(. means multiply)

The** simplification **of the equation [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex] is 2453.5.

How to simplify the equation?

Consider the **equation** [tex]\frac{(7^{2}.3-1 )^{4} }{(3^{2}.7-6)^{3} }[/tex]

Solve for **Numarator** [tex](7^{2} .3-1)^{4}[/tex]= [tex](7^{2} .3-1)^{2} (7^{2} .3-1)^{2}[/tex]

= [tex](147-1)^{2}[/tex][tex](147-1)^{2}[/tex]

= (21316) (21316)

Solve for** Denominator ** [tex](3^{2}.7-1)^{3\\}[/tex]

= [tex](63-6)^{3}[/tex]

= 57³

Solve both, and** simplify** the equation.

= [tex]\frac{(21316) (21316)}{185193}[/tex]

= 2453.5

∴ Simplification is 2453.5

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In the problems below, copy the problems and the picture, mark the givens, and prove the statements.

**Answer:**

**Step-by-step explanation:**

Givens

OF = RF

OU = UR

Draw a line from U to F

UF = UF Reflexive property.

Solution

ΔOUF = ΔRUF SSS

<O = < R Congruent parts are congruent when the triangles are congruent.

Please answer if blurry let me know

**Answer:**

[tex]P'(-6,4)[/tex]

**Step-by-step explanation:**

P(x,y) -> rotate 90 degrees -> P'(-y,x)

P'(-6,4)

:]

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Determine the minimum sample size required when you want to be % confident that the sample mean is within one unit of the population mean and. Assume the population is normally distributed.

The **minimum sample size** of the given condition is 89.

In given condition,

For 95% **confidence level**, critical value of z is z* = 1.96

The margin of **error** given is E = 1

Standard deviation ( α ) = 4.8

Final required sample size is;

n = [tex](\frac{z*\alpha }{E} )^{2}[/tex]

= [tex](\frac{1.96 * 4.8}{1} )^2[/tex]

= 88.51

n ≅ 89

The **minimum sample size** of the given condition is 89.

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Evaluate. Write your answer as a whole number or as a simplified fraction.

**Answer:**

1000

**Step-by-step explanation:**

Hello!

Use the **Quotient Property of Exponents** to evaluate the expression:

[tex]\frac{a^b}{a^c} = a^{b-c[/tex]

In this case, a is 10, b is 5, and c is 2.

Evaluate:[tex]\frac{10^5}{10^2}[/tex][tex]10^{5-2}[/tex][tex]10^3[/tex]If we simplify 10³, we should get **1000**.

the head of institutional research at a university believed that the mean age of full-time students was declining. in 1995, the mean age of a full-time student was known to be 27.4 years. after looking at the enrollment records of all 4934 full-time students in the current semester, he found that the mean age was 27.1 years, with a standard deviation of 7.3 years. he conducted a hypothesis of : 27.4 years versus : 27.4 years and obtained a p-value of 0.0020. he concluded that the mean age of full-time students did decline. is there anything wrong with his research?

No, there is nothing wrong in the research that is done by the head of the institution. He said correct that the **mean **age of the full time students has declined.

Given above that a university's director of institutional research thought that the average age of full-time students was lowering. The average age of a full-time student in 1995 was 27.4 years old.

He registered all 4934 pupils for this and the average age was 27.1 years.

The fact that the inquiry concerns the average age of a full-time student makes this situation ideal. This is a trustworthy approach when the **mean** is calculated after accounting for all full-time students at the university.

Given that this is a left-tailed test, the hypothesis is also correct.

He rejected the null hypothesis because p = 0.0020.05.

The average age did decrease, in conclusion. The situation is ideal.

Therefore his hypothesis is absolutely correct. There is nothing wrong with it.

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solve for t

300,000 = 300 (1+.0375/12) ^ (12t) / (.0375/12)

If the **equation **be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the **value **of t = 30.43236.

