identify the range of the function

Answer:

-198

Step-by-step explanation:

you will deal with the ones in the bracket first

that is [3×104]=312

[5×102]=510

312-510=-198

according to me there is no answer in your option my answer is negative198

Answer:

Step-by-step explanation:

2/310=5/c

simplify 2/310 into 1/155

1/155=5/c

cross product

155*5=1*c

775=c

c=775

---------------------------------

m/3=32/4

simplify 32/4 into 8,

m/3=8,

m=8*3=24

m=24

Answer:

34

Step-by-step explanation:

i just know t hat this is th answer

Answer:

width =5.5ft

length =18

Step-by-step explanation:

w=x

L=2x+7

area=w*L

99 = x(2x+7)

[tex]99=2x^{2} +7x[/tex]

[tex]2x^{2} +7x-99=0[/tex]

[tex]2x^{2} +18x-11x-99=0[/tex]

2x(x+9)-11(x+9)=0

(2x-11)(x+9)=0

2x-11=0

2x=11

x=11/2

x=5.5

L=2x+7=2*5.5+7=11+7=18

Answer:

A, C, F

Step-by-step explanation:

Answer:

1,3&6

Step-by-step explanation:

line

distance along a line

point

Answer: 9.5

Step-by-step explanation: 57 divided by 6 is 9.5

Answer:

216 sq. cm.

Step-by-step explanation:

If we fold the paper of the given dimensions then we will get a rectangular prism with dimension 10 cm by 6 cm by 3 cm.

Now, a rectangular prism has the total surface area given by  

A = 2(LW + WH + HL)

where, L = length = 10 cm.

W = width = 6 cm. and  

H = height = 3 cm.

Therefore, total surface area = A = 2(10 × 6 + 6 × 3 + 3 × 10) = 216 sq. cm. (Answer)

Answer:

216 sq. cm.

Step-by-step explanation:

Answer:

{6, 8, 10} is a set which represents the side length of a right triangle.

Step-by-step explanation:

In a right triangle:

[tex](Base)^{2}  + (Perpendicular)^{2}   = (Hypotenuse)^{2}[/tex]

Now, in the given triplets:

(a) {4, 8, 12}

Here, [tex](4)^{2}  + (8)^{2}   = 16 + 64  = 80\\\implies H = \sqrt{80}  =  8.94[/tex]

So, third side of the triangle   8.94 ≠ 12

Hence,  {4, 8, 12} is NOT a triplet.

(b) {6, 8, 10}

Here, [tex](6)^{2}  + (8)^{2}   = 36 + 64  = 100\\\implies H = \sqrt{100}  =  10[/tex]

So, third side of the triangle  10

Hence,  {6, 8, 10} is  a triplet.

(c) {6, 8, 15}

Here, [tex](6)^{2}  + (8)^{2}   = 36 + 64  = 100\\\implies H = \sqrt{100}  =  10[/tex]

So, third side of the triangle  10  ≠ 15

Hence,  {6, 8, 15} is  NOT a triplet.

(d) {5, 7, 13}

Here, [tex](5)^{2}  + (7)^{2}   = 25 + 49  = 74\\\implies H = \sqrt{74}  =  8.60[/tex]

So, third side of the triangle  8.60  ≠ 13

Hence, {5, 7, 13} is  NOT a triplet.

Answer:

3

Step-by-step explanation:

Answer: 6, 570

Step by step explanation:  If Minnie and Mickey have 5 girls and 5 boys every 3 weeks for 52 weeks this means they will have 17 pregnancies. At the end of one year Minnie and Mickey alone will have produced 170 children. It takes these children 6 weeks to grow up and be ready to reproduce. Every 6 weeks 10 new rats will be able to have children at a rate of 10 per 3 weeks. This means that a single set of 10 offspring will have 100 children every 3 weeks. There will be 8 sets of offspring that can reproduce before the year is over. This means if the sets have 100 children every 3 weeks starting with one set and adding one more set every 6 weeks, at the end of the year the offspring's offspring will total 6,400. 6,400 + 170 will equal 6,570. The total population is 6,570.

Answer:

√125 + 5 or 16.180

Step-by-step explanation:

√5 · 5 · 5 + √5 · 5

√25 · 5 + √25

√125 + 5 or 16.18

Answer:

False.  [tex]8x^2-36[/tex] is not a Linear expression.

Step-by-step explanation:

Given: [tex]8x^2-36[/tex]

we need to find whether it is a linear expression or not.

