Which two of the following expressions can be simlified by using the Quotient of Powers Property?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies \begin{array}{llll} y+4=4(x-3)\implies y-(\stackrel{y_1}{-4})=\stackrel{m}{4}(x-\stackrel{x_1}{3})\\\\ ~\hfill (\stackrel{x_1}{3}~~,~~\stackrel{y_1}{-4}) \end{array}[/tex]

if there was a random selection of  cartons from each of the groups to measure grams of fat. This is an example of stratified sampling

Stratified sampling can be defined as a method of sampling that involves  division of a population into smaller groups or items, these are called strata.

This groups or strata are then arranged or organized based on the shared characteristics or attributes of the members in the group of the given population.

Stratification is the process of classifying the population into groups.

Features of  stratified sampling are;

From the information given, we can see that it is an example of stratified sampling.

Thus, if there was a random selection of cartons from each of the groups to measure grams of fat. This is an example of stratified sampling

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Answer:

7

Step-by-step explanation:

Given the information from the question:

[tex]fg - f = f \times g - f[/tex]

Next we can use the order of operations to find the value of the expression.

[tex]fg - f = - 6 \times - 1 - ( - 1) \\ = 6 - ( - 1) \\ = 6 + 1 \\ = 7[/tex]

Therefore the hour hand travels 40.192in in 5 hours

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;

β = 360/5

β = 72 degrees

Given the following parameters

r = 16/2

r = 8in

Substitute into the formula

A = 8²(72π)/360
A = 40.192in

Therefore the hour hand travels 40.192in in 5 hours

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Answer:

3; 1

Step-by-step explanation:

when there are six spots we can see that there are 2 eyes

so

divide both sides by 2

6:2

6 / 2 : 2 / 2

3 : 1

that is your answer

Answer:

$6455.

Step-by-step explanation:

The formula for this investment is:

A = P(1 + r/4)^4t      where P = amount deposited ,  A amount after t years,

                                r = rate (as a decimal fraction).

So we have:

7160.06 = P(1 + 0.026/4)^16

7160.06 = P * 1.109227

P = 7160.06 / 1.109227

  =  $6455.

Answer:

c if lsrt lstr name two congruent segments

Answer:

  (0, -2)

Step-by-step explanation:

The solution to a system of equations is the point on the graph where the lines intersect.

Here, both lines have a y-intercept of -2, so intersect there. The solution is ...

  (x, y) = (0, -2)

The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.

The location of the receiver = 15 inches above the vertex

Width of the dish = 84 inches

The receiver of a satellite dish is normally located at the focus (focal point).

Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;

Coordinates of the focus = (0, a)

Where;

a = The distance of the focus above the vertex

Therefore;

a = 15 inches

The dish is horizontally spaced equally about the vertex.

The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.

At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;

X = 84 ÷ 2 = 42

Which gives;

42² = 4 × 15 × Y

Y = 42² ÷ (4 × 15) = 29.4

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[tex]-2(-1+2w)[/tex]

distribute

[tex]2-4w[/tex]

put in standard form

[tex]-4w+2[/tex]

Answer:

The graph of g(x) has a y-intercept at (0,0) and a slope of -2.

The gallons needed to paint the silo is 10.

A cylinder is a three-dimensional object. It is a prism with a circular base. The total surface area of cylinder can be determined by adding the area of all its faces.

Total surface area of the cylinder excluding its base = 2πrh +πr²

Where:

TSA = (2 x 3.14 x 10 x 30) + (3.14 x 10²)

314 + 1884 = 2198 ft²

Number of gallons needed = 2198 / 224 = 9.81 = 10 gallons

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For the given functions, the domains are:

1) All real numbers.

2) D: x≥ -3

3) D: set of all real numbers such that x ≠ 0

4) D: 7 ≥ x ≥-7

5)  All real numbers.

For any function, we assume that the domain is the set of all real numbers, and then we remove all the values of x that generate problems (like a denominator equal to zero or something like that).

1) f(x) = x^2 - 4

This is just a quadratic equation, the domain is the set of all real numbers.

2) f(x) = √(x + 3)

Remember that the argument of a square root must be equal to or larger than zero, so here the domain is defined by:

x + 3 ≥ 0

x≥ -3

The domain is:

D: x ≥ -3

3) f(x) = 1/x

We can assume that the domain is the set of all real numbers, but, we can see that when x = 0 the denominator becomes zero, then we need to remove that value from the domain.

Thus, we conclude that the domain is:

D: set of all real numbers such that x ≠ 0

4) f(x) = √(49 - x^2)

Here we must have:

49 - x^2 ≥ 0

49 ≥ x^2

√49  ≥ x ≥-√49

7 ≥ x ≥-7

The domain of this function is:

D:  7 ≥ x ≥-7

5) f(x) = √(x^2 + 1)

Notice that x^2 is always a positive number, then the argument of the above square root is always positive, then the domain of that function is the set of all real numbers.

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Answer:

$50

Step-by-step explanation:

x is distance and y is cost because the cost is dependent on the distance which makes the distance the independent variable. you can always use y=mx+b for these problems!!

[tex](k \circ p)(x)=k(p(x))=k(x-3) \\ \\ =2(x-3)^2-5 \\ \\ =2(x^2 - 6x+9)-5 \\ \\ =\boxed{2x^2 - 12x+13}[/tex]

For instance, f[g (x)] exists the composite function of f(x) and g(x). The composite function f[g (x)] exists read as “f of g of x”.

The composite function exists [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex]

Therefore, the correct answer is option b. [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex].

A composite function exists generally as a function that exists written inside another function. The composition of a function exists done by replacing one function with another function.