Let the **equation **be

[tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]

**Multiply **both sides by 0.0375 / 12, and we get

[tex]$300000 \cdot \frac{0.0375}{12}=\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{\frac{0.0375}{12}} \cdot \frac{0.0375}{12}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{1875}{2}=300\left(1+\frac{0.0375}{12}\right)^{12 t}$$[/tex]

Switch sides of the equation,

[tex]$300\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{1875}{2}$$[/tex]

**Divide **both sides by 300, and we get

[tex]$\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{300}=\frac{\frac{1875}{2}}{300}$$[/tex]

Simplifying the above equation, we get

[tex]$\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{25}{8}$$[/tex]

Apply **exponent rules**, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right)$$[/tex]

Solving the above equation, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right): \quad t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$[/tex]

[tex]$t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$$[/tex]

simplifying the above value of t, we get

t = 30.43236.

If the **equation **be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the **value **of t = 30.43236.

Therefore, the **value **of t = 30.43236.

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The current population of a city is about 2,130,000 people, and it's increasing at a rate of 10 percent per year. Arrange the steps in the correct order to

show how to determine the population of the city in five years.

The **population** of the city in 5 years is 3430386 as the **population** is **increasing** 10% per year

**What is percentage and how to calculate?**

**Percentage** is the **ratio** which can be expressed as **fraction** of 100. And to calculate **percentage** we **multiply** by 100.

We are given that **population** of a city is 2130000

And the population is **increasing** at a rate of 10%

We are asked to find the population after 5 years

The **equation** can be given as (1.1)^x*2130000

We put x =5

We get

[tex](1.1)^5*2130000\\1.61051*2130000\\=3430386[/tex]

Hence the **population** will be 3430386 after 5 years at a rate of 10% increase per year

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Need help! Finding Missing Angles !

**Step-by-step explanation:**

Since right angles are 90°

11 = 90°

12 = 90°

13 = 90°

A cylinder with radius r and height h is inscribed in a cone with radius of 4m and height of 10m. Express the volume V of the cylinder as a function of h.

The** volume of the cylinder** is **502.4m³**

**Volume of the cylinder:**

Volume of the cylinder can be calculated by the product of the area of base and height.

For any cylinder with base **radius **‘r’, and **height **‘h’, the volume will be base times the height.

**V = πr²h cubic units.**

Given,

A cylinder with radius r and height h is inscribed in a cone with radius of 4m and height of 10m.

Here we need to find the volume of the cylinder,

We know that the values of,

Radius = 4m

height = 10m.

Now we have to apply the value on the formula, then we get,

V = π x (4)² x 10

Apply the value of π as 3.14 then we get,

V = 3.14 x 16 x 10

V = 502.4

Therefore, the volume of the cylinder is 502.4 m³.

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I have no idea what I’m doing And could use help! Anyone who takes time out of their day to help I appreciate you!!

**Answer: It is impossible for two obtuse angles to be a straight angle**

**Step-by-step explanation:**

**Definition of a straight angle: An angle that is exactly 180 degrees**

**Definition of obtuse angle: An angle that is more than 90 degrees**

**1) X = obtuse angle**

x > 90

Set minimum to test:

x = 91

**2) Set up the question**

**(<= less than or equal to)**

2x <= 180

**3) Sub the first equation**

2(91) <= 180

**182 <= 180**

**4) Answer the question**

**It is impossible for two obtuse angles to be a straight angle**

Solve the inequality.8(x-1) >12(x-2)

SOLUTION

Solve the inequality.

[tex]8(x-1)>12(x-2)[/tex][tex]\begin{gathered} 8(x-1)>12(x-2) \\ 8x-8>12x-24 \\ 8x-12x>-24+8 \\ -4x>-16 \end{gathered}[/tex]divide both sides by -4

[tex]\begin{gathered} -4x>-16 \\ x<\frac{16}{4} \\ x<4 \end{gathered}[/tex]Carlos sold half of his comic books then bought 14 more. He now has 33 comics books. How many did he start with?

Answer: Carlos started with 38 comic books.

