(Surds)

Write

√99 + √44

in the form a√b where a and b are integers

Given :

Sierra is getting her car fixed at a mechanics. The total cost after tax is represented by 0.065(30h) + 30h, where h represents the number of hours it takes to repair the car.

To Find :

What part of the expression represents the amount of money she will have to pay in tax.

Solution :

Total cost , T = 30h( 1 + 0.065)

T = 30h + 30h(0.065)

T = (30h) + (30h )× 6.5 %

Here, 30h is the cost of repairing the car.

Other part shows the tax she have to pay which is 6.5% of the total amount.

Hence, this is the required solution.

Answer:

x=0 or x=6

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

Answer:

(g - f)(x) = 3x - 6

Step-by-step explanation:

Step 1: Define

f(x) = 5 - x

g(x) = 2x - 1

Step 2: Find (g - f)(x)

(g - f)(x) = 2x - 1 - (5 - x)

(g - f)(x) = 2x - 1 - 5 + x

(g - f)(x) = 3x - 6

Answer:

3x-6

Step-by-step explanation:

f(x) = 5 - x

g(x) = 2x - 1

(g - f)(x) = 2x - 1 - (5 - x )

Distribute the minus sign

         =2x - 1 - 5 + x

Combine like terms

        = 3x-6

In the "Sum of Minterms" form of the function F = xy + xz + yz, the terms that are part of this form are: x'y'z', xy'z, x'yz', and xyz.

x'y'z' is part of the "Sum of Minterms" form because it represents the minterm where x', y', and z' are complemented (negated).

xy'z is also part of the "Sum of Minterms" form because it represents the minterm where x, y', and z are complemented.

x'yz' is included in the form as it represents the minterm where x', y, and z' are complemented.

Lastly, xyz is part of the "Sum of Minterms" form because it represents the minterm where x, y, and z are not complemented.

These terms represent the individual minterms that are summed together to express the function F in the "Sum of Minterms" form. Each term corresponds to a specific combination of input variables (x, y, and z) where the function evaluates to true.

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Answer:

x=-4 or 2

Step-by-step explanation:

x(x+1)=8-x

x^2+x=8-x

x^2+2x-8=0

x^2+4x-2x-8=0

x(x+4)-2(x+4)

(x-2)(x+4)=0

x-2=0

x=2

or

x+4=0

x=-4

ANSWER: 155.25

EXPLANATION: -81 ÷ (-9)× 23(3/4)

9×69/4

621/4

155.25 answer

please mark as brainliest if it helps

Answer:

[tex] \frac{621}{4} [/tex]

or

[tex]155.25[/tex]

Answer:

Step-by-step explanation:

P=2975 + r and 4= p - 225

The circumference of the circle is about 10.05 meters

From the question, we have the following parameters that can be used in our computation:

Diameter, d = 3.2 inches

The circumference of the circle is calculated as

C = πd

Substitute the known values in the above equation, so, we have the following representation

C = 3.14 * 3.2

Evaluate

C = 10.05

Hence, the circumference of the circle is 10.05 meters

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Question

Complete the sentence. Calculate the circumference of the circle. Use 3.14 for pi . Round the answer to the nearest hundredth.

Diameter = 3.2 inches

The circumference of the circle is about __ meters.

Answer:

D (11)

Step-by-step explanation:

77 / 11 = 7

66/11 = 6

Answer:

the factors and prime factorization of 66 and 77. The biggest common factor number is the GCF number. So the greatest common factor 66 and 77 is 11.

Step-by-step explanation:

Answer:

Step-by-step explanation:

3/4 is 0.75 and 1 1/2 is 1.5

plot the numbers:

1.1, 3/4 , -0.9 , -1, 1 1/2 ( the line is not up to scale)

_|_______|__|_______|_____|___|__|_____|____|_

 -2           -1  -0.9            0       3/4    1  1.1      1 1/2       2

the number the least is -1

the number greatest  1 1/2

the correct order from least to greatest is  

-1  , -0.9 , 3/4  , 1.1 , 1 1/2  

Answer:

(a) there are 12 ways to choose 2 letters, taking the order of the choices into consideration.

(b)  there are 6 ways to choose 2 letters, without considering the order of the choices.

Step-by-step explanation:

(a) If the order of the choices is taken into consideration, we are dealing with permutations. We want to choose 2 letters out of 4 without replacement. The number of ways this can be done is calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

In this case, n = 4 (number of letters) and r = 2 (number of choices). Plugging in these values, we get:

P(4, 2) = 4! / (4 - 2)!

= 4! / 2!

= 4 x 3

= 12

Therefore, there are 12 ways to choose 2 letters, taking the order of the choices into consideration.

(b) If the order of the choices is not taken into consideration, we are dealing with combinations. We still want to choose 2 letters out of 4 without replacement, but the order of the choices doesn't matter. The number of ways this can be done is calculated using the formula for combinations:

C(n, r) = n! / (r! * (n - r)!)

In this case, n = 4 (number of letters) and r = 2 (number of choices). Plugging in these values, we get:

C(4, 2) = 4! / (2! * (4 - 2)!)

= 4! / (2! * 2!)

= 4 x 3 / 2

= 6

Therefore, there are 6 ways to choose 2 letters, without considering the order of the choices.

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Answer:

1/32

Step-by-step explanation:

2^13/ (2^9)^2 = 2^13/2^18 = 1/2^5 = (2x2x2x2x2=32) = 1/32

The value of the expression 2¹³ / 2¹⁸ is 1/32.

An expression is combination of variables, numbers and operators.

We have to find the value of 2¹³ / (2⁹)²

From the exponential property [tex](a^m)^n=a^m^n[/tex]

Let us simplify the denominator  (2⁹)² = 2¹⁸

The expression becomes of 2¹³ / 2¹⁸

Now let use the property [tex]\frac{a^m}{a^n} =a^m^-^n[/tex]

2¹³ / 2¹⁸

[tex]2^-^5[/tex]

We can write this in the form of fraction 1/2⁵

1/2×2×2×2×2

1/32

Hence, the value of the expression 2¹³ / 2¹⁸ is 1/32.

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The radio station gives away a total of $315.79 during the contest.

In the first day of the contest, the radio station gives a prize of $300 to the first listener who answers the trivia question correctly. The amount of the prize decreases by 5% for each day that passes. We are required to find the total amount of prize money the radio station gives away during the contest.Let X be the total amount of prize money given away during the contest. Then we can write the following equation:X = $300 + $285 + $270.75 + $257.21 + …After solving this infinite geometric series, we can find the total amount of prize money that the radio station gives away during the contest.X = a1 / (1 - r), where a1 is the first term and r is the common ratio.Substituting the values of a1 and r, we get:X = $300 / (1 - 0.05) = $300 / 0.95 = $315.79 (rounded to two decimal places)

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Subtract miles traveled from total miles:

1500 - 600 = 900 more miles to go

Divide miles to go by speed:

900 / 300 = 3 hours

3 more hours

Answer:

3 more hours

Step-by-step explanation:

Answer:

0.32

Step-by-step explanation:

0.2 to the fifth power is 0.00032, so that simplified is 0.32.

Answer

0.32

Step-by-step explanation:

"0.2222" was replaced by "(2222/10000)". 4 more similar replacement(s)

                  1111

Simplify   ————

                  5000

       22            222        2              1111

 (((———•4)•{————}3——)•5)•(————2)

      100           1000      10            5000

1111 = 11•101

(1111)2 = (11•101)2 = 112 • 1012  2.2     5000 = 23•54 (5000)2 = (23•54)2 = 26 • 58

22    ( 222   2     (112•1012)

 (((———•4)•{————}3——)•5)•——————————

    100     1000  10      (26•58)  

           1

Simplify   —

           5

     22    ( 222  1     (112•1012)

 (((———•4)•{————}3—)•5)•——————————

    100     1000  5      (26•58)  

           111

Simplify   ———

           500

     22    111  1     (112•1012)

 (((———•4)•———3)—)•5)•——————————

    100    500  5      (26•58)  

5.1     111 = 3•37

(111)3 = (3•37)3 = 33 • 373  5.2     500 = 22•53 (500)3 = (22•53)3 = 26 • 59

     22    (33•373)   1     (112•1012)

 (((———•4)•———————— ÷ —)•5)•——————————

    100    (26•59)    5      (26•58)  

        (33•373)      1

Divide  ————————  by  —

        (26•59)       5

6.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

(33•373)     1       (33•373)     5

————————  ÷  —   =   ————————  •  —

(26•59)      5       (26•59)      1

Dividing exponents:

6.2    51   divided by   59   = 5(1 - 9) = 5(-8) = 1/58

     22        (33•373)         (112•1012)

 (((——— • 4) • ————————) • 5) • ——————————

    100        (26•58)           (26•58)  

           11

Simplify   ——

           50

    11        (33•373)         (112•1012)

 (((—— • 4) • ————————) • 5) • ——————————

    50        (26•58)           (26•58)  

Multiplying exponents

8.1    52  multiplied by  58   = 5(2 + 8) = 510

Dividing exponents:

8.2    21   divided by   26   = 2(1 - 6) = 2(-5) = 1/25

Equation at the end of step

8

:

  (11•33•373)        (112•1012)

 (——————————— • 5) • ——————————

   (510•25)           (26•58)  

Dividing exponents

9.1    51   divided by   510   = 5(1 - 10) = 5(-9) = 1/59

 (11•33•373)   (112•1012)

 ——————————— • ——————————

   (59•25)      (26•58)  

Multiplying exponents

10.1    111  multiplied by  112   = 11(1 + 2) = 113

Multiplying exponents:

10.2    59  multiplied by  58   = 5(9 + 8) = 517

Multiplying exponents:

10.3    25  multiplied by  26   = 2(5 + 6) = 211

Final result :

 (113•33•373•1012)          

 ————————— = 0.32

     (517•211)              

Answer:

32

Step-by-step explanation:

Step 1: Define

f(x) = 3x² - 5x - 4

g(x) = -4x - 12

Step 2: Find f(g(x))

f(g(x)) = 3(-4x - 12)² - 5(-4x - 12) - 4

f(g(x)) = 3(16x² + 96x + 144) + 20x + 60 + 4

f(g(x)) = 48x² + 288x + 432 + 20x + 64

f(g(x)) = 48x² + 308x + 496

Step 3: Find f(g(-4))

f(g(-4)) = 48(-4)² + 308(-4) + 496

f(g(-4)) = 48(16) - 1232 + 496

f(g(-4)) = 768 - 736

f(g(-4)) = 32

Answer:  see proof below

Step-by-step explanation:

[tex]x^a=y^b=z^c\ =k\\[/tex]

Then   [tex]x^a=k\qquad \rightarrow \qquad x=k^{\frac{1}{a}}[/tex]

and    [tex]y^b=k\qquad \rightarrow \qquad y=k^{\frac{1}{b}}[/tex]

and    [tex]z^c=k\qquad \rightarrow \qquad z=k^{\frac{1}{c}}[/tex]

 y³ = x · z

[tex](k^{\frac{1}{b}})^3=k^{\frac{1}{a}}\cdot k^{\frac{1}{c}}\\\\k^\frac{3}{b}}=k^{\frac{1}{a}+\frac{1}{c}}\\\\\\\bold{\dfrac{3}{b}=\dfrac{1}{a}+\dfrac{1}{c}}\quad \checkmark[/tex]

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Using this formula, we can write the equation of the circle with center (2, 4) and radius √215 as follows:(x - 2)² + (y - 4)² = (√215)²

Simplifying this equation, we get:(x - 2)² + (y - 4)² = 215

Thus, the standard form equation of this circle is (x - 2)² + (y - 4)² = 215.

The center of the circle is (2, 4) and the radius is √215.

To write the standard form equation of the circle, we use the formula (x - h)² + (y - k)² = r².

Plugging in the values of the center and radius, we get the equation (x - 2)² + (y - 4)² = 215.

What is Standard Form means?

Standard form refers to a specific way of writing mathematical equations, typically used in algebra. It involves representing an equation as a linear combination of variables and constants, where the variables are raised to the power of one and the coefficients are integers.

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Answer:

There are 192 employees in the company.

Step-by-step explanation:

Let x be the total number of employees

Use ratio and proportion

[tex]\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192[/tex]

x = 192

Answer:

The polygon has 9 sides (a regular nonagon).

Step-by-step explanation:

Angles in a Regular Polygon

A polygon with n sides has a total sum of internal angles equal to 180°(n-2). This means that each angle (in a regular polygon) measures

[tex]\displaystyle \frac{180(n-2)}{n}[/tex]

The regular polygon used by Dina for the logo is such that each interior angle measures 140°, thus:

[tex]\displaystyle \frac{180(n-2)}{n}=140[/tex]

Multiply by n:

[tex]180(n-2)=140n[/tex]

Operate:

[tex]180n-360=140n[/tex]

Reducing:

[tex]40n=360[/tex]

Solving:

n=9

The polygon has 9 sides (a regular nonagon).

66 is the correct answer

Answer:

x=-90

Step-by-step explanation:

The mean weight of 150 pounds is rejected. The evidence suggests that the mean weight is significantly different from 150 pounds.

To determine whether we can conclude that the mean weight of 150 pounds is rejected based on the given data, we need to perform a hypothesis test.

In this case, our null hypothesis (H0) is that the mean weight is equal to 150 pounds, and the alternative hypothesis (Ha) is that the mean weight is not equal to 150 pounds.

H0: μ = 150

Ha: μ ≠ 150

Where:

μ is the population mean

σ is the population standard deviation

n is the sample size

In this case, we have the following information:

Sample mean = 160

Population standard deviation (σ) = 50

Sample size (n) = 1600

Population mean (μ) = 150 (null hypothesis value)

Let's calculate the z-score:

z = (160 - 150) / (50 / √1600)

z = 10 / (50 / 40)

z = 10 / 1

z = 10

The z-score of 10 indicates that the sample mean is 10 standard deviations away from the null hypothesis mean of 150.

Next, we need to determine the critical value(s) for our hypothesis test. We choose a significance level, often denoted as α, which represents the probability of rejecting the null hypothesis when it is true. Let's assume a significance level of α = 0.05, commonly used in hypothesis testing.

For a two-tailed test at α = 0.05, the critical z-value(s) can be found by dividing α by 2 (since we are looking for values in both tails of the distribution). Using a standard normal distribution table or calculator, the critical z-value is approximately 1.96.

Since our calculated z-score (10) is greater than the critical z-value (1.96), we can reject the null hypothesis.

Therefore, based on the given data, we can conclude that the mean weight of 150 pounds is rejected. The evidence suggests that the mean weight is significantly different from 150 pounds.

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Answer:

19 = x :)

Step-by-step explanation:

(see attachment for explanation)

answer _------Three or more points , , , ..., are said to be collinear if they lie on a single straight line. .

Answer:

23 kids

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Since there are n sides and each exterior angle = [tex]\frac{5n}{2}[/tex] , then

n × [tex]\frac{5n}{2}[/tex] = 360 ( multiply both sides by 2 to clear the fraction )

5n² = 720 ( divide both sides by 5 )

n² = 144 ( take the square root of both sides )

n = [tex]\sqrt{144}[/tex] = 12

The polygon has 12 sides