Given function exists, [tex]$k(x)=2 x^{2}-5[/tex] and p(x) = (x - 3)

To find composite function k(p(x)).

k(p(x)) = k(x-3)

[tex]$&k(p(x))=2(x-3)^{2}-5 \\[/tex]

simplifying the above equation, we get

[tex]$&k(p(x))=2\left(x^{2}+9-6 x\right)-5 \\[/tex]

[tex]$&k(p(x))=2 x^{2}+18-12 x-5 \\[/tex]

[tex]$&k(p(x))=2 x^{2}-12 x+13[/tex]

The composite function exists [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex]

Therefore, the correct answer is option b. [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex].

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Answer:

1 boy to 15 girls.

Step-by-step explanation:

Since there is only two boys, I divided each number by two and got 1 to 15. Have an amazing day!

The ratio of boys to all children in the group is 1:16.

Given that in a group there are 2 boys and 30 girls.

We need to find the ratio of boys to all children.

To find the ratio of boys to all children in the group, we need to add the number of boys and girls together to get the total number of children.

Then, we can express the number of boys as a fraction of the total number of children.

Number of boys = 2

Number of girls = 30

Total number of children = Number of boys + Number of girls

Total number of children = 2 + 30 = 32

Now, we can express the number of boys as a fraction of the total number of children:

Ratio of boys to all children = Number of boys / Total number of children

Ratio of boys to all children = 2 / 32

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

Ratio of boys to all children = 1 / 16

So, the ratio of boys to all children in the group is 1:16.

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Answer:

320 pages.

Step-by-step explanation:

We can simply multiply and add to find how many pages are in the book.

So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.

Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:

[tex]\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320[/tex]

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

⨠ use the distributive property

[tex]\sf{7x-3(x-6)=30}[/tex]

[tex]\sf{7x-3x+18=30}[/tex]

⨠ combine like terms

[tex]\sf{4x+18=30}[/tex]

⨠ subtract both sides by 18

[tex]\sf{4x=30-18}[/tex]

[tex]\sf{4x=12}[/tex]

⨠ divide both sides by 4

[tex]\boxed{\sf x=3}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Answer:

Identity property of addition 8 + 0 = 8

Identity property of multiplication 8 x 1 = 8

Step-by-step explanation:

He mixed up his properties.  8 + 1  does not equal 8.  I want to know what I can add to 8 and that I would still get 8, the answer is zero.

The identity property of multiplication is showing that any number multiplied by 1 is itself.

Answer:

10

Step-by-step explanation:

Every number with exponent zero is equal to 1

(7³×8)⁰ = 1

5⁰ = 1

then:

(3² + 5⁰) / (7³×8)⁰

= (3² + 1) / 1

= (9+1) / 1

= 10

3^2 = 9

3^2 = 95^0 =1

(7^3 x 8)^0 is 1

(anything to power of zero is one)

9 + 1 / 1 gives us the fraction 10/1

10/1 + 1/3 => make denominator the same, so I'll multiply 10/1 by 3

We get : 30/3 + 1/3 => 31/3

Thus answer is 31/3

Hope this helps!

Answer:

  9.08

Step-by-step explanation:

To find the predicted value of y, put the x-value where x is in the equation and do the arithmetic.

  [tex]\hat{y}=134.63-2.79x\qquad\text{given}\\\\\hat{y}=134.63-2.79(45) = 134.63-125.55\qquad\text{use 45 for x}\\\\\boxed{\hat{y}=9.08}\qquad\text{simplify}[/tex]

The true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer

The complete question is added as an attachment

From the table, we have

Divisor = x^2 - 3x + 4

Quotient = 2x + 5

Dividend = -2x^3 + 11x^2 - 23x + 20

See that the signs of the leading coefficients of the dividend and the divisor are different

This means that the leading coefficient of the quotient must be negative

From the question, we have:

Quotient = 2x + 5

The expression 2x + 5 has a positive leading coefficient

Hence, the true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer

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Check the picture below.

Answer:

a polygon with an interior angle of 108 is a pentagon

Answer:

a) $20,771.76

b) $20,817.67

c) $20,484.80

d) $20,864.52

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Part (a): semiannually

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{2}\right)^{2 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1.0275}{2}\right)^{12}[/tex]

[tex]\implies \sf A=20771.76[/tex]

Part (b): quarterly

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{4}\right)^{4 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1.01375}\right)^{24}[/tex]

[tex]\implies \sf A=20817.67[/tex]

Part (c): monthly

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{12 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{72}[/tex]

[tex]\implies \sf A=20484.80[/tex]

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Part (d): continuous

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000e^{0.055 \times 6}[/tex]

[tex]\implies \sf A=20864.52[/tex]

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0.8926 percent of the time, the shipment will be rejected.

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A delivery of 50 cheap digital watches, 10 of which are flawed.

A digital watch's likelihood of malfunctioning

P = 10/50

= 0.2

Size of sample: n = 10

Additionally, if they find one or more samples to be defective, they reject the entire cargo.

Making use of the binomial probability formula:

[tex]P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}[/tex]

The random variable x should stand in for the quantity of defective watches.

The chance that the delivery will be refused is:

[tex]\begin{aligned}&P(x \geq 1)=1-P(0) \\&=1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}\end{aligned}[/tex]

= 1 - (0.8)

= 0.8926

As a result, 0.8926 percent of the time, the shipment will be rejected.

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I understand that the question you are looking for is:

A shipment of 50 inexpensive digital​ watches, including 10 that are​ defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be​ rejected

Answer:

[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]

Explanation:

Let the total water required water the entire ground be g

Equation:

[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]

rearranging

[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]

simplify

[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]

rewrite in mixed fraction

[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]

The water required to water the entire ground is  1 1/6 liters.