Step-by-step explanation:

33 - 14 = 19

19 x 2 = 38

PLEASE HELP ME IT WOULD MAKE MY MONTH!!! ILYSM

How many pounds of apples will he get if he goes to David’s orchard?

**Answer:**

David's orchid: 20 +x

Pam's orchid: 25 + 0.75x

**Step-by-step explanation:**

**Framing linear equations:**

** **Cost of first 10 pounds = 10 * 2 = $ 20

Let the weight of additional apples picked = x pounds

Cost of 'x' pounds = 1 * x = $ x

Total cost = cost of first 10 pounds + cost of additional 'x' pounds

= 20 + x

Pam's orchid:Entry fee = $ 10

Cost of first 10 pounds = 10 * 1.50 = $ 15

Cost of 'x' pounds = 0.75*x = 0.75x

Total cost = Entry fee + cost of first 10 pounds + cost of additional 'x' pounds

= 10 + 15 + 0.75x

= 25 + 0.75x

** **

Add parentheses to make true3 + 4 × 2 = 1472 ÷ 12 - 6 = 12

We want to find where to put the parentheses on each expression to make the expression true.

First, we identify the symbols +, x, / and - to identify the pairs of numbers. For example, in the expression

[tex]3+4\cdot2[/tex]we have two symbols (+, *).

Now, this would give us two pairs of expression where we can put the parentheses. That is, one possibility per symbol. So we have

[tex](3+4)[/tex]and

[tex](4\cdot2)[/tex]Now, let us try the first choice. Remember that first we have to evaluate what is inside the parentheses. This would give us

[tex](3+4)\cdot2=7\cdot2=14[/tex]which coincides to the value we wanted.

In the second case, we have the following symbols / and -

This would give us two pairs for grouping, namely

[tex](72/12)[/tex]and

[tex](12\text{ -6)}[/tex]as before, we will first evaluet the first option

[tex](\frac{72}{12})\text{ - 6=6 -6 =0}[/tex]If we try the second option, we woud get

[tex]\frac{72}{(12\text{ -6)}}=\frac{72}{6}=12[/tex]which would give us the correct value.

A model car has a list price of $46.20. The model is on

sale at 15% off. Find the total cost to the nearest cent

after a 4.5% sales tax is added to the sale price.

** Answer:The total cost is $41.04 **

**Step-by-step explanation:**

Using the graph, determine the coordinates of the x-intercepts of the parabola.

**Answer:**

2 points

Step-by-step explanation:

According to the graph, the parabola has two x-intercept, where is (0,-2) and (0,-8).

PLEASE HELP QUICK. NOW NEEDED

pls tell me u understand the drawing

According to the Empirical Rule, what percent of values in a normal distribution will fall between 1 standard deviations above the mean and 3 standard deviations above the mean?

According to the **Empirical Rule**, 99.7% percent of values in a normal distribution will fall between 1 **standard deviations** above the **mean** and 3 standard deviations above the mean.

The** Empirical Rule** is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:

In this context, we can reasonably infer and logically deduce that 99.7% of a normal distribution would fall within three (3) **standard deviations** of its **mean **in accordance with the **Empirical Rule**.

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find the indicated sum in each sequence 7,10,17,27,44,71,115...,a10

The **sequence** of **numbers**, 7, 10, 17, 27, 44, 71, 115... in which each new term is given by the **sum** of the previous two terms, gives the sum of the first 10 terms as 1,265

A **number sequence** consists of a **listing** of numbers that are connected to each other by a rule.

The given sequence is presented as follows;

7, 10, 17, 27, 44, 71, 115..., [tex] a_{10}[/tex]

From the given sequence, we have;

a_n = a_{(n-1)} + a_{(n-2)}

The **first** 10 **terms** of the **sequence** is therefore;

7, 10, 17, 27, 44, 71, 115, (71+115), (115+(71+115)), ((71+115)+(115+(71+115)))

Which gives;

7, 10, 17, 27, 44, 71, 115, 186, 301, 487

The sum of the first 10 terms of the sequence is therefore;

7 + 10 + 17 + 27 + 44 + 71 + 115 + 186 + 301 + 487 = 1265

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Factor by Grouping.. I know there is no common GCF but i don't know how to continue!

xy^2 − 3xy − 6y + 18

**Answer:**

(xy-6)(y-3)

**Step-by-step explanation:**

i don't know if you needed this, but if you need this i can explain step by step

xy(y-3)-6(y-3). we take the common ones out and than simplify as:. (xy-6)(y-3)

One card is drawn from a standard deck of 52 cards. Find the probability of drawing the following. an eight or a diamond

The probability of a simple event to occur is this:

[tex]P(x)=\frac{\text{total number of favorable outcomes}}{\text{total }number\text{ of possible outcomes}}[/tex]In the question given, the favorable outcomes are either 8 or diamond.

In a deck of cards, there are 13 diamond cards and 4 eights however one of the diamond cards is also 8. Therefore, total favorable outcome is 13 + 4 - 1 = 16.

Of course, the total number of possible outcomes is 52. So, the probability of getting an eight or a diamond is:

[tex]p(x)=\frac{16}{52}=\frac{4}{13}\approx0.3077[/tex]**The probability, in fraction, is 4/13. **

**In decimal form, it is 0.3077. **

**In percentage form, it is 30.77%**

Solve using augmented matrices.

x+y=1

3x-y=7

The **solution **to the system of **equation **{x + y = 1, 3x - y = 7 } using augmented matrices is ( 2,-1 ).

Given the system of **equation **in the question;

x + y = 1

3x - y = 7

First, we write the system of **equation **in **matrix form**.

[tex]\left[\begin{array}{ccc}1&1&1\\3&-1&7\\\end{array}\right][/tex]

Next, we find the reduced row echelon form

Row operation R₂ = R₂ - 3R₁ to make the entry at 2, 1 a 0.

[tex]\left[\begin{array}{ccc}1&1&1\\3-3*1&-1-3*1&7-3*1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&-1\4&4\\\end{array}\right][/tex]

Next, multiply each element of R₂ by -1/4 to make the entry at 2, 2 a 1.

[tex]\left[\begin{array}{ccc}1&1&1\\-\frac{1}{4}*0 &-\frac{1}{4}*-4 &-\frac{1}{4}*4 \\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&1&-1\\\end{array}\right][/tex]

Now, perform the operation, R₁ = R₁ - R₂, to make the entry at 1,2 a 0.

[tex]\left[\begin{array}{ccc}1-0&1-1&1+1\\0&1&-1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&0&2\\0&1&-1\\\end{array}\right][/tex]

Using the result from the **matrix**, **x **= 2 and **y **= -1.

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X-intercept

Find f(-2)

Find x for f(x)=2

By using the **graph **we can see:

First, we want to find the value of x such that the graph touches (**intercepts**) the x-axis.

On the graph, we can see that it intercepts the x-axis at x = 0, so that is the x-intercept.

Now we want to find f(-2), this is the value of the **function **when x = -2, to find that we first need to find x = -2 in the horizontal axis.

f(-2) = 4

Now we want to find the value of x such that:

f(x) = 2

so now we need to find 2 in the vertical axis. we can see that the **function **is equal to 2 for x = -1.3 (approximation).

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The diameter of a basketball rim is 18 inches. What is the circumference of the rim? Write your answer using pi. Show your work.

Answer: 18Pi

Explanation:

The equation of the circumference of a circle is 2 x Pi x radius

The radius is one half of the diameter. So to find the radius we can divide the diameter by 2.

18 divided by 2 is 9

So to find the circumference we can just do Pi x 9 x 2

9 x 2 = 18

So the answer is 18Pi, or 56.52

Explanation:

The equation of the circumference of a circle is 2 x Pi x radius

The radius is one half of the diameter. So to find the radius we can divide the diameter by 2.

18 divided by 2 is 9

So to find the circumference we can just do Pi x 9 x 2

9 x 2 = 18

So the answer is 18Pi, or 56.52

**Answer:**

18 pi

**Step-by-step explanation:**

2xpixr d divided by 2 equals 9 pi x 2 x 9 =18

-4(w + 5) + 5w simplify use distributive property

**Answer:**

w - 20

**Step-by-step explanation:**

**Remove the parenthesis **by multiplying each term of (w + 5) by (-4)

-4(w + 5) + 5w = -4*w + 5*(-4) + 5w

= -4w - 20 + 5w

= -4w + 5w - 20

**Combine **like terms. **Like terms** have same variable with same power.

= w - 20

the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group. now using only theorems about the structure of cyclic groups, describe each of the subgroups of u(49) by specifying its order and by giving an explicit generator. do not repeat any of the subgroups — in other words, present each subgroup exactly once

then the **generator **is the element which can generate whole set

therefore U(49) has 12 generator

What is meant by **cyclic group**?

A cyclic group is a group that can be generated by a single element. (the group generator). **Cyclic groups **are Abelian.

the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group.

elements of U(49) are {1,2,3,5,,7,11,,13,17,19,23,29,31,37,39,,41,47}

then the generator is the element which can generate whole set

therefore U(49) has 12 **generator**

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Hurry Pls) Enter the rational number as

a/b where a and b are integers.

7 1/3

(Note: this isn't my work, it's my siblings and I have no idea how to answer it.)

The rational number of 7¹/₃ as; a/b where a and b are integers.

How to convert a rational number?A **rational number** is defined as any number that can be written as a fraction, where both the **numerator** (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero

Now, we are given the fraction as; 7¹/₃

This given number is expressed as a mixed fraction and so we convert it to **improper fraction** to get; 22/7

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Which method can't you use to solve this problem? x^2 + 7x =0

A) Factoring

B) Square roots

C) Quadratic formula

It should be B)Square Roots!

Hope this helps :)

Hope this helps :)

please answer the question below the top question. on both.

The **value of x **is 6 degrees.

It is given in the question that:-

HI is **parallel** to JK and FG is the** transversal** intersecting HI at L and JK at M.

∠LMK = 115 degrees

∠MLI = (8x + 17) degrees

We have to find the value of x.

We know that,

**Angles** on the same side of the transversal sum up to 180 degrees.

Hence, we can write,

∠LMK + ∠MLI = 180 degrees.

115 + (8x + 17) = 180 degrees

8x + 132 = 180 degrees

8x = 180 - 132

8x = 48 degrees

x = 48/8 degrees

x = 6 **degrees**

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Consider the chart of millionaires and population

The number of **millionaires** Los Angeles should have will be **equal** to 5,065 millionaires.

**Proportion** may be defined as part or share of a complete unit compared with respect to the **whole unit**. A proportion is basically the equality of ratios. Two different **ratios** can be treated as equals if they are in **proportion** to each other. Now, the number of **millionaires** in Los Angeles will be equal to the Proportion of Millionaires in Dubai **multiplied **by the Population of Los Angeles that is

= 0.00124 × 4,085,014

= 5,065 millionaires

The Data and Calculations will be given as:

**City ** **Millionaires** **Population** **Proportion**

Los Angeles 11,560 4,085,014 0.00283 (11,560/4,085,014)

Casablanca 6,900 3,752,357 0.00184 (6,900/3,752,357)

Berlin 6,750 3,562,038 0.00189 (6,750/3,52,038)

Dubai 3,570 2,878,344 0.00124 (3,570/2,878,344)

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**Complete Question:**

**City Millionaires Population**

**Los Angeles 11,560 4,085,014**

**Casablanca 6,900 3,752,357**

**Berlin**

**6,750**

**3,562,038**

**Dubai**

**3,570**

**2,878,344**

**Consider the chart of Millionaires and Population. If Los Angeles were**

**proportional to Dubai with respect to population, how many millionaires**

**should we expect Los Angeles to have? Round your answer to a whole number.**

When you get through kiss back there? BLACK BOY CHPATER 2 WHAT IT MEAN!???? PLEASEEEE!!!!
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