By Definition of Linear expression we say,

Linear expression is an algebraic expression where the power of variable(s) is equals to 1

Or we can say that:

Polynomial having power of variable(s) as 1, is known as Linear Expression

In the above expression the power of variable is 2 hence it is not a linear expression.

Hence the statement is False, the [tex]8x^2-36[/tex] is not a Linear expression.

Answer:16

Step-by-step explanation:

If 4x=18 then 4x-2=16

Answer:

The population will be 240,116

Step-by-step explanation:

Exponential growth can be represented by the expression:

[tex]P(t) = P_i\,(1+r)^t[/tex]

where:

[tex]P(t)[/tex] is the population at time (t)

[tex]P_i[/tex] is the initial value of the population

"r" is the annual rate of growth (written in decimal form)

and "t" is the time in years.

Therefore in this situation, P(16) is what we want to find [the population after 16 years]

the initial population [tex]P_i[/tex] is 110,000

the rate of growth is 0.05 [decimal form of 5%]

and t is 16 years.

Replacing all these in the given functional form gives:

[tex]P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116[/tex]

An exponential function to model a population of 110,000 that grows at 5% per year for 16 years is P(t) = 110,000 ∙ (1.05)^t. After 16 years, using this exponential function, the population would be approximately 242,884.

To model the population growth using an exponential function, we can use the formula P(t) = P0 ∙ (1 + r)t, where P(t) is the population after t years, P0 is the initial population, r is the growth rate, and t is the time in years. In this case, the initial population P0 is 110,000, the growth rate r is 5% (or 0.05), and the time t is 16 years.

The exponential growth function would be:

P(16) = 110,000 ∙ (1 + 0.05)16

To find the projected population after 16 years, we'll calculate:

P(16) = 110,000 ∙ (1.05)16
P(16) = 110,000 ∙ 2.20804
P(16) = 242,884.4

After rounding, the population would be approximately 242,884 after 16 years.

Answer: The wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]

Step-by-step explanation:

To calculate the wavelength of light, we use the equation:

[tex]\lambda=\frac{c}{\nu}[/tex]

where,

[tex]\lambda[/tex] = wavelength of the light  

c = speed of light = [tex]3\times 10^8m/s[/tex]

[tex]\nu[/tex] = frequency of light = [tex]3\times 10^{18}s^{-1}[/tex]

Putting the values in above equation, we get:

[tex]\lambda=\frac{3\times 10^8m/s}{3\times 10^{19}s^{-1}}=1\times 10^{-10}m[/tex]

Hence, the wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]

Answer:

1 x 10 ^-10 m

Step-by-step explanation:

Answer:

$5000

Step-by-step explanation:

A nickel is worth 5 cents, or 0.05 dollars.

Multiply the number of nickels by the worth of a nickel in dollars.

100,000 * $0.05

= $5000

Therefore, 100,000 nickels is worth $5000.

Answer:

THE ANSWER IS $5000

Step-by-step explanation:

A NICKLE IS WORTH 5 CENTS, OR $0.05. SO YOU MULTIPLY THE 100,000 BY THE WORTH OF NICKLES IN A DOLLAR. SO YOU DO 100,000 X 0.05= $5000. SO 100,000 NICKLES IS WORTH $5000.

Answer:

the answer is c

Step-by-step explanation:

Answer:

90°, 60°, and 30°

60°.

Step-by-step explanation:

The triangle ABC has side lengths √6, √2, and 2√2 units.

It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.

Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is [tex]\theta[/tex], then

[tex]\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} }  = \frac{1}{2}[/tex]

Hence, [tex]\theta[/tex] = 60°

Therefore, the three angles of the triangle are 90°, 60°, and 30°.

Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.

And in that case the base angle will remain 60°. (Answer)

Answer:

f=2

Step-by-step explanation:

1.25f+2.75f= 10-2

You must take positive two to the other side to get negative 2. Also, you should take the negative 2.75f to the other side to get positive 2.75f.

4f= 8

f= 2

Answer:

f=2

Step-by-step explanation:

Tj hit 85% of the balls pitched to him.

Step-by-step explanation:

Baseballs pitched to Tj = 20

Baseballs hit by Tj = 17

Percentage = [tex]\frac{baseballs\ hit\ by\ Tj}{baseballs\ pitched\ to\ Tj}*100\\[/tex]

Percentage= [tex]\frac{17}{20}*100[/tex]

Percentage=[tex]\frac{1700}{20} = 85\%\\[/tex]

Tj hit 85% of the balls pitched to him.

Keywords: percentage, division

Learn more about division at:

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Answer:

B

Step-by-step explanation:

Using the rules of exponents

[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

[tex]t^{-\frac{2}{7} }[/tex]

= [tex]\frac{1}{t^{\frac{2}{7} } }[/tex]

= [tex]\frac{1}{\sqrt[7]{t^{2} } }[/tex]

Answer:

OPTION B: y = [tex]$ \frac{1}{2} $[/tex]x - 2

Step-by-step explanation:

To find the equation of the line substitute the value of x and compare the corresponding value of y.

OPTION A:  

y = 2x + 4

Substitute x = 0. We get, 2(0) + 4 = 4

When x = 0, y = -2 [tex]$ \ne $[/tex] 4.

OPTION B:

y = [tex]$ \frac{1}{2} $[/tex]x - 2

Substitute x = 0, we get [tex]$ \frac{1}{2} (0) - 2$[/tex]

= -2

When x = 2, [tex]$ \frac{1}{2}(2) - 2 $[/tex] = 1 - 2

=-1

Similarly, When x = 4, [tex]$ \frac{1}{2}(4) - 2 = 2 - 2 $[/tex]

= 0.

Since, all the values are satisfied, OPTION B is the answer.

Substitute OPTION C and OPTION D. They do not satisfy the values either.

Answer:

Median = 46.5

Minimum = 32

Maximum = 62

Lower quartile = 38

Upper quartile = 59

Step-by-step explanation:

Before we can proceed to solving any of these, it is best you arrange your data first from least to greatest

32  34  37  39  41  45  48  53  58  60  61  62

First we have the median. The Median is the middle value. In this case we an even number of data, which is 12 data points. The middle value of the data would be found in between the 6th and 7th data point:

45 and 48

To get the middle value, you need to solve for the value that is in the middle of 45 and 48 by getting the sum of both numbers and dividing it by two.

45 + 48 = 93

93 ÷ 2 = 46.5

The minimum and maximum value is merely the least and greatest number.

Here we have:

Minimum = 32

Maximum = 62

To get the lower and upper quartiles, just remember that quartiles divide the data into 4 equal parts. All you need to do is find the value that is in between each quarters of the data:

            Q1 (Lower)  Q2(Median) Q3(Upper)

32  34  37 |  39  41  45 | 48  53  58 | 60  61  62

Like the median, we will find the value that comes in between each quarter.

Q1

37 + 39 = 76

76 ÷ 2 = 38

Lower quartile = 38

Q3:

58 + 60 = 118

118 ÷ 2 = 59

Upper quartile = 59

Answer:

the person on top has it right ^^^^^^^^^^ did the work and it right thx :))

Ben's gross income was $28,500.

Step-by-step explanation:

Sales for the month = $950000

Commission rate = 3%

Amount of commission = 3% of sales for the month

Amount of commission = [tex]\frac{3}{100}*950000[/tex]

Amount of commission = [tex]\frac{2850000}{100}[/tex]

Amount of commission = $28500

Ben's gross income was $28,500.

Keywords: percentage, division

Learn more about division at:

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The lengths of the sides are 24cm, 27cm and 30cm.

Step-by-step explanation:

The ratio of lengths is 8:9:10

Perimeter = 81 cm

Let x be the length of side.

Therefore,

The length of sides is 8x, 9x and 10x.

Perimeter is the sum of 3 sides, therefore,

[tex]8x+9x+10x=81\\27x=81[/tex]

Dividing both sides by 27;

[tex]\frac{27x}{27}=\frac{81}{27}\\x=3[/tex]

Therefore, the lengths of sides are [tex]8(3), 9(3)\ and\ 10(3)[/tex]

The lengths of the sides are 24cm, 27cm and 30cm.

Keywords: triangles, perimeter

Learn more about triangles at:

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The lengths of the sides of the triangle are 24 cm, 27 cm, and 30 cm.

To find the lengths of the sides of the triangle, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter. Let's assume the common ratio between the sides is 'x'. So, the lengths of the sides can be written as 8x, 9x, and 10x. According to the problem, the perimeter of the triangle is 81 cm.

Therefore, 8x + 9x + 10x = 81.

Combining like terms, we get 27x = 81.

Dividing both sides by 27, we find that x = 3.

Substituting this value back into the lengths of the sides, we find that the lengths are 8x = 8(3) = 24 cm, 9x = 9(3) = 27 cm, and 10x = 10(3) = 30 cm.

Answer:

Step-by-step explanation:

[tex]x,\ y-numbers\\\\\text{The system of equations:}\\\\\underline{+\left\{\begin{array}{ccc}x+y=126\\x-y=42\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=168\qquad\text{divide both sides by 2}\\.\qquad x=84\\\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\84+y=126\qquad\text{subtract 84 from both sides}\\y=42[/tex]

Final answer:

The two numbers that have a sum of 126 and a difference of 42 are 84 and 42.

Explanation:

To find the two numbers whose sum is 126 and whose difference is 42, we can set up a system of equations:

x + y = 126 (Sum of the numbers)

x - y = 42 (Difference of the numbers)

By adding these two equations, we can eliminate y and solve for x:

x + y + x - y = 126 + 42

2x = 168

x = 84

Now that we have the value of x, we can find y by substituting x back into either of the equations. For example:

84 + y = 126

y = 126 - 84

y = 42

Therefore, the two numbers are 84 and 42.

Answer:

The weekly savings of first person = $900

The weekly savings of second person = $700.

Step-by-step explanation:

Let us assume the income of first person = $ m

Now, as the difference in the income is $200.

⇒ And the income of first person  -  income of first person =  $200

⇒ Income of second person    =    m -  $200

So, according to the question:

Ratio of   Income of First person : Second Person's Income  =  9: 7

or, m : ( m - 200)   =  9: 7  

[tex]\implies  \frac{m}{m - 200 }  = \frac{9}{7}[/tex]

[tex]7 \times m = (m - 200) \times 9\\\implies 7 m = 9m - 1800\\\implies 7m - 9m = -1800\\\implies -2m = -1800\\m = \frac{1800}{2}   = 900[/tex]

or,m = $900

Hence, the weekly savings of first person = $900

and the weekly savings of second person = m - 200 = $900 - 200 = $700.

Final answer:

To find the weekly incomes of two persons with a ratio of 9:7 and a difference of $200, represent their incomes as 9x and 7x. Solving for x, we get $100, so their incomes are $900 and $700 respectively.

Explanation:

The question asks us to solve for the weekly incomes of two persons given that the ratio of their incomes is 9:7 and the difference between their incomes is $200.

Let's represent the incomes of the two persons as 9x and 7x respectively, where x is a common multiplier. According to the information provided,

9x - 7x = $200

Solving for x:

(9x - 7x) = 2x

2x = $200

x = $200 / 2

x = $100

Now calculating each person's income:

Person A: 9x = 9 * $100 = $900

Person B: 7x = 7 * $100 = $700

Therefore, the weekly incomes of the two persons are $900 and $700 respectively.

Answer:

(a) P  =  - 200 T + 9,400

(b) After 22  months the student  will owe $5000.

Step-by-step explanation:

Here, the amount loaned out to the student = $9,400

The installment amount of each month  = $200

(a) P : Amount remaining to be paid

    T: time in months

Now, the remaining amount = Actual amount - Amount paid in T months

or,      P = 9,400 - $200 (T)

⇒ P  =  - 200 T + 9,400 ( y = mx + C form)

(b) The remaining amount left = $5000

As we know, P = 9,400 - $200 (T)

⇒ 5,000 = 9,400 - 200 T

⇒200 T = 9,400 - 5,000 = 4,400

⇒ T = 4400/200 =  22

or T = 22 Months

Hence,  After 22  months the student  will owe $5000.

Answer:

33.33%

Step-by-step explanation:

The value of a variable change from 12 units to 16 units in a month.

We have to calculate the percentage increase for that month.

Therefore, the increase of value from 12 to 16 means by (16 - 12) = 4 units

So, the percentage increase for the month is [tex]\frac{4}{12} \times 100 = 33.33[/tex]%. (Rounded to the two decimal). (Answer)

Answer:

[tex]\large\boxed{\log_6\dfrac{1}{36}=-2}[/tex]

Step-by-step explanation:

[tex]\text{We know:}\\\\\log_ab=c\iff a^c=b\\\\\log_6\dfrac{1}{36}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_636^{-1}=\log_6(6^2)^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\log_66^{(2)(-1)}=\log_66^{-2}\qquad\text{use}\log_ab^n=n\log_ab\\\\=-2\log_66\qquad\text{use}\ \log_aa=1\\\\=-2(1)=-2[/tex]

[tex]\log_6\dfrac{1}{36}=-2\ \text{because}\ 6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}[/tex]

The solution of logarithmic function is, - 2

We have to given that,

Logarithmic function is,

⇒ log ₆ (1/36)

Now, We can apply the logarithmic rule to solve as,

⇒ log ₆ (1/36)

⇒ log ₆ (36)⁻¹

⇒ log ₆ (6)⁻²

⇒ - 2 log ₆ (6)

⇒ - 2 × 1

⇒ - 2

Therefore, The solution of logarithmic function is, - 2

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