

PV=initial investment=$100,000

r=rate of return=6%

n=365 days a year

t=1 year

FV=$100,000*(1+6%/365)^(365*1)

FV=$106,183.13

Interest=$106,183.13 -$100,000

interest=$6,183.13

Annual yield=effective annual interest

EAR=(1+6%/365)^(365)-1

EAR=6.18%

What is monthly compounding?

It means interest is compounded or computed every month, 12 months a year

FV=PV*(1+r/n)^(n*t)

PV=initial investment=$100,000

r=rate of return=6%

n=12 months a year

t=1 year

FV=$100,000*(1+6%/12)^(12*1)

FV=$ 106,167.78  

Interest=$ 106,167.78  -$100,000

interest=$6,167.68

Annual yield=effective annual interest

EAR=(1+6%/12)^(12)-1

EAR=6.17%

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Answer:

Step-by-step explanation:

No, Cherise did not use algebra tiles to correctly represent the product of (x - 2)(x - 3).

The correct algebra tile configuration for the product of (x - 2)(x - 3) would have 2 tiles in the Factor 1 spot, labeled -x and -2, respectively, and 3 tiles in the Factor 2 spot, labeled -x and -3 twice, respectively. The Product spot would have 6 tiles, labeled +x², -5x and +6 twice, respectively.

The given algebra tile configuration has 3 tiles in the Factor 1 spot and 4 tiles in the Factor 2 spot, which do not match the correct configuration for (x - 2)(x - 3). Additionally, the tile configuration in the Product spot is also incorrect, as it has 5 negative x tiles, whereas the correct configuration should have 3 negative x tiles.

Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer:

Square Root of 7 = 7^1/2    = 2.646

Cubed Root of 7 = 7^1/3    = 1.913

Square Root of 7^3 = 7^3/2     = 3.659

Answer:

A person (or institution) who invest the money or makes the funds available is called the lender or creditor.

Step-by-step explanation:

Answer:

Sophia should start her homework at 5:55

Step-by-step explanation:

If it takes her 10 minutes to go to school, 30 minutes to do her homework, and 25 minutes to eat dinner, you should add those numbers together to get 65 because then you can subtract 65 minutes from 7:00 so you get the time she needs to start her homework in order to get to school at 7:00. So basically 10+30+25=65 and then 65 minutes subtracted from 7:00 is 5:55.

I hope this helps you :D

Answer:

5:55 pm

Step-by-step explanation:

30+25+10=65

or

1 hour and 5 minutes

The actual distance from Columbus to Midway is,

⇒ 99 miles

Multiplication means to add number to itself a particular number of times. And, Multiplication can be viewed as a process of repeated addition.

We have to given that;

A map scale shows that, 1 cm = 30 miles.

And, Jeanne measured the distance from Columbus to Midway on the map as 3.3 cm.

Now, We get;

1 cm = 30 miles

3.3 cm = 3.3 x 30 miles

          = 99 miles

Thus, The actual distance from Columbus to Midway would be,

⇒ 99 miles

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Answer:

Harry made 9 resolutions.

Step-by-step explanation:

Tim made x resolutions.

Harry made five more, x + 5.

Harry and Tim's together was 13.

x + x + 5 = 13

combine like terms.

2x + 5 = 13

subtract 5

2x = 8

divide by 2

x = 4

Tim made 4 resolutions.

Harry made 4 + 5, that is, 9 resolutions.

Check:

Harry and Tim together is 13.

4 + 9 = 13

Harry made 9 resolutions.

Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

Answer:

i. daily charge = £13

ii. fixed charge = £6

Step-by-step explanation:

Number of days (x) | Cost in £ (y)

1 | 19

2 | 32

3 | 45

4 | 58

5 | 71

Using the given table, we can represent this situation with an equation in slope-intercept form, y = mx + b, where,

m = slope = daily charge

b = y-intercept = fixed charge

✔️Thus, using the coordinates of any two given pairs, say (1, 19) and (2, 32):

Slope (m) = ∆y/∆x = (32 - 19)/(2 - 1) = 13/1

Slope (m) = 13

Therefore daily charge = £13

✔️To find y-intercept (b), substitute (x, y) = (1, 19) and m = 13 into y = mx + b.

Thus:

19 = (13)(1) + b

19 = 13 + b

b = 19 - 13

b = 6

Therefore, fixed charge = £6

✔️Substitute m = 13 and b = 6 into y = mx + b to represent the function given for the situation:

y = 13x + 6

The given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

What is Euclid's algorithm?

The Euclidean algorithm, also known as Euclid's algorithm, is an effective way to determine the greatest common divisor of two integers, or the biggest number that divides them both evenly without leaving a remainder. It is named after the Greek mathematician Euclid, who first discussed it in his Elements and gave it that name.

A common fraction can be reduced to its simplest terms using the Euclidean algorithm. For instance, the algorithm will demonstrate that the GCD of 765 and 714 is 51, and that 765/714 = 15/14 as a result. Additionally, it has several applications in more complex mathematics.

Hence, the given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

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Answer:

(a)The x-intercepts are 3, -4 and 1.

(b)f(x)=-0.5

Step-by-step explanation:

Given the function:

\(f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}\)

x-Intercepts

When y=f(x)=0

\(f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}=0\\(x - 3)(x + 4)(x - 1)=0\\x - 3=0$ or $ x + 4=0 $ or $ x - 1=0\\x=3$ or $ -4$ or $ 1\)

The x-intercepts are 3, -4 and 1.

y-intercepts

When x=0

\(f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}\\f(x) = \dfrac{(0 - 3)(0 + 4)(0 - 1)}{(0 + 2)(0 - 12)}\\= \dfrac{(- 3)( 4)( - 1)}{( 2)( - 12)}\\= \dfrac{12}{-24}\\\\=-0.5\)

The y-intercept is -0.5

Answer:

( − 1 , ∞ )

Step-by-step explanation:

( − 1 , ∞ )

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

\(y = -x^2 - 4x + 2\)

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

Answer: let x = the amt over the weight limit

17x + 17 = 19x + 15

17 - 15 = 19x - 17x

2 = 2x

x = 1 kg over the limit

"How large was each airline's fee?"

17(1) + 17 = $34

19(1) + 15 = $34

Step-by-step explanation: