CAN YOU HELP ME
Explain the differences between expressions and equations.

Answer:

(9x - 1)²

Step-by-step explanation:

If you can tell, the square root of 81 is 9. This should be a clue that the polynomial could be one binomial squared. If you tried factoring starting out with 9x in both parenthesis, you could see that you would get (9x - 1)² as your answer.

Answer:

(9x-1)²

Step-by-step explanation:

81x² - 18x + 1= (9x)²- 2*9x+1²= (9x-1)²

The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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Answer:

20. A. 357.8 in³

B. 1231.5 yd³

Step-by-step explanation:

20.

A.

Volume of Pyramid : ⅓*base area * height

here,

Base area = area of rectangle=length*breadth =10*8=80in²

Now

Height can be calculated by using Pythagorous theorem

height =\(\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}\)

height =\(\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in\)

height =13.4 in

Now

Volume of pyramid = ⅓*base area *height

Volume of Pyramid=⅓*80*13.42

Volume of Pyramid=357.8 in³

B.

Volume of cone = ⅓*area of base* height

Here

slant height=24 yd

height =?

diameter=14yd

radius =14/2=7 yd

Let's find the height:

By using the Pythagorous theorem,

slight height²=radius²+height²

substituting value

25²=7²+height²

height²=25²-7²

height =\(\sqrt{576}\)=24 yd

Now

Area of Base= πr²=π*7²=153.94 yd²

Now

Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³

So,

Volume of cone is 1231.52 yd³.

Answer:

(See bolded numbers)

Factoring -1 out of negative numbers:

11) (-6) • (3)= (-1 • 6) • 3= -1 • 6 • 3= -18

-6 is the negative number here and factoring out -1 from -6 will give us -1(6). In the second last step, multiply 6 and 3 together then multiply the product by -1.

-1(6 ×3)= -1(18)= -18

12) (-4) • (-8)= (-1 • 4) • (-1 • 8)= 1 • 4 • 8= 32

Multiplying 2 negative numbers will give us a positive number. The 3rd step is 1 as (-1)(-1)= 1.

13) (-9) • (-5)= (-1 • 9) • (-1 • 5)= 1 • 9 • 5= 45

14) (2) • (-8)= 2 • (-1 • 8)= -1 • 2 • 8= -16

Negative numbers are numbers with a negative sign and are numbers less than zero. Factoring -1 out of negative numbers will leave us with the positive number.

The people that would not be sampled would be:

We have to do this by considering the people that would be seen present in the roster of the school. The people that are dropouts as well as homeschooled cannot appear in a school register because they are not students.

The students that are sick and on the trip are all students of the high school so they can be included in the sampling that is being done by the school.

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Answer:

3. f(3) = 16

4. h(3) = 4

Step-by-step explanation:

3.

f(x) = x² + 7

f(3) = 3² + 7

f(3) = 16

4.

h(x) = 12/x

h(3) = 12/3

h(3) = 4

Answer:

A.  True

Step-by-step explanation:

Figure D follows the congruence transformation of the rule

(x, y) → (-x, y)

Option D is the correct answer.

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Congruence transformation follows the rule (x, y) → (-x, y).

Figure A is a reflection that follows the rule (x, y) → (x, -y).

Figure B is a reflection that follows the rule of (x, y) → (x + 4, y).

Figure C is a reflection that follows the rule of (x, y) → (x - 7, y).

Figure D is a reflection that follows the rule of (x, y) → (-x, y)

Thus,

Figure D follows the congruence transformation of the rule

(x, y) → (-x, y)

Option D is the correct answer.

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The opposite angles of a rhombus are congruent

It is true that rhombus ABCD is a square

A rhombus has the following features

The above highlights mean that:

So, the four angles in the rhombus are right angle, and the side lengths are equal.

Hence, the rhombus is a square

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(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer: A = 7x

Step-by-step explanation:

Area = Length x  Width

A = L * W

L = 5x + 1        W = x

Plug the length and width into the equation for area.

A = (5x + 1) * x

A = 6x + x

A = 7x

Answer:

80 mm²

Step-by-step explanation:

Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.

Answer:

120 Girls

Step-by-step explanation:

First, you have to combine the dark shade girls and the light shade girls together to get 7.

Then, you should divide 210 by 7, to get 30

Finally, using 30 as your multiplier,

you go and multiply 30 x 4 to get 120 girls :D

The equation representing the situation is y = 240 - 5x

the amount reaming is 195 connecting cubes

The equation is written from the following information

there are 240 connecting cubes in the box

five students each take 9 connecting cubes from the box

let the number of box be x such that

5x = 5 students each taking from the box

let the number remaining be y

y = 240 - 5x

for x = 9

y = 240 - 5 * 9

y = 240 - 45

y = 195

The connecting cubes remaining after each of the 5 students take 9 is 195 connecting cubes

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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Answer:

83.4

Step-by-step explanation:

Answer:

10x - 2y

Step-by-step explanation:

simplify the expression.

8x–2y + x + x

combine numbers that have the same variables

8x + x + x

*those x have 1 coefficient each.

it will be 8x+1x+1x = 10x then –2y

10x–2y.

Hope it helps :)

Answer:

736

Step-by-step explanation:

25*32=800

16*4=64

800-64

\(57=\cfrac{5}{8}z+7\implies 57=\cfrac{5z}{8}+7\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8(57)=8\left( \cfrac{5z}{8}+7 \right)} \\\\\\ 456=5z+56\implies 400=5z\implies \cfrac{400}{5}=z\implies 80=z\)

Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5

Answer:

angles 4 is 88 degrees

Angles 3 is 92 degrees

Step-by-step explanation:

all 3 of angles of a triangle equal 180

47+45=92

180-92=88

Angles 4 is 88 degrees

Now since 3 is on a flat plane next to 4 we subtract 88 from 180 to find angle 3

180-88=92

92 degrees is angle 3

Hopes this helps please mark brainliest

Answer:

We conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.

Step-by-step explanation:

We are given that slab avalanches studied in a region of Canada had an average thickness of μ = 66 cm.

A random sample of avalanches in spring gave the following thicknesses (in cm);

X: 59, 51, 76, 38, 65, 54, 49, 62, 68, 55, 64, 67, 63, 74, 65, 79.

Let \(\mu\) = true mean slab thickness in the Vail region

So, Null Hypothesis, \(H_0\) : \(\mu\) = 66 cm      {means that the mean slab thickness in the Vail region is the same as that in the region of Canada}

Alternate Hypothesis, \(H_A\) : \(\mu\) \(\neq\) 66 cm      {means that the mean slab thickness in the Vail region is different from that in the region of Canada}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                             T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean thickness = \(\frac{\sum X}{n}\) = 61.81 cm

             s = sample standard deviation = \(\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }\) = 10.64

             n = sample of avalanches = 16

So, the test statistics =  \(\frac{61.81-66}{\frac{10.64}{\sqrt{16} } }\)  ~  \(t_1_5\)

                                    =  -1.575

The value of t-test statistics is -1.575.

Now, at a 1% level of significance, the t table gives a critical value of -2.947 and 2.947 at 15 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.

39x - 11 = 17x + 6

Answer is A

A probability mass function (pmf) for a random variable X must satisfy the following two conditions:
1. f(x) ≥ 0 for all x
2. Σf(x) = 1

(a) f(x) = x/c
To find the constant c, we can use the second condition and sum over all possible values of x:
Σf(x) = Σ(x/c) = 1/c Σx = 1
Since we don't have a specified range for x, we cannot solve for c.

(b) f(x) = cx
Again, we can use the second condition to find the constant c:
Σf(x) = Σ(cx) = cΣx = 1
Without a specified range for x, we cannot solve for c.

(c) f(x) = c(1/4)^x
Using the second condition:
Σf(x) = Σ(c(1/4)^x) = cΣ(1/4)^x = 1
We can use the formula for an infinite geometric series to find the sum:
Σ(1/4)^x = 1/(1 - 1/4) = 4/3
So, c = 3/4

(d) f(x) = c(x + 1)^2
Using the second condition:
Σf(x) = Σ(c(x + 1)^2) = cΣ(x + 1)^2 = 1
Without a specified range for x, we cannot solve for c.

(e) f(x) = x/c
This is the same as part (a), so we cannot solve for c without a specified range for x.

(f) f(x) = c/(x+1)(x+2)
Using the hint, we can rewrite f(x) as:
f(x) = c(1/(x+1) - 1/(x+2))
Using the second condition:
Σf(x) = Σ(c(1/(x+1) - 1/(x+2))) = cΣ(1/(x+1) - 1/(x+2)) = 1
We can use the formula for a telescoping series to find the sum:
Σ(1/(x+1) - 1/(x+2)) = 1 - 1/(x+2)
As x approaches infinity, the sum approaches 1.
So, c = 1

To depict each pmf as a line graph, we would plot the values of f(x) on the y-axis and the values of x on the x-axis. However, without a specified range for x, we cannot create accurate graphs for parts (a), (b), (d), and (e). For part (c), the graph would be a decreasing exponential curve, with f(x) approaching 0 as x increases. For part (f), the graph would be a decreasing curve, with f(x) approaching 0 as x increases.

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Answer:

a) \( P(X \geq 1) = 1-P(X<1) = 1-P(X=0)\)

\(P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}\)

And replacing we got:

\( P(X \geq 1) =1 -1x10^{-18} \approx 1\)

b) \(P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355\)

\(P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047\)

\(P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517\)

And adding we got:

\( P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992\)

c) \( P(X \leq 8) =1 -P(X>8) = 1-P(X=9)\)

\(P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517\)

And replacing we got:

\( P(X \leq 8)= 1-0.913517=0.086483\)

Step-by-step explanation:

Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:

\(X \sim Binom(n=9, p=0.99)\)

The probability mass function for the Binomial distribution is given as:

\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)

Where (nCx) means combinatory and it's given by this formula:

\(nCx=\frac{n!}{(n-x)! x!}\)

Part a

We want to find this probability:

\( P(X \geq 1) = 1-P(X<1) = 1-P(X=0)\)

\(P(X=0)=(9C0)(0.99)^0 (1-0.99)^{9-0}=1x10^{-18}\)

And replacing we got:

\( P(X \geq 1) =1 -1x10^{-18} \approx 1\)

Part b

\( P(X \geq 7)= P(X=7) +P(X=8)+ P(X=9) \)

\(P(X=7)=(9C7)(0.99)^7 (1-0.99)^{9-7}=0.003355\)

\(P(X=8)=(9C8)(0.99)^8 (1-0.99)^{9-8}=0.083047\)

\(P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517\)

And adding we got:

\( P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992\)

Part c

\( P(X \leq 8) =1 -P(X>8) = 1-P(X=9)\)

\(P(X=9)=(9C9)(0.99)^9 (1-0.99)^{9-9}=0.913517\)

And replacing we got:

\( P(X \leq 8)= 1-0.913517=0.086483\)

Answer:

13lb 2oz

Step-by-step explanation:

Using the Empirical Rule, the percentage of students who scored greater than 700 is:

b. 2.5%

It states that, for a normally distributed random variable:

700 is two standard deviations above the mean. 5% of the measures are more than two standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of these measures are below 300 and 2.5% are above 700, hence option B is correct.

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Answer:

5

Step-by-step explanation:

5 + 2 = 7

7(3) = 21

_

5 + 16 